465 Sentences With "reducible" | Random Sentence Generator

Truth is, Trump's popularity isn't reducible to any one thing.

Jewish identity isn't reducible to how we remember the Holocaust.

Hence as persons we inhabit a life-world that is not reducible to the world of nature, any more than the life in a painting is reducible to the lines and pigments from which it is composed.

The controversy over transmissions isn't reducible to a discussion about laws and regulations.

But is something as complex as talking to a therapist reducible to genes?

Kaku believes we are all reducible to patterns of connected neurons in our brains.

They're not some flattened version of humanity, reducible to a collection of parts and attributes.

The moral meaning of a country is not reducible to any president and/or his administration.

It is important to remind ourselves that conversations include, but are not reducible to, exchanges of information.

Our anxiety before death is not reducible to a psychological condition that can or should be overcome.

I don't think anyone's saying that a religion is reducible to the concretized doctrines in its holy text.

"Social marginalization is not reducible to single variables," wrote Steven Woolf and Jason Purnell in a JAMA editorial.

The arts of escalation are inseparable from — though not reducible to — the infrastructures and ecosystems of social media.

And that means that even the phenomena that are not reducible to Cold War tensions were affected by it.

And the other powers all have their own agendas, none of which are reducible to anything as simple as justice.

I admire the way you make paintings that deal with relationships in a way that is not reducible to sex.

Character is not reducible to private morality alone, but the person of the statesman makes an inescapable difference in politics.

She was aware that she possessed some kind of power that was connected to her storytelling but not reducible to it.

He said that physics was initially thought to be about the study of physical objects, that everything was reducible to particles.

Officers are not emotionless robots any more than death-row prisoners are reducible to the crimes for which we have been convicted and sentenced.

In other words, white identity is not defined by racial animus, and whites who identify with their racial group are not simply reducible to bigots.

My sense is that it's not reducible to a single variable, though ethno-nationalism is a bigger factor than a lot of people care to admit.

If we say that a religion is reducible to the concretized doctrines in its holy text, then we don't leave much room for evolution or reformation.

When we talk about anti-fascism we need to see it as a tradition of pan-left politics that is not reducible simply to opposition to fascism.

To deny that is to deny that both identity and the past matter, to assume everything is reducible to some kind of material or economic ultimate cause.

The 2016 election brought forward real disagreements in the Democratic Party, disagreements that aren't reducible to empirical arguments, or arguments about what an achievable political agenda might be.

Big data can't bring objectivity to a subjective world It may slip our notice, but technological innovation is often reducible to an innovation in the marketing and conceptualization of technology.

It's been suggested that the "ice" in "Ice" translates to a junkie's relationship to her drug, yet the book is hardly reducible to this or any other form of allegory.

Class reductionism is the supposed view that inequalities apparently attributable to race, gender, or other categories of group identification are either secondary in importance or reducible to generic economic inequality.

For the poet, democracy wasn't simply the least bad form of government, it wasn't reducible to dreary policy and endless debate, but it was rather a vital, transformative and regenerative ethos.

The fact that Johns's art is not swiftly reducible to easily consumable bits of meaning seems to irk people as well as lead to accusations of being cool, detached, aloof, and remote.

The health care industry has reached $3.5 trillion and is "growing at an unsustainable rate," said Merlo, who pointed out that an estimated quarter of health care spending is wasteful and reducible.

The chief pointed out an estimated quarter of health care spending is wasteful and reducible and his company, in collaboration with Aetna, has a plan to reduce costs and boost the company's earnings.

I am more skeptical about claims that the causes of violence are reducible to a single category—private property, a lack of love, whatever—and can therefore be easily eliminated at its root.

Our politicians mourn, our media serves the familiar narratives, and we end the day in the same place where we started it, bewildered by reducible catastrophes but unwilling to do anything about it.

"Making the numbers go up" in video games feels good because the problems in our own lives are rarely even reducible to "numbers," let alone solved with a simple mixture of determination and time.

Microbes: Our tiny crucial allies The key conceptual breakthrough in analyzing the microbiome came with the recognition that the complex array of so many different organisms living together in a community may not be reducible.

Not long after I noticed the pattern of my personal writing — that all my inquiries were reducible to the same bottom line — I decided that I was going to withdraw myself from my work entirely.

But while you might expect a complicated explanation for his choice to name a release after a math equation, Haslam nonchalantly explains that the title mainly just applies to the fact that all music is reducible to quantitative analysis.

That vernacular, he said, is used to articulate a "very coherent story about what America is, and what it should be, that is not reducible to a set of policy positions" — but only if you know how to hear it.

"When I think about Durham's work — the 40 plus years that he put into it and also looking at the impact that he had on various discourses — like Jean Fisher I think that art is not reducible to identity," she said.

" Human brains are more complex, of course, and "are not only affected by immediate recent losses," Dr. Deisseroth said, but "your appetite for risk in many circumstances might be at least possibly reducible to what a particular set of cells in a particular brain area is doing.

Taking its title from a line from Giovanni's Room by James Baldwin, the show rejects the notion that "home" is reducible to a fixed place or static dream, conceiving of it instead as an animating force that sets people adrift in the pursuit of intimacy and belonging.

But her belief—and her unwillingness to think of the universe as a directionless accident, or of the human mind as a collection of brute responses, totally reducible to the brain and blind to values originating outside itself—isn't stuck in the past; it determines her future, too.

For instance, the endless and often tiresome contretemps over the 1619 Project—last year's examination of slavery's centrality to the American story in The New York Times Magazine—is essentially reducible to a disagreement over whether our country is defined by a set of founding ideals, now and then betrayed or undermined by bad actors, or by a set of structural forces that have materially shaped our political and societal outcomes.

In general, a problem in NP is called self-reducible if its function variant can be solved in polynomial time using an oracle deciding the original problem. Every NP- complete problem is self-reducible. It is conjectured that the integer factorization problem is not self-reducible.

Historically, positivism has been criticized for its reductionism, i.e., for contending that all "processes are reducible to physiological, physical or chemical events," "social processes are reducible to relationships between and actions of individuals," and that "biological organisms are reducible to physical systems." Max Horkheimer criticized the classic formulation of positivism on two grounds. First, he claimed that it falsely represented human social action.

Each of the Petersen family graphs forms a minimal forbidden minor for the family of YΔY-reducible graphs.. However, Neil Robertson provided an example of an apex graph (a linkless embeddable graph formed by adding one vertex to a planar graph) that is not YΔY-reducible, showing that the YΔY- reducible graphs form a proper subclass of the linkless embeddable graphs and have additional forbidden minors. In fact, as Yaming Yu showed, there are at least 68,897,913,652 forbidden minors for the YΔY-reducible graphs beyond the seven of the Petersen family..

Noether identities need not be independent, but satisfy first-stage Noether identities, which are subject to the second-stage Noether identities and so on. Higher-stage Noether identities also are separated into the trivial and non-trivial once. A degenerate Lagrangian is called reducible if there exist non-trivial higher-stage Noether identities. Yang-Mills gauge theory and gauge gravitation theory exemplify irreducible Lagrangian field theories. Different variants of second Noether’s theorem state the one-to-one correspondence between the non-trivial reducible Noether identities and the non-trivial reducible gauge symmetries. Formulated in a very general setting, second Noether’s theorem associates to the Koszul-Tate complex of reducible Noether identities, parameterized by antifields, the BRST complex of reducible gauge symmetries parameterized by ghosts.

Robertson's example of a non-YΔY-reducible apex graph. A connected graph is YΔY-reducible if it can be reduced to a single vertex by a sequence of steps, each of which is a Δ-Y or Y-Δ transform, the removal of a self-loop or multiple adjacency, the removal of a vertex with one neighbor, and the replacement of a vertex of degree two and its two neighboring edges by a single edge.. Like the apex graphs and the linkless embeddable graphs, the YΔY-reducible graphs are closed under graph minors. And, like the linkless embeddable graphs, the YΔY-reducible graphs have the seven graphs in the Petersen family as forbidden minors, prompting the question of whether these are the only forbidden minors and whether the YΔY-reducible graphs are the same as the linkless embeddable graphs. However, Neil Robertson provided an example of an apex graph that is not YΔY-reducible.

Every sufficiently smooth DAE is almost everywhere reducible to this semi-explicit index-1 form.

A Kleinian group is called elementary if its limit set is finite, in which case the limit set has 0, 1, or 2 points. Examples of elementary Kleinian groups include finite Kleinian groups (with empty limit set) and infinite cyclic Kleinian groups. A Kleinian group is called reducible if all elements have a common fixed point on the Riemann sphere. Reducible Kleinian groups are elementary, but some elementary finite Kleinian groups are not reducible.

However, this does not imply any special dynamical structure. To explain quantum integrability, it is helpful to consider the free particle setting. Here all dynamics are one-body reducible. A quantum system is said to be integrable if the dynamics are two-body reducible.

A closed curve is called essential if it is not homotopic to a point, a puncture, or a boundary component. A Heegaard splitting is reducible if there is an essential simple closed curve \alpha on H which bounds a disk in both V and in W. A splitting is irreducible if it is not reducible. It follows from Haken's Lemma that in a reducible manifold every splitting is reducible. A Heegaard splitting is stabilized if there are essential simple closed curves \alpha and \beta on H where \alpha bounds a disk in V, \beta bounds a disk in W, and \alpha and \beta intersect exactly once.

Reductivists think subjective representations are reducible to objective. Non-reductivists think that subjective representations are real and distinct.

If the final graph consists of a single node, then the original graph is said to be reducible.

A simple entity is not reducible to conceptual forms, or conventional designations, nor is it compositely existent entity.

Unlike older lattice based cryptographic algorithms, the RLWE-KEX is provably reducible to a known hard problem in lattices.

The strong reducibilities include: ;One-one reducibility: A is one-one reducible (or 1-reducible) to B if there is a total computable injective function f such that each n is in A if and only if f(n) is in B. ;Many-one reducibility: This is essentially one-one reducibility without the constraint that f be injective. A is many-one reducible (or m-reducible) to B if there is a total computable function f such that each n is in A if and only if f(n) is in B. ;Truth-table reducibility: A is truth-table reducible to B if A is Turing reducible to B via an oracle Turing machine that computes a total function regardless of the oracle it is given. Because of compactness of Cantor space, this is equivalent to saying that the reduction presents a single list of questions (depending only on the input) to the oracle simultaneously, and then having seen their answers is able to produce an output without asking additional questions regardless of the oracle's answer to the initial queries. Many variants of truth-table reducibility have also been studied.

It follows from Waldhausen's Theorem that every reducible splitting of an irreducible manifold is stabilized. A Heegaard splitting is weakly reducible if there are disjoint essential simple closed curves \alpha and \beta on H where \alpha bounds a disk in V and \beta bounds a disk in W. A splitting is strongly irreducible if it is not weakly reducible. A Heegaard splitting is minimal or minimal genus if there is no other splitting of the ambient three-manifold of lower genus. The minimal value g of the splitting surface is the Heegaard genus of M.

That is, given such sets A and B, there is a total computable function f such that A = {x : f(x) ∈ B}. These sets are said to be many-one equivalent (or m-equivalent). Many-one reductions are "stronger" than Turing reductions: if a set A is many-one reducible to a set B, then A is Turing reducible to B, but the converse does not always hold. Although the natural examples of noncomputable sets are all many-one equivalent, it is possible to construct recursively enumerable sets A and B such that A is Turing reducible to B but not many-one reducible to B. It can be shown that every recursively enumerable set is many-one reducible to the halting problem, and thus the halting problem is the most complicated recursively enumerable set with respect to many-one reducibility and with respect to Turing reducibility. Post (1944) asked whether every recursively enumerable set is either computable or Turing equivalent to the halting problem, that is, whether there is no recursively enumerable set with a Turing degree intermediate between those two.

In 1928 Dörnte published the first main results: An n-ary groupoid which is reducible is an n-ary group, however for all n > 2 there exist n-ary groups which are not reducible. In some n-ary groups there exists an element e (called an n-ary identity or neutral element) such that any string of n-elements consisting of all e's, apart from one place, is mapped to the element at that place. E.g., in a quaternary group with identity e, eeae = a for every a. An n-ary group containing a neutral element is reducible.

Non-reductive physicalism is the predominant contemporary form of property dualism according to which mental properties are mapped to neurobiological properties, but are not reducible to them. Non-reductive physicalism asserts that mind is not ontologically reducible to matter, in that an ontological distinction lies in the differences between the properties of mind and matter. It asserts that while mental states are physical in that they are caused by physical states, they are not ontologically reducible to physical states. No mental state is the same one thing as some physical state, nor is any mental state composed merely from physical states and phenomena.

The first problem is reducible to the second one, by taking the intersection of the output gate and n. Indeed, the new output get will be empty if and only if n was not an element of the former output gate. The first problem is reducible to the third one, by asking if the node n is a subset of the output node. The second problem is reducible to the first one, it suffices to multiply the output gate by 0, then 0 will be in the output gate if and only if the former output gate were not empty.

Given any two of these, their intersection has exactly the four points. The reducible quadratics, in turn, may be determined by expressing the quadratic form as a matrix: reducible quadratics correspond to this matrix being singular, which is equivalent to its determinant being zero, and the determinant is a homogeneous degree three polynomial in and and corresponds to the resolvent cubic.

The theory emerged from efforts to unify the dynamic selection process for these three learning algorithms to a regulatory mechanism reducible to individual neurotransmitters.

A topological space X is reducible if it can be written as a union X = X_1 \cup X_2 of two closed proper subsets X_1, X_2 of X. A topological space is irreducible (or hyperconnected) if it is not reducible. Equivalently, all non empty open subsets of X are dense or any two nonempty open sets have nonempty intersection. A subset F of a topological space X is called irreducible or reducible, if F considered as a topological space via the subspace topology has the corresponding property in the above sense. That is, F is reducible if it can be written as a union F = (G_1\cap F)\cup(G_2\cap F), where G_1,G_2 are closed subsets of X, neither of which contains F. An irreducible component of a topological space is a maximal irreducible subset.

Nevertheless, significant interarea differences in patterns of rights creation or in the distribution of property will not be reducible to differences in rates of testacy.

Gold nanoparticles in the size range of 2 to 5 nm catalyze CO oxidation with a TOF of about 1 s−1 at temperatures below 273 K (0 °C). The catalytic activity of nanoparticles is brought about in the absence of moisture when the support is semiconductive or reducible, e.g. TiO2, MnO2, Fe2O3, ZnO, ZrO2, or CeO2. However, when the support is insulating or non-reducible, e.g.

The difference between bounded weak truth- table and bounded Turing reduction is that in the first case, the up to n queries have to be made at the same time while in the second case, the queries can be made one after the other. For that reason, there are cases where A is bounded Turing reducible to B but not weak truth-table reducible to B.

Therefore, it is at least equal to the minimum of these two distances, the requirement for being reducible. For average distance, d(A\cup B,C) is just a weighted average of the distances d(A,C) and d(B,C). Again, this is at least as large as the minimum of the two distances. Thus, in both of these cases, the distance is reducible.

Since 2000, high-performance water-reducible CARCs were commonly used. These materials met DoD’s VOC objective of 1.8 lb/gal and contained no hazardous air pollutants.

After adding a rule to R , remove any rules in R that might have reducible left sides. Repeat the procedure until all overlapping left sides have been checked.

A set B is called many-one complete, or simply m-complete, iff B is recursively enumerable and every recursively enumerable set A is m-reducible to B.

The discrete logarithm problem, the quadratic residuosity problem, the RSA inversion problem, and the problem of computing the permanent of a matrix are each random self-reducible problems.

This smaller map has the condition that if it can be colored with four colors, this also applies to the original map. This implies that if the original map cannot be colored with four colors the smaller map cannot either and so the original map is not minimal. Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist. Their proof reduced the infinitude of possible maps to 1,834 reducible configurations (later reduced to 1,482) which had to be checked one by one by computer and took over a thousand hours.

Biological Naturalism states that consciousness is a higher level function of the human brain's physical capabilities. Another argument for non-reductive physicalism has been expressed by John Searle, who is the advocate of a distinctive form of physicalism he calls biological naturalism. His view is that although mental states are not ontologically reducible to physical states, they are causally reducible (see causality). He believes the mental will ultimately be explained through neuroscience.

These dimensions are taken to be inter-linked, but not equatable or reducible to one another.Le Goff, J.F. (2001). Boszormenyi-Nagy and Contextual Therapy: An Overview, ANZJFT, 22 (3) : 147–157.

Special sciences are those sciences other than fundamental physics, that are presumed to be reducible to fundamental physics, at least in principle. In this view, chemistry, biology, and neuroscience—indeed, all sciences except fundamental physics—are special sciences. The status of the special sciences, and their relation to physics, is unresolved in the philosophy of science. Jerry Fodor, for instance, has argued for strong autonomy, concluding that the special sciences are not even in principle reducible to physics.

The results of this section show that the computation of the pseudoinverse is reducible to its construction in the Hermitian case. It suffices to show that the putative constructions satisfy the defining criteria.

Compactification of moduli spaces generally require allowing certain degeneracies – for example, allowing certain singularities or reducible varieties. This is notably used in the Deligne–Mumford compactification of the moduli space of algebraic curves.

The Lorentz group and its Lie algebra have the complete reducibility property. This means that every representation reduces to a direct sum of irreducible representations. The reducible representations will therefore not be discussed.

There was also philosophical calcination, which was said to occur when horns, hooves, etc., were hung over boiling water, or other liquor, until they had lost their mucilage, and were easily reducible into powder.

Since all computational problems are reducible into the accept/reject question on inputs, (all problem instances can be represented in a finite length of symbols), automata theory plays a crucial role in computational theory.

Applicative order evaluation is an evaluation strategy in which an expression is evaluated by repeatedly evaluating its leftmost innermost reducible expression. This means that a function's arguments are evaluated before the function is applied.

For any given choice of cube root and its conjugate, this contains nested radicals involving complex numbers, yet it is reducible (even though not obviously so) to one of the solutions 1, 2, or –3.

Regardless of the jungle influences, few of the album's rhythms are reducible to drum and bass, with subtler beat layering and "rhythmic eruptions" comparable to experimental ambient techno acts like Tournesol and The Black Dog.

Thus . Define to be the polynomial . Since is a root of , the minimal polynomial for is a factor of . Because has degree 3, if it is reducible over by then it has a rational root.

Normal order evaluation is an evaluation strategy in which an expression is evaluated by repeatedly evaluating its leftmost outermost reducible expression. This means that a function's arguments are not evaluated before the function is applied.

Neuroheuristics (or Neuristics) studies the dynamic relations between the complex knowledge acquired by neuroscience by means of an approach not reducible in an expertise since it is continuously renewed at every stage of progress towards scientific discovery.

The AllMusic review by "Blue" Gene Tyranny called it "Wonderful acoustic music that winds its way through many textures and energy levels, not reducible to a simple description. Enjoyable, as well as music of a grand vision".

This result (a "remarkable theorem", as Lee Neuwirth called it in his review), was published in 1975 in the highly respected journal, Annals of Mathematics. In 1978, together with José María Montesinos, he answered a question posed by Fox, proving the existence of 2-knots whose groups have infinitely many ends. With Hamish Short, González- Acuña proposed and worked on the cabling conjecture: the only knots in the 3-sphere which admit a reducible Dehn surgery, i.e. a surgery which results in a reducible 3-manifold, are the cable knots.

To simplify the Euclidean division, for one commonly chooses polynomials of the form :X^n+aX+b, which make the needed Euclidean divisions very efficient. However, for some fields, typically in characteristic , irreducible polynomials of the form may not exist. In characteristic , if the polynomial is reducible, it is recommended to choose with the lowest possible that makes the polynomial irreducible. If all these trinomials are reducible, one chooses "pentanomials" , as polynomials of degree greater than , with an even number of terms, are never irreducible in characteristic , having as a root.

Every reducible configuration contains a cycle, so for every finite set S of reducible configurations there is a number γ such that all configurations in the set contain a cycle of length at most γ. However, there exist snarks with arbitrarily high girth, that is, with arbitrarily high bounds on the length of their shortest cycle.. A snark G with girth greater than γ cannot contain any of the configurations in the set S, so the reductions in S are not strong enough to rule out the possibility that G might be a minimal counterexample.

Since every apex graph is linkless embeddable, this shows that there are graphs that are linkless embeddable but not YΔY-reducible and therefore that there are additional forbidden minors for the YΔY-reducible graphs. Robertson's apex graph is shown in the figure. It can be obtained by connecting an apex vertex to each of the degree-three vertices of a rhombic dodecahedron, or by merging two diametrally opposed vertices of a four-dimensional hypercube graph. Because the rhombic dodecahedron's graph is planar, Robertson's graph is an apex graph.

Dupré advocates a pluralistic model of science as opposed to the common notion of reductionism. Physical Reductionism suggests that all science may be reduced to physical explanations due to causal or mereological links that obtain between the objects studied in the higher sciences and the objects studied by physics. For example, a physical reductionist would see psychological facts as (in principle) reducible to neurological facts, which is in turn are reducible to biological facts. Biology could then be explained in terms of chemistry, and chemistry could then be explained in terms of physical explanation.

The resulting diagram is an immersed plane curve with the additional data of which strand is over and which is under at each crossing. (These diagrams are called knot diagrams when they represent a knot and link diagrams when they represent a link.) Analogously, knotted surfaces in 4-space can be related to immersed surfaces in 3-space. A reduced diagram is a knot diagram in which there are no reducible crossings (also nugatory or removable crossings), or in which all of the reducible crossings have been removed.

Dedekind's path to logicism had a turning point when he was able to construct a model satisfying the axioms characterizing the real numbers using certain sets of rational numbers. This and related ideas convinced him that arithmetic, algebra and analysis were reducible to the natural numbers plus a "logic" of classes. Furthermore by 1872 he had concluded that the naturals themselves were reducible to sets and mappings. It is likely that other logicists, most importantly Frege, were also guided by the new theories of the real numbers published in the year 1872.

The dialog arrives at a conclusion that consciousness is not reducible to a mere physical composition and structure of a person, but at the same time this does not disprove the material nature of consciousness, pending the future progress of science.

In computability theory, many reducibility relations (also called reductions, reducibilities, and notions of reducibility) are studied. They are motivated by the question: given sets A and B of natural numbers, is it possible to effectively convert a method for deciding membership in B into a method for deciding membership in A? If the answer to this question is affirmative then A is said to be reducible to B. The study of reducibility notions is motivated by the study of decision problems. For many notions of reducibility, if any noncomputable set is reducible to a set A then A must also be noncomputable.

An outer automorphism φ of Fk is said to be reducible if there exists a free product decomposition :F_k=H_1\ast\dots H_m\ast U where all Hi are nontrivial, where m ≥ 1 and where φ permutes the conjugacy classes of H1,...,Hm in Fk. An outer automorphism φ of Fk is said to be irreducible if it is not reducible. It is known that φ ∈ Out(Fk) be irreducible if and only if for every topological representative f : Γ → Γ of φ, where Γ is finite, connected and without degree-one vertices, any proper f-invariant subgraph of Γ is a forest.

For example, the case described in degree 4 vertex situation is the configuration consisting of a single vertex labelled as having degree 4 in G. As above, it suffices to demonstrate that if the configuration is removed and the remaining graph four-colored, then the coloring can be modified in such a way that when the configuration is re- added, the four-coloring can be extended to it as well. A configuration for which this is possible is called a reducible configuration. If at least one of a set of configurations must occur somewhere in G, that set is called unavoidable. The argument above began by giving an unavoidable set of five configurations (a single vertex with degree 1, a single vertex with degree 2, ..., a single vertex with degree 5) and then proceeded to show that the first 4 are reducible; to exhibit an unavoidable set of configurations where every configuration in the set is reducible would prove the theorem.

Reductions with metal alkoxyaluminium hydrides are chemical reactions that involve either the net hydrogenation of an unsaturated compound or the replacement of a reducible functional group with hydrogen by metal alkoxyaluminium hydride reagents.Málek, J. Org. React. 1985, 34, 1. Málek, J. Org. React.

They are not one of the same thing. Philosophical rationalism in its most extreme form is the doctrine that knowledge can ultimately be founded on pure reason, while logicism is the doctrine that mathematical concepts, among others are reducible to pure logic.

The cabling conjecture states that if Dehn surgery on a knot in the 3-sphere yields a reducible 3-manifold, then that knot is a (p,q)-cable on some other knot, and the surgery must have been performed using the slope pq.

More recently, Lieto and Vernero have also shown that arguments reducible to logical fallacies are a class of widely adopted persuasive techniques in both web and mobile technologies. These techniques have shown their efficacy also on large scale studies about persuasive news recommendations .

It is an essential aspect for cross-claims, especially when there exits overlapping obligations. Common features of set- off are that they are confined to situations where claim and cross claim are for money or reducible to money and it requires mutuality.

Mautner Geodesic flows on symmetric Riemannian spaces, Annals of Mathematics, vol. 65, 1957, pp. 416-430 With a ground-breaking paper in 1958, Mautner became an important pioneer in the representation theory of reducible p-adic groups.Mautner Spherical functions over p-adic fields.

The number of bonds that are unmoved is the character of that operation. This reducible representation is decomposed into the sum of irreducible representations. These irreducible representations correspond to the symmetry of the orbitals involved. MO diagrams provide simple qualitative LCAO treatment.

Again, denote the set of rational numbers by . Theorem: An angle of measure may be trisected if and only if is reducible over the field extension . The proof is a relatively straightforward generalization of the proof given above that a angle is not trisectible.

SSPACE(S(n)) is the class of the languages accepted by a symmetric Turing machine running in space O(S(n)) and SL=SSPACE(log(n)). SL can equivalently be defined as the class of problems logspace reducible to USTCON. Lewis and Papadimitriou by their definition showed this by constructing a nondeterministic machine for USTCON with properties that they showed are sufficient to make a construction of an equivalent symmetric Turing machine possible. Then, they observed that any language in SL is logspace reducible to USTCON as from the properties of the symmetric computation we can view the special configuration as the undirected edges of the graph.

As of 2000, two different CARC topcoats included: 1) One-component, moisture-cure urethane (MCU): MCU CARCs cured in a two-stage process where water and isocyanate groups combined to produce a cured paint film. The materials were designed for resistance to windblown dust, sand and chemical agents. An improvement to solvent-borne polyurethanes, MCU materials offered both lower levels of volatile organic compounds and elimination of hazardous air pollutants. 2) Two-component, high-performance, water-reducible polyurethane: Waterbased CARCs, most commonly used by the military, were composed of water-reducible polyurethane resins, marking the first time a water-based two-component CARC was commercially available.

Ontological reductionism is the belief that reality is composed of a minimum number of kinds of entities or substances. This claim is usually metaphysical, and is most commonly a form of monism, in effect claiming that all objects, properties and events are reducible to a single substance. (A dualist who is an ontological reductionist would believe that everything is reducible to two substances—as one possible example, a dualist might claim that reality is composed of "matter" and "spirit".) Richard Jones divides ontological reductionism into two: the reductionism of substances (e.g., the reduction of mind to matter) and the reduction of the number of structures operating in nature (e.g.

The potential is measured between the working electrode and the reference electrode, while the current is measured between the working electrode and the counter electrode. These data are plotted as current (i) versus applied potential (E, often referred to as just 'potential'). In Figure 2, during the initial forward scan (from t0 to t1) an increasingly reducing potential is applied; thus the cathodic current will, at least initially, increase over this time period assuming that there are reducible analytes in the system. At some point after the reduction potential of the analyte is reached, the cathodic current will decrease as the concentration of reducible analyte is depleted.

"Species selection operates on variation provided by the largely random process of speciation and favors species that speciate at high rates or survive for long periods and therefore tend to leave many daughter species." Species selection comprises (a) effect-macroevolution, where organism-level traits (aggregate traits) affect speciation and extinction rates (Stanley’s original concept), and (b) strict-sense species selection, where species-level traits (e.g. geographical range) affect speciation and extinction rates. It has been argued that effect macroevolution is reducible to microevolution because both operate through selection on organismic traits, but Grantham demonstrated that effect macroevolution can oppose selection at the organismic level and is therefore not reducible microevolution.

In the framework of many-body quantum mechanics, models solvable by the Bethe ansatz can be contrasted with free fermion models. One can say that the dynamics of a free model is one-body reducible: the many-body wave function for fermions (bosons) is the anti- symmetrized (symmetrized) product of one-body wave functions. Models solvable by the Bethe ansatz are not free: the two-body sector has a non-trivial scattering matrix, which in general depends on the momenta. On the other hand, the dynamics of the models solvable by the Bethe ansatz is two-body reducible: the many-body scattering matrix is a product of two-body scattering matrices.

Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one says that E is Borel reducible to F, in symbols E ≤B F, if and only if there is a Borel function : Θ : X → Y such that for all x,x' ∈ X, one has :x E x' ⇔ Θ(x) F Θ(x'). Conceptually, if E is Borel reducible to F, then E is "not more complicated" than F, and the quotient space X/E has a lesser or equal "Borel cardinality" than Y/F, where "Borel cardinality" is like cardinality except for a definability restriction on the witnessing mapping.

The aforementioned dependency of some catalysts on water or moisture also relates to oxygen activation. The ability of certain reducible oxides, such as MnO2, Co3O4, and NiO to activate oxygen in dry conditions (< 0.1 ppm H2O) can be ascribed to the formation of oxygen defects during pretreatment.

Computability theory is closely related to the branch of mathematical logic called recursion theory, which removes the restriction of studying only models of computation which are reducible to the Turing model. Many mathematicians and computational theorists who study recursion theory will refer to it as computability theory.

Mild conditions allow this reaction to take place while not affecting complex or reducible groups in the reactant-acid. The reaction requires the presence of a nucleophile (water). A metal catalyst is required. Usually Ag2O is chosen but other metals and even light effect the reaction.

One possible attack on the cycle double cover problem would be to show that there cannot exist a minimum counterexample, by proving that any graph contains a reducible configuration, a subgraph that can be replaced by a smaller subgraph in a way that would preserve the existence or nonexistence of a cycle double cover. For instance, if a cubic graph contains a triangle, a Δ-Y transform will replace the triangle by a single vertex; any cycle double cover of the smaller graph can be extended back to a cycle double cover of the original cubic graph. Therefore, a minimal counterexample to the cycle double cover conjecture must be a triangle-free graph, ruling out some snarks such as Tietze's graph which contain triangles. Through computer searches, it is known that every cycle of length 11 or less in a cubic graph forms a reducible configuration, and therefore that any minimal counterexample to the cycle double cover conjecture must have girth at least 12.. Unfortunately, it is not possible to prove the cycle double cover conjecture using a finite set of reducible configurations.

Thus an oracle machine with a noncomputable oracle will be able to compute sets that a Turing machine without an oracle cannot. Informally, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set (in this case, the set A is also said to be (relatively) computable from B and recursive in B). If a set A is Turing reducible to a set B and B is Turing reducible to A then the sets are said to have the same Turing degree (also called degree of unsolvability). The Turing degree of a set gives a precise measure of how uncomputable the set is. The natural examples of sets that are not computable, including many different sets that encode variants of the halting problem, have two properties in common: #They are recursively enumerable, and #Each can be translated into any other via a many-one reduction.

In folk music a tune-family is, "a seeming multiplicity of melodies," reducible, "to a small number of 'models' or sets." One can think of the models or sets as deep structures. Often, "different tunes are the same," and, "the same tune is different."Burke 1978, p.124-5.

Logicism is the thesis that mathematics is reducible to logic, and hence nothing but a part of logic.Carnap, Rudolf (1931), "Die logizistische Grundlegung der Mathematik", Erkenntnis 2, 91-121. Republished, "The Logicist Foundations of Mathematics", E. Putnam and G.J. Massey (trans.), in Benacerraf and Putnam (1964). Reprinted, pp.

Schwartz's reagent will selectively reduce the amide over any readily reducible esters that may be present in the reaction mixture. Vinylation of ketones in high yields is a possible use of Schwartz's reagent. Schwartz's reagent is used in the synthesis of some macrolide antibiotics, (−)-motuporin, and antitumor agents.

W is not primitive if it is periodic, where the population can perpetually cycle through different disjoint sets of compositions, or if it is reducible, where the dominant species (or quasispecies) that develops can depend on the initial population, as is the case in the simple example given below.

The problem of detecting DDH tuples is random self-reducible, meaning, roughly, that if it is hard for even a small fraction of inputs, it is hard for almost all inputs; if it is easy for even a small fraction of inputs, it is easy for almost all inputs.

If the four-color conjecture were false, there would be at least one map with the smallest possible number of regions that requires five colors. The proof showed that such a minimal counterexample cannot exist, through the use of two technical concepts:; ; # An unavoidable set is a set of configurations such that every map that satisfies some necessary conditions for being a minimal non-4-colorable triangulation (such as having minimum degree 5) must have at least one configuration from this set. # A reducible configuration is an arrangement of countries that cannot occur in a minimal counterexample. If a map contains a reducible configuration, the map can be reduced to a smaller map.

A subspace W of V that is invariant under the group action is called a subrepresentation. If V has exactly two subrepresentations, namely the zero-dimensional subspace and V itself, then the representation is said to be irreducible; if it has a proper subrepresentation of nonzero dimension, the representation is said to be reducible. The representation of dimension zero is considered to be neither reducible nor irreducible, just like the number 1 is considered to be neither composite nor prime. Under the assumption that the characteristic of the field K does not divide the size of the group, representations of finite groups can be decomposed into a direct sum of irreducible subrepresentations (see Maschke's theorem).

Non-reductive physicalism is the idea that while mental states are physical they are not reducible to physical properties, in that an ontological distinction lies in the differences between the properties of mind and matter. According to non-reductive physicalism all mental states are causally reducible to physical states where mental properties map to physical properties and vice versa. A prominent form of non- reductive physicalism, called anomalous monism, was first proposed by Donald Davidson in his 1970 paper "Mental events", in which he claims that mental events are identical with physical events, and that the mental is anomalous, i.e. under their mental descriptions these mental events are not regulated by strict physical laws.

Another possibility to transform a polynomial so as to satisfy the criterion, which may be combined with applying a shift, is reversing the order of its coefficients, provided its constant term is nonzero (without which it would be divisible by anyway). This is so because such polynomials are reducible in if and only if they are reducible in (for any integral domain ), and in that ring the substitution of for reverses the order of the coefficients (in a manner symmetric about the constant coefficient, but a following shift in the exponent amounts to multiplication by a unit). As an example satisfies the criterion for after reversing its coefficients, and (being primitive) is therefore irreducible in .

In recursion theory, \phi_e denotes the computable function with index (program) e in some standard numbering of computable functions, and \phi^B_e denotes the eth computable function using a set B of natural numbers as an oracle. A set A of natural numbers is Turing reducible to a set B if there is a computable function that, given an oracle for set B, computes the characteristic function χA of the set A. That is, there is an e such that \chi_A = \phi^B_e. This relationship is denoted A ≤T B; the relation ≤T is a preorder. Two sets of natural numbers are Turing equivalent if each is Turing reducible to the other.

9-Borabicyclo[3.3.1]nonane or 9-BBN is an organoborane compound. This colourless solid is used in organic chemistry as a hydroboration reagent. The compound exists as a hydride-bridged dimer, which easily cleaves in the presence of reducible substrates. 9-BBN is also known by its nickname 'banana borane'.

Symptoms and signs vary depending on the type of hernia. Symptoms may or may not be present in some inguinal hernias. In the case of reducible hernias, a bulge in the groin or in another abdominal area can often be seen and felt. When standing, such a bulge becomes more obvious.

Ethical non-naturalism is the meta-ethical view which claims that: # Ethical sentences express propositions. # Some such propositions are true. # Those propositions are made true by objective features of the world, independent of human opinion. # These moral features of the world are not reducible to any set of non-moral features.

"Evolution in (Brownian) space: a model for the origin of the bacterial flagellum ." \- the three examples Behe proposed. John H. McDonald even showed his example of a mousetrap to be reducible. If irreducible complexity is an insurmountable obstacle to evolution, it should not be possible to conceive of such pathways.

In mathematics, a fibrifold is (roughly) a fiber space whose fibers and base spaces are orbifolds. They were introduced by , who introduced a system of notation for 3-dimensional fibrifolds and used this to assign names to the 219 affine space group types. 184 of these are considered reducible, and 35 irreducible.

Cohomology of the variational bicomplex leads to the global first variational formula and first Noether's theorem. Extended to Lagrangian theory of even and odd fields on graded manifolds, the variational bicomplex provides strict mathematical formulation of classical field theory in a general case of reducible degenerate Lagrangians and the Lagrangian BRST theory.

According to the 1999 Cambridge Dictionary of Philosophy,"Laws of thought". The Cambridge Dictionary of Philosophy. Robert Audi, Editor, Cambridge: Cambridge UP. p. 489. laws of thought are laws by which or in accordance with which valid thought proceeds, or that justify valid inference, or to which all valid deduction is reducible.

23, available here Scaled down to a non-reducible minimum, Traditionalism is politics understood as implementation of social reign of Jesus Christ; in practical terms it stands for a loosely organized confessional monarchy with strong royal power, with some checks-and-balances provided by organicist representation and with society organized on a corporative basis.

Bakhtin argues that dialogic interactions are not reducible to forms that are analyzable by linguistic methods. While dialogic relations presuppose a language, they do not reside within the system of language and are impossible among the elements of a language.Bakhtin, M. M. (1986) Speech Genres and Other Late Essays. Trans. by Vern W. McGee.

One then expects that the circular functions should be reducible to rational functions. Geometrically, the construction goes like this: for any point (cos φ, sin φ) on the unit circle, draw the line passing through it and the point . This point crosses the -axis at some point . One can show using simple geometry that .

A module over a (not necessarily commutative) ring with unity is said to be semisimple (or completely reducible) if it is the direct sum of simple (irreducible) submodules. For a module M, the following are equivalent: # M is semisimple; i.e., a direct sum of irreducible modules. # M is the sum of its irreducible submodules.

A is a base for Martin-Löf-randomness if A is Turing reducible to Z for some set Z that is Martin-Löf random relative to A. More equivalent characterizations of K-triviality have been studied, such as: # Lowness for weakly-2-randomness; # Lowness for difference-left-c.e. reals (notice here no randomness is mentioned).

Sidgwick's meta-ethics involve an explicit defense of a non-naturalist form of moral realism. He is committed to moral cognitivism: that moral language is robustly truth-apt, and that moral properties are not reducible to any natural properties. This non-naturalist realism is combined with an ethical intuitionist epistemology to account for the possibility of knowing moral truths.

For quadratic polynomials, the above method may be adapted, leading to the so-called ac method of factorization.Stover, Christopher AC Method - Mathworld Consider the quadratic polynomial :ax^2 + bx + c with integer coefficients. If it has a rational root, its denominator must divide evenly. So, it may be written as a possibly reducible fraction \frac ra.

This is the geometric interpretation of the fact that, in a polynomial ring over a field, the height of an ideal is 1 if and only if the ideal is a principal ideal. In the case of possibly reducible hypersurfaces, this result may be restated as follows: hypersurfaces are exactly the algebraic sets whose all irreducible components have dimension .

Demonology is the study of demons or beliefs about demons. They may be human, or nonhuman, separable souls, or discarnate spirits which have never inhabited a body. A sharp distinction is often drawn between these two classes, notably by the Melanesians, several African groups, and others. The Islamic jinn, for example, are not reducible to modified human souls.

On the other hand, our aim will be to show that all such are logically reducible to formulation 1. We offer this conclusion at the present moment as a working hypothesis. And to our mind such is Church's identification of effective calculability with recursivness.8" (italics in original) ::7 [he sketches an approach to a proof] ::8 "Cf.

Clearly, APT algorithms are included in our class GenP. We have seen several NP complete problems in GenP, but Meyer and Paterson show that this is not the case for APT. They prove that an NP complete problem is reducible to a problem in APT if and only if P = NP. Thus APT seems much more restrictive than GenP.

Contractarian libertarianism holds that any legitimate authority of government derives not from the consent of the governed, but rather from contract or mutual agreement, although this can be seen as reducible to consequentialism or deontologism depending on what grounds contracts are justified. Some libertarian socialists reject deontological and consequential approaches and use historical materialism to justify their political beliefs.

Thus, an n-ary group that is not reducible does not contain such elements. There exist n-ary groups with more than one neutral element. If the set of all neutral elements of an n-ary group is non-empty it forms an n-ary subgroup.Wiesław A. Dudek, Remarks to Głazek's results on n-ary groups, Discussiones Mathematicae.

For a reductive group G over a field of characteristic zero, all finite-dimensional representations of G (as an algebraic group) are completely reducible, that is, they are direct sums of irreducible representations.Milne (2017), Theorem 22.42. That is the source of the name "reductive". Note, however, that complete reducibility fails for reductive groups in positive characteristic (apart from tori).

The mapping class groups satisfy the Tits alternative: that is, any subgroup of it either contains a non-abelian free subgroup or it is virtually solvable (in fact abelian). Any subgroup which is not reducible (that is it does not preserve a set of isotopy class of disjoint simple closed curves) must contain a pseudo-Anosov element.

Stephen Jay Gould wrote that the "entire argument" of the authors of The Bell Curve rests on four unsupported, and mostly false, assumptions about intelligence: # Intelligence must be reducible to a single number. # Intelligence must be capable of rank ordering people in a linear order. # Intelligence must be primarily genetically based. # Intelligence must be essentially immutable.

Assign a zero when there is no influence. Thus obtain the weighted column stochastic supermatrix. #Compute the limit priorities of the stochastic supermatrix according to whether it is irreducible (primitive or imprimitive [cyclic]) or it is reducible with one being a simple or a multiple root and whether the system is cyclic or not. Two kinds of outcomes are possible.

The mathematical proof of the parallelogram of force is not generally accepted to be mathematically valid. Various proofs were developed (chiefly Duchayla's and Poisson's), and these also caused objections. That the parallelogram of force was true was not questioned, but why it was true. Today the parallelogram of force is accepted as an empirical fact, non-reducible to Newton's first principles.

The distinctive claim of verificationism is that the result of such verifications is, by definition, truth. That is, truth is reducible to this process of verification. According to perspectivism and relativism, a proposition is only true relative to a particular perspective. Roughly, a proposition is true relative to a perspective if and only if it is accepted, endorsed, or legitimated by that perspective.

For instance, two individuals who, while sharing the labor of hollandaise-sauce production, each believe the proposition "We are making hollandaise sauce", have formed a collective intention. This would not exist if they only held beliefs to the effect of "I am stirring", or "I am pouring". It is thus, Searle claims, that collective intentionality is not reducible to individual intentionality.

By honestly applying "form follows function", industrial designers had the potential to put their clients out of business. Some simple single-purpose objects like screwdrivers and pencils and teapots might be reducible to a single optimal form, precluding product differentiation. Some objects made too durable would prevent sales of replacements. (cf. planned obsolescence) From the standpoint of functionality, some products are simply unnecessary.

Another example of a popular fast ion conductor is beta-alumina solid electrolyte. Unlike the usual forms of alumina, this modification has a layered structure with open galleries separated by pillars. Sodium ions (Na+) migrate through this material readily since the oxide framework provides an ionophilic, non-reducible medium. This material is considered as the sodium ion conductor for the sodium–sulfur battery.

The Ortolani test is part of the physical examination for developmental dysplasia of the hip, along with the Barlow maneuver. Specifically, the Ortolani test is positive when a posterior dislocation of the hip is reducible with this maneuver. This is part of the standard infant exam performed preferably in early infancy.The Ortolani test is named after Marino Ortolani, who developed it in 1937.

One of the most distinctive stances of the Montreal School approach, birthed in the Université de Montréal by James Taylor, Francois Cooren (see particularly Cooren, 2004), and Bruno Latour amongst others, is that texts have agency. Texts do something to humans that is not reducible to certain human interactions and human actions.Cooren, F. (2004). Textual Agency: How Texts Do Tings in Organizational Settings.

Mr Beavis left his car parked for 56 minutes over the permitted two-hour period. He argued that the £85 charge demanded of him by ParkingEye (reducible to £50 if he had paid within 14 days) was an unenforceable penalty. Further or alternatively, he maintained that it is unfair and invalid within the meaning of the Unfair Terms in Consumer Contracts Regulations 1999.

Franz Boas's The Mind of Primitive Man (1911) established a program that would dominate American anthropology for the next 15 years. In this study, he established that in any given population, biology, language, material, and symbolic culture, are autonomous; that each is an equally important dimension of human nature, but that no one of these dimensions is reducible to another.

In the early 1950s, studying philosophy of quantum mechanics under Popper at the London School of Economics, Paul Feyerabend found falsificationism to be not a breakthrough but rather obvious, and thus the controversy over it to suggest instead endemic poverty in the academic discipline philosophy of science. And yet, there witnessing Popper's attacks on inductivism—"the idea that theories can be derived from, or established on the basis of, facts"—Feyerabend was impressed by a Popper talk at the British Society for the Philosophy of Science. Popper showed that higher-level laws, far from reducible to, often conflict with laws supposedly more fundamental. Popper's prime example, already made by the French classical physicist and philosopher of science Pierre Duhem decades earlier, was Kepler's laws of planetary motion, long famed to be, and yet not actually, reducible to Newton's law of universal gravitation.

In "Life's irreducible structure" (1968), Polanyi argues that the information contained in the DNA molecule is not reducible to the laws of physics and chemistry. Although a DNA molecule cannot exist without physical properties, these properties are constrained by higher-level ordering principles. In "Transcendence and Self-transcendence" (1970), Polanyi criticises the mechanistic world view that modern science inherited from Galileo. Polanyi advocates emergence i.e.

A reducible femoral hernia occurs when a femoral hernia can be pushed back into the abdominal cavity, either spontaneously or with manipulation. However, it is more likely to occur spontaneously. This is the most common type of femoral hernia and is usually painless. An irreducible femoral hernia occurs when a femoral hernia cannot be completely reduced, typically due to adhesions between the hernia and the hernial sac.

Another argument for this has been expressed by John Searle, who is the advocate of a distinctive form of physicalism he calls biological naturalism. His view is that although mental states are ontologically irreducible to physical states, they are causally reducible. He has acknowledged that "to many people" his views and those of property dualists look a lot alike, but he thinks the comparison is misleading.

Hence, a Langmuir-Hinshelwood mechanism has been proposed, in which CO adsorbed on gold surfaces reacts with O adsorbed at the edge sites of the gold nanoparticles. The need to use oxide supports, and more specifically reducible supports, is due to their ability to activate dioxygen. Gold nanoparticles supported on inert materials such as carbon or polymers have been proven inactive in CO oxidation.

Because only reactive electrophiles undergo reduction, selectivity is possible in reactions of substrates with multiple reducible functional groups. Chiral Lewis acids and metal complexes may be used for the enantioselective reduction of ketones with hydrosilanes.Hayashi, T.; Hayashi, C.; Uozumi, Y. Tetrahedron: Asymmetry 1995, 6, 2503. (1)File:HSGen.png Upon the generation of a carbocation, rate-determining hydride transfer from the organosilane occurs to yield a reduced product.

Note that this problem is in NP—given a solution it may be verified using the circuit that the solution is correct. A function computation problem belongs to PPA if it admits a polynomial-time reduction to this graph search problem. A problem is complete for the class PPA if in addition, this graph search problem is reducible to that problem. PPA contains PPAD as a subclass.

In the 2-ary case, i.e. for an ordinary group, the existence of an identity element is a consequence of the associativity and inverse axioms, however in n-ary groups for n ≥ 3 there can be zero, one, or many identity elements. An n-ary groupoid (G, ƒ) with ƒ = (x1 ◦ x2 ◦ . . . ◦ xn), where (G, ◦) is a group is called reducible or derived from the group (G, ◦).

A module over a (not necessarily commutative) ring with unity is said to be semisimple (or completely reducible) if it is the direct sum of simple (irreducible) submodules. A ring is said to be (left)-semisimple if it is semisimple as a left module over itself. Surprisingly, a left-semisimple ring is also right-semisimple and vice versa. The left/right distinction is therefore unnecessary.

The earliest methods for solving quadratic equations were geometric. Babylonian cuneiform tablets contain problems reducible to solving quadratic equations. The Egyptian Berlin Papyrus, dating back to the Middle Kingdom (2050 BC to 1650 BC), contains the solution to a two-term quadratic equation. The Greek mathematician Euclid (circa 300 BC) used geometric methods to solve quadratic equations in Book 2 of his Elements, an influential mathematical treatise.

This ensemble is readily formed at the metal-oxide interface and explains the much higher activity of oxide-supported transition metals relative to extended metal surfaces. The turn-over-frequency for the WGSR is proportional to the equilibrium constant of hydroxyl formation, which rationalizes why reducible oxide supports (e.g. CeO2) are more active than irreducible supports (e.g. SiO2) and extended metal surfaces (e.g. Pt).

Vaisheshika, also Vaisesika, (Sanskrit: वैशेषिक) is one of the six Hindu schools of Indian philosophy. It came to be closely associated with the Hindu school of logic, Nyaya. Vaisheshika espouses a form of atomism and postulates that all objects in the physical universe are reducible to a finite number of atoms. Originally proposed by Kanāda (or Kana- bhuk, literally, atom-eater) from around the 2nd century BCE.

Any semisimple algebra (possibly of infinite dimension) is one whose modules are completely reducible, i.e. they decompose into the direct sum of simple modules. Let A_0 \subseteq A_1 \subseteq A_2 \subseteq \cdots be a chain of split semisimple algebras, and let \hat A_i be the indexing set for the irreducible representations of A_i. Denote by A_i^\lambda the irreducible module indexed by \lambda \in \hat A_i.

The most fundamental reducibility notion is Turing reducibility. A set A of natural numbers is Turing reducible to a set B if and only if there is an oracle Turing machine that, when run with B as its oracle set, will compute the indicator function (characteristic function) of A. Equivalently, A is Turing reducible to B if and only if there is an algorithm for computing the indicator function for A provided that the algorithm is provided with a means to correctly answer questions of the form "Is n in B?". Turing reducibility serves as a dividing line for other reducibility notions because, according to the Church-Turing thesis, it is the most general reducibility relation that is effective. Reducibility relations that imply Turing reducibility have come to be known as strong reducibilities, while those that are implied by Turing reducibility are weak reducibilities.

In code optimization during the translation of computer programs into an executable form, and in mathematical reduction generally, a reduction strategy for a term rewriting system determines which reducible subterms (or reducible expressions, redexes) should be reduced (contracted) within a term; it may be the case that a term may contain multiple redexes which are disjoint from one another and that choosing to contract one redex before another may have no influence on the resulting reduced form of the term, or that the redexes in a term do overlap and that choosing to contract one of the overlapping redexes over the other may result in a different reduced form of the term. It is the choice of which redex at each step in the reduction to contract that determines the strategy chosen. This can be seen as a practical application of the theoretical notion of reduction strategy in lambda calculus.

PLS (standing for "Polynomial Local Search") is a class of problems designed to model the process of searching for a local optimum for a function. In particular, it is the class of total function problems that are polynomial-time reducible to the following problem :Given input circuits A and B each with n input and output bits, find x such that A(B(x)) ≤ A(X). It contains the class CLS.

For a point among generally intersecting segments, the visibility polygon problem is reducible, in linear time, to the lower envelope problem. By the Davenport–Schinzel argument, the lower envelope in the worst case has \Theta(n\alpha(n)) number of vertices, where \alpha(n) is the inverse Ackermann function. A worst case optimal divide-and-conquer algorithm running in \Theta(n\log n) time was created by John Hershberger in 1989.

Her attention became famous because of his warmth and closeness with the patients and their children, who could go to the office to hundreds in a single day. In 1910, Aleixandre registered a patent (nº 47109) in favor of two metal pessaries of reducible rings. The pessary is a device that is placed in the vagina to correct the descent or prolapse of the uterus, usually as a result of childbirth.

In geometry, an enneagrammic antiprism is a star antiprism constructed with enneagrammic bases. There are two forms, built on the two enneagrams {9/2} and {9/4}, and one crossed form {9/5}. A nonuniform 9/7 cross-antiprism can be constructed without equal edge-lengths. A 9/3 ratio is reducible and so represents a compound polyhedron of 3 triangular antiprisms with 120 degree rotations between them.

An algebraic hypersurface is an algebraic variety that may be defined by a single implicit equation of the form :p(x_1, \ldots, x_n)=0, where is a multivariate polynomial. Generally the polynomial is supposed to be irreducible. When this is not the case, the hypersurface is not an algebraic variety, but only an algebraic set. It may depend on the authors or the context whether a reducible polynomial defines a hypersurface.

Gold can be a very active catalyst in oxidation of carbon monoxide (CO), i.e. the reaction of CO with molecular oxygen to produce carbon dioxide (CO2). Supported gold clusters, thin films and nanoparticles are one to two orders of magnitude more active than atomically dispersed gold cations or unsupported metallic gold. Possible mechanism of CO oxidation on an Au catalyst supported on a reducible metal oxide at room temperature.

A variety of allylic ethers undergo the Wittig rearrangement—the fundamental requirement is the ability to generate the appropriate carbanion in the substrate. This demands either acidic hydrogens, a reducible functional group, or a carbon-metal bond. Historically, alkenyl, alkynyl, and phenyl groups have been used to acidify the α position. Free terminal alkynes are tolerated, although yields are higher when silyl-protected alkynes are used. (7)File:23Scope3.

Cartesian dualism and Popper's three worlds are two forms of what is called epistemological pluralism, that is the notion that different epistemological methodologies are necessary to attain a full description of the world. Other forms of epistemological pluralist dualism include psychophysical parallelism and epiphenomenalism. Epistemological pluralism is one view in which the mind-body problem is not reducible to the concepts of the natural sciences. A contrasting approach is called physicalism.

Suppose A and B are subsets of Baire space ωω. Then A is Wadge reducible to B or A ≤W B if there is a continuous function f on ωω with A = f^{-1}[B]. The Wadge order is the preorder or quasiorder on the subsets of Baire space. Equivalence classes of sets under this preorder are called Wadge degrees, the degree of a set A is denoted by [A]W.

A vibration will be active in the IR if there is a change in the dipole moment of the molecule and if it has the same symmetry as one of the x, y, z coordinates. To determine which modes are IR active, the irreducible representation corresponding to x, y, and z are checked with the reducible representation of Γvib.Kunju, A. Salahuddin. Group Theory and Its Applications in Chemistry.

Because they lack intentionality they will lack any intentional content. Lacking intentional content their phenomenal character will not be reducible to intentional content, refuting the representational doctrine. Though emotions are typically considered as having directedness and intentionality this idea has also been called into question. One might point to emotions a person all of a sudden experiences that do not appear to be directed at or about anything in particular.

Several variants of this model are also equivalent to DFAs. In particular, the nondeterministic case (in which the transition from one state can be to multiple states given the same input) is reducible to a DFA. Other variants of this model allow more computational complexity. With a single infinite stack the model can parse (at least) any language that is computable by a Turing machine in linear time.

Although many anthropologists have hypothesized that language evolved to help humans describe their world, this ignores the fact that intra-species violence, not the environment, poses the greatest threat to human existence. Human representation, according to Gans, is not merely a "natural" evolutionary development of animal communication systems, but is a radical departure from it. The signifier implies a symbolic dimension that is not reducible to empirical referents.

A function may be recursively defined in terms of itself. A familiar example is the Fibonacci number sequence: F(n) = F(n − 1) + F(n − 2). For such a definition to be useful, it must be reducible to non-recursively defined values: in this case F(0) = 0 and F(1) = 1. A famous recursive function is the Ackermann function, which, unlike the Fibonacci sequence, cannot be expressed without recursion.

By a broadly similar process sodium sulfide can react with alkenes in the thiol-ene reaction to give thioethers. Sodium sulfide can be used as nucleophile in Sandmeyer type reactions. Sodium sulfide reduces1,3-dinitrobenzene derivatives to the 3-nitroanilines. Aqueous solution of sodium sulfide can be refluxed with nitro carrying azo dyes dissolved in dioxane and ethanol to selectively reduce the nitro groups to amine; while other reducible groups, e.g.

In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic.Logicism Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.

G. E. M. Anscombe wrote about how facts can be brute relative to other facts. Simply put, some facts cannot be reducible to other facts, such that if some set of facts holds true, it does not entail the fact brute relative to it. The example she uses is that of someone owing a grocer money for supplying them with potatoes. In such a case, the set of facts, e.g.

The strong reductions listed above restrict the manner in which oracle information can be accessed by a decision procedure but do not otherwise limit the computational resources available. Thus if a set A is decidable then A is reducible to any set B under any of the strong reducibility relations listed above, even if A is not polynomial-time or exponential-time decidable. This is acceptable in the study of recursion theory, which is interested in theoretical computability, but it is not reasonable for computational complexity theory, which studies which sets can be decided under certain asymptotical resource bounds. The most common reducibility in computational complexity theory is polynomial-time reducibility; a set A is polynomial-time reducible to a set B if there is a polynomial-time function f such that for every n, n is in A if and only if f(n) is in B. This reducibility is, essentially, a resource-bounded version of many-one reducibility.

Although there are many known types of oracles, the choice of which to use can be simplified, because many of them are equivalent in computational power. An oracle \scriptstyle X is said to be polynomially reducible to another oracle \scriptstyle Y if any call to \scriptstyle X may be simulated by an algorithm that accesses the matroid using only oracle \scriptstyle Y and takes polynomial time as measured in terms of the number of elements of the matroid; in complexity-theoretic terms, this is a Turing reduction. Two oracles are said to be polynomially equivalent if they are polynomially reducible to each other. If \scriptstyle X and \scriptstyle Y are polynomially equivalent, then every result that proves the existence or nonexistence of a polynomial time algorithm for a matroid problem using oracle \scriptstyle X also proves the same thing for oracle \scriptstyle Y. For instance, the independence oracle is polynomially equivalent to the circuit-finding oracle of .

Roughly, a reduction strategy is a function that maps a lambda calculus term with reducible expressions to one particular reducible expression, the one to be reduced next. Mathematical logicians have studied the properties of this system for decades, and the superficial similarity between the description of evaluation strategies and reduction strategies originally misled programming language researchers to speculate that the two were identical, a belief that is still visible in popular textbooks from the early 1980s;Structure and Interpretation of Computer Programs by Abelson and Sussman, MIT Press 1983 these are, however, different concepts. PlotkinCall- by-name, call-by-value, and the lambda calculus showed in 1973, however, that a proper model of an evaluation strategy calls for the formulation of a new axiom for function calls, that is, an entirely new calculus. He validates this idea with two different calculi: one for call-by-name and another one for call-by-value, each for purely functional programming languages.

Contrary to the views of his colleague and friend Alan Turing, whose work at the Victoria University of Manchester prepared the way for the first modern computer, he denied that minds are reducible to collections of rules. His work influenced the critique by Hubert Dreyfus of "First Generation" artificial intelligence. It was while writing Personal Knowledge that he identified the "structure of tacit knowing". He viewed it as his most important discovery.

Appel and Haken's final discharging procedure was extremely complex and, together with a description of the resulting unavoidable configuration set, filled a 400-page volume, but the configurations it generated could be checked mechanically to be reducible. Verifying the volume describing the unavoidable configuration set itself was done by peer review over a period of several years. A technical detail not discussed here but required to complete the proof is immersion reducibility.

It may be wonderful to have access to an unlimited number of distinctions to define what one means, but not all scholars would agree that any concept is equal to, or reducible to, a mathematical set.Susan L. Epstein, "Memory and concepts in reactive learning". Proceedings of the Canadian Workshop on Machine Learning 1992. Some phenomena are difficult or impossible to quantify and count, in particular if they lack discrete boundaries (for example, clouds).

The security of the NTRU encryption scheme and the BLISS signature is believed to be related to, but not provably reducible to, the Closest Vector Problem (CVP) in a Lattice. The CVP is known to be NP-hard. The Post Quantum Cryptography Study Group sponsored by the European Commission suggested that the Stehle–Steinfeld variant of NTRU which does have a security reduction be studied for long term use instead of the original NTRU algorithm.

Kneale p. 435 Frege went much further than any of his predecessors in his rigorous and formal approach to logic, and his calculus or Begriffsschrift is important. Frege also tried to show that the concept of number can be defined by purely logical means, so that (if he was right) logic includes arithmetic and all branches of mathematics that are reducible to arithmetic. He was not the first writer to suggest this.

Born in Autrecourt, near Verdun, he was educated at Paris and earned bachelor's degrees in theology and law and a master's degree in arts. Nicholas is known principally for developing skepticism to extreme logical conclusions. He is sometimes considered the sole genuinely skeptic philosopher of medieval times. Nicholas founded his skeptical position on arguments that knowledge claims were not "reducible to the first principle," that is, that it was not contradictory to deny them.

Painting not being reducible to drawing, it is a source of disunity and disorder in our systems of knowledge, one which elicits an experience of "lack" (insuffisance). The history of this conflict, she argued, begins in Platonic thought, which condemns color and rhetoric equally. The arts of speech and those of imagery are thus definitively linked. A central later figure is Roger de Piles, the leader of the Rubenists, the partisans of color (coloris).

The SAT problem is self-reducible, that is, each algorithm which correctly answers if an instance of SAT is solvable can be used to find a satisfying assignment. First, the question is asked on the given formula Φ. If the answer is "no", the formula is unsatisfiable. Otherwise, the question is asked on the partly instantiated formula Φ{x1=TRUE}, i.e. Φ with the first variable x1 replaced by TRUE, and simplified accordingly.

The collapse of L and SL has a number of significant consequences. Most obviously, all SL-complete problems are now in L, and can be gainfully employed in the design of deterministic log-space and polylogarithmic-space algorithms. In particular, we have a new set of tools to use in log-space reductions. It is also now known that a problem is in L if and only if it is log-space reducible to USTCON.

Adding NaN3, a toxic substance, also significantly reduces the sequestration rates of the fungal BMOs. Heat treatments revealed that temperatures below 85 °C do not alter the conformation of the Mn(II) oxidase in the BMOs. Freezing the fungal BMOs at -80 °C for 4 weeks did not affect the Mn(II) ability, and the reducible Mn was still dominated in solution. This makes fungal BMOs an effective Mn(II) sequestering material if needed.

In algebra, an analytically normal ring is a local ring whose completion is a normal ring, in other words a domain that is integrally closed in its quotient field. proved that if a local ring of an algebraic variety is normal, then it is analytically normal, which is in some sense a variation of Zariski's main theorem. gave an example of a normal Noetherian local ring that is analytically reducible and therefore not analytically normal.

In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.

The apex graphs include graphs that are themselves planar, in which case again every vertex is an apex. The null graph is also counted as an apex graph even though it has no vertex to remove. Apex graphs are closed under the operation of taking minors and play a role in several other aspects of graph minor theory: linkless embedding, Hadwiger's conjecture,. YΔY-reducible graphs, and relations between treewidth and graph diameter.

Furthermore, this problem is random self- reducible, which ensures that for a given N, every public key is just as secure as every other public key. The GM cryptosystem has homomorphic properties, in the sense that if c0, c1 are the encryptions of bits m0, m1, then c0c1 mod N will be an encryption of m_0 \oplus m_1. For this reason, the GM cryptosystem is sometimes used in more complex cryptographic primitives.

Any sentence that is not purely logical, or is unverifiable is devoid of meaning. As a result, most metaphysical, ethical, aesthetic and other traditional philosophical problems came to be considered pseudoproblems.Barone, Francesco (1986), Il neopositivismo logico, Laterza, Roma Bari. In the extreme empiricism of the neopositivists—at least before the 1930s—any genuinely synthetic assertion must be reducible to an ultimate assertion (or set of ultimate assertions) that expresses direct observations or perceptions.

Problems that require some privacy in the data (typically cryptographic problems) can use randomization to ensure that privacy. In fact, the only provably secure cryptographic system (the one-time pad) has its security relying totally on the randomness of the key data supplied to the system. The field of cryptography utilizes the fact that certain number-theoretic functions are randomly self-reducible. This includes probabilistic encryption and cryptographically strong pseudorandom number generation.

If the state has no intentional content its phenomenal character will not be reducible to that state's intentional content, for it has none to begin with. A common example of this kind of state are moods. Moods are states with phenomenal character that are generally thought to not be directed at anything in particular. Moods are thought to lack directedness, unlike emotions, which are typically thought to be directed at particular things e.g.

In Aristotelian logic, dictum de omni et nullo (Latin: "the maxim of all and none") is the principle that whatever is affirmed or denied of a whole kind K may be affirmed or denied (respectively) of any subkind of K. This principle is fundamental to syllogistic logic in the sense that all valid syllogistic argument forms are reducible to applications of the two constituent principles dictum de omni and dictum de nullo.

However, in this example, vowel reduction occurred when the infixes were added before the vowel, causing the infixes -in- and -om- to become -inm-. When forming binombomtak, "were exploding," from betak, "explode," the reducible vowel and reduplication steps were re-ordered so no vowel reduction was experienced. Some highly marked affixes have an infixed glottal stop leading the second vowel such as when forming bangbangʡa, "little old pots, toy pots," from banga, "pot".

Waterborne resins are sometimes called water-based resins. They are resins or polymeric resins that use water as the carrying medium as opposed to solvent or solvent-less. Resins are used in the production of coatings, adhesives, sealants, elastomers and composite materials..When the phrase waterborne resin is used it usually describes all resins which have water as the main carrying solvent. The resin could be water soluble, water reducible or water dispersed.

Over fields of characteristic 0 the Specht modules are irreducible, and form a complete set of irreducible representations of the symmetric group. A partition is called p-regular if it does not have p parts of the same (positive) size. Over fields of characteristic p>0 the Specht modules can be reducible. For p-regular partitions they have a unique irreducible quotient, and these irreducible quotients form a complete set of irreducible representations.

Another theorem named partly after Castelnuovo is the Kronecker–Castelnuovo theorem (1894): If the sections of an irreducible algebraic surface, having at most isolated singular points, with a general tangent plane turn out to be reducible curves, then the surface is either ruled surface and in fact a scroll, or the Veronese surface. Kronecker never published it but stated it in a lecture. Castelnuovo proved it. In total, Castelnuovo published over 100 articles, books and memoirs.

In mathematics, computer science and logic, overlap, as a property of the reduction rules in term rewriting system, describes a situation where a number of different reduction rules specify potentially contradictory ways of reducing a reducible expression, also known as a redex, within a term. More precisely, if a number of different reduction rules share function symbols on the left-hand side, overlap can occur. Often we do not consider trivial overlap with a redex and itself.

A text is inscribed at the bottom-left: "But the sand or clay to which by one or the other process we are reducible are turned to glass and foam." Surf art has manifested as cave drawings by old native Hawaiians along with painters, surrealists, graphic designers, sculptures and installation artists. Many are surfers themselves. Surf art has spread from coastal areas to urban cities, such as New York, where surf culture and art exhibitions can now be found.

It can be interpreted as taking multiple paths of computation simultaneously through a finite number of states. However, it is possible to prove that any NFA is reducible to an equivalent DFA. ;Pushdown automaton: Similar to the finite state machine, except that it has available an execution stack, which is allowed to grow to arbitrary size. The state transitions additionally specify whether to add a symbol to the stack, or to remove a symbol from the stack.

An equivalent definition is the class of problems AC0 reducible to CCVP. As an example, a sorting network can be used to compute majority by designating the middle wire as an output wire: If the middle wire is designated as output, and the wires are annotated with 16 different input variables, then the resulting comparator circuit computes majority. Since there are sorting networks which can be constructed in AC0, this shows that the majority function is in CC.

The concept of reduction, also called multivariate division or normal form computation, is central to Gröbner basis theory. It is a multivariate generalization of the Euclidean division of univariate polynomials. In this section we suppose a fixed monomial ordering, which will not be defined explicitly. Given two polynomials f and g, one says that f is reducible by g if some monomial m in f is a multiple of the leading monomial lm(g) of g.

However, Eliade argues against those he calls "historicist or existentialist philosophers" who do not recognize "man in general" behind particular men produced by particular situations (Eliade cites Immanuel Kant as the likely forerunner of this kind of "historicism".)Eliade, Images and Symbols, p. 32. He adds that human consciousness transcends (is not reducible to) its historical and cultural conditioning,Eliade, Images and Symbols, p. 33. and even suggests the possibility of a "transconscious".Eliade, Images and Symbols, p. 17.

Rice showed that for every nontrivial class C (which contains some but not all r.e. sets) the index set E = {e: the eth r.e. set We is in C} has the property that either the halting problem or its complement is many-one reducible to E, that is, can be mapped using a many-one reduction to E (see Rice's theorem for more detail). But, many of these index sets are even more complicated than the halting problem.

Another distance measure commonly used in agglomerative clustering is the distance between the centroids of pairs of clusters, also known as the weighted group method. It can be calculated easily in constant time per distance calculation. However, it is not reducible. For instance, if the input forms the set of three points of an equilateral triangle, merging two of these points into a larger cluster causes the inter- cluster distance to decrease, a violation of reducibility.

In an interview with Amy Taubin, Hanson said, "The very things that made Michael and I want to do the movie so badly were the reasons it was so tricky to market. Since films go out on so many screens at once, there's a need for instant appeal. But Wonder Boys isn't easily reducible to a single image or a catchy ad line". Hanson felt that the studio played it safe with the original ad campaign.

One major philosophical view which was rejected by all the schools mentioned above was the view held by the Pudgalavadin or 'personalist' schools. They seemed to have held that there was a sort of 'personhood' in some ultimately real sense which was not reducible to the five aggregates. This controversial claim was in contrast to the other Buddhists of the time who held that a personality was a mere conceptual construction (prajñapti) and only conventionally real.

In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring that is a semisimple module over itself is known as an Artinian semisimple ring. Some important rings, such as group rings of finite groups over fields of characteristic zero, are semisimple rings. An Artinian ring is initially understood via its largest semisimple quotient.

The planar graphs and the apex graphs are linklessly embeddable, as are the graphs obtained by Y-Δ transforms from these graphs. The YΔY reducible graphs are the graphs that can be reduced to a single vertex by Y-Δ transforms, removal of isolated vertices and degree-one vertices, and compression of degree-two vertices; they are also minor-closed, and include all planar graphs. However, there exist linkless graphs that are not YΔY reducible, such as the apex graph formed by connecting an apex vertex to every degree-three vertex of a rhombic dodecahedron.. There also exist linkless graphs that cannot be transformed into an apex graph by Y-Δ transforms, removal of isolated vertices and degree-one vertices, and compression of degree-two vertices: for instance, the ten-vertex crown graph has a linkless embedding, but cannot be transformed into an apex graph in this way. Related to the concept of linkless embedding is the concept of knotless embedding, an embedding of a graph in such a way that none of its simple cycles form a nontrivial knot.

A Y-Δ transform, an operation that replaces a degree-three vertex in a graph by a triangle connecting its neighbors, is sufficient (together with the removal of parallel edges) to reduce any Apollonian network to a single triangle, and more generally the planar graphs that can be reduced to a single edge by Y-Δ transforms, removal of parallel edges, removal of degree-one vertices, and compression of degree- two vertices are exactly the planar partial 3-trees. The dual graphs of the planar partial 3-trees form another minor-closed graph family and are exactly the planar graphs that can be reduced to a single edge by Δ-Y transforms, removal of parallel edges, removal of degree-one vertices, and compression of degree-two vertices. introduced the Δ-Y reducible planar graphs and characterized them in terms of forbidden homeomorphic subgraphs. The duality between the Δ-Y and Y-Δ reducible graphs, the forbidden minor characterizations of both classes, and the connection to planar partial 3-trees are all from .

For each factor mod p^a, we can test if it corresponds to a "true" factor, and if so, find that "true" factor, provided that p^a exceeds 2B. This way, all irreducible "true" factors can be found by checking at most 2^r cases. This is reduced to 2^{r-1} cases by skipping complements. If f(x) is reducible, the number of cases is reduced further by removing those f_i(x) that appear in an already found "true" factor.

Since the proving of the theorem, efficient algorithms have been found for 4-coloring maps requiring only O(n2) time, where n is the number of vertices. In 1996, Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas created a quadratic-time algorithm, improving on a quartic-time algorithm based on Appel and Haken's proof.; ). This new proof is similar to Appel and Haken's but more efficient because it reduces the complexity of the problem and requires checking only 633 reducible configurations.

Then one "flows" the charge by systematically redistributing the charge from a vertex to its neighboring vertices according to a set of rules, the discharging procedure. Since charge is preserved, some vertices still have positive charge. The rules restrict the possibilities for configurations of positively charged vertices, so enumerating all such possible configurations gives an unavoidable set. As long as some member of the unavoidable set is not reducible, the discharging procedure is modified to eliminate it (while introducing other configurations).

To motivate the definition, consider the case of a reducible complex algebraic curve X consisting of two nonsingular components, X_1 and X_2, which transversally intersect at the points Q_1 and Q_2. Further, assume that the components are not compact, but can be compactified by adding the points P_1,\dots ,P_n. The first cohomology group of the curve X (with compact support) is dual to the first homology group, which is easier to visualize. There are three types of one-cycles in this group.

IV., W. Foerst, Ed., Academic Press, New York, 1968, pp. 163–335. These two reagents are on the extremes of reactivity—whereas lithium aluminium hydride reacts with nearly all reducible functional groups, sodium borohydride reacts with a much more limited range of functional groups. Diminished or enhanced reactivity may be realized by the replacement of one or more of the hydrogens in these reagents with alkoxy groups. Additionally, substitution of hydrogen for chiral alkoxy groups in these reagents enables asymmetric reductions.

The result is a world in which human agency and social structure each presuppose the other though neither is reducible to, or completely explicable in terms of, the other. More specifically, Lawson argues that social reality is everywhere constituted through positioning people and things as components of social totalities, whereupon human actions and uses of positioned objects are guided by rights and obligations associated with the positions. Whole communities can also be so positioned, as in the formation of corporations.

The context- free nature of the language makes it simple to parse with a pushdown automaton. Determining an instance of the membership problem; i.e. given a string w, determine whether w \in L(G) where L is the language generated by a given grammar G; is also known as recognition. Context-free recognition for Chomsky normal form grammars was shown by Leslie G. Valiant to be reducible to boolean matrix multiplication, thus inheriting its complexity upper bound of O(n2.3728639).

"Why I Am Not a Property Dualist." Archived from the original on 10 December 2006. Non-reductive physicalism is a form of property dualism in which it is asserted that all mental states are causally reducible to physical states. One argument for this has been made in the form of anomalous monism expressed by Donald Davidson, where it is argued that mental events are identical to physical events, however, relations of mental events cannot be described by strict law-governed causal relationships.

Some scholars conjecture that a quantum mechanical system which somehow uses an infinite superposition of states could compute a non-computable function.There have been some claims to this effect; see or and the ensuing literature. For a retort see . This is not possible using the standard qubit- model quantum computer, because it is proven that a regular quantum computer is PSPACE-reducible (a quantum computer running in polynomial time can be simulated by a classical computer running in polynomial space).

Lignite can be separated into two types. The first is xyloid lignite or fossil wood and the second form is the compact lignite or perfect lignite. Although xyloid lignite may sometimes have the tenacity and the appearance of ordinary wood, it can be seen that the combustible woody tissue has experienced a great modification. It is reducible to a fine powder by trituration, and if submitted to the action of a weak solution of potash, it yields a considerable quantity of humic acid.

The smallest unit in Stoic logic is an assertible (the Stoic equivalent of a proposition) which is the content of a statement such as "it is day". Assertibles have a truth-value such that at any moment of time they are either true or false. Compound assertibles can be built up from simple ones through the use of logical connectives. The resulting syllogistic was grounded on five basic indemonstrable arguments to which all other syllogisms were claimed to be reducible.

Every reducibility relation (in fact, every preorder) induces an equivalence relation on the powerset of the natural numbers in which two sets are equivalent if and only if each one is reducible to the other. In recursion theory, these equivalence classes are called the degrees of the reducibility relation. For example, the Turing degrees are the equivalence classes of sets of naturals induced by Turing reducibility. The degrees of any reducibility relation are partially ordered by the relation in the following manner.

One of the wires is designated as the output wire. The function computed by the circuit is evaluated by initializing the wires according to the input variables, executing the comparator gates in order, and outputting the value carried by the output wire. The comparator circuit value problem (CCVP) is the problem of evaluating a comparator circuit given an encoding of the circuit and the input to the circuit. The complexity class CC is defined as the class of problems logspace reducible to CCVP.

The ECOH hash functions are based on concrete mathematical functions. They were designed such that the problem of finding collisions should be reducible to a known and hard mathematical problem (the subset sum problem). It means that if one could find collisions, one would be able to solve the underlying mathematical problem which is assumed to be hard and unsolvable in polynomial time. Functions with these properties are known provably secure and are quite unique among the rest of hash functions.

This sense of emotional wonder appears evident at the root of all religious experiences. Through this emotional wonder, we suspend our rational mind for non-rational possibilities. The Idea of the Holy also set out a paradigm for the study of religion that focuses on the need to realize the religious as a non-reducible, original category in its own right. This paradigm was under much attack between approximately 1950 and 1990 but has made a strong comeback since then.

Polymethylhydrosiloxane (PMHS) is a polymer with the general structure -(CH3(H)Si-O)-. It is used in organic chemistry as a mild and stable reducing agent easily transferring hydrides to metal centers and a number of other reducible functional groups.J. M. Lavis, R. E. Maleczka, Jr. "Polymethylhydrosiloxane" Encyclopedia of Reagents for Organic Synthesis 2003, John Wiley & Sons. A variety of related materials are available under the following CAS registry numbers 9004-73-3, 16066-09-4, 63148-57-2, 178873-19-3.

Ginsberg manifested an 'objectivist' theory of ethics in the tradition of Plato, Aristotle, Mill, Sidgwick and Hobhouse. This led him to maintain that 'value' and 'obligation', 'good' and 'bad' are terms not further reducible or analysable into each other or into terms not implying them. He also deals positively with the notion of levels of moral development, and suggests criteria for assessing these. Using these criteria it is possible to detect unmistakable differences of level between different societies in the modern world.

He thought the two-limbed test was well-settled and there was no need to alter it. On the application of the first limb (discrimination), he found the Commonwealth law in singling out (and thus discriminating against) state judges placed a burden upon the states and was thus invalid. His reasoning thus implicitly links the two limbs of the test. Kirby J agreed with the majority's assessment that the Melbourne Corporation principle is actually reducible to a one-limbed test.

Morphological analysis was designed for multi-dimensional, non-quantifiable problems where causal modeling and simulation do not function well or at all. Fritz Zwicky developed this approach to seemingly non-reducible complexity (Zwicky, 1966, 1969). Using the technique of cross consistency assessment (CCA) (Ritchey, 2002), the system however does allow for reduction, not by reducing the number of variables involved, but by reducing the number of possible solutions through the elimination of the illogical solution combinations in a grid box.

In more detail: an affine group scheme G of finite type over a field k is called linearly reductive if its finite-dimensional representations are completely reducible. For k of characteristic zero, G is linearly reductive if and only if the identity component Go of G is reductive.Milne (2017), Corollary 22.43. For k of characteristic p>0, however, Masayoshi Nagata showed that G is linearly reductive if and only if Go is of multiplicative type and G/Go has order prime to p.

A decision problem C is co-NP-complete if it is in co-NP and if every problem in co-NP is polynomial-time many-one reducible to it. This means that for every co-NP problem L, there exists a polynomial time algorithm which can transform any instance of L into an instance of C with the same truth value. As a consequence, if we had a polynomial time algorithm for C, we could solve all co-NP problems in polynomial time.

In representation theory, a branch of mathematics, the Gelfand–Graev representation is a representation of a reductive group over a finite field introduced by , induced from a non-degenerate character of a Sylow subgroup. The Gelfand–Graev representation is reducible and decomposes as the sum of irreducible representations, each of multiplicity at most 1. The irreducible representations occurring in the Gelfand–Graev representation are called regular representations. These are the analogues for finite groups of representations with a Whittaker model.

This is done by using the symmetry of the molecules and orbitals involved in bonding, and thus is sometimes called Symmetry Adapted Linear Combination (SALC). The first step in this process is assigning a point group to the molecule. A common example is water, which is of C2v symmetry. Then a reducible representation of the bonding is determined demonstrated below for water: :The irreducible representation as derived from the point group's operations Each operation in the point group is performed upon the molecule.

One way that leads to generalizations is to allow reducible algebraic sets (and fields that aren't algebraically closed), so the rings R may not be integral domains. A more significant modification is to allow nilpotents in the sheaf of rings, that is, rings which are not reduced. This is one of several generalizations of classical algebraic geometry that are built into Grothendieck's theory of schemes. Allowing nilpotent elements in rings is related to keeping track of "multiplicities" in algebraic geometry.

The liability incurred by a surety under his guarantee depends upon its terms, and is not necessarily coextensive with that of the principal debtor. It is, however, obvious that the surety's obligation cannot exceed that of the principal.de Colyar, Law of Guarantees, 3rd ed. p. 233; Burge, Suretyship, p. 5 By many existing civil codes, however, a guarantee which imposes on the surety a greater liability than that of the principal is not invalidated but is merely reducible to that of the principal.

Mirecourt reasoned that there are two kinds of certain knowledge: (1) 'the principle of non-contradiction,' and (2) 'the immediate intuition of one's existence'. The most undoubtedly of all things that can be known fall to this first kind of knowledge, as well as all analytic judgements that are reducible to it. Mirecourt distinguishes between two kinds of evidence of these kinds of knowledge: (1) special and (2) natural. Special evidence comes from the principle of non-contradiction, and natural evidence is that which is gained empirically.

In Valiant's paper, O(n2.81) was the then-best known upper bound. See Matrix multiplication#Algorithms for efficient matrix multiplication and Coppersmith–Winograd algorithm for bound improvements since then. Conversely, Lillian Lee has shown O(n3−ε) boolean matrix multiplication to be reducible to O(n3−3ε) CFG parsing, thus establishing some kind of lower bound for the latter. Practical uses of context-free languages require also to produce a derivation tree that exhibits the structure that the grammar associates with the given string.

PWPP is the corresponding class of problems that are polynomial-time reducible to it. WEAK-PIGEON is the following problem: :Given a Boolean circuit C having n input bits and n-1 output bits, find x e y such that C(x) = C(y). Here, the range of the circuit is strictly smaller than its domain, so the circuit is guaranteed to be non-injective. WEAK-PIGEON reduces to PIGEON by appending a single 1 bit to the circuit's output, so PWPP \subseteq PPP.

The long Hotshot, introduced for $849, weighed just . But to go racing, the weight was further reducible to , by temporarily discarding such things as the detachable windscreen, and the non-folding (stowed) soft-top and side-curtains. There was no trunk lid — the spare wheel was mounted on the down-sloping rear deck, above the rear bumper, and access to the rear stowage room was by folding the seat-backs forward. Powered by a 26.5 HP CIBA engine, the Hotshot was capable of more than .

In algebra, an analytically irreducible ring is a local ring whose completion has no zero divisors. Geometrically this corresponds to a variety with only one analytic branch at a point. proved that if a local ring of an algebraic variety is a normal ring, then it is analytically irreducible. There are many examples of reduced and irreducible local rings that are analytically reducible, such as the local ring of a node of an irreducible curve, but it is hard to find examples that are also normal.

Due to his dissatisfaction with the ability hypothesis, Earl Conee presents another variant. Conee's acquaintance hypothesis identifies a third category of knowledge, "knowledge by acquaintance of an experience," that is not reducible to factual knowledge nor to knowing-how. He argues that the knowledge Mary actually acquires post-release is acquaintance knowledge. Knowing an experience by acquaintance "requires the person to be familiar with the known entity in the most direct way that it is possible for a person to be aware of that thing".

The braid group can be shown to be isomorphic to the mapping class group of a punctured disk with punctures. This is most easily visualized by imagining each puncture as being connected by a string to the boundary of the disk; each mapping homomorphism that permutes two of the punctures can then be seen to be a homotopy of the strings, that is, a braiding of these strings. Via this mapping class group interpretation of braids, each braid may be classified as periodic, reducible or pseudo-Anosov.

One can also phrase this differently, as a question of reduction of the structure group of the tangent bundle from to a reducible subgroup. The conditions in the Frobenius theorem appear as integrability conditions; and the assertion is that if those are fulfilled the reduction can take place because local transition functions with the required block structure exist. For example, in the codimension 1 case, we can define the tangent bundle of the foliation as , for some (non-canonical) (i.e. a non-zero co-vector field).

This effect is potentially reducible, such as in China where commercially farmed turtles may be reducing some of the pressure to poach endangered species. Another problem with the listing species is its effect of inciting the use of the "shoot, shovel, and shut-up" method of clearing endangered species from an area of land. Some landowners currently may perceive a diminution in value for their land after finding an endangered animal on it. They have allegedly opted to kill and bury the animals or destroy habitat silently.

The strategy followed in the classification of the irreducible infinite-dimensional representations is, in analogy to the finite-dimensional case, to assume they exist, and to investigate their properties. Thus first assume that an irreducible strongly continuous infinite-dimensional representation on a Hilbert space of is at hand. Since is a subgroup, is a representation of it as well. Each irreducible subrepresentation of is finite-dimensional, and the representation is reducible into a direct sum of irreducible finite-dimensional unitary representations of if is unitary.

Delhi: Phi Learning, 2015, 83-86. An IR mode is active if the same irreducible representation is present in both. Furthermore, a vibration will be Raman active if there is a change in the polarizability of the molecule and if it has the same symmetry as one of the direct products of the x, y, z coordinates. To determine which modes are Raman active, the irreducible representation corresponding to xy, xz, yz, x2, y2, and z2 are checked with the reducible representation of Γvib.

A string rewriting system is a special type of Post canonical system with a single initial word, and the productions are each of the form : P_1 g P_2 \ \rightarrow \ P_1 h P_2 That is, each production rule is a simple substitution rule, often written in the form g -> h. It has been proved that any Post canonical system is reducible to such a substitution system, which, as a formal grammar, is also called a phrase-structure grammar, or a type-0 grammar in the Chomsky hierarchy.

The Vaiśeṣika philosophy is a naturalist school. It is a form of atomism in natural philosophy.Analytical philosophy in early modern India J Ganeri, Stanford Encyclopedia of Philosophy It postulates that all objects in the physical universe are reducible to paramāṇu (atoms), and that one's experiences are derived from the interplay of substance (a function of atoms, their number and their spatial arrangements), quality, activity, commonness, particularity and inherence. Knowledge and liberation are achievable by complete understanding of the world of experience, according to Vaiśeṣika school.

Analytical philosophy in early modern India J Ganeri, Stanford Encyclopedia of Philosophy It postulated that all objects in the physical universe are reducible to paramāṇu (atoms), and one's experiences are derived from the interplay of substance (a function of atoms, their number and their spatial arrangements), quality, activity, commonness, particularity and inherence.Oliver Leaman, Key Concepts in Eastern Philosophy. Routledge, , 1999, page 269. Everything was composed of atoms, qualities emerged from aggregates of atoms, but the aggregation and nature of these atoms was predetermined by cosmic forces.

Postmodernism is a reaction to modernism, but it can also be viewed as a response to a deep- seated shift in societal attitude. According to this latter view, postmodernism began when historic (as opposed to personal) optimism turned to pessimism, at the latest by 1930 . John Cage is a prominent figure in 20th- century music, claimed with some justice both for modernism and postmodernism because the complex intersections between modernism and postmodernism are not reducible to simple schemata . His influence steadily grew during his lifetime.

Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism.

In general, solutions of the isomonodromy equations cannot be expressed in terms of simpler functions such as solutions of linear differential equations. However, for particular (more precisely, reducible) choices of extended monodromy data, solutions can be expressed in terms of such functions (or at least, in terms of 'simpler' isomonodromy transcendents). The study of precisely what this transcendence means has been largely carried out by the invention of 'nonlinear differential Galois theory' by Hiroshi Umemura and Bernard Malgrange. There are also very special solutions which are algebraic.

Another key elements to Durkheim's theory of knowledge outlined in Elementary Forms is the concept of ("collective representations"). ' are the symbols and images that come to represent the ideas, beliefs, and values elaborated by a collectivity and are not reducible to individual constituents. They can include words, slogans, ideas, or any number of material items that can serve as a symbol, such as a cross, a rock, a temple, a feather etc. As Durkheim elaborates, ' are created through intense social interaction and are products of collective activity.

In this text Nietzsche was either not effective at, or not concerned with, persuading his readers to accept any specific point of view. Yet the discerning reader can note here the prefigurations of many of the ideas more fully developed in his later books. For example, the materialism espoused in this book might seem reducible to a naive scientific objectivism which reduces all phenomena to their natural, mechanical causes. Yet that is very straightforwardly not Nietzsche's strongest perspective, perhaps traditionally most well-expressed in The Gay Science.

One of the most fundamental debates in philosophy concerns the "true" nature of the world—whether it is some ethereal plane of ideas or a reality of atomic particles and energy. Materialism posits a real 'world out there,' as well as in and through us, that can be sensed—seen, heard, tasted, touched and felt, sometimes with prosthetic technologies corresponding to human sensing organs. (Materialists do not claim that human senses or even their prosthetics can, even when collected, sense the totality of the 'universe'; simply that they collectively cannot sense what cannot in any way be known to us.) Materialists do not find this a useful way of thinking about the ontology and ontogeny of ideas, but we might say that from a materialist perspective pushed to a logical extreme communicable to an idealist, ideas are ultimately reducible to a physically communicated, organically, socially and environmentally embedded 'brain state'. While reflexive existence is not considered by materialists to be experienced on the atomic level, the individual's physical and mental experiences are ultimately reducible to the unique tripartite combination of environmentally determined, genetically determined, and randomly determined interactions of firing neurons and atomic collisions.

PPAD (standing for "Polynomial time Parity Argument, Directed") is a restriction of PPA to problems whose solutions are guaranteed by a directed version of the handshake lemma. It is often defined as the set of problems that are polynomial-time reducible to End-of-a-Line: :Given circuits S and P with n input and output bits S(0) ≠ 0 and P(0) = 0, find x such that P(S(x)) ≠ x or x ≠ 0 such that S(P(x)) ≠ x. PPAD is in the intersection of PPA and PPP, and it contains CLS.

Chalmers characterizes his view as "naturalistic dualism": naturalistic because he believes mental states supervenes "naturally" on physical systems (such as brains); dualist because he believes mental states are ontologically distinct from and not reducible to physical systems. He has also characterized his view by more traditional formulations such as property dualism. In support of this, Chalmers is famous for his commitment to the logical (though, importantly, not natural) possibility of philosophical zombies. These zombies, unlike the zombie of popular fiction, are complete physical duplicates of human beings, lacking only qualitative experience.

"God or the Divine is" without being able to attribute qualities about "what He is" would be the prerequisite of positive theology in negative theology that distinguishes theism from atheism. "Negative theology is a complement to, not the enemy of, positive theology". Since religious experience—or consciousness of the holy or sacred, is not reducible to other kinds of human experience, an abstract understanding of religious experience cannot be used as evidence or proof that religious discourse or praxis can have no meaning or value.Lonergan, Bernard (1972), "Method in Theology", New York, N.Y.: Seabury Press, .

The graph automorphism problem is the problem of testing whether a graph has a nontrivial automorphism. It belongs to the class NP of computational complexity. Similar to the graph isomorphism problem, it is unknown whether it has a polynomial time algorithm or it is NP- complete.. There is a polynomial time algorithm for solving the graph automorphism problem for graphs where vertex degrees are bounded by a constant. The graph automorphism problem is polynomial-time many-one reducible to the graph isomorphism problem, but the converse reduction is unknown.

In fact, the system does not have to even be liquid. A tube plugged with cotton with a little ammonium hydroxide at one end, and a solution of hydrochloric acid at the other will show rings of deposited ammonium chloride where the two gases meet, if the conditions are chosen correctly. Ring formation has also been observed in solid glasses containing a reducible species. For example, bands of silver have been generated by immersing silicate glass in molten AgNO3 for extended periods of time (Pask and Parmelee, 1943).

A hernia is caused by the protrusion of a viscus (in the case of groin hernias, an intra-abdominal organ) through a weakness in the abdominal wall. This weakness may be inherent, as in the case of inguinal, femoral and umbilical hernias. On the other hand, the weakness may be caused by previous surgical incision through the muscles and fascia in the area; this is termed an incisional hernia. A femoral hernia may be either reducible or irreducible, and each type can also present as obstructed and/or strangulated.

The idea of the explanatory gap is that an unbridgeable gap exists when trying to comprehend consciousness from the perspective of natural science as a scientific explanation of mental states would require a reduction from a physical process to phenomenal experience. The property of mental states to be experienced from a subjective point of view (see Qualia) might not be reducible from the objective, i.e. outside perspective of science. In this sense there would be a gap between the outside perspective of science and the internal perspective of phenomenal experience.

In this approach, we base the security of hash function on some hard mathematical problem and we prove that finding collisions of the hash functions is as hard as breaking the underlying problem. This gives a somewhat stronger notion of security than just relying on complex mixing of bits as in the classical approach. A cryptographic hash function has provable security against collision attacks if finding collisions is provably polynomial-time reducible from problem P which is supposed to be unsolvable in polynomial time. The function is then called provably secure, or just provable.

Gabriel Sudan (1927) and Wilhelm Ackermann (1928) display recursive functions that are not primitive recursive: :"Are there recursions that are not reducible to primitive recursion; and in particular can recursion be used to define a function which is not primitive recursive? :"This question arose from a conjecture of Hilbert in 1926 on the continuum problem, and was answered [yes: there are recursions that are not primitive recursive] by Ackermann 1928."Kleene 1952:271 In subsequent years Kleenecf. Kleene 1952:272-273 observes that Rózsa Péter (1935) simplified Ackermann's example ("cf.

Moral shock as a concept is especially important because it pinpoints a factor that motivates individuals to protest that is not reducible to factors highlighted by resource mobilization and political opportunity theories (e.g., social networks, preexisting beliefs). The Art of Moral Protest shows that would-be protestors do not always know other protestors and often formulate their beliefs on the fly, so to speak. Hence, Jasper’s concept is able to account for an additional path into protest, a path emphasizing the relative importance of events and their initial consciousness-raising effects on individuals.

If a group of organisms, owing to their interactions or division of labor, provides superior fitness compared to other groups, where the fitness of the group is higher or lower than the mean fitness of the constituent individuals, group selection can be declared to occur. Specific syndromes of selective factors can create situations in which groups are selected because they display group properties which are selected- for. Many common examples of group traits are reducible to individual traits, however. Selection of these traits is thus more simply explained as selection of individual traits.

Physicalism is a philosophical theory holding that everything that exists is no more extensive than its physical properties; that is, that there are no non-physical substances (for example physically independent minds). Physicalism can be reductive or non- reductive. Reductive physicalism is grounded in the idea that everything in the world can actually be reduced analytically to its fundamental physical, or material, basis. Alternatively, non-reductive physicalism asserts that mental properties form a separate ontological class to physical properties: that mental states (such as qualia) are not ontologically reducible to physical states.

In short, identity was not reducible to belonging to one or another segmentary division of a tribe, but involved far more concrete traits. Throughout the Australian totemic system he believed he could isolate a logic, which in its fullest form, evinced 8 combinations of three paired terms of primary properties. Two totems in a binary tribal moiety could be shown to each involve a set of up to 20 features that could be distributed as traits over all human and non-human members of each of the two groups.

Richard H. Jones (2000), Reductionism: Analysis and the Fuullness of Reality, pp. 27-28, 32. Lewisburg, Pa.: Bucknell University Press and by Jaegwon Kim: that form of reductionism concerning a program of replacing the facts or entities entering statements claimed to be true in one type of discourse with other facts or entities from another type, thereby providing a relationship between them. Such an association is provided where the same idea can be expressed by "levels" of explanation, with higher levels reducible if need be to lower levels.

This statement alone negates dualism, idealism and mental causation. Whereas, it is redundant to state the remaining of the causal exclusion argument because if all physical effects have sufficient physical causes, then no physical effects would be caused twice over by any substance other than physical. Also, if all physical effects have sufficient physical causes, then there clearly would not be any reducible or irreducible mental causes. Secondly, if a person does not support physicalism, then they are not going to support the view that all physical effects have sufficient physical causes.

Dry oxygen does not react with crystalline LiH unless heated strongly, when an almost explosive combustion occurs. LiH is highly reactive toward water and other protic reagents: :LiH + H2O → Li+ \+ H2 \+ OH− LiH is less reactive with water than Li and thus is a much less powerful reducing agent for water, alcohols, and other media containing reducible solutes. This is true for all the binary saline hydrides. LiH pellets slowly expand in moist air, forming LiOH; however, the expansion rate is below 10% within 24 hours in a pressure of 2 Torr of water vapor.

In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics. They appear as the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations (i.e., a reducible representation into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly).

A reductionism is the opposite view, that colors are identical to or reducible to other properties. Typically a reductionist view of color explains colors as an object's disposition to cause certain effects in perceivers or the very dispositional power itself (this sort of view is often dubbed "relationalism", since it defines colors in terms of effects on perceivers, but it also often called simply dispositionalism - various forms of course exist). An example of a notable theorist that defends this kind of view is the philosopher Jonathan Cohen. Another type of reductionism is color physicalism.

A reflectance type is a set, or type, of reflectances, and a reflectance is a surface's disposition to reflect certain percentages of light specified for each wavelength within the visible spectrum. Both relationalism and physicalism of these kinds are so called realist theories, since apart from specifying what colors are, they maintain that colored things exist. Primitivism may be either realist or antirealist, since primitivism simply claims that colors aren't reducible to anything else. Some primitivists further accept that, though colors are primitive properties, no real or nomologically possible objects have them.

This makes ethical non-naturalism a non-definist form of moral realism, which is in turn a form of cognitivism. Ethical non- naturalism stands in opposition to ethical naturalism, which claims that moral terms and properties are reducible to non-moral terms and properties, as well as to all forms of moral anti-realism, including ethical subjectivism (which denies that moral propositions refer to objective facts), error theory (which denies that any moral propositions are true), and non-cognitivism (which denies that moral sentences express propositions at all).

As early as 1984, in analyzing the municipal elections in Paris, he showed the existence of a political space that was not reducible to the distribution of social groups defined on the basis of socio-economic criteria. His doctoral thesis focused on the intersection of the two dimensions of the social: the political and the spatial. The resulting book, L’Espace Légitime, is an exploration of the junction of these dimensions. First, it clarifies the concepts of politics regulated within a society by legitimacy versus geopolitics regulated between societies through violence.

By Menger's theorem, for any two vertices and in a connected graph , the numbers and can be determined efficiently using the max-flow min-cut algorithm. The connectivity and edge-connectivity of can then be computed as the minimum values of and , respectively. In computational complexity theory, SL is the class of problems log-space reducible to the problem of determining whether two vertices in a graph are connected, which was proved to be equal to L by Omer Reingold in 2004. Hence, undirected graph connectivity may be solved in space.

A boxology is a representation of an organized structure as a graph of labeled nodes ("boxes") and connections between them (as lines or arrows). The concept is useful because many problems in systems design are reducible to modular "black boxes" and connections or flow channels between them. The term is somewhat tongue-in-cheek and refers to the generic nature of diagrams containing labelled nodes and (sometimes directed) paths between them. The archetypical example of a boxology is a corporate "org chart", which describes lines of control through the corporation.

CLS (standing for "Continuous Local Search") is a class of search problems designed to model the process of finding a local optima of a continuous function over a continuous domain. It is defined as the class of problems that are polynomial-time reducible to the Continuous Localpoint problem: :Given two Lipschitz continuous functions f and p and parameters ε and λ, find an ε-approximate fixed point of f with respect to p or two points that violate the λ-continuity of p or f. This class was first defined by Daskalakis and Papadimitriou in 2011.Daskalakis and Papadimitriou.

In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electromagnetic interactions, which produce significant long-range forces whose effects can be seen directly in everyday life, and the strong and weak interactions, which produce forces at minuscule, subatomic distances and govern nuclear interactions. Some scientists hypothesize that a fifth force might exist, but these hypotheses remain speculative. Each of the known fundamental interactions can be described mathematically as a field.

In the 19th century, the case of Phineas Gage, a railway worker who was injured by a stout iron rod passing through his brain, convinced both researchers and the public that cognitive functions were localised in the brain. Following this line of thinking, a large body of empirical evidence for a close relationship between brain activity and mental activity has led most neuroscientists and contemporary philosophers to be materialists, believing that mental phenomena are ultimately the result of, or reducible to, physical phenomena.Schwartz, J.H. Appendix D: Consciousness and the Neurobiology of the Twenty-First Century. In Kandel, E.R.; Schwartz, J.H.; Jessell, T.M. (2000).

Also, stories with a single source or without any context of previous research mean that the subject at hand is presented as more definitive and certain than it is in reality. There is often a "product over process" approach to science journalism that aids, too, in the downplaying of uncertainty. Finally, and most notably for this investigation, when science is framed by journalists as a triumphant quest, uncertainty is erroneously framed as "reducible and resolvable". Some media routines and organizational factors affect the overstatement of uncertainty; other media routines and organizational factors help inflate the certainty of an issue.

Whereas knowledge is traditionally thought to be reducible to a form of belief, i.e., a justified and true belief, Nagel argues that knowledge should itself be counted among the fundamental types of mental state, on a par with beliefs, desires, intentions, and so on. Nagel is the author of Knowledge: A Very Short Introduction, which has been praised as an "admirably clear and engaging" introduction to epistemology. Nagel considers classic questions, including about skepticism, rationalism, and empiricism, as well as more contemporary concerns, such as whether Wikipedia, "where most articles have multiple and anonymous authors", can be a reliable source of knowledge.

Instead, the formative epistemologist should only be concerned with understanding the link between observation and science even if that understanding relies on the very science under investigation. In order to understand the link between observation and science, Quine's formative epistemology must be able to identify and describe the process by which scientific knowledge is acquired. One form of this investigation is reliabilism which requires that a belief be the product of some reliable method if it is to be considered knowledge. Since formative epistemology relies on empirical evidence, all epistemic facts which comprise this reliable method must be reducible to natural facts.

The Petersen family is named after Danish mathematician Julius Petersen, the namesake of the Petersen graph. Any of the graphs in the Petersen family can be transformed into any other graph in the family by Δ-Y or Y-Δ transforms, operations in which a triangle is replaced by a degree-three vertex or vice versa. These seven graphs form the forbidden minors for linklessly embeddable graphs, graphs that can be embedded into three-dimensional space in such a way that no two cycles in the graph are linked. They are also among the forbidden minors for the YΔY-reducible graphs.

Some CFG examples: (a) an if-then-else (b) a while loop (c) a natural loop with two exits, e.g. while with an if...break in the middle; non-structured but reducible (d) an irreducible CFG: a loop with two entry points, e.g. goto into a while or for loop In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a program during its execution. The control-flow graph is due to Frances E. Allen, who notes that Reese T. Prosser used boolean connectivity matrices for flow analysis before.

For a period of time encompassing Newton's working life, the discipline of analysis was a subject of controversy in the mathematical community. Although analytic techniques provided solutions to long-standing problems, including problems of quadrature and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry. Instead, analysts were often forced to invoke infinitesimal, or "infinitely small", quantities to justify their algebraic manipulations. Some of Newton's mathematical contemporaries, such as Isaac Barrow, were highly skeptical of such techniques, which had no clear geometric interpretation.

In 1997, she proved Lange's conjecture for the generic curve, with Barbara Russo, which states that "If 0, then there exist stable vector bundles with s_{n'}(E)=s." They also clarified what happens in the interval n'(n-n')(g-1) using a degeneration argument to a reducible curve.On Lange's Conjecture She took up an appointment as an Associate Professor of Mathematics at Tufts University, and has been on the faculty of Tufts since 1989. She has been a reviewer for several journals, including the Bulletin of the American Mathematical Society, the Duke Mathematical Journal, and the journal of algebraic geometry.

Edmund Burke, Reflections on the Revolution in France [1790] (Pearson Longman, 2006), p. 144. Following St. Augustine and Cicero, he believed in "human heart"-based government. Nevertheless, he was contemptuous and afraid of the Enlightenment, inspired by the writings of such intellectuals such as Jean-Jacques Rousseau, Voltaire and Anne Robert Jacques Turgot, who disbelieved in divine moral order and original sin. Burke said that society should be handled like a living organism and that people and society are limitlessly complicated, leading him to conflict with Thomas Hobbes' assertion that politics might be reducible to a deductive system akin to mathematics.

There is currently no medical recommendation about how to manage an inguinal hernia condition in adults, due to the fact that, until recently, elective surgery used to be recommended. The hernia truss is intended to contain a reducible inguinal hernia within the abdomen. It is not considered to provide a cure, and if the pads are hard and intrude into the hernia aperture they may cause scarring and enlargement of the aperture. In addition, most trusses with older designs are not able effectively to contain the hernia at all times, because their pads do not remain permanently in contact with the hernia.

Ajivika is a "Nastika" school of thought whose metaphysics included a theory of atoms or atomism which was later adapted in Vaiśeṣika school, which postulated that all objects in the physical universe are reducible to paramāṇu (atoms), and one's experiences are derived from the interplay of substance (a function of atoms, their number and their spatial arrangements), quality, activity, commonness, particularity and inherence.Oliver Leaman, Key Concepts in Eastern Philosophy. Routledge, , 1999, page 269. Everything was composed of atoms, qualities emerged from aggregates of atoms, but the aggregation and nature of these atoms was predetermined by cosmic forces.

Intellectuals have disagreed about the extent to which the social sciences should mimic the methods used in the natural sciences. The founding positivists of the social sciences argued that social phenomena can and should be studied through conventional scientific methods. This position is closely allied with scientism, naturalism and physicalism; the doctrine that all phenomena are ultimately reducible to physical entities and physical laws. Opponents of naturalism, including advocates of the verstehen method, contended that there is a need for an interpretive approach to the study of human action, a technique radically different from natural science.

Matzinger argues that the idea of DAMPs may explain why Toll-like receptors seem to respond both to external and endogenous signals (while acknowledging controversy over this issue). By emphasizing her theory that the tissues drive the nature of the immune response (i.e., the "what type" rather than the "whether" of immune response), Matzinger describes a dynamic immune system with complex webs of signalling, rather than an immune system that can be explained by a simple and easily reducible set of molecular signals that initiate response or by a small set of cells (e.g., regulatory T cells) that shut it down.

The Australian Cricket Board received widespread criticism for not immediately announcing the scandal. A later report by Rob O'Regan QC concluded that cricketers were not fully informed about the dangers of interacting with bookmakers, and although no further punishment could be given to either Waugh or Warne, in future players should be punished by not only fines, but also by suspensions. The ICC was slow to react, but did eventually in 2000 set up an Anti-Corruption and Security Unit headed by Sir Paul Condon, former head of London's Metropolitan Police. It claims to have reduced corruption in cricket to a "reducible minimum".

These are central to the analytic process because they are central to human and social life in general. Concerning love’s significance, Lothane agrees in principle (1) with Ferenczi that love and bodily tenderness include sexuality but are not reducible to it; (2) with Michael Balint, Ferenczi’s most prominent follower, who unified primary love and psychoanalytic technique for "love, or primary love (in Balint's phrase), is the necessary leaven...the true mover of the therapeutic process that makes exploration of underlying frustration and conflict, and their eventual overcoming, possible."Lothane, Z. (1998). The feud between Freud and Ferenczi over love.

Theory reduction is the process by which a more general theory absorbs a special theory. For example, both Kepler's laws of the motion of the planets and Galileo's theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because Newtonian mechanics is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.

In philosophy, emergentism is the belief in emergence, particularly as it involves consciousness and the philosophy of mind, and as it contrasts with and also does not contrast with reductionism. A property of a system is said to be emergent if it is a new outcome of some other properties of the system and their interaction, while it is itself different from them.O'Connor, Timothy and Wong, Hong Yu, "Emergent Properties", The Stanford Encyclopedia of Philosophy (Summer 2015 Edition), Edward N. Zalta (ed.), URL = . Emergent properties are not identical with, reducible to, or deducible from the other properties.

Other scholars point to the diachronous character of the physical strata of the Anthropocene, arguing that onset and impact are spread out over time, not reducible to a single instant or date of start. A January 2016 report on the climatic, biological, and geochemical signatures of human activity in sediments and ice cores suggested the era since the mid-20th century should be recognised as a geological epoch distinct from the Holocene. The Anthropocene Working Group met in Oslo in April 2016 to consolidate evidence supporting the argument for the Anthropocene as a true geologic epoch.

A reducible pair can be decomposed into a direct product of irreducible ones, and for many purposes, it is enough to restrict one's attention to the irreducible case. Several classes of reductive dual pairs had appeared earlier in the work of André Weil. Roger Howe proved a classification theorem, which states that in the irreducible case, those pairs exhaust all possibilities. An irreducible reductive dual pair (G, G′) in Sp(W) is said to be of type II if there is a lagrangian subspace X in W that is invariant under both G and G′, and of type I otherwise.

Miners had long used the name kobold ore (German for goblin ore) for some of the blue-pigment-producing minerals; they were so named because they were poor in known metals, and gave poisonous arsenic-containing fumes when smelted. In 1735, such ores were found to be reducible to a new metal (the first discovered since ancient times), and this was ultimately named for the kobold. Today, some cobalt is produced specifically from one of a number of metallic- lustered ores, such as cobaltite (CoAsS). The element is, however, more usually produced as a by-product of copper and nickel mining.

Dissent regarding the value of intuition in a logical or mathematical context may often hinge on the breadth of the definition of intuition and the psychological underpinning of the word. Dissent regarding the implications of logical intuition in the fields of artificial intelligence and cognitive computing may similarly hinge on definitions. However, similarity between the potentially infinite nature of logical intuition posited by Gödel and the hard problem of consciousness posited by David Chalmers suggest that the realms of intuitive knowledge and experiential consciousness may both have aspects that are not reducible to classical physics concepts.

However, irreducibility depends on the ambient field, and a polynomial may be irreducible over and reducible over some extension of . Similarly, divisibility by a square depends on the ambient field. If an irreducible polynomial over is divisible by a square over some field extension, then (by the discussion above) the greatest common divisor of and its derivative is not constant. Note that the coefficients of belong to the same field as those of , and the greatest common divisor of two polynomials is independent of the ambient field, so the greatest common divisor of and has coefficients in .

Many problems in NP, including many NP-complete problems, ask whether a particular object exists, such as a satisfying assignment, a graph coloring, or a clique of a certain size. The FNP versions of these problems ask not only if it exists but what its value is if it does. This means that the FNP version of every NP- complete problem is NP-hard. Bellare and Goldwasser showed in 1994 using some standard assumptions that there exist problems in NP such that their FNP versions are not self-reducible, implying that they are harder than their corresponding decision problem.

The causal interaction of mind and brain can be described thus in naturalistic terms: Events at the micro-level (perhaps at that of individual neurons) cause consciousness. Changes at the macro-level (the whole brain) constitute consciousness. Micro-changes cause and then are impacted by holistic changes, in much the same way that individual football players cause a team (as a whole) to win games, causing the individuals to gain confidence from the knowledge that they are part of a winning team. He articulates this distinction by pointing out that the common philosophical term 'reducible' is ambiguous.

It is easily seen that the Perron and peripheral projections of L are both equal to P, thus when the original matrix is reducible the projections may lose non-negativity and there is no chance of expressing them as limits of its powers. The matrix T is an example of a primitive matrix with zero diagonal. If the diagonal of an irreducible non-negative square matrix is non-zero then the matrix must be primitive but this example demonstrates that the converse is false. M is an example of a matrix with several missing spectral teeth.

The study of pseudo-Anosov diffeomorphisms of a surface is fundamental. They are the most interesting diffeomorphisms, since finite-order mapping classes are isotopic to isometries and thus well understood, and the study of reducible classes indeed essentially reduces to the study of mapping classes on smaller surfaces which may themselves be either finite order or pseudo- Anosov. Pseudo-Anosov mapping classes are "generic" in the mapping class group in various ways. For example, a random walk on the mapping class group will end on a pseudo-Anosov element with a probability tending to 1 as the number of steps grows.

The S-unit equation is a Diophantine equation :u + v = 1 with u, v restricted to being S-units of K. The number of solutions of this equation is finite and the solutions are effectively determined using estimates for linear forms in logarithms as developed in transcendental number theory. A variety of Diophantine equations are reducible in principle to some form of the S-unit equation: a notable example is Siegel's theorem on integral points on elliptic curves, and more generally superelliptic curves of the form yn=f(x). A computational solver for S-unit equation is available in the software SageMath.

The nearest-neighbor chain algorithm may be used in conjunction with this array of distances to find the same clustering as the greedy algorithm for these cases. Its total time and space, using this array, is also . The same time and space bounds can also be achieved in a different way, by a technique that overlays a quadtree-based priority queue data structure on top of the distance matrix and uses it to perform the standard greedy clustering algorithm. This quadtree method is more general, as it works even for clustering methods that are not reducible.

The Colin de Verdière graph invariant is an integer defined for any graph using algebraic graph theory. The graphs with Colin de Verdière graph invariant at most μ, for any fixed constant μ, form a minor-closed family, and the first few of these are well-known: the graphs with μ ≤ 1 are the linear forests (disjoint unions of paths), the graphs with μ ≤ 2 are the outerplanar graphs, and the graphs with μ ≤ 3 are the planar graphs. As conjectured and proved, the graphs with μ ≤ 4 are exactly the linklessly embeddable graphs. A linkless apex graph that is not YΔY reducible.

The philosophy of mathematics is a branch of philosophy of science; but in many ways mathematics has a special relationship to philosophy. This is because the study of logic is a central branch of philosophy, and mathematics is a paradigmatic example of logic. In the late nineteenth and twentieth centuries, logic made great advances, and mathematics has been proven to be reducible to logic (at least, to first-order logic with some set theory). The use of formal, mathematical logic in philosophy now resembles the use of mathematics in science, although it is not as frequent.

The B-theorist could argue that "now" is reducible to a token- reflexive phrase such as "simultaneous with this utterance," yet Smith states that even such an argument fails to eliminate tense. One can think the statement "I am not uttering anything now," and such a statement would be true. The statement "I am not uttering anything simultaneous with this utterance" is self-contradictory, and cannot be true even when one thinks the statement. Finally, while tensed statements can express token-independent truth values, no token-reflexive statement can do so (by definition of the term "token-reflexive").

This does depend on having a K-rational point, which serves as the point at infinity in Weierstrass form. There are many cubic curves that have no such point, for example when K is the rational number field. The singular points of an irreducible plane cubic curve are quite limited: one double point, or one cusp. A reducible plane cubic curve is either a conic and a line or three lines, and accordingly have two double points or a tacnode (if a conic and a line), or up to three double points or a single triple point (concurrent lines) if three lines.

A particular example is when and are fields containing a common subfield . The tensor product of fields is closely related to Galois theory: if, say, , where is some irreducible polynomial with coefficients in , the tensor product can be calculated as :A \otimes_R B \cong B[x] / f(x) where now is interpreted as the same polynomial, but with its coefficients regarded as elements of . In the larger field , the polynomial may become reducible, which brings in Galois theory. For example, if is a Galois extension of , then :A \otimes_R A \cong A[x] / f(x) is isomorphic (as an -algebra) to the .

Certeau claims that places are different from spaces because places are "ultimately reducible to being there" while spaces are specified "by the actions of historical subjects." While places could be pointed to on a map and are defined by what is physically inside of them, spaces are sites where things have happened. A space is defined by the interactions that individual agents have with it, not by its physical features. Certeau gives the examples that the place of a street becomes a space only when people walk on it and the places of texts only become spaces when people read them.

In the mathematical field of knot theory, a split link is a link that has a (topological) 2-sphere in its complement separating one or more link components from the others.. A split link is said to be splittable, and a link that is not split is called a non-split link or not splittable. Whether a link is split or non-split corresponds to whether the link complement is reducible or irreducible as a 3-manifold. A link with an alternating diagram, i.e. an alternating link, will be non-split if and only if this diagram is connected.

Instead, the naturalized epistemologist should only be concerned with understanding the link between observation and science even if that understanding relies on the very science under investigation. In order to understand the link between observation and science, Quine's naturalized epistemology must be able to identify and describe the process by which scientific knowledge is acquired. One form of this investigation is reliabilism which requires that a belief be the product of some reliable method if it is to be considered knowledge. Since naturalized epistemology relies on empirical evidence, all epistemic facts which comprise this reliable method must be reducible to natural facts.

Occurrence of hydrogen spillover on reducible supports such as titanium oxide is established, yet questions remain about whether hydrogen spillover can take place on nonreducible supports such as aluminium oxide. The study shows a convincing proof of the spillover effect at well-defined distances away from the metal catalyst explaining why hydrogen spillover is slower on an aluminum oxide catalyst support than on a titanium oxide catalyst support. The results reveal that hydrogen spillover is fast and efficient on titanium oxide, and extremely slow and short-ranged on aluminium oxide. Figure 2: Dissociative chemisorption of H2 on metal catalysts.

Hypermodernism holds that an object is by definition non-composable toward its attributes; and no one attribute of an object can act as a proxy for the object itself. No whole, or object, is reducible to ONLY its attributes; and the attributes may not be mutually exclusive to the object itself. Furthermore, an object may have extraneous functions independent of its composing attributes (postmodern theory); this potential supra-functionality is a key concern to hypermodernism's attempt to replace objects with attributes. Attributes, while having the functions of an object, are not building blocks toward an object in hypermodernism.

In classical gauge theory, spontaneous symmetry breaking occurs if the structure group G of a principal bundle P\to X is reducible to a closed subgroup H, i.e., there exists a principal subbundle of P with the structure group H.L. Nikolova, V. Rizov, "Geometrical approach to the reduction of gauge theories with spontaneous broken symmetries", Reports on Mathematical Physics 20 (1984) 287. By virtue of the well-known theorem, there exists one-to-one correspondence between the reduced principal subbundles of P with the structure group H and the global sections of the quotient bundle . These sections are treated as classical Higgs fields.

Oort studied from 1952 to 1958 at Leiden University, where he graduated with a thesis on elliptic curves. He received his doctorate in 1961 in Leiden from and Jaap Murre with thesis Reducible and Multiple Algebraic Curves, but had previously studied under Jean-Pierre Serre in Paris and Aldo Andreotti in Pisa. Oort was from 1961 at the University of Amsterdam, where he became a professor in 1967. In 1977, until his retirement in 2000, he was a professor at Utrecht University. He was a visiting scholar at several academic institutions, including Harvard University (1966/67) and Aarhus University (1972/73).

Surgical options have been shown to be successful in patients with unstable extra-articular or minimal articular distal radius fractures. These options include percutaneous pinning, external fixation, and ORIF using plating. Patients with low functional demand of their wrists can be treated successfully with nonsurgical management; however, in more active and fit patients with fractures that are reducible by closed means, nonbridging external fixation is preferred, as it has less serious complications when compared to other surgical options. The most common complication associated with nonbridging external fixation is pin tract infection, which can be managed with antibiotics and frequent dressing changes, and rarely results in reoperation.

The notion of irreducible component is fundamental in algebraic geometry and rarely considered outside this area of mathematics: consider the algebraic subset of the plane :. For the Zariski topology, its closed subsets are itself, the empty set, the singletons, and the two lines defined by and . The set is thus reducible with these two lines as irreducible components. The spectrum of a commutative ring is the set of the prime ideals of the ring, endowed with the Zariski topology, for which a set of prime ideals is closed if and only if it is the set of all prime ideals that contain a fixed ideal.

In 2002, the ICS played a tremendous role in campaigns over the Gujarat communal massacres. But this in turn intensified conflicts, with one wing arguing that communalism was reducible to an economic determinist analysis, and also arguing that the other side, in campaigning for secularism, had been projecting individuals rather than the party. Thus, in 2002, the ICS brought out the first major book documenting the Gujarat violence anywhere in India (The Genocidal Pogrom in Gujarat: Anatomy of Indian Fascism), and Prajapati and Trupti Shah in Vadodara played key roles in PUCL's documentation of the violence in Gujarat. Yet by the end of 2002 Prajapati had resigned from the ICS.

He endeavored to establish a discipline that would base its claims on a rigorous empirical study. One of Boas's most important books, The Mind of Primitive Man (1911), integrated his theories concerning the history and development of cultures and established a program that would dominate American anthropology for the next fifteen years. In this study, he established that in any given population, biology, language, material, and symbolic culture, are autonomous; that each is an equally important dimension of human nature, but that no one of these dimensions is reducible to another. In other words, he established that culture does not depend on any independent variables.

Moral realism (in the robust sense; cf. moral universalism for the minimalist sense) holds that such propositions are about robust or mind-independent facts, that is, not facts about any person or group's subjective opinion, but about objective features of the world. Meta- ethical theories are commonly categorized as either a form of realism or as one of three forms of "anti-realism" regarding moral facts: ethical subjectivism, error theory, or non-cognitivism. Realism comes in two main varieties: # Ethical naturalism holds that there are objective moral properties and that these properties are reducible or stand in some metaphysical relation (such as supervenience) to entirely non-ethical properties.

General tau theory deals with the guidance of bodily movements. It was developed from work on J. J. Gibson's notion of ecological invariants in the visual flow-field during a perception-in-action event, and subsequently generalised by David N. Lee in the late 1990s to an amodal theory of perceptuomotor control. The theory considers the organism acting as a unified whole in dynamic relations with its environment, rather than conceiving of the organism as a complex mechanical device reducible into analysable parts. The theory is embedded in ecological thinking, paying attention to both organism and environment, and drawing information from their forms of interaction.

On Leibniz and physics, see the chapter by Garber in Jolley (1995) and Wilson (1989). Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, he anticipated Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute: "As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions."See H. G. Alexander, ed.

His chosen field of research were the Dinka of southern Sudan, a people closely related to the Nuer studied by his mentor, (1947–50) and the Anuak (1952-1954). His work on the former, culminating in Divinity and Experience: the Religion of the Dinka, is regarded as unsurpassed as a study of African religion. His central, ultimately Durkheimian premise here is that religion is not reducible to a matter of beliefs and practices, but rather to a complex set of natural and social practices.T. M. S. Evens "Contradiction and Choice among the Dinka and in Genesis" in Anthropology as ethics: nondualism and the conduct of sacrifice, Berghahn Books, 2008 ch.

Morphological analysis is a technique developed by Fritz Zwicky (1966, 1969) for exploring all the possible solutions to a multi-dimensional, non-quantified problem complex. As a problem structuring and problem solving technique, morphological analysis was designed for multi-dimensional, non-quantifiable problems where causal modeling and simulation do not function well or at all. Zwicky developed this approach to address seemingly non-reducible complexity. Using the technique of cross consistency assessment (CCA), the system however does allow for reduction, not by reducing the number of variables involved, but by reducing the number of possible solutions through the elimination of the illogical solution combinations in a grid box.

In a finite field, the product of two non-squares is a square; this implies that the polynomial x^4 + 1, which is irreducible over the integers, is reducible modulo every prime number. For example, :x^4 + 1 \equiv (x+1)^4 \pmod 2; :x^4 + 1 \equiv (x^2+x-1)(x^2-x-1) \pmod 3,\qquadsince 1^2 \equiv -2 \pmod 3; :x^4 + 1 \equiv (x^2+2)(x^2-2) \pmod 5,\qquadsince 2^2 \equiv -1 \pmod 5; :x^4 + 1 \equiv (x^2+3x+1)(x^2-3x+1) \pmod 7,\qquadsince 3^2 \equiv 2 \pmod 7.

This in turn gives a solution to the problem of partitioning tri-partite graphs into triangles, which could then be used to find solutions for the special case of SAT known as 3-SAT, which then provides a solution for general Boolean satisfiability. So a polynomial time solution to Sudoku leads, by a series of mechanical transformations, to a polynomial time solution of satisfiability, which in turn can be used to solve any other NP-problem in polynomial time. Using transformations like this, a vast class of seemingly unrelated problems are all reducible to one another, and are in a sense "the same problem".

A decision problem \scriptstyle C is NP-complete if: # \scriptstyle C is in NP, and # Every problem in NP is reducible to \scriptstyle C in polynomial time. \scriptstyle C can be shown to be in NP by demonstrating that a candidate solution to \scriptstyle C can be verified in polynomial time. Note that a problem satisfying condition 2 is said to be NP-hard, whether or not it satisfies condition 1. A consequence of this definition is that if we had a polynomial time algorithm (on a UTM, or any other Turing-equivalent abstract machine) for \scriptstyle C, we could solve all problems in NP in polynomial time.

In the definition of NP-complete given above, the term reduction was used in the technical meaning of a polynomial-time many-one reduction. Another type of reduction is polynomial-time Turing reduction. A problem \scriptstyle X is polynomial-time Turing-reducible to a problem \scriptstyle Y if, given a subroutine that solves \scriptstyle Y in polynomial time, one could write a program that calls this subroutine and solves \scriptstyle X in polynomial time. This contrasts with many-one reducibility, which has the restriction that the program can only call the subroutine once, and the return value of the subroutine must be the return value of the program.

Epiphenomenalism states that all mental events are caused by a physical event and have no physical consequences, and that one or more mental states do not have any influence on physical states. So, the mental event of deciding to pick up a rock ("M1") is caused by the firing of specific neurons in the brain ("P1"). When the arm and hand move to pick up the rock ("P2") this is not caused by the preceding mental event M1, nor by M1 and P1 together, but only by P1. The physical causes are in principle reducible to fundamental physics, and therefore mental causes are eliminated using this reductionist explanation.

PPP is the set of all function computation problems that admit a polynomial-time reduction to the PIGEON problem, defined as follows: :Given a Boolean circuit C having the same number n of input bits as output bits, find either an input x that is mapped to the output C(x) = 0^n, or two distinct inputs x e y that are mapped to the same output C(x) = C(y). A problem is PPP-complete if PIGEON is also polynomial-time reducible to it. Note that the pigeonhole principle guarantees that PIGEON is total. We can also define WEAK-PIGEON, for which the weak pigeonhole principle guarantees totality.

The year 2011 was declared by the United Nations as the International Year of Chemistry. It was an initiative of the International Union of Pure and Applied Chemistry, and of the United Nations Educational, Scientific, and Cultural Organization and involves chemical societies, academics, and institutions worldwide and relied on individual initiatives to organize local and regional activities. Organic chemistry was developed by Justus von Liebig and others, following Friedrich Wöhler's synthesis of urea which proved that living organisms were, in theory, reducible to chemistry. Other crucial 19th century advances were; an understanding of valence bonding (Edward Frankland in 1852) and the application of thermodynamics to chemistry (J.

Attenborough is a lifelong supporter of the BBC, public service broadcasting and the television licence. He has said that public service broadcasting "is one of the things that distinguishes this country and makes me want to live here", and believes that it is not reducible to individual programmes, but "can only effectively operate as a network [...] that measures its success not only by its audience size but by the range of its schedule".“The future of public service broadcasting” . BBC. Retrieved 15 September 2019 > ... the BBC per minute in almost every category is as cheap as you can find > anywhere in the world and produces the best quality.

In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t connectivity), which is the problem of determining whether there exists a path between two vertices in an undirected graph, otherwise described as the problem of determining whether two vertices are in the same connected component. This problem is also called the undirected reachability problem. It does not matter whether many-one reducibility or Turing reducibility is used. Although originally described in terms of symmetric Turing machines, that equivalent formulation is very complex, and the reducibility definition is what is used in practice.

Let p and q be two unary predicates. Then ⊓x(p(x)⊔¬p(x))⟜⊓x(q(x)⊔¬q(x)) expresses the problem of Turing-reducing q to p (in the sense that q is Turing reducible to p if and only if the interactive problem ⊓x(p(x)⊔¬p(x))⟜⊓x(q(x)⊔¬q(x)) is computable). ⊓x(p(x)⊔¬p(x))→⊓x(q(x)⊔¬q(x)) does the same but for the stronger version of Turing reduction where the oracle for p can be queried only once. ⊓x⊔y(q(x)↔p(y)) does the same for the problem of many-one reducing q to p.

This inference is less reliable (and thus more likely commit the fallacy of hasty generalization) than a statistical generalization, first, because the sample events are non-random, and second because it is not reducible to mathematical expression. Statistically speaking, there is simply no way to know, measure and calculate as to the circumstances affecting performance that will obtain in the future. On a philosophical level, the argument relies on the presupposition that the operation of future events will mirror the past. In other words, it takes for granted a uniformity of nature, an unproven principle that cannot be derived from the empirical data itself.

The security of the keystream generation of QUAD is provably reducible to the conjectured intractability of the MQ problem, namely solving a multivariate system of quadratic equations. The first proof was done over field GF(2) for an old-fashioned stream cipher (where the key is the initial state). It was later extended by Berbain and Gilbert in order to take into account the set-up procedure of a modern cipher (with a setup stage deriving the initial state from the key). The security of the whole cipher as a Pseudo Random Function can be related to the conjectured intractability of the MQ problem.

Even though the graph isomorphism problem is polynomial time reducible to crystal net topological equivalence (making topological equivalence a candidate for being "computationally intractable" in the sense of not being polynomial time computable), a crystal net is generally regarded as novel if and only if no topologically equivalent net is known. This has focused attention on topological invariants. One invariant is the array of minimal cycles (often called rings in the chemistry literature) arrayed about generic vertices and represented in a Schlafli symbol. The cycles of a crystal net are related to another invariant, that of the coordination sequence (or shell map in topology), which is defined as follows.

A bounded form of each of the above strong reducibilities can be defined. The most famous of these is bounded truth-table reduction, but there are also bounded Turing, bounded weak truth-table and others. These first three are the most common ones and they are based on the number of queries. For example, a set A is bounded truth-table reducible to B if and only if the Turing machine M computing A relative to B computes a list of up to n numbers, queries B on these numbers and then terminates for all possible oracle answers; the value n is a constant independent of x.

In the same way, a color-blind person is not necessarily able to perceive the green color of grass although he is capable of vision. Suppose we give a name to this ability to appreciate the beauty in things we see: one might call it the aesthetic sense. This aesthetic sense does not come automatically to all people with perfect vision and hearing, so it is fair to describe it as something extra, something not wholly reducible to vision and hearing. As the aesthetic sense informs us about what is beautiful, we can analogically understand the moral sense as informing us of what is good.

By no means…there is > a necessary connexion to be taken into consideration. Angela Coventry writes that, for Hume, "there is nothing in any particular instance of cause and effect involving external objects which suggests the idea of power or necessary connection" and "we are ignorant of the powers that operate between objects". However, while denying the possibility of knowing the powers between objects, Hume accepted the causal principle, writing: "I never asserted so absurd a proposition as that something could arise without a cause." It has been argued that, while Hume did not think that causation is reducible to pure regularity, he was not a fully fledged realist either.

In complexity theory, the complexity class NP-easy is the set of function problems that are solvable in polynomial time by a deterministic Turing machine with an oracle for some decision problem in NP. In other words, a problem X is NP-easy if and only if there exists some problem Y in NP such that X is polynomial-time Turing reducible to Y., p. 117, 120. This means that given an oracle for Y, there exists an algorithm that solves X in polynomial time (possibly by repeatedly using that oracle). NP-easy is another name for FPNP (see the function problem article) or for FΔ2P (see the polynomial hierarchy article).

Clearly, the graph canonization problem is at least as computationally hard as the graph isomorphism problem. In fact, graph isomorphism is even AC0-reducible to graph canonization. However it is still an open question whether the two problems are polynomial time equivalent. While the existence of (deterministic) polynomial algorithms for graph isomorphism is still an open problem in computational complexity theory, in 1977 László Babai reported that with probability at least 1 − exp(−O(n)), a simple vertex classification algorithm produces a canonical labeling of a graph chosen uniformly at random from the set of all n-vertex graphs after only two refinement steps.

In May 1902, anthracite coal miners went on strike, threatening a national energy shortage. After threatening the coal operators with intervention by federal troops, Roosevelt won their agreement to an arbitration of the dispute by a commission, which succeeded in stopping the strike. The accord with J.P. Morgan resulted in the miners getting more pay for fewer hours, but with no union recognition.. Roosevelt said, "My action on labor should always be considered in connection with my action as regards capital, and both are reducible to my favorite formula—a square deal for every man." Roosevelt was the first president to help settle a labor dispute.

Regarding the first form of designation, Dan Lusthaus adds that: > If the appropriator is something different from the skandhas themselves, > then there is a sixth skandha, which is doctrinally impermissible. If the > skandhas appropriate themselves, that leads to a vicious cycle of infinite > regress. Hence, the Vātsīputrīya argue, the nominal person (pudgala) is > neither the same as nor different from the skandhas. It is a heuristic > fiction that avoids these unwarranted consequences and lends coherence by > also corresponding to how actual persons experience themselves—that is, as > distinct individuals continuous with, but not absolutely identical to or > reducible to, their own pasts and futures.

In computer science, interactive computation is a mathematical model for computation that involves input/output communication with the external world during computation. This is in contrast to the traditional understanding of computation which assumes reading input only before computation and writing output only after computation, thus defining a kind of "closed" computation. The Church-Turing thesis attempts to define computation and computability in terms of Turing machines. Because the Turing machine model only provides an answer to the question of what computability of functions means, but interactive tasks are not always reducible to functions, it fails to capture a broader intuition of computation and computability.

In other words, if we begin from the perspective that movement (not space, time, or force) is primary, then motion is not reducible to spacetime. Matter-in- motion is not in spacetime but rather produces spacetime itself. This conclusion is consistent with, but not identical to, recent physical theories of motion in quantum gravity. From the perspective of movement, according to Nail, all seemingly discrete bodies are the result of moving flows of matter that continually fold themselves up in various patterns or what he calls “fields of motion.” Nail's philosophy of movement provides a conceptual framework for the study of these patterns of motion through history.

According to Umberto Eco, Medieval conceptions of beauty were based on the earlier Classical attempt to link mathematics with beauty: '[This conception of beauty's] many variations are reducible to the one fundamental principle of unity in variety.' These aesthetics also had a moral dimension borrowed from Pythagoras, for whom, for instance, certain musical proportions were believed to lead to sins. Musical principles were often enacted into architecture so that buildings would be built according to an 'order reminiscent of a musical melody'. For this reason, architects were frequently called 'composers' who created beautiful buildings according to a 'divine arrangement' whereby correct proportions of latitude, longitude and altitude harmonised.

Tyndall said in 1879: "During nine years of labour on the subject of radiation [in the 1860s], heat and light were handled throughout by me, not as ends, but as instruments by the aid of which the mind might perchance lay hold upon the ultimate particles of matter."Quoted from Tyndall's Fragments of Science, Volume II. This agenda is explicit in the title he picked for his 1872 book Contributions to Molecular Physics in the Domain of Radiant Heat. It is present less explicitly in the spirit of his widely read 1863 book Heat Considered as a Mode of Motion. Besides heat he also saw magnetism and sound propagation as reducible to molecular behaviours.

The English to be, and its equivalents in certain other languages, also have a non-copular use as an existential verb, meaning "to exist." This use is illustrated in the following sentences: I want only to be, and that is enough; I think therefore I am; To be or not to be, that is the question. In these cases, the verb itself expresses a predicate (that of existence), rather than linking to a predicative expression as it does when used as a copula. In ontology it is sometimes suggested that the "is" of existence is reducible to the "is" of property attribution or class membership; to be, Aristotle held, is to be something.

A general conic is defined by five points: given five points in general position, there is a unique conic passing through them. If three of these points lie on a line, then the conic is reducible, and may or may not be unique. If no four points are collinear, then five points define a unique conic (degenerate if three points are collinear, but the other two points determine the unique other line). If four points are collinear, however, then there is not a unique conic passing through them – one line passing through the four points, and the remaining line passes through the other point, but the angle is undefined, leaving 1 parameter free.

In 1995/6 Dascal coordinated in Jerusalem an international research project called "Leibniz the Polemicist", which was aimed to find new ways to develop an understanding of the importance of debate in shaping knowledge. It was inspired in Leibniz's eclectic and pluralistic approach, according to which knowledge arises out of the synthesis of the "grains of truth" present in every doctrine, a synthesis that is to be achieved through rational controversy governed by a notion of rationality not reducible to logical deduction and yet not arbitrary. One of the results of this project was the creation of the International Association for the Study of Controversies (IASC, read I ASK). The association has conducted since 1996 yearly workshops and conferences.

Thus, mind is not reducible to the neurophysiology of the organic individual, but is emergent in "the dynamic, ongoing social process" that constitutes human experience. For Mead, mind arises out of the social act of communication. Mead's concept of the social act is relevant, not only to his theory of mind, but to all facets of his social philosophy. His theory of "mind, self, and society" is, in effect, a philosophy of the act from the standpoint of a social process involving the interaction of many individuals, just as his theory of knowledge and value is a philosophy of the act from the standpoint of the experiencing individual in interaction with an environment.

The notion of a reductive dual pair makes sense over any field F, which we assume to be fixed throughout. Thus W is a symplectic vector space over F. If W1 and W2 are two symplectic vector spaces and (G1, G′1), (G2, G′2) are two reductive dual pairs in the corresponding symplectic groups, then we may form a new symplectic vector space W = W1 ⊕ W2 and a pair of groups G = G1 × G2, G′ = G′1 × G′,2 acting on W by isometries. It turns out that (G, G′) is a reductive dual pair. A reductive dual pair is called reducible if it can be obtained in this fashion from smaller groups, and irreducible otherwise.

Russell continued to defend logicism, the view that mathematics is in some important sense reducible to logic, and along with his former teacher, Alfred North Whitehead, wrote the monumental Principia Mathematica, an axiomatic system on which all of mathematics can be built. The first volume of the Principia was published in 1910, and is largely ascribed to Russell. More than any other single work, it established the speciality of mathematical or symbolic logic. Two more volumes were published, but their original plan to incorporate geometry in a fourth volume was never realised, and Russell never felt up to improving the original works, though he referenced new developments and problems in his preface to the second edition.

Instead, it was the Bolshevik Revolution that attracted their attention. Poet and ABB member Claude McKay had previously been active in the Left Communist Workers Socialist Federation in London and subsequently visited the Soviet Union several times in the mid-1920s, writing about conferences of the Communist International for African-American audiences. McKay's book, The Negroes in America (published in Russian in 1924 but not in the U.S. until 1979) argued, against the official Communist position of the time, that the oppression of black people in the U.S. was not reducible to economic oppression, but was unique. He argued against the color blindness that the Communists had inherited from the Socialist Party.

In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem a successively harder decision problem with the property that is not decidable by an oracle machine with an oracle for . The operator is called a jump operator because it increases the Turing degree of the problem . That is, the problem is not Turing-reducible to . Post's theorem establishes a relationship between the Turing jump operator and the arithmetical hierarchy of sets of natural numbers.. Informally, given a problem, the Turing jump returns the set of Turing machines which halt when given access to an oracle that solves that problem.

Given the definition of the permanent of a matrix, it is clear that PERM(M) for any n-by-n matrix M is a multivariate polynomial of degree n over the entries in M. Calculating the permanent of a matrix is a difficult computational task--PERM has been shown to be #P-complete (proof). Moreover, the ability to compute PERM(M) for most matrices implies the existence of a random program that computes PERM(M) for all matrices. This demonstrates that PERM is random self-reducible. The discussion below considers the case where the matrix entries are drawn from a finite field Fp for some prime p, and where all arithmetic is performed in that field.

There is an alternative solution using algebraic geometry In brief, one interprets the roots as the intersection of two quadratic curves, then finds the three reducible quadratic curves (pairs of lines) that pass through these points (this corresponds to the resolvent cubic, the pairs of lines being the Lagrange resolvents), and then use these linear equations to solve the quadratic. The four roots of the depressed quartic may also be expressed as the coordinates of the intersections of the two quadratic equations and i.e., using the substitution that two quadratics intersect in four points is an instance of Bézout's theorem. Explicitly, the four points are for the four roots of the quartic.

Society and culture are related but dissimilar concepts, so the scope of each is different. Thus, a society is an interdependent community, while societal as distinct from individual culture is an attribute of a community, including the complex web of shifting patterns that links some individuals together. In any case, both cultures and societies must deal with death; and various cultural studies (many of which overlap with each other) examine this response taking a variety of approaches. Thanatology is by no means reducible to a section of forensic science and the notion that it can be is symptomatic of the pathological urge of scientism to force all disciplines into its own Procrustean bed.

General morphology was developed by Fritz Zwicky, the Bulgarian- born, Swiss-national astrophysicist based at the California Institute of Technology. Among others, Zwicky applied morphological analysis (MA) to astronomical studies and jet and rocket propulsion systems. As a problem- structuring and problem-solving technique, MA was designed for multi- dimensional, non-quantifiable problems where causal modelling and simulation do not function well, or at all. Zwicky developed this approach to address seemingly non-reducible complexity: using the technique of cross-consistency assessment (CCA), the system allows for reduction by identifying the possible solutions that actually exist, eliminating the illogical solution combinations in a grid box rather than reducing the number of variables involved.

The power of Parmenides' logic was such that some subsequent philosophers abandoned the monism of the Milesians, Xenophanes, Heraclitus, and Parmenides, where one thing was the arche, and adopted pluralism, such as Empedocles and Anaxagoras.Burnet, Greek Philosophy, 69. There were, they said, multiple elements which were not reducible to one another and these were set in motion by love and strife (as in Empedocles) or by Mind (as in Anaxagoras). Agreeing with Parmenides that there is no coming into being or passing away, genesis or decay, they said that things appear to come into being and pass away because the elements out of which they are composed assemble or disassemble while themselves being unchanging.

These are essentials used by Goethe and Schiller: # Gehalt: the inexpressible "felt-thought", or "import", which is alive in the artist and the percipient that he or she finds means to express within the aesthetic form, hence Gehalt is implicit with form. A work's Gehalt is not reducible to its Inhalt. # Gestalt: the aesthetic form, in which the import of the work is stratified, that emerges from the regulation of forms (these being rhetorical, grammatical, intellectual, and so on) abstracted from the world or created by the artist, with sense relationships prevailing within the employed medium. # Stoff: Schiller and Goethe reserve this (almost solely) for the forms taken from the world or that are created.

Structure-reactivity relationships are investigated, for example the transfer of electronic effects through an N-N single bond, ring formation of some 2-amino-1,4-benzoquinones, or interactions between two reducible groups in a molecule. Polarographic reduction of pesticides has been used to study their adsorption on lignin, to determine their bioavailability in applications in forest nurseries. Studies of alkaline cleavage of lignin at room temperature will form a basis for the use of lignin (which is a renewable raw material) for future industrial applications. He has won numerous awards, including the prestigious 1975 Benedetti–Pichler award given annually by the American Microchemical Society, as well as numerous visiting professorships at institutions around the world.

The flagella of certain bacteria constitute a molecular motor requiring the interaction of about 40 different protein parts. Behe presents this as a prime example of an irreducibly complex structure defined as "a single system composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning", and argues that since "an irreducibly complex system that is missing a part is by definition nonfunctional", it could not have evolved gradually through natural selection. Reducible complexity. In contrast to Behe's claims, many proteins can be deleted or mutated and the flagellum still works, even though sometimes at reduced efficiency.

A person or entity who buys insurance is known as an insured or as a policyholder. The insurance transaction involves the insured assuming a guaranteed and known relatively small loss in the form of payment to the insurer in exchange for the insurer's promise to compensate the insured in the event of a covered loss. The loss may or may not be financial, but it must be reducible to financial terms, and usually involves something in which the insured has an insurable interest established by ownership, possession, or pre-existing relationship. The insured receives a contract, called the insurance policy, which details the conditions and circumstances under which the insurer will compensate the insured.

He called his ontological position "monism sui generis", since it unites monism and pluralism; it is an emergentism in which the elements assemble themselves by virtue of their properties or functions, or properties-functions. Each structure, although it depends to exist on the elements that compose it, is not reducible to them because it acquires new properties-functions that cannot be explained based on those of the element. The structure also becomes an element for a new structure. Self-assembly begins from the physical level to the point where structures acquire more complex properties-functions and of a different order to give rise to a new biological level, and thus the continuum progresses until reaching the social and then the cultural level.

For example consider , in which the coefficient 1 of is not divisible by any prime, Eisenstein's criterion does not apply to . But if one substitutes for in , one obtains the polynomial , which satisfies Eisenstein's criterion for the prime number . Since the substitution is an automorphism of the ring , the fact that we obtain an irreducible polynomial after substitution implies that we had an irreducible polynomial originally. In this particular example it would have been simpler to argue that (being monic of degree 2) could only be reducible if it had an integer root, which it obviously does not; however the general principle of trying substitutions in order to make Eisenstein's criterion apply is a useful way to broaden its scope.

The problem can be shown to be in NL, as a non-deterministic Turing machine can guess the next node of the path, while the only information which has to be stored is the total length of the path and which node is currently under consideration. The algorithm terminates if either the target node t is reached, or the length of the path so far exceeds n, the number of nodes in the graph. The complement of st-connectivity, known as st-non-connectivity, is also in the class NL, since NL = coNL by the Immerman–Szelepcsényi theorem. In particular, the problem of st-connectivity is actually NL-complete, that is, every problem in the class NL is reducible to connectivity under a log-space reduction.

Bakhtin argues that dialogic interactions of the kind found in Dostoevsky are not reducible to forms that are studiable by linguistics and can only be understood as discourse. The discursive word is never separate from a subject who utters it in address to another subject: the word must be embodied for it to have any dialogical status. Bakhtin identifies three main types of discourse: (i) unmediated discourse directed exclusively toward its referential object; (ii) objectified discourse (of a represented person); (iii) discourse with an orientation toward someone else's discourse (double voiced discourse). It is this third type in its various forms (for example, internal dialogization) that is of primary interest to Bakhtin in his investigation into the dialogical process and its striking presence in Dostoevsky's writing.

The role of reduction in computer science can be thought as a (precise and unambiguous) mathematical formalization of the philosophical idea of "theory reductionism". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "hard" to solve as the former. Reduction in theoretical computer science is pervasive in both: the mathematical abstract foundations of computation; and in real-world performance or capability analysis of algorithms.

Electoral law in Maine and Nebraska makes it possible for those states to split their electoral votes: winner-take-all both by congressional district and statewide. Despite the prevalent winner-take-all practice, the minority always gets a sizable vote. While the red/blue paradigm encourages hardening into ideological camps, political parties, candidates in those parties and individuals members of those parties have a variety of positions and outlooks—nearly every town, city and patch of farmland in the country is "purple", a mix of neighbors, friends and family, each of whose own mixed political preferences tip the scale to vote for one side or the other in a contest. Individually and collectively, they are not reducible to red or blue.

This is the explicit form in this case of the abstract result that over an algebraically closed field K (such as the complex numbers) the regular representation of G is completely reducible, provided that the characteristic of K (if it is a prime number p) doesn't divide the order of G. That is called Maschke's theorem. In this case the condition on the characteristic is implied by the existence of a primitive n-th root of unity, which cannot happen in the case of prime characteristic p dividing n. Circulant determinants were first encountered in nineteenth century mathematics, and the consequence of their diagonalisation drawn. Namely, the determinant of a circulant is the product of the n eigenvalues for the n eigenvectors described above.

The theory continues by introducing the concept of reducible measure, meaning that the quotient ρ/μ is element of L2(I, R, μ). The following results are then established: The reducer φ of ρ is an antecedent of ρ/μ for the operator Tρ. (In fact the only antecedent which belongs to Hρ). For any function square integrable for ρ, there is an equality known as the reducing formula: : \langle f/\varphi \rangle_\rho = \langle T_\rho (f)/1 \rangle_\rho. The operator :f\mapsto \varphi\times f -T_\rho (f) defined on the polynomials is prolonged in an isometry Sρ linking the closure of the space of these polynomials in L2(I, R, ρ2μ−1) to the hyperplane Hρ provided with the norm induced by ρ.

Intuitively, problem A is reducible to problem B if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B. "Harder" means having a higher estimate of the required computational resources in a given context (e.g., higher time complexity, greater memory requirement, expensive need for extra hardware processor cores for a parallel solution compared to a single-threaded solution, etc.). The existence of a reduction from A to B can be written in the shorthand notation A ≤m B, usually with a subscript on the ≤ to indicate the type of reduction being used (m : mapping reduction, p : polynomial reduction).

Epiphenomenalism is a doctrine about mental-physical causal relations which holds that one or more mental states and their properties are the by-products (or epiphenomena) of the states of a closed physical system, and are not causally reducible to physical states (do not have any influence on physical states). According to this view mental properties are as such real constituents of the world, but they are causally impotent; while physical causes give rise to mental properties like sensations, volition, ideas, etc., such mental phenomena themselves cause nothing further - they are causal dead ends. Huxley explained mental properties as like the steam on a locomotive The position is credited to English biologist Thomas Huxley (Huxley 1874), who analogised mental properties to the whistle on a steam locomotive.

In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine solving the second problem exists, then the first problem can be solved by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times. If both the time required to transform the first problem to the second, and the number of times the subroutine is called is polynomial, then the first problem is polynomial-time reducible to the second. A polynomial-time reduction proves that the first problem is no more difficult than the second one, because whenever an efficient algorithm exists for the second problem, one exists for the first problem as well.

Most of Hume's followers have disagreed with his conclusion that belief in an external world is rationally unjustifiable, contending that Hume's own principles implicitly contained the rational justification for such a belief, that is, beyond being content to let the issue rest on human instinct, custom and habit.Morick, H. (1980), Challenges to Empiricism, Hackett Publishing, Indianapolis, IN. According to an extreme empiricist theory known as phenomenalism, anticipated by the arguments of both Hume and George Berkeley, a physical object is a kind of construction out of our experiences.Marconi, Diego (2004), "Fenomenismo"', in Gianni Vattimo and Gaetano Chiurazzi (eds.), L'Enciclopedia Garzanti di Filosofia, 3rd edition, Garzanti, Milan, Italy. Phenomenalism is the view that physical objects, properties, events (whatever is physical) are reducible to mental objects, properties, events.

She returned to Johns Hopkins, where she completed her dissertation on "absolute reducibility of maps of at most 19 regions" in 1966 at the age of 47. Bari's dissertation explored chromatic polynomials and the Birkhoff-Lewis conjecture. She determined that “Because of the fact that all other cubic maps with fewer than 20 regions contain at least one absolutely reducible configuration, it follows that the Birkhoff-Lewis conjecture holds for all maps with fewer than 20 regions.”Bari, Ruth. Abstract: “Absolute Reducibility of Maps of at Most 19 Regions.” Biographies of Women Mathematicians Her Ph.D. advisor was Daniel Lewis, Jr.Mathematics Genealogy Project After she received her degree, mathematician William Tutte invited Bari to spend two weeks lecturing on her work in Canada at the University of Waterloo.

In the theory of cluster analysis, the nearest-neighbor chain algorithm is an algorithm that can speed up several methods for agglomerative hierarchical clustering. These are methods that take a collection of points as input, and create a hierarchy of clusters of points by repeatedly merging pairs of smaller clusters to form larger clusters. The clustering methods that the nearest-neighbor chain algorithm can be used for include Ward's method, complete-linkage clustering, and single-linkage clustering; these all work by repeatedly merging the closest two clusters but use different definitions of the distance between clusters. The cluster distances for which the nearest- neighbor chain algorithm works are called reducible and are characterized by a simple inequality among certain cluster distances.

Marx argues that products have different objective costs of production, reducible to different amounts of labour-time. Against this view, one could also argue that the physical amounts of comparable resources (such as energy, land, water, etc.), necessary to manufacture a car, are much larger than resources necessary for growing a carrot, explaining why the cost (and, hence, minimal price) of a car is larger than the cost of a carrot. In other words, it is the total input costs (including costs of labour), not the amount of labour per se, which create the difference in costs (and, therefore minimal equilibrium prices) of the goods. However, Marx argues in the first chapters of Das Kapital that most of such costs (i.e.

In about two out of every seven cases it arises from the inferior epigastric and descends almost vertically to the upper part of the obturator foramen. The artery in this course usually lies in contact with the external iliac vein, and on the lateral side of the femoral ring (Figure A on diagram). It can also pass medial to the femoral ring along the margin of the lacunar ligament (Figure B). In either case it would be at risk of injury during the operation to repair a femoral hernia, whether the hernia is reducible, incarcerated or strangulated. When the obturator artery travels along the lacunar ligament, it nearly encircles the femoral ring and can be lacerated during a femoral hernia repair.

Some ancient philosophies held that the universe is reducible to completely mechanical principles—that is, the motion and collision of matter. This view was closely linked with materialism and reductionism, especially that of the atomists and to a large extent, stoic physics. Later mechanists believed the achievements of the scientific revolution of the 17th century had shown that all phenomena could eventually be explained in terms of "mechanical laws": natural laws governing the motion and collision of matter that imply a determinism. If all phenomena can be explained entirely through the motion of matter under physical laws, as the gears of a clock determine that it must strike 2:00 an hour after striking 1:00, all phenomena must be completely determined, past, present or future.

Take facial recognition as an illustration: we can recognize our acquaintance's face out of a million others while we are not conscious about the knowledge of his face. It would be difficult for us to describe the precise arrangement of his eyes, nose and mouth, since we memorize the face unconsciously. As a prelude to The Tacit Dimension, in his book Personal Knowledge (1958), Polanyi claims that all knowing is personal, emphasizing the profound effects of personal feelings and commitments on the practice of science and knowledge. Arguing against the then dominant Empiricists view that minds and experiences are reducible to sense data and collections of rules, he advocates a post- positivist approach that recognizes human knowledge is often beyond their explicit expression.

The Kundu equation is a completely integrable system, allowing Lax pair representation, exact solutions, and higher conserved quantity. Along with its different particular cases, this equation has been investigated for finding its exact travelling wave solutions, exact solitary wave solutions via bilinearization, and Darboux transformation together with the orbital stability for such solitary wave solutions. The Kundu equation has been applied to various physical processes such as fluid dynamics, plasma physics, and nonlinear optics. It is linked to the mixed nonlinear Schrödinger equation through a gauge transformation and is reducible to a variety of known integrable equations such as the nonlinear Schrödinger equation (NLSE), derivative NLSE, higher nonlinear derivative NLSE, Chen–Lee–Liu, Gerjikov-Vanov, and Kundu–Eckhaus equations, for different choices of the parameters.

The new output is not reducible to the sum of inputs, because it is a new use-value to which new value has been added by living labor. Once the output has been produced and sold, a production price (or a unit cost price) can be fixed "after the fact", but that price is based on the preceding capital outlays which are fixed once the output has been produced, plus a profit mark-up, and usually cannot change later (at least not very significantly, in the ordinary situation). That aside, in practice it is not really true that every commodity has a uniquely formed production price, as Machover suggests. At best one could say that a particular type of commodity (for example, a good quality vacuum cleaner) exhibits a normal, average production price.

That means that the sadist is exhilarated by the emotional distress of the victim because they seek a subjectivity that views the victim as both subject and object. This argument may appear stronger if it is understood that this "Look of the Other" theory is either only an aspect of the faculties of desire, or somehow its primary faculty. This does not account for the turn that Deleuze took for his own theory of these matters, but the premise of "desire as 'Look'" is associated with theoretical distinctions always detracted by Deleuze, in what he regarded as its essential error to recognize "desire as lack"—which he identified in the philosophical temperament of Plato, Socrates, and Lacan. For Deleuze, insofar as desire is a lack it is reducible to the "Look".

Computer scientist Scott Aaronson analyzed the computational power of the Digi-Comp II. There are several ways to mathematically model the device's computational capabilities. A natural abstraction is a directed acyclic graph in which each internal vertex has an out-degree of 2, representing a toggle cam that routes balls to one of two other vertices. A fixed number of balls are placed at a designated source vertex, and the decision problem is to determine whether any balls ever reach a designated sink vertex. Aaronson showed that this decision problem, given as inputs a description of the DAG and the number of balls to run (encoded in unary), is complete under log-space reduction for CC, the class of problems log-space reducible to the stable marriage problem.

It has been argued that research endeavours working within the conventional linear paradigm necessarily end up in replication difficulties. Problems arise if the causal processes in the system under study are "interaction-dominant" instead of "component dominant", multiplicative instead of additive, and with many small non-linear interactions producing macro-level phenomena, that are not reducible to their micro-level components. In the context of such complex systems, conventional linear models produce answers that are not reasonable, because it is not in principle possible to decompose the variance as suggested by the General Linear Model (GLM) framework – aiming to reproduce such a result is hence evidently problematic. The same questions are currently being asked in many fields of science, where researchers are starting to question assumptions underlying classical statistical methods.

Whereas propositional attitudes approach to analyze points of view internally, the "location/access" approach analyzes points of view externally, by their role. The term "access" refers to the statement of Liz Gutierrez that "points of views, or perspectives, are ways of having access to the world and to ourselves", and the term "location" is in reference to the provided quotation of Jon Moline that points of view are "ways of viewing things and events from certain locations". Moline rejects the notion that points of view are reducible to some rules based on some theories, maxims or dogmas. Moline considers the concept of "location" in two ways: in a direct way as a vantage point, and in an extended way, the way how a given vantage point provides a perspective, i.e.

Orthogonality as a property of term rewriting systems describes where the reduction rules of the system are all left-linear, that is each variable occurs only once on the left hand side of each reduction rule, and there is no overlap between them. Orthogonal term rewriting systems have the consequent property that all reducible expressions (redexes) within a term are completely disjoint -- that is, the redexes share no common function symbol. For example, the term rewriting system with reduction rules : \rho_1\ :\ f(x, y) \rightarrow g(y) : \rho_2\ :\ h(y) \rightarrow f(g(y), y) is orthogonal -- it is easy to observe that each reduction rule is left-linear, and the left hand side of each reduction rule shares no function symbol in common, so there is no overlap. Orthogonal term rewriting systems are confluent.

It is a world- economy and it is by definition capitalist in form." Robert Brenner has pointed out that the prioritization of the world market means the neglect of local class structures and class struggles: "They fail to take into account either the way in which these class structures themselves emerge as the outcome of class struggles whose results are incomprehensible in terms merely of market forces." Another criticism is that of reductionism made by Theda Skocpol: she believes the interstate system is far from being a simple superstructure of the capitalist world economy: "The international states system as a transnational structure of military competition was not originally created by capitalism. Throughout modern world history, it represents an analytically autonomous level [... of] world capitalism, but [is] not reducible to it.

Since the focus on controlling student behavior interferes with relationship, his work suggests a preference for small schools and an implied criticism of large schools, especially in their ability to be effective with high risk students. He believed teaching was an art, not really a science and, as such, it was never technique that caused learning to occur, but rather the full complexity of individual relationships between students and teachers that were not reducible to the predictability of technique. Further, he felt that much of significant learning occurs strictly within the student's individual motivation and between students, when the teachers are wise enough to stand aside and allow it to occur. His plays were produced at the Judson Memorial Church in New York and elsewhere, and his essays and fiction appeared in many periodicals.

However, a major drawback of the constraint network is that it does not provide a computational framework for leveraging the numerical structure of the weighted constraints. Unlike the constraint network, the constraint composite graph provides a unifying framework for representing both the graphical structure of the variable- interactions as well as the numerical structure of the weighted constraints. It can be constructed using a simple polynomial-time procedure; and a given weighted constraint satisfaction problem is reducible to the problem of computing the minimum weighted vertex cover for its associated constraint composite graph. The "hybrid" computational properties of the constraint composite graph are reflected in the following two important results: (Result 1) The constraint composite graph of a given weighted constraint satisfaction problem has the same treewidth as its associated constraint network.

A Grammar is said to be SLR(1) if and only if, for each and every state s in the SLR(1) automaton, none of the following conditions are violated: # For any reducible rule A → a • Xb in state s (where X is some terminal), there must not exist some irreducible rule, B → a • in the same state s such that the follow set of B contains the terminal X. In more formal terms, the intersection of set containing the terminal X and the follow set of B must be empty. Violation of this rule is a Shift-Reduce Conflict. # For any two complete items A → a • and B → b • in s, Follow(A) and Follow(B) are disjoint (their intersection is the empty set). Violation of this rule is a Reduce-Reduce Conflict.

He rejects the claim that myth developed to explain ritual as an overly reductive and unknowable hypothesis. Auxier argues that the experience we call “religious” in the higher phases of experience is not reducible either to aesthetic or to cognitive experience and is a distinctive and nearly universal characteristic of human life. Auxier holds that religious experience can be engendered both through the repetition of rituals and through the experience of novelty (in nature or other cultures), but the novelty must be integrated into the familiar patterns in order for the feeling of value it carries to be retained. Thus Auxier believes that the religious community in which a human being is raised becomes the basis for the integration of future religious experiences that are not explicit in the experience of that community.

"This perspective stresses that Hart and Sacks 'believed that it was possible to distinguish legitimate and illegitimate exercises of official power while simultaneously transcending the centuries-old debate between ... the 'is' and the 'ought'.' The Legal Process demonstrated that lawyers did not have to engage in substantive moral or political reasoning, since 'there could be a kind of natural, functional correlation between different kinds of disputes and different kinds of institutions, so that the categories of dispute could be matched up with the kinds of institutional procedures corresponding to them.' Thus, by adopting the value pluralism of pragmatists like John Dewey, legal process was able to argue - contra the realists - that the analysis of legal validity is not reducible to political ideology.", citing Gary Peller, Neutral Principles in the 1950s, 21 U. Mich.

Prior to Fichte's writings, the idea of life as a power and principle independent of and not reducible to matter or substance had been put forward in England and Scotland in the mid-1700s, by the philosopher, Thomas Reid and John Hunter (surgeon), a highly influential anatomist and surgeon as well as an observational scientist in the true Baconian tradition. Hunter rested the idea of the life principle on solid observation of nature. For him, anatomy and structure, matter and form were simply outer expressions of a vital dynamics. This idea found a receptive soil in German philosophy and eclectic medicine, as represented by Christoph Hufeland (1762–1836), which had developed the concept of a life force or energy (Lebenskraft) as well, but one that had remained largely speculative or metaphorical.

12, Fernández Riquelme 2008, p. 562 and should participate in state politics represented in the Cortes by delegates of various "gremios, hermandades, agrupaciones, cámaras, comunidades y cofradías";Fernandez de la Mora 1989, p. 12, Fernández Riquelme 2008, p. 562 Tejada juxtaposed Spanish communitarian fuerosby no means reducible to "regionalism", Ayuso 1997, p. 29; the question whether fuero was a law or a norm seems left open, see Cantero 1996, p. 148 against the French individual liberties.Cecotti 2005, p. 206 According to some, the proposal advanced by Tejada was intended as a discussion how Spain should look like after Franco.Cuenca Toribio 1994, p. 374 160px Tejada's works on theory of politics are visibly less numerous than those on theory of law or on history of political thought; moreover, some of them resemble political manifestos rather than scholarly writings.

Queer international relations scholarship aims to broaden the scope and method of traditional international relations theory to include sexed and gendered approaches that are often excluded in the discipline at large. While affiliated with feminist theory and gender studies, as well as post-structuralism, queer IR theory is not reducible to any other field of international relations scholarship. Queer international relations theory works to expose the many ways in which sexualities and gender affect international politics. This includes the ways in which queer subjects and practices are disciplined, normalized, or capitalized on by traditional sites of power; how queer identities have often been the focus of domestic and foreign policy in heteronormative states; and how the order-versus-anarchy dichotomy in traditional international relations theory socially manifests itself in normal-versus-perverse and hetero/homo-normative versus queer dichotomies.

NP-complete problems are in NP, the set of all decision problems whose solutions can be verified in polynomial time; NP may be equivalently defined as the set of decision problems that can be solved in polynomial time on a non-deterministic Turing machine. A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) into p in polynomial time. It is not known whether every problem in NP can be quickly solved—this is called the P versus NP problem. But if any NP-complete problem can be solved quickly, then every problem in NP can, because the definition of an NP-complete problem states that every problem in NP must be quickly reducible to every NP-complete problem (that is, it can be reduced in polynomial time).

The rules as to when contracts did or did not require consent, and which were potentially reducible by court were complex. The age to enter into marriage was originally the age of minority, but this was raised to 16 years by the Age of Marriage Act 1929, and confirmed in the Marriage (Scotland) Act 1977. Under the Age Legal Capacity Scotland Act 1991 the old rules and terms were replaced. The basic rule under the replacement regime is that under 16s have no legal capacity. This is qualified by section 2 which provides that under 16s can: 1) enter into a contract of a kind commonly entered into by persons of their age group, and on terms which are not unreasonable; 2) from age 12, make a Will, and are deemed to have capacity to instruct a lawyer to act on their behalf.

For Kantor, because the interaction between organism and environment is continuous in time this event should be analyzed in terms of all of its interdependent components. This led to the proposal of the interbehavioral field as the unit of analysis. Kantor represented this field with the formula PE = C(k, sf, rf, hi, st, md) where PE is the psychological event, consisting of the interdependence (C) of the factors in the field, k stands for the specificity of every behavior segment, sf is the stimulus function, rf is the response function, hi stands for the history of interactions, st corresponds to the interactional setting, and md is the medium of contact. According to Kantor, this interbehavioral field is at the core of every psychological event, and this event is not reducible to any of the individual factors.

In Euclidean and projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines. Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate; this is true over both the Euclidean plane and any pappian projective plane. Indeed, given any five points there is a conic passing through them, but if three of the points are collinear the conic will be degenerate (reducible, because it contains a line), and may not be unique; see further discussion.

In The Idea of the Holy and other works, Otto set out a paradigm for the study of religion that focused on the need to realize the religious as a non-reducible, original category in its own right. The eminent Romanian-American historian of religion and philosopher Mircea Eliade used the concepts from The Idea of the Holy as the starting point for his own 1954 book, The Sacred and the Profane. The paradigm represented by Otto and Eliade was then heavily criticized for viewing religion as a sui generis category, until around 1990, when it began to see a resurgence as a result of its phenomenological aspects becoming more apparent. Ninian Smart, who was a formative influence on religious studies as a secular discipline, was influenced by Otto in his understanding of religious experience and his approach to understanding religion cross-culturally.

It is parametrized therefore by the unitary dual, the set of isomorphism classes of such representations, which is given the hull-kernel topology. The analogue of the Plancherel theorem is abstractly given by identifying a measure on the unitary dual, the Plancherel measure, with respect to which the direct integral is taken. (For Pontryagin duality the Plancherel measure is some Haar measure on the dual group to G, the only issue therefore being its normalization.) For general locally compact groups, or even countable discrete groups, the von Neumann group algebra need not be of type I and the regular representation of G cannot be written in terms of irreducible representations, even though it is unitary and completely reducible. An example where this happens is the infinite symmetric group, where the von Neumann group algebra is the hyperfinite type II1 factor.

Marx proposed that in a society where independent, private producers trade their products with each other, of their own volition and initiative, and without much coordination of market exchange, the volumes of production and commercial activities are adjusted in accordance with the fluctuating values of the products (goods and services) as they are bought and sold, and in accordance with the fluctuations of supply and demand. Because their social coexistence, and its meaning, is expressed through market exchange (trade and transaction), people have no other relations with each other. Therefore, social relations are continually mediated and expressed with objects (commodities and money). How the traded commodities relate will depend upon the costs of production, which are reducible to quantities of human labour, although the worker has no control over what happens to the commodities that he or she produces.

In computability theory and computational complexity theory, especially the study of approximation algorithms, an approximation-preserving reduction is an algorithm for transforming one optimization problem into another problem, such that the distance of solutions from optimal is preserved to some degree. Approximation-preserving reductions are a subset of more general reductions in complexity theory; the difference is that approximation-preserving reductions usually make statements on approximation problems or optimization problems, as opposed to decision problems. Intuitively, problem A is reducible to problem B via an approximation-preserving reduction if, given an instance of problem A and a (possibly approximate) solver for problem B, one can convert the instance of problem A into an instance of problem B, apply the solver for problem B, and recover a solution for problem A that also has some guarantee of approximation.

The industrial nature of these facilities means that many routine procedures or animal husbandry practices impinge on the welfare of the animals and could be considered as cruelty, with Henry Stephen Salt claiming in 1899 that "it is impossible to transport and slaughter vast numbers of large and highly-sensitive animals in a really humane manner".Salt, H.S. (1899) The Logic of Vegetarianism: Essays and Dialogues. London. It has been suggested the number of animals hunted, kept as companions, used in laboratories, reared for the fur industry, raced, and used in zoos and circuses, is insignificant compared to farm animals, and therefore the "animal welfare issue" is numerically reducible to the "farm animal welfare issue". Similarly, it has been suggested by campaign groups that chickens, cows, pigs, and other farm animals are among the most numerous animals subjected to cruelty.

This property was identified by in connection with an earlier clustering method that used mutual nearest neighbor pairs but not chains of nearest neighbors.. A distance function on clusters is defined to be reducible if, for every three clusters , and in the greedy hierarchical clustering such that and are mutual nearest neighbors, the following inequality holds: :. If a distance function has the reducibility property, then merging two clusters and can only cause the nearest neighbor of to change if that nearest neighbor was one of and . This has two important consequences for the nearest neighbor chain algorithm. First, it can be shown using this property that, at each step of the algorithm, the clusters on the stack form a valid chain of nearest neighbors, because whenever a nearest neighbor becomes invalidated it is immediately removed from the stack.

Sandis' research has primarily focused on the philosophy of action but he has also written about reasons, moral psychology, and understanding, as well as exegetical accounts of related works by Hume, Hegel, Anscombe, and Wittgenstein. His 2012 book The Things We Do and Why We Do Them argues for a pluralist account of actions and their explanations, and includes the controversial view that the reasons for which we act cannot in themselves explain why any action occurs. Since then he has published numerous articles defending the view that understanding others is not reducible to obtaining information about their 'mental contents' and that, consequently, no theory about the nature of such access can account for understanding others, which requires the sharing of behaviour. He has also collaborated with Microsoft Research on designing intelligible AI and co-written papers on the ethics of risk-taking with Nassim Nicholas Taleb.

Tegmark moves from the epistemic claim that mathematics is the only known symbol system which can in principle express absolutely everything, to the methodological claim that everything is reducible to mathematical relationships, and then to the ontological claim, that ultimately everything that exists is mathematical (the mathematical universe hypothesis). The argument is then reversed, so that because everything is mathematical in reality, mathematics is necessarily the ultimate universal symbol system. The main criticisms of Tegmark's approach are that (1) the steps in this argument do not necessarily follow, (2) no conclusive proof or test is possible for the claim that such an exhaustive mathematical expression or reduction is feasible, and (3) it may be that a complete reduction to mathematics cannot be accomplished, without at least partly altering, negating or deleting a non-mathematical significance of phenomena, experienced perhaps as qualia.See also Raphael van Riel & Robert Van Gulick, "Scientific reduction".

Similarly, for a projective curve defined by a homogeneous polynomial P(x,y,z) of degree d, the singular points have the solutions of the system :P'_x(x,y,z)=P'_y(x,y,z)=P'_z(x,y,z)=0 as homogeneous coordinates. (In positive characteristic, the equation P(x,y,z) has to be added to the system.) This implies that the number of singular points is finite as long as p(x,y) or P(x,y,z) is square free. Bézout's theorem implies thus that the number of singular points is at most (d−1)2, but this bound is not sharp because the system of equations is overdetermined. If reducible polynomials are allowed, the sharp bound is d(d−1)/2, this value is reached when the polynomial factors in linear factors, that is if the curve is the union of d lines.

Particularly the latter idea was widely rejected by the modern synthesis and is disproved today, but the hopeful monster concept based on evo-devo explanations found a moderate revival in recent times. As an alternative to saltational evolution, Dobzhansky suggested that the difference between macroevolution and microevolution reflects essentially a difference in time- scales, and that macroevolutionary changes were simply the sum of microevolutionary changes over geologic time. This view became broadly accepted, and accordingly, the term macroevolution has been used widely as a neutral label for the study of evolutionary changes that take place over a very large time-scale. However, the tenet that large-scale evolutionary patterns were ultimately reducible to microevolution has been challenged by the concept of species selection, which suggests that selection among species is a major evolutionary factor that is independent from and complementary to selection among organisms.

A crude version of this algorithm to find a basis for an ideal I of a polynomial ring R proceeds as follows: :Input A set of polynomials F that generates I :Output A Gröbner basis G for I :# G := F :# For every fi, fj in G, denote by gi the leading term of fi with respect to the given ordering, and by aij the least common multiple of gi and gj. :# Choose two polynomials in G and let Sij = (aij / gi) fi − (aij / gj) fj (Note that the leading terms here will cancel by construction). :# Reduce Sij, with the multivariate division algorithm relative to the set G until the result is not further reducible. If the result is non-zero, add it to G. :# Repeat steps 1-4 until all possible pairs are considered, including those involving the new polynomials added in step 4.

1, pp. 109-140. Bestvina and Handel applied the train track techniques to obtain an effective proof of Thurston's classification of homeomorphisms of compact surfaces (with or without boundary) which says that every such homeomorphism is, up to isotopy, either reducible, of finite order or pseudo-anosov. Since then train tracks became a standard tool in the study of algebraic, geometric and dynamical properties of automorphisms of free groups and of subgroups of Out(Fn). Train tracks are particularly useful since they allow to understand long-term growth (in terms of length) and cancellation behavior for large iterates of an automorphism of Fn applied to a particular conjugacy class in Fn. This information is especially helpful when studying the dynamics of the action of elements of Out(Fn) on the Culler-Vogtmann Outer space and its boundary and when studying Fn actions of on real trees.

Modern views often center around physicalism and functionalism, which hold that the mind is roughly identical with the brain or reducible to physical phenomena such as neuronal activitySmart, J.J.C., "The Mind/Brain Identity Theory", The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.), though dualism and idealism continue to have many supporters. Another question concerns which types of beings are capable of having minds (New Scientist 8 September 2018 p10). For example, whether mind is exclusive to humans, possessed also by some or all animals, by all living things, whether it is a strictly definable characteristic at all, or whether mind can also be a property of some types of human-made machines. Whatever its nature, it is generally agreed that mind is that which enables a being to have subjective awareness and intentionality towards their environment, to perceive and respond to stimuli with some kind of agency, and to have consciousness, including thinking and feeling.

In mathematics, the unitarian trick is a device in the representation theory of Lie groups, introduced by for the special linear group and by Hermann Weyl for general semisimple groups. It applies to show that the representation theory of some group G is in a qualitative way controlled by that of some other compact group K. An important example is that in which G is the complex general linear group, and K the unitary group acting on vectors of the same size. From the fact that the representations of K are completely reducible, the same is concluded for those of G, at least in finite dimensions. The relationship between G and K that drives this connection is traditionally expressed in the terms that the Lie algebra of K is a real form of that of G. In the theory of algebraic groups, the relationship can also be put that K is a dense subset of G, for the Zariski topology.

A resurgence of interest in classical integrable systems came with the discovery, in the late 1960s, that solitons, which are strongly stable, localized solutions of partial differential equations like the Korteweg–de Vries equation (which describes 1-dimensional non-dissipative fluid dynamics in shallow basins), could be understood by viewing these equations as infinite-dimensional integrable Hamiltonian systems. Their study leads to a very fruitful approach for "integrating" such systems, the inverse scattering transform and more general inverse spectral methods (often reducible to Riemann–Hilbert problems), which generalize local linear methods like Fourier analysis to nonlocal linearization, through the solution of associated integral equations. The basic idea of this method is to introduce a linear operator that is determined by the position in phase space and which evolves under the dynamics of the system in question in such a way that its "spectrum" (in a suitably generalized sense) is invariant under the evolution, cf. Lax pair.

A raster data type is, in essence, any type of digital image represented by reducible and enlargeable grids. Anyone who is familiar with digital photography will recognize the Raster graphics pixel as the smallest individual grid unit building block of an image, usually not readily identified as an artifact shape until an image is produced on a very large scale. A combination of the pixels making up an image color formation scheme will compose details of an image, as is distinct from the commonly used points, lines, and polygon area location symbols of scalable vector graphics as the basis of the vector model of area attribute rendering. While a digital image is concerned with its output blending together its grid based details as an identifiable representation of reality, in a photograph or art image transferred into a computer, the raster data type will reflect a digitized abstraction of reality dealt with by grid populating tones or objects, quantities, cojoined or open boundaries, and map relief schemas.

Ethical naturalism has been criticized most prominently by ethical non-naturalist G. E. Moore, who formulated the open-question argument. Garner and Rosen say that a common definition of "natural property" is one "which can be discovered by sense observation or experience, experiment, or through any of the available means of science." They also say that a good definition of "natural property" is problematic but that "it is only in criticism of naturalism, or in an attempt to distinguish between naturalistic and nonnaturalistic definist theories, that such a concept is needed." R. M. Hare also criticised ethical naturalism because of its fallacious definition of the terms 'good' or 'right' explaining how value-terms being part of our prescriptive moral language are not reducible to descriptive terms: "Value-terms have a special function in language, that of commending; and so they plainly cannot be defined in terms of other words which themselves do not perform this function".

In one of his works G. Dumézil has postulated the existence of a structural difference in level between the Indo-European gods of beginning and ending and the other gods who fall into a tripartite structure, reflecting the most ancient organization of society. So in IE religions there is an introducer god (as Vedic Vâyu and Roman Janus) and a god of ending, a nurturer goddess and a genie of fire (as Vedic Saraswati and Agni, Avestic Armaiti, Anâitâ and Roman Vesta) who show a sort of mutual solidarity: the concept of 'god of ending' is defined in connection to the human referential, i.e. the current situation of man in the universe, and not to endings as transitions, which are under the jurisdiction of the gods of beginning owing to the ambivalent nature of the concept. Thus the god of beginning is not structurally reducible to a sovereign god, nor the goddess of ending to any of the three categories on to which the goddesses are distributed.

Even to an agnostic or atheist the poems here will almost certainly evoke a powerful sense of strangeness, of something quite-conceivably real but not reducible to words' Geoff Page reviews The Sunset Assumption in Southerly (journal)Southerly Vol 72 No 2 2012 p 197 '...technically skilled and careful, in the service of precise notations of scenes from the poet's emotional life.' Commentary on Light Pressure in the Oxford Companion to 20th Century PoetryIan Hamilton (ed) Oxford Companion to Twentieth Century Poetry in English OUP 1994 p171 'Foulcher is not a poet of dramatic gestures or strident convictions; rather, he is a poet of implications, implications that come from closely observed and imaginatively recreated particulars; ones that readers will almost certainly recognise as part of their own lives'. Geoff Page (ed) A Reader's Guide to Contemporary Australian Poetry UQP 1995.Geoff Page (ed) A Reader's Guide to Contemporary Australian Poetry UQP 1995.

In economics, Saari has shown that natural price mechanisms that set the rate of change of the price of a commodity proportional to its excess demand can lead to chaotic behavior rather than converging to an economic equilibrium, and has exhibited alternative price mechanisms that can be guaranteed to converge. However, as he also showed, such mechanisms require that the change in price be determined as a function of the whole system of prices and demands, rather than being reducible to a computation over pairs of commodities. In celestial mechanics, Saari's work on the -body problem "revived the singularity theory" of Henri Poincaré and Paul Painlevé, and proved Littlewood's conjecture that the initial conditions leading to collisions have measure zero. He also formulated the "Saari conjecture", that when a solution to the Newtonian -body problem has an unchanging moment of inertia relative to its center of mass, its bodies must be in relative equilibrium.

According to Zhang & Norman (1994), the distributed cognition approach has three key components: # Embodiment of information that is embedded in representations of interaction # Coordination of enaction among embodied agents # Ecological contributions to a cognitive ecosystem DCog studies the "propagation of representational states across media" (Rogers and Ellis, ibid.). Mental content is considered to be non- reducible to individual cognition and is more properly understood as off- loaded and extended into the environment, where information is also made available to other agents (Heylighen, Heath, & Overwalle, 2003). It is often understood as an approach in specific opposition to earlier and still prevalent "brain in a vat" models which ignore "situatedness, embodiment and enaction" as key to any cognitive act (Ibid.). These representation-based frameworks consider distributed cognition as "a cognitive system whose structures and processes are distributed between internal and external representations, across a group of individuals, and across space and time" (Zhang and Patel, 2006).

Truemper observed that every grid graph is reducible by Δ-Y and Y-Δ transforms in this way, that this reducibility is preserved by graph minors, and that every planar graph is a minor of a grid graph.. This idea can be used to replace Steinitz's lemma that a reduction sequence exists, in a proof of Steinitz's theorem using induction in the same way. However, there exist graphs that require a nonlinear number of steps in any sequence of Δ-Y and Y-Δ transforms. More precisely, Ω(n3/2) steps are sometimes necessary, and the best known upper bound on the number of steps is even worse, O(n2).. An alternative form of induction proof is based on removing edges (and compressing out the degree-two vertices that might be performed by this removal) or contracting edges and forming a minor of the given planar graph. Any polyhedral graph can be reduced to K4 by a linear number of these operations, and again the operations can be reversed and the reversed operations performed geometrically, giving a polyhedral realization of the graph.

Robertson's irreducible apex graph, showing that the YΔY- reducible graphs have additional forbidden minors beyond those in the Petersen family. A minor of a graph G is another graph formed from G by contracting and removing edges. As the Robertson–Seymour theorem shows, many important families of graphs can be characterized by a finite set of forbidden minors: for instance, according to Wagner's theorem, the planar graphs are exactly the graphs that have neither the complete graph K5 nor the complete bipartite graph K3,3 as minors. Neil Robertson, Paul Seymour, and Robin Thomas used the Petersen family as part of a similar characterization of linkless embeddings of graphs, embeddings of a given graph into Euclidean space in such a way that every cycle in the graph is the boundary of a disk that is not crossed by any other part of the graph.. Horst Sachs had previously studied such embeddings, shown that the seven graphs of the Petersen family do not have such embeddings, and posed the question of characterizing the linklessly embeddable graphs by forbidden subgraphs.. Robertson et al.

Formally, this reduction is executed via a log-space transducer. Such a machine has polynomially-many configurations, so log-space reductions are also polynomial-time reductions. However, log-space reductions are probably weaker than polynomial-time reductions; while any non- empty, non-full language in P is polynomial-time reducible to any other non- empty, non-full language in P, a log-space reduction from an NL-complete language to a language in L, both of which would be languages in P, would imply the unlikely L = NL. It is an open question if the NP-complete problems are different with respect to log-space and polynomial-time reductions. Log- space reductions are normally used on languages in P, in which case it usually does not matter whether many-one reductions or Turing reductions are used, since it has been verified that L, SL, NL, and P are all closed under Turing reductions, meaning that Turing reductions can be used to show a problem is in any of these classes.

In his resignation letter, published in English and Spanish, he recollected that > One of the most basic splits in contemporary human rights work – sometimes > mapped onto a division between "global South" and "global North," though not > quite reducible to it – is between rights as a set of legal norms, and > rights as a complex of human dreams and political aspirations. The split has > to do, as well, with the difference between institutions and movements, the > former ones formal and developing their own standards and needs, the latter > fluid and chaotic and responsible to individuals' and communities' desires > and drives … Human Rights Watch – and other international organizations like > it – needs a far deeper understanding of what social movements are, why they > are important, how they turn human rights into living values rather than > legal abstractions. In fall 2010, Long was a senior fellow at the Center for Gender and Sexuality Law at Columbia University Law School. From January 2011 - September 2012, he was a visiting fellow at the Human Rights Program at Harvard Law School.

In mathematics, a multivariate polynomial defined over the rational numbers is absolutely irreducible if it is irreducible over the complex field.... For example, x^2+y^2-1 is absolutely irreducible, but while x^2+y^2 is irreducible over the integers and the reals, it is reducible over the complex numbers as x^2+y^2 = (x+iy)(x-iy), and thus not absolutely irreducible. More generally, a polynomial defined over a field K is absolutely irreducible if it is irreducible over every algebraic extension of K,. and an affine algebraic set defined by equations with coefficients in a field K is absolutely irreducible if it is not the union of two algebraic sets defined by equations in an algebraically closed extension of K. In other words, an absolutely irreducible algebraic set is a synonym of an algebraic variety,. which emphasizes that the coefficients of the defining equations may not belong to an algebraically closed field. Absolutely irreducible is also applied, with the same meaning to linear representations of algebraic groups.

They may be cosmological (describing existence at large), personal (describing development of an individual), or both. They can be holistic (holding that higher realities emerge from and are not reducible to the lower), idealist (holding that reality is primarily mental or spiritual) or nondual (holding that there is no ultimate distinction between mental and physical reality). One can regard all of them as teleological to a greater or lesser degree. Philosophers, scientists, and educators who have proposed theories of spiritual evolution include Schelling (1775-1854), Hegel (1770-1831), Carl Jung (1875-1961), Max Théon (1848-1927), Helena Petrovna Blavatsky (1831-1891), Henri Bergson (1859-1941), Rudolf Steiner (1861-1925), Sri Aurobindo (1872-1950), Nikolai Berdyaev (1874-1948), Jean Gebser (1905-1973), Pierre Teilhard de Chardin (1881-1955), Owen Barfield (1898-1997), Arthur M. Young (1905-1995), Edward Haskell (1906-1986), E. F. Schumacher (1911-1977), Erich Jantsch (1929-1980), Clare W. Graves (1914-1986), Alfred North Whitehead (1861-1947), Terence McKenna (1946-2000), and P. R. Sarkar (1921-1990).

In the posthumously published Sense and Sensibilia (the title is Austin's own, and wittily echoes the title of Sense and Sensibility, Jane Austen's first book, just as his name echoes hers),Austin had lectured on the material of this book many times in Oxford from about 1947 to 1959, and once at the University of California at Berkeley. See Warnock's Foreword. Austin criticizes the claims put forward by A. J. Ayer's The Foundations of Empirical Knowledge (1940), and to a lesser extent, H. H. Price's Perception (1932) and G. J. Warnock's Berkeley (1953), concerning the sense-data theory. He states that perceptual variation, which can be attributed to physical causes, does not involve a figurative disconnect between sense and reference, due to an unreasonable separation of parts from the perceived object. Central to his argument, he shows that "there is no one kind of thing that we ‘perceive’ but many different kinds, the number being reducible if at all by scientific investigation and not by philosophy" (Austin 1962a, 4).

Romantic medicine is part of the broader movement known as Romanticism, most predominant in the period 1800–1840, and involved both the cultural (humanities) and natural sciences, not to mention efforts to better understand man within a spiritual context ('spiritual science'). Romanticism in medicine was an integral part of Romanticism in science. :Romantic writers were far better read in medicine than we tend to remember: Byron consulted popular health manuals by Adair and Solomon; Coleridge read deeply in his physician, James Gillman's, library; Percy Shelley ordered Spallanzani's complete works and immersed himself in the vitalist controversy, while Mary Shelley read Gall and Spurzheim; Blake engraved plates for medical literature published by Joseph Johnson; and Keats, of course, was trained as a physician. The impetus for Romantic ideas in medicine came from the Great Britain, and more specifically Scotland - John Hunter (1728–93) - and the idea of life as a principle not reducible to material constructs, and John Brown (1735–88), founder of the Brunonian system of medicine (see also, Romanticism in Scotland#Science).

On the purely visual level, Hoolboom notes Cockburn's montage consists of deliberately banal images, "indifferently shot and largely illustrative of the voice-over" to emphasize the fact that, to all appearances and for all practical purposes, nothing has changed. Norman Wilner notes that as is typical of him, Cockburn's narrator is both prankster and serious inquisitor, calmly offering philosophical and metaphysical insights while his thesis plays out on the screen; "there's no way anything he's talking about is even plausible, let alone probable, but he's going to explore the possibilities as if it were." Treating the narrator exclusively as a persona, Martinson remarks that he is both rattled by and curious about the uniquely private and perturbing knowledge that he has mysteriously acquired, and, if we take the narrator at his word, a universal expansion is reducible to "a blip in the order of things, barely perceptable." The narrator is certain about what happened and yet nervous about it at the same time, aware that the "residue" of the event exists "only in this mind" in the form of a "barely sensed sense" which, having happened once, may happen again.

The older doctrine, here called universal mechanism, is the ancient philosophies closely linked with materialism and reductionism, especially that of the atomists and to a large extent, stoic physics. They held that the universe is reducible to completely mechanical principles—that is, the motion and collision of matter. Later mechanists believed the achievements of the scientific revolution had shown that all phenomena could eventually be explained in terms of 'mechanical' laws, natural laws governing the motion and collision of matter that implied a thorough going determinism: if all phenomena could be explained entirely through the motion of matter under the laws of classical physics, then even more surely than the gears of a clock determine that it must strike 2:00 an hour after striking 1:00, all phenomena must be completely determined: whether past, present or future. (One of the philosophical implications of modern quantum mechanics is that this view of determinism is not defensible.) The French mechanist and determinist Pierre Simon de Laplace formulated the sweeping implications of this thesis by saying: One of the first and most famous expositions of universal mechanism is found in the opening passages of Leviathan by Thomas Hobbes (1651).

Take two smooth curves C and D in a smooth projective 3-fold P, intersecting in two points c and d that are nodes for the reducible curve C\cup D. For some applications these should be chosen so that there is a fixed-point-free automorphism exchanging the curves C and D and also exchanging the points c and d. Hironaka's example V is obtained by blowing up the curves C and D, with C blown up first at the point c and D blown up first at the point d. Then V has two smooth rational curves L and M lying over c and d such that L+M is algebraically equivalent to 0, so V cannot be projective. For an explicit example of this configuration, take t to be a point of order 2 in an elliptic curve E, take P to be E\times E/(t)\times E/(t), take C and D to be the sets of points of the form (x,x,0) and (x,0,x), so that c and d are the points (0,0,0) and (t,0,0), and take the involution σ to be the one taking (x,y,z) to (x+t,z,y).