127 Sentences With "multiplicities" | Random Sentence Generator

He was probably referring to Deleuze and Guattari's famously influential writing on multiplicities.

"Multiplicities" refers to the philosophical concept of a space in which difference is retained.

He is typically framed as an artist of mulatto ecologies, voodoo assemblages, and transcultural multiplicities.

Just as the model Mr. Gesnouin had, Mr. Michele referenced Deleuze and Guattari's multiplicities in his show notes.

The artists represent a new polycultural future for curator Modou Dieng, one where binaries are exploded into multiplicities.

It's praiseworthy that Disney has hired Mr. Coogler and Ms. DuVernay; Disney understands the audience in all its multiplicities.

Listening through to Jesus Loves Me Too—which we're premiering in full here—you can hear those multiplicities at play.

Ingels seems to be attracted to the dialectical relationship between the unitary building and the multiplicities of urban space that surround it.

The book itself offers a glimpse of the reality of living with schizophrenia and the multiplicities and contradictions that accompany the disease.

Zadie Smith told me a wonderful thing about the way that you can look at a person and see that there are multiplicities.

"People confuse masculine and feminine with being male and female and restricting those multiplicities in a single body's form creates conflict," Verma told me.

Insofar as there is a healthy way to do that, Frank seems to offer, it is in determining a personal reality that supersedes external markers and reconciles internal multiplicities.

Multiplicities marks the New York debut of Brett Seiler, a queer Zimbabwean man living in South Africa; Helina Metaferia, an female, Ethiopian-American performance artist; and Blake Daniels, a queer American man who studied in South Africa.

The curatorial theme of the current Biennale, Forming in the pupil of the eye, is derived from an old story about a young traveler who seeks a meeting with a wise sage to try to understand the complicated multiplicities of all that is.

By not only ignoring, but actively suppressing these narratives the Lebanese left mirrors for the shortcomings of western liberalism and white feminism, and ignore the various racial, socioeconomic contexts and multiplicities of feminist and refugee struggles in favor of bourgeois political discourse, which is an ill-disguised means to accumulate further labor.

We looked back at some of our past coverage on this auspicious day with an essay by the mathematician Steven Strogatz, who wrote that π is the perfect symbol for our species' long effort to tame infinity, and another by the columnist Natalie Angier on the multiplicities of infinity in science. 10.

Thankfully, progress seems to have been made in recent years: the UK was home to its first same-sex marriage in 2017, while a number of projects founded for and by queer British Muslims have sought to reflect on—and provide space for—the multiplicities of its community, from London Queer Muslims and Imaan LGBTQ to Hidayah.

So then what we thought was this: Given that the film itself is all layers and multiplicities of disciplines, inputs, and chronologies, it could be more interesting to present a layered, multiple-voiced exchange between the two of us — a kind of review-qua-pastiche or pastiche-qua-review, not unlike the pastiche that is this film.

Puncture one of the exogenous rituals surrounding the game, this critique says, and the entire enterprise collapses into chaos—the intrusion of multiplicities of opinions loudly expressed, the possibility of unintended material consequences, the inconvenient facts of other people's lived realities, the carnage and challenge and thrill of living in this world with your eyes open.

As a result, the masses and spin multiplicities of such particles are then arbitrary.

Proof of equivalence: If a set is well-ordered, then its cardinality is an aleph since the alephs are the cardinals of well-ordered sets. If a set's cardinality is an aleph, then it can be well-ordered since there is a one-to-one correspondence between it and the well-ordered set defining the aleph. First, he defined two types of multiplicities: consistent multiplicities (sets) and inconsistent multiplicities (absolutely infinite multiplicities). Next he assumed that the ordinals form a set, proved that this leads to a contradiction, and concluded that the ordinals form an inconsistent multiplicity.

However, in this case there are additional constraints on the divisor beyond having zero sum of multiplicities..

In differential geometry, a Dupin hypersurface is a submanifold in a space form, whose principal curvatures have globally constant multiplicities.

File:Datamodel.jpg Figure 7: Overall data model This data model shows all the concepts with multiplicities and relations in a full project context.

The integrating processes of his physical form energies and his mental energies perfect themselves until the multiplicities have progressively reintegrated themselves back to Omneity.

The philosopher Gilles Deleuze describes The Archaeology of Knowledge as, "the most decisive step yet taken in the theory-practice of multiplicities."Deleuze, Foucault (1986, p.14).

More generally, the fundamental theorem of algebra asserts that the complex solutions of a polynomial equation of degree always form a multiset of cardinality . A special case of the above are the eigenvalues of a matrix, whose multiplicity is usually defined as their multiplicity as roots of the characteristic polynomial. However two other multiplicities are naturally defined for eigenvalues, their multiplicities as roots of the minimal polynomial, and the geometric multiplicity, which is defined as the dimension of the kernel of (where is an eigenvalue of the matrix ). These three multiplicities define three multisets of eigenvalues, which may be all different: Let be a matrix in Jordan normal form that has a single eigenvalue.

In his Foucault (1986), Deleuze describes Michel Foucault's The Archaeology of Knowledge (1969) as "the most decisive step yet taken in the theory-practice of multiplicities."Deleuze (1986, 14).

Deleuze and Guattari's rhizomatic and Benjamin's montage dismantle the top-down and hierarchical social reality and bring into attention the micro-politics of mapping multiplicities of networks and assemblages.

In mathematics, the Nagata conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass through a collection of very general points with prescribed multiplicities.

Eguchi and Hikami showed that the N=(4,4) multiplicities are mock modular forms, and Miranda Cheng suggested that characters of elements of M24 should also be mock modular forms. This suggestion became the Mathieu Moonshine conjecture, asserting that the virtual representation of N=(4,4) given by the K3 elliptic genus is an infinite dimensional graded representation of M24 with non-negative multiplicities in the massive sector, and that the characters are mock modular forms. In 2012, Terry Gannon proved that the representation of M24 exists.

1\. The two conjectures are known to be equivalent. Moreover, Borho–Jantzen's translation principle implies that can be replaced by for any dominant integral weight . Thus, the Kazhdan–Lusztig conjectures describe the Jordan–Hölder multiplicities of Verma modules in any regular integral block of Bernstein–Gelfand–Gelfand category O. 2\. A similar interpretation of all coefficients of Kazhdan–Lusztig polynomials follows from the Jantzen conjecture, which roughly says that individual coefficients of are multiplicities of in certain subquotient of the Verma module determined by a canonical filtration, the Jantzen filtration.

Rhizome as a philosophical concept was developed by Gilles Deleuze and Félix Guattari in their Capitalism and Schizophrenia (1972–1980) project. It is what Deleuze calls an "image of thought", based on the botanical rhizome, that apprehends multiplicities.

Normaliz also computes enumerative data, such as multiplicities (volumes) and Hilbert series. The kernel of Normaliz is a templated C++ class library. For multivariate polynomial arithmetic it uses CoCoALib. Normaliz has interfaces to several general computer algebra systems: CoCoA, GAP, Macaulay2 and Singular.

This axiom implies that these big classes are not sets, which eliminates the paradoxes since they cannot be members of any class.Hallett 1986, pp. 288, 290–291. Cantor had pointed out that inconsistent multiplicities face the same restriction: they cannot be members of any multiplicity.

In the prime factorization, for example, : the multiplicity of the prime factor 2 is 2, while the multiplicity of each of the prime factors 3 and 5 is 1. Thus, 60 has four prime factors allowing for multiplicities, but only three distinct prime factors.

The fundamental theorem of algebra states that every polynomial of degree n has n complex roots, counted with their multiplicities. The non-real roots of polynomials with real coefficients come in conjugate pairs. Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.

The methods have been extended, however, to deal with other types of processes like intersystem crossing (ISC; transfer between states of different multiplicities) and field-induced transfers. NA-MQC dynamics has been often used in theoretical investigations of photochemistry and femtochemistry, especially when time-resolved processes are relevant.

A comprehensive overview is to be found in Craig Huneke's article "Hilbert-Kunz multiplicities and the F-signature" arXiv:1409.0467. This article is also found on pages 485-525 of the Springer volume "Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday", edited by Irena Peeva.

In the philosophy of mathematics, specifically the philosophical foundations of set theory, limitation of size is a concept developed by Philip Jourdain and/or Georg Cantor to avoid Cantor's paradox. It identifies certain "inconsistent multiplicities", in Cantor's terminology, that cannot be sets because they are "too large". In modern terminology these are called proper classes.

Black Is...Black Ain't is an exploration and comprehensive commentary of the Black experience in America. Riggs establishes that there is no singular definition of what it means "to be Black." The very form and content illustrate Blackness in its multiplicities. The film presents a plethora of black identities disallowing for generalization or stereotyping of the larger Black community.

After this cycle has been completed a version of the system is ready and a new cycle begins to create a new version. The phases are explained in the following sections and are shown through a meta-modeling technique. More details about multiplicities and concepts in a project context can be seen in the overall data model later on.

The signature of a metric tensor is defined as the signature of the corresponding quadratic form. It is the number of positive and zero eigenvalues of any matrix (i.e. in any basis for the underlying vector space) representing the form, counted with their algebraic multiplicities. Usually, is required, which is the same as saying a metric tensor must be nondegenerate, i.e.

Two closed Riemannian manifolds are said to be isospectral if the eigenvalues of their Laplace–Beltrami operator (Laplacians), counted multiplicities, coincide. One of fundamental problems in spectral geometry is to ask to what extent the eigenvalues determine the geometry of a given manifold. There are many examples of isospectral manifolds which are not isometric. The first example was given in 1964 by John Milnor.

The notion of the singular art world is problematic, since Becker and others show art worlds are, instead, independent multiplicities scattered worldwide that are always in flux: there is no "center" to the art world any more. The art world, along with the definition of fine art, is constantly changing as works of art previously excluded move into the "avant garde" and then into mainstream culture.

Nagata's conjecture on curves concerns the minimum degree of a plane curve specified to have given multiplicities at given points; see also Seshadri constant. Nagata's conjecture on automorphisms concerns the existence of wild automorphisms of polynomial algebras in three variables. Recent work has solved this latter problem in the affirmative.I. P. Shestakov, & U. U. Umirbaev (2004) Journal of the American Mathematical Society 17, 197–227.

William Fulton in Intersection Theory (1984) writes > ... if and are subvarieties of a non-singular variety , the intersection > product should be an equivalence class of algebraic cycles closely related > to the geometry of how , and are situated in . Two extreme cases have been > most familiar. If the intersection is proper, i.e. , then is a linear > combination of the irreducible components of , with coefficients the > intersection multiplicities.

Virtual Private LAN Service (VPLS) is a way to provide Ethernet-based multipoint to multipoint communication over IP or MPLS networks. It allows geographically dispersed sites to share an Ethernet broadcast domain by connecting sites through pseudowires. The term 'sites' includes multiplicities of both servers and clients. The technologies that can be used as pseudo-wire can be Ethernet over MPLS, L2TPv3 or even GRE.

The ratio of mean multiplicities of positively charged kaons and pions as a function of collision energy in collisions of two lead nuclei and proton–proton interactions The onset of deconfinement refers to the beginning of the creation of deconfined states of strongly interacting matter produced in nucleus-nucleus collisions with increasing collision energy (a quark–gluon plasma). The onset of deconfinement was predicted by Marek Gazdzicki and Mark I. Gorenstein to be located in the low energy range of the Super Proton Synchrotron (SPS) at the European Organization for Nuclear Research (CERN). These predictions have been confirmed by the NA49 experiment at the CERN SPS within the energy scan programme. The most famous of these is the "horn" in the ratio of mean multiplicities of positively charged kaons and pions observed in collisions of two lead nuclei at the low energies of the SPS.

The paradoxical title of Sister Outsider expresses Lorde’s commitment to her identity and the multiplicities gathering together to assemble her unique identity – multiplicities that often placed her “on the line,” in a space that refused safety of an inside parameter, demonstrating Lorde's ability to embrace difficulty in the path to create change. Lorde informs readers through these essays that the histories of westernized culture have conditioned inhabitants to view “human differences in simplistic opposition to each other” – good/bad, superior/inferior – and to always be suspicious of the latter, instead of as Lorde suggests, using differences as a catalyst for change . Throughout the collection, Lorde also emphasizes the use of poetry as a profound form of knowledge, a powerful tool for diagnosing and challenging power relations within a racist, patriarchal society. In this charged collection, Lorde challenges sexism, racism, ageism, homophobia, and classism with determination.

Given a polynomial equation or a system of polynomial equations it is often useful to compute or to bound the number of solutions without computing explicitly the solutions. In the case of a single equation, this problem is solved by the fundamental theorem of algebra, which asserts that the number of complex solutions is bounded by the degree of the polynomial, with equality, if the solutions are counted with their multiplicities. In the case of a system of polynomial equations in unknowns, the problem is solved by Bézout's theorem, which asserts that, if the number of complex solutions is finite, their number is bounded by the product of the degrees of the solutions. Moreover, if the number of solutions at infinity is also finite, then the product of the degrees equals the number of solutions counted with multiplicities and including the solutions at infinity.

When a chief series for a group exists, it is generally not unique. However, a form of the Jordan–Hölder theorem states that the chief factors of a group are unique up to isomorphism, independent of the particular chief series they are constructed from. In particular, the number of chief factors is an invariant of the group G, as well as the isomorphism classes of the chief factors and their multiplicities.

They can be used to calculate the level of deuteration in a molecule. Analogous signals are not observed in 2H NMR spectra because of the low sensitivity of this technique compared to the 1H analysis. Deuterons typically exhibit very similar chemical shifts to their analogous protons. Analysis via 13C NMR spectroscopy is also possible: the different spin values of hydrogen (1/2) and deuterium (1) gives rise to different splitting multiplicities.

She went to Purdue University for graduate study, completing her Ph.D. in mathematics in 1992. Her dissertation, Tight Closure, Joint Reductions, And Mixed Multiplicities, was supervised by Craig Huneke. After postdoctoral research at the University of Michigan, she joined the faculty at New Mexico State University, and moved from there back to Reed in 2005. Swanson returned to Purdue in 2020 as Head of the Department of Mathematics.

They are additive rather than > substitutive, and immanent rather than transcendent: executed by functional > complexes of currents, switches, and loops, caught in scaling > reverberations, and fleeing through intercommunications, from the level of > the integrated planetary system to that of atomic assemblages. > Multiplicities captured by singularities interconnect as desiring-machines; > dissipating entropy by dissociating flows, and recycling their machinism as > self-assembling chronogenic circuitry.Nick Land, Fanged Noumena (2011, 442).

Watanabe and Yoshida strengthened some of Kunz's results, showing that in the unmixed case, the ring is regular precisely when c=1. Hilbert–Kunz functions and multiplicities have been studied for their own sake. Brenner and Trivedi have treated local rings coming from the homogeneous co-ordinate rings of smooth projective curves, using techniques from algebraic geometry. Han, Monsky and Teixeira have treated diagonal hypersurfaces and various related hypersurfaces.

Influenced by Hermeneutic tradition, Clifford Geertz developed an interpretive anthropology of understanding the meaning of the society. The hermeneutic approach allows Geertz to close the distance between an ethnographer and a given culture similar to reader and text relationship. The reader reads a text and generates his/her own meaning. Instead of imposing concepts to represent reality, ethnographers should read the culture and interpret the multiplicities of meaning expressed or hidden in the society.

Huff + Gooden, an African-American firm based in Charleston, South Carolina, have designed a small museum for the Virginia Key Beach Park (2005–8) that underscores the ambiguities of racial pride and segregation…. The structure and the larger landscape by Walter Hood continue the theme of multiplicities and changes over time. This new sensibility in American modern architecture encourages visitors to contemplate multiple dimensions of the past and the future, buildings and their surroundings.

Mashayekhi's music circulates between a range of styles and genres, from classical compositions inspired by Persian rhythms and Iranian folk music that incorporate meditated repetition and polyphony, to atonal compositions, to works for tape and live electronics that combine traditional Iranian and Western instruments. Mashayekhi calls his compositional practice "Meta-X," referring to the sonic multiplicities present in his work (as contradictions of tonal/atonal, improvised/pre-defined, Persian/non-Persian) that unify within a single musical piece.

By using the Goddard–Thorn theorem, Borcherds showed that the homogeneous pieces of the Lie algebra are naturally isomorphic to graded pieces of the Moonshine module, as representations of the monster simple group. Earlier applications include Frenkel's determination of upper bounds on the root multiplicities of the Kac-Moody Lie algebra whose Dynkin diagram is the Leech lattice, and Borcherds's construction of a generalized Kac-Moody Lie algebra that contains Frenkel's Lie algebra and saturates Frenkel's 1/∆ bound.

Badiou is therefore – against Georg Cantor, from whom he draws heavily – staunchly atheist. However, secondly, this prohibition prompts him to introduce the event. Because, according to Badiou, the axiom of foundation 'founds' all sets in the void, it ties all being to the historico-social situation of the multiplicities of de-centred sets – thereby effacing the positivity of subjective action, or an entirely 'new' occurrence. And whilst this is acceptable ontologically, it is unacceptable, Badiou holds, philosophically.

The places where the pieces meet are known as knots. The key property of spline functions is that they and their derivatives may be continuous, depending on the multiplicities of the knots. B-splines of order n are basis functions for spline functions of the same order defined over the same knots, meaning that all possible spline functions can be built from a linear combination of B-splines, and there is only one unique combination for each spline function.

Other commonly used isomeric descriptors normal-, iso-, and neo- are translated as 正 (zhèng, 'proper'), 异 (yì, 'different'), and 新 (xīn, 'new'), respectively. The numerical prefix bis- is translated as 双 (shuāng, 'double'), while larger multiplicities are simply given by the Chinese word for the number (e.g., 四 (sì, 'four') for tetrakis-). For example, tetrakis(triphenylphosphine)palladium is rendered 四(三苯基膦)钯, in which 三苯基膦 is triphenylphosphine and 钯 is palladium.

This chapter expands on the argument that difference underlies thought by proposing a conception of Ideas based on difference. Deleuze returns to his substitution of the differential (dx) for negation (-x), arguing that Ideas can be conceived as "a system of differential relations between reciprocally determined genetic elements" (173-4). Ideas are multiplicities—that is, they are neither many nor one, but a form of organization between abstract elements that can be actualized in different domains. One example is of organisms.

Let R \to S be a local homomorphism of complete local domains. Then there exists an R-algebra BR that is a balanced big Cohen–Macaulay algebra for R, an S-algebra B_S that is a balanced big Cohen- Macaulay algebra for S, and a homomorphism BR → BS such that the natural square given by these maps commutes. # Serre's Conjecture on Multiplicities. (cf. Serre's multiplicity conjectures.) Suppose that R is regular of dimension d and that M \otimes_R N has finite length.

For two Young diagrams λ and μ consider the composition of the corresponding Schur functors Sλ(Sμ(-)). This composition is called a plethysm of λ and μ. From the general theory it's known that, at least for vector spaces over a characteristic zero field, the plethysm is isomorphic to a direct sum of Schur functors. The problem of determining which Young diagrams occur in that description and how to calculate their multiplicities is open, aside from some special cases like Symm(Sym2(V)).

These isospectral Riemannian manifolds have the same local geometry but different topology. They can be found using the "Sunada method," due to Toshikazu Sunada. In 1993 she found isospectral Riemannian manifolds which are not locally isometric and, since that time, has worked with coauthors to produce a number of other such examples. Gordon has also worked on projects concerning the homology class, length spectrum (the collection of lengths of all closed geodesics, together with multiplicities) and geodesic flow on isospectral Riemannian manifolds.

Despite this emphasis on interconnection, throughout his individual writings and more famous collaborations with Gilles Deleuze, Guattari has resisted calls for holism, preferring to emphasize heterogeneity and difference, synthesizing assemblages and multiplicities in order to trace rhizomatic structures rather than creating unified and holistic structures. Guattari's concept of the three interacting and interdependent ecologies of mind, society, and environment stems from the outline of the three ecologies presented in Steps to an Ecology of Mind, a collection of writings by cyberneticist Gregory Bateson.

Bôcher's theorem states that the finite zeros of the derivative r'(z) of a nonconstant rational function r(z) that are not multiple zeros of r(z) are the positions of equilibrium in the field of force due to particles of positive mass at the zeros of r(z) and particles of negative mass at the poles of r(z) , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.

The Clebsch–Gordan coefficients are the coefficients appearing in the expansion of the product of two spherical harmonics in terms of spherical harmonics themselves. A variety of techniques are available for doing essentially the same calculation, including the Wigner 3-jm symbol, the Racah coefficients, and the Slater integrals. Abstractly, the Clebsch–Gordan coefficients express the tensor product of two irreducible representations of the rotation group as a sum of irreducible representations: suitably normalized, the coefficients are then the multiplicities.

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.

Esther Shalev-Gerz questions the perpetual construction of the relationship between an experience and the telling one gives of it. She analyses portraiture, which she understands as the reflection of a person, place or event. Her work invites the spectator to an opening to the ambiguities and multiplicities acting in the collective memory. Her installations, photography, video and public sculpture are developed through dialogue, consultation and negotiation with people whose participation provides an emphasis to their individual and collective memories, accounts, opinions and experiences.

Some authors propose extending basic feature models with UML-like multiplicities of the form [n,m] with n being the lower bound and m the upper bound. These are used to limit the number of sub-features that can be part of a product whenever the parent is selected.Czarnecki, K. and Helsen, S. and Eisenecker, U., "Staged configuration using feature models", Proceedings of the Third International Conference on Software Product Lines (SPLC '04), volume 3154 of Lecture Notes in Computer Science. Springer Berlin/Heidelberg, August 2004. download.

In algebra, a hypoalgebra is a generalization of a subalgebra of a Lie algebra introduced by . The relation between an algebra and a hypoalgebra is called a subjoining , which generalizes the notion of an inclusion of subalgebras. There is also a notion of restriction of a representation of a Lie algebra to a subjoined hypoalgebra, with branching rules similar to those for restriction to subalgebras except that some of the multiplicities in the branching rule may be negative. calculated many of these branching rules for hypoalgebras.

Singmaster's conjecture is a conjecture in combinatorial number theory in mathematics, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times). It is clear that the only number that appears infinitely many times in Pascal's triangle is 1, because any other number x can appear only within the first x + 1 rows of the triangle.

In computational chemistry, spin contamination is the artificial mixing of different electronic spin-states. This can occur when an approximate orbital- based wave function is represented in an unrestricted form – that is, when the spatial parts of α and β spin-orbitals are permitted to differ. Approximate wave functions with a high degree of spin contamination are undesirable. In particular, they are not eigenfunctions of the total spin-squared operator, Ŝ2, but can formally be expanded in terms of pure spin states of higher multiplicities (the contaminants).

Multiplicity () is a philosophical concept developed by Edmund Husserl and Henri Bergson from Riemann's description of the mathematical concept."It was Riemann in the field of physics and mathematics who dreamed about the notion of 'multiplicity' and other different kinds of multiplicities. The philosophical importance of this notion then appeared in Husserl's Formal and Transcendental Logic, as well as in Bergson's Essay on the Immediate Given of Awareness" (Deleuze 1986, 13). It forms an important part of the philosophy of Gilles Deleuze, particularly in his collaboration with Félix Guattari, Capitalism and Schizophrenia (1972–80).

Screen theory is a Marxist–psychoanalytic film theory associated with the British journal Screen in the early 1970s. It considers filmic images as signifiers that do not only encode meanings but also mirrors in which viewers accede to subjectivity. The theory attempts to discover a way of theorizing a politics of freedom through cinema that focuses on diversity instead of unity. Here, the Marxist emphasis on universal consciousness as a basis for defining emancipation shifted to the articulation of diversities and multiplicities of individual and collective experience due to the psychoanalytic elaboration of the unconscious.

The key point is that a positive projection always has rank one. This means that if A is an irreducible non-negative square matrix then the algebraic and geometric multiplicities of its Perron root are both one. Also if P is its Perron projection then AP = PA = ρ(A)P so every column of P is a positive right eigenvector of A and every row is a positive left eigenvector. Moreover, if Ax = λx then PAx = λPx = ρ(A)Px which means Px = 0 if λ ≠ ρ(A).

CLEO-c was the final version of the detector, and it was optimized for taking data at the reduced beam energies needed for studies of the charm quark. It replaced the CLEO III silicon detector, which suffered from lower-than-expected efficiency, with a six layer, all stereo drift chamber (ZD). CLEO-c also operated with the solenoid magnet at a reduced magnetic field of 1 T to improve the detection of low momentum charged particles. The low particle multiplicities at these energies allowed efficient reconstruction of D mesons.

In 2012, Gannon proved that all but the first of the multiplicities are non-negative integral combinations of representations of M24, and Gaberdiel–Persson–Ronellenfitsch–Volpato computed all analogues of generalized moonshine functions, strongly suggesting that some analogue of a holomorphic conformal field theory lies behind Mathieu moonshine. Also in 2012, Cheng, Duncan, and Harvey amassed numerical evidence of an umbral moonshine phenomenon where families of mock modular forms appear to be attached to Niemeier lattices. The special case of the A124 lattice yields Mathieu Moonshine, but in general the phenomenon does not yet have an interpretation in terms of geometry.

Gilles Deleuze et les médecins In the last years of his life, simple tasks such as writing required laborious effort. On 4 November 1995, he committed suicide, throwing himself from the window of his apartment. Before his death, Deleuze had announced his intention to write a book entitled La Grandeur de Marx (The Greatness of Marx), and left behind two chapters of an unfinished project entitled Ensembles and Multiplicities (these chapters have been published as the essays "Immanence: A Life" and "The Actual and the Virtual").François Dosse, Gilles Deleuze and Felix Guattari: Intersecting Lives, pp. 454–455.

The continuous, ageless dynamism of mana wāhine is rather a more applicable term for this discussion. Additionally, because mana wāhine envelops these works within its matrices, they speak with a richer prescience than a work that is simply an expression of art in and of itself and necessarily gives way to a more expansive function and understanding of art, as such. Catriona Moore, speaking of feminist art more broadly, notes the multiplicities of purposes, directions, and outcomes that are characteristics of feminist art and aesthetics – these make the artworld a dynamic space for discussion, development and advancement.

Every real polynomial of odd degree has an odd number of real roots (counting multiplicities); likewise, a real polynomial of even degree must have an even number of real roots. Consequently, real odd polynomials must have at least one real root (because the smallest odd whole number is 1), whereas even polynomials may have none. This principle can be proven by reference to the intermediate value theorem: since polynomial functions are continuous, the function value must cross zero, in the process of changing from negative to positive or vice versa (which always happens for odd functions).

Miłosz's work is known for its complexity; according to the scholars Leonard Nathan and Arthur Quinn, Miłosz "prided himself on being an esoteric writer accessible to a mere handful of readers". Nevertheless, some common themes are readily apparent throughout his body of work. The poet, critic, and frequent Miłosz translator Robert Hass has described Miłosz as "a poet of great inclusiveness", with a fidelity to capturing life in all of its sensuousness and multiplicities. According to Hass, Miłosz's poems can be viewed as "dwelling in contradiction", where one idea or voice is presented only to be immediately challenged or changed.

The ratio of mean multiplicities of positively charged kaons and pions as a function of collision energy in collisions of two lead nuclei and proton–proton interactions.One of most interesting questions is if there is a threshold in reaction energy and/or volume size which needs to be exceeded in order to form a domain in which quarks can move freely. It is natural to expect that if such a threshold exists the particle yields/ratios we have shown above should indicate that. One of the most accessible signatures would be the relative Kaon yield ratio.

Once a choice of such a bijection is fixed, the Brauer character of a representation assigns to each group element of order coprime to p the sum of complex roots of unity corresponding to the eigenvalues (including multiplicities) of that element in the given representation. The Brauer character of a representation determines its composition factors but not, in general, its equivalence type. The irreducible Brauer characters are those afforded by the simple modules. These are integral (though not necessarily non-negative) combinations of the restrictions to elements of order coprime to p of the ordinary irreducible characters.

For the need of Intersection theory, Jean-Pierre Serre introduced a general notion of the multiplicity of a point, as the length of an Artinian local ring related to this point. The first application was a complete definition of the intersection multiplicity, and, in particular, a statement of Bézout's theorem that asserts that the sum of the multiplicities of the intersection points of algebraic hypersurfaces in a -dimensional projective space is either infinite or is exactly the product of the degrees of the hypersurfaces. This definition of multiplicity is quite general, and contains as special cases most of previous notions of algebraic multiplicity.

Vladimir Vernadsky, The Biosphere, (New York: Copernicus, 1998) The biosphere or milieu has also been going through the process of social engineering. Foucault particularly focuses on space and demonstrates the ways in which urban forms have been subjected to discipline and regulation to enhance circulation. It seems that Foucault was moving towards the direction of bridging the gap between the nature and culture by proposing the idea of a milieu. This collapsing of given spaces also signifies that merely unpacking or de-centering the Cartesian subject will not be enough; in fact the milieu or biosphere requires careful collapsing into multiplicities.

Doyle began his magnum opus, Babel, in 1989 – a 5-CD set that took ten years to compose. Each track corresponds to a 'room' or place within an imagined giant tower city, a kind of aural virtual reality. It celebrates the multiplicity of musical language.Barbara Jillian Dignam: "Multiplicities of Musical Language and Select Compositional Devices in Roger Doyle's Babel (1989–99)", in: Gareth Cox and Julian Horton (eds.): Irish Musical Analysis (Irish Musical Studies vol. 11) (Dublin: Four Courts Press, 2014), p. 277–297. 103 pieces of music were composed for it and he worked with 48 collaborators.

Selberg's trace formula shows that for an hyperbolic surface of finite volume it is equivalent to know the length spectrum (the collection of lengths of all closed geodesics on S, with multiplicities) and the spectrum of \Delta. However the precise relation is not explicit. Another relation between spectrum and geometry is given by Cheeger's inequality, which in the case of a surface S states roughly that a positive lower bound on the spectral gap of S translates into a positive lower bound for the total length of a collection of smooth closed curves separating S into two connected components.

If is a nonzero polynomial, there is a highest power such that divides , which is called the multiplicity of the root in . When is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots, as, with the above definitions, every number is a root of the zero polynomial, with an undefined multiplicity. With this exception made, the number of roots of , even counted with their respective multiplicities, cannot exceed the degree of . The relation between the coefficients of a polynomial and its roots is described by Vieta's formulas.

But there is no known technique for determining the Hilbert–Kunz function or c in general. In particular the question of whether c is always rational wasn't settled until recently (by Brenner—it needn't be, and indeed can be transcendental). Hochster and Huneke related Hilbert-Kunz multiplicities to "tight closure" and Brenner and Monsky used Hilbert–Kunz functions to show that localization need not preserve tight closure. The question of how c behaves as the characteristic goes to infinity (say for a hypersurface defined by a polynomial with integer coefficients) has also received attention; once again open questions abound.

They are known for their "Me and My Higher Self" memes on Instagram which started when Michael was undergoing a major spiritual transformation of their own. This project is aimed at increasing self-love, and much like Michael's music and visual art, also explores the multiplicities within the self. Remezcla reports that Michael is a "queer multimedia artist...[who] utilizes music, art videos, and memes as their mediums to explore themes of self love and acceptance, spirituality, and sexuality in a time when our 'deepest truths are being revealed'." Michael is the host of “Broadly Hotline,” a web series on Broadly.

The class of C may be defined as the number of tangents that may be drawn to C from a point not on C (counting multiplicities and including imaginary tangents). Each of these tangents touches C at one of the points of intersection of C and the first polar, and by Bézout's theorem there are at most n(n−1) of these. This puts an upper bound of n(n−1) on the class of a curve of degree n. The class may be computed exactly by counting the number and type of singular points on C (see Plücker formula).

In mathematics, a univariate polynomial of degree with real or complex coefficients has complex roots, if counted with their multiplicities. They form a set of points in the complex plane. This article concerns the geometry of these points, that is the information about their localization in the complex plane that can be deduced from the degree and the coefficients of the polynomial. Some of these geometrical properties are related to a single polynomial, such as upper bounds on the absolute values of the roots, which define a disk containing all roots, or lower bounds on the distance between two roots.

At age 19, Brenner began photographing Orthodox Jews in the Mea Shearim neighborhood of Jerusalem. Initially, he believed this was "authentic Judaism," but his approach quickly evolved into an exploration of the multiplicities of dissonant identities. In 1981, Brenner began photographing Jewish communities around the world, exploring what it means to live and survive with a portable identity and how Jews adopted the traditions and manners of their home countries and yet remained part of the Jewish people. He spent 25 years chronicling the diaspora of the Jews across the world from Rome to New York, India to Yemen, Morocco to Ethiopia, Sarajevo to Samarkand.

In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. The adjacency matrix of a simple graph is a real symmetric matrix and is therefore orthogonally diagonalizable; its eigenvalues are real algebraic integers. While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdière number.

The Riemann singularity theorem was extended by George Kempf in 1973, building on work of David Mumford and Andreotti - Mayer, to a description of the singularities of points p = class(D) on Wk for 1 ≤ k ≤ g − 1\. In particular he computed their multiplicities also in terms of the number of independent meromorphic functions associated to D (Riemann-Kempf singularity theorem).Griffiths and Harris, p.348 More precisely, Kempf mapped J locally near p to a family of matrices coming from an exact sequence which computes h0(O(D)), in such a way that Wk corresponds to the locus of matrices of less than maximal rank.

In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces. Maschke's theorem allows one to make general conclusions about representations of a finite group G without actually computing them. It reduces the task of classifying all representations to a more manageable task of classifying irreducible representations, since when the theorem applies, any representation is a direct sum of irreducible pieces (constituents). Moreover, it follows from the Jordan–Hölder theorem that, while the decomposition into a direct sum of irreducible subrepresentations may not be unique, the irreducible pieces have well-defined multiplicities.

Some polynomials, such as , do not have any roots among the real numbers. If, however, the set of accepted solutions is expanded to the complex numbers, every non-constant polynomial has at least one root; this is the fundamental theorem of algebra. By successively dividing out factors , one sees that any polynomial with complex coefficients can be written as a constant (its leading coefficient) times a product of such polynomial factors of degree 1; as a consequence, the number of (complex) roots counted with their multiplicities is exactly equal to the degree of the polynomial. There may be several meanings of "solving an equation".

Yet this Absolute is different from Hegel's, which necessarily a telos or end result of the dialectic of multiplicities of consciousness throughout human history. For Schelling, the Absolute is a causeless 'ground' upon which relativity (difference and similarity) can be discerned by human judgement (and thus permit 'freedom' itself) and this ground must be simultaneously not of the 'particular' world of finites but also not wholly different from them (or else there would be no commensurability with empirical reality, objects, sense data, etc. to be compared as 'relative' or otherwise): > The particular is determined in judgements, but the truth of claims about > the totality cannot be proven because judgements are necessarily > conditioned, whereas the totality is not.

In mathematics, the degree of an affine or projective variety of dimension is the number of intersection points of the variety with hyperplanes in general position.In the affine case, the general-position hypothesis implies that there is no intersection point at infinity. For an algebraic set, the intersection points must be counted with their intersection multiplicity, because of the possibility of multiple components. For (irreducible) varieties, if one takes into account the multiplicities and, in the affine case, the points at infinity, the hypothesis of general position may be replaced by the much weaker condition that the intersection of the variety has the dimension zero (that is, consists of a finite number of points).

With the posthumanist turn, however, the art of ethnographic writing has suffered serious challenges. Anthropologists are now thinking of experimenting with a new style of writing – for instance, writing with natives or multiple authorship. It also undermines the discipline of identity politics and postcolonialism. Postcolonial scholars’ claims of subaltern identity or indigeneity and their demand of liberal rights from a state is actually falling back into the same signifying Western myth of Oedipal complex of ego and the Id. Instead of looking for a non-unitary subject in multiplicities organized into assemblage and montage; postcolonial studies limit flows into the same Western category of identity thus undermining the networks that sustain people's everyday lives.

This detached view of the history makes historian a master signifier who imposes concepts onto the materiality of the process. Historicism is thus a history of silences. Historical materialism, on the other hand, is the history of the present that is past and present are not detached from each other but constitutes a single interrupting and non-linear temporality. “History is the object of a construction whose place is formed not in homogenous and empty time, but in that which is fulfilled by the here-and-now [Jetztzeit].”Walter Benjamin, Thesis on the Philosophy of History Writing history of present that is now- here releases differences and multiplicities from the clutches of historical categories that impose silence.

"After spending a lot of time trying to estimate success by combinatorial calculations, I wondered whether a more practical method...might be to lay it out say one hundred times and simply observe and count the number of successful plays." In 1947, John von Neumann sent a letter to Robert Richtmyer proposing the use of a statistical method to solve neutron diffusion and multiplication problems in fission devices. His letter contained an 81-step pseudo code and was the first formulation of a Monte Carlo computation for an electronic computing machine. Von Neumann's assumptions were: time-dependent, continuous-energy, spherical but radially- varying, one fissionable material, isotropic scattering and fission production, and fission multiplicities of 2, 3, or 4.

Thus, the specific case of a = b = 1/2 is known as an odd-time odd-frequency discrete Fourier transform (or O2 DFT). Such shifted transforms are most often used for symmetric data, to represent different boundary symmetries, and for real-symmetric data they correspond to different forms of the discrete cosine and sine transforms. Another interesting choice is a=b=-(N-1)/2, which is called the centered DFT (or CDFT). The centered DFT has the useful property that, when N is a multiple of four, all four of its eigenvalues (see above) have equal multiplicities (Rubio and Santhanam, 2005) The term GDFT is also used for the non-linear phase extensions of DFT.

Bézout's theorem predicts that the number of points of intersection of two curves is equal to the product of their degrees (assuming an algebraically closed field and with certain conventions followed for counting intersection multiplicities). Bézout's theorem predicts there is one point of intersection of two lines and in general this is true, but when the lines are parallel the point of intersection is infinite. Homogeneous coordinates are used to locate the point of intersection in this case. Similarly, Bézout's theorem predicts that a line will intersect a conic at two points, but in some cases one or both of the points is infinite and homogeneous coordinates must be used to locate them.

Image for 9-points theorem, special case, when both and are unions of 3 lines In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane . The original form states: :Assume that two cubics and in the projective plane meet in nine (different) points, as they do in general over an algebraically closed field. Then every cubic that passes through any eight of the points also passes through the ninth point. A more intrinsic form of the Cayley–Bacharach theorem reads as follows: :Every cubic curve on an algebraically closed field that passes through a given set of eight points also passes through a certain (fixed) ninth point , counting multiplicities.

In mathematics and theoretical physics, fusion rules are rules that determine the exact decomposition of the tensor product of two representations of a group into a direct sum of irreducible representations. The term is often used in the context of two-dimensional conformal field theory where the relevant group is generated by the Virasoro algebra, the relevant representations are the conformal families associated with a primary field and the tensor product is realized by operator product expansions. The fusion rules contain the information about the kind of families that appear on the right hand side of these OPEs, including the multiplicities. More generally, integrable models in 2 dimensions which aren't conformal field theories are also described by fusion rules for their charges.

Daniella Trimboli argues that instead of focusing on multiplicities, Fleming deconstructs the idea of singular truth by blending traditional documentary forms with her non-conventional storytelling techniques. Fleming does this by combining comic-book strips for Sam's origin stories and animation of characters in old photographs with interviews, first-person narration and old footage. The Magical Life of Long Tack Sam is part of a subgenre that Jim Lane calls the 'family portrait documentary' in which the boundaries of private and public histories intersect as the filmmaker's life interweaves with the family in focus, as an autobiography layering the biography of the family. An example as such is Fleming's profession directly affecting Sam's; the movies were overtaking vaudeville in the American mainstream entertainment business.

In complex analysis, the theorem states that the finite zeros of the derivative r'(z) of a nonconstant rational function r(z) that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of r(z) and particles of negative mass at the poles of r(z) , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance. Furthermore, if C1 and C2 are two disjoint circular regions which contain respectively all the zeros and all the poles of r(z) , then C1 and C2 also contain all the critical points of r(z) .

In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety and different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Schemes were introduced by Alexander Grothendieck in 1960 in his treatise "Éléments de géométrie algébrique"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).Introduction of the first edition of "Éléments de géométrie algébrique". Strongly based on commutative algebra, scheme theory allows a systematic use of methods of topology and homological algebra.

She contended that female primatologists focus on different observations that require more communication and basic survival activities, offering very different perspectives of the origins of nature and culture than the currently accepted ones. Drawing on examples of Western narratives and ideologies of gender, race and class, Haraway questioned the most fundamental constructions of scientific human nature stories based on primates. In Primate Visions, she wrote: > "My hope has been that the always oblique and sometimes perverse focusing > would facilitate revisionings of fundamental, persistent western narratives > about difference, especially racial and sexual difference; about > reproduction, especially in terms of the multiplicities of generators and > offspring; and about survival, especially about survival imagined in the > boundary conditions of both the origins and ends of history, as told within > western traditions of that complex genre".

When trying to find out whether two square matrices A and B are similar, one approach is to try, for each of them, to decompose the vector space as far as possible into a direct sum of stable subspaces, and compare the respective actions on these subspaces. For instance if both are diagonalizable, then one can take the decomposition into eigenspaces (for which the action is as simple as it can get, namely by a scalar), and then similarity can be decided by comparing eigenvalues and their multiplicities. While in practice this is often a quite insightful approach, there are various drawbacks this has as a general method. First, it requires finding all eigenvalues, say as roots of the characteristic polynomial, but it may not be possible to give an explicit expression for them.

This theorem may be viewed as a generalization of Bézout's identity, which provides a condition under which an integer or a univariate polynomial h may be expressed as an element of the ideal generated by two other integers or univariate polynomials f and g: such a representation exists exactly when h is a multiple of the greatest common divisor of f and g. The AF+BG condition expresses, in terms of divisors (sets of points, with multiplicities), a similar condition under which a homogeneous polynomial H in three variables can be written as an element of the ideal generated by two other polynomials F and G. This theorem is also a refinement, for this particular case, of Hilbert's Nullstellensatz, which provides a condition expressing that some power of a polynomial h (in any number of variables) belongs to the ideal generated by a finite set of polynomials.

In 2010, Tohru Eguchi, Hirosi Ooguri, and Yuji Tachikawa observed that the elliptic genus of a K3 surface can be decomposed into characters of the N=(4,4) superconformal algebra, such that the multiplicities of massive states appear to be simple combinations of irreducible representations of the Mathieu group M24. This suggests that there is a sigma-model conformal field theory with K3 target that carries M24 symmetry. However, by the Mukai–Kondo classification, there is no faithful action of this group on any K3 surface by symplectic automorphisms, and by work of Gaberdiel–Hohenegger–Volpato, there is no faithful action on any K3 sigma-model conformal field theory, so the appearance of an action on the underlying Hilbert space is still a mystery. By analogy with McKay–Thompson series, Cheng suggested that both the multiplicity functions and the graded traces of nontrivial elements of M24 form mock modular forms.

Once a metal complex undergoes metal-to-ligand charge transfer, the system can undergo intersystem crossing, which, in conjunction with the tunability of MLCT excitation energies, produces a long-lived intermediate whose energy can be adjusted by altering the ligands used in the complex. Another species can then react with the long-lived excited state via oxidation or reduction, thereby initiating a redox pathway via tunable photoexcitation. Complexes containing high atomic number d6 metal centers, such as Ru(II) and Ir(III), are commonly used for such applications due to them favoring intersystem crossing as a result of their more intense spin-orbit coupling. Complexes that have access to d orbitals are able to access spin multiplicities besides the singlet and triplet states, as some complexes have orbitals of similar or degenerate energies so that it is energetically favorable for electrons to be unpaired.

The prehistory of Mathieu moonshine starts with a theorem of Mukai, asserting that any group of symplectic automorphisms of a K3 surface embeds in the Mathieu group M23. The moonshine observation arose from physical considerations: any K3 sigma-model conformal field theory has an action of the N=(4,4) superconformal algebra, arising from a hyperkähler structure. When computed the first few terms of the decomposition of the elliptic genus of a K3 CFT into characters of the N=(4,4) superconformal algebra, they found that the multiplicities matched well with simple combinations of representations of M24. However, by the Mukai–Kondo classification, there is no faithful action of this group on any K3 surface by symplectic automorphisms, and by work of Gaberdiel–Hohenegger–Volpato, there is no faithful action on any K3 CFT, so the appearance of an action on the underlying Hilbert space is still a mystery.

The composition factors of the projective indecomposable modules may be calculated as follows: Given the ordinary irreducible and irreducible Brauer characters of a particular finite group, the irreducible ordinary characters may be decomposed as non-negative integer combinations of the irreducible Brauer characters. The integers involved can be placed in a matrix, with the ordinary irreducible characters assigned rows and the irreducible Brauer characters assigned columns. This is referred to as the decomposition matrix, and is frequently labelled D. It is customary to place the trivial ordinary and Brauer characters in the first row and column respectively. The product of the transpose of D with D itself results in the Cartan matrix, usually denoted C; this is a symmetric matrix such that the entries in its j-th row are the multiplicities of the respective simple modules as composition factors of the j-th projective indecomposable module.

Michael Tippett's Concerto for Double String Orchestra (1938–39) is one of his most popular and frequently performed works. Like other works of the composer's early maturity such as the First Piano Sonata and the First String Quartet, the Concerto is characterized by rhythmic energy and a direct melodic appeal. Representing both a meeting point for many of his early influences and a release for the catalytic experiences that defined the decade after leaving London and the Royal College of Music, the Concerto was an experiment in multiplicities, where the diversity of the thematic material (invented and imported) became synthesized through the timbral unity of the ensemble—two ensembles in fact, a further manifestation of the opposition and divisions contributing to the work’s multi-dimensionality.Thomas Schuttenhelm, The Orchestral Music of Michael Tippett: Creative Development and the Compositional Process (London: Cambridge University Press, 2013) 35.

A crucial property of compact operators is the Fredholm alternative, which asserts that the existence of solution of linear equations of the form (\lambda K + I)u=f \, (where K is a compact operator, f is a given function, and u is the unknown function to be solved for) behaves much like as in finite dimensions. The spectral theory of compact operators then follows, and it is due to Frigyes Riesz (1918). It shows that a compact operator K on an infinite-dimensional Banach space has spectrum that is either a finite subset of C which includes 0, or the spectrum is a countably infinite subset of C which has 0 as its only limit point. Moreover, in either case the non-zero elements of the spectrum are eigenvalues of K with finite multiplicities (so that K − λI has a finite-dimensional kernel for all complex λ ≠ 0).

In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed field K. Given functions f and g in K(C), i.e. rational functions on C, then :f((g)) = g((f)) where the notation has this meaning: (h) is the divisor of the function h, or in other words the formal sum of its zeroes and poles counted with multiplicity; and a function applied to a formal sum means the product (with multiplicities, poles counting as a negative multiplicity) of the values of the function at the points of the divisor. With this definition there must be the side-condition, that the divisors of f and g have disjoint support (which can be removed). In the case of the projective line, this can be proved by manipulations with the resultant of polynomials.

What is crucial for Badiou is that the structural form of the count-as-one, which makes multiplicities thinkable, implies (somehow or other) that the proper name of being does not belong to an element as such (an original 'one'), but rather the void set (written Ø), the set to which nothing (not even the void set itself) belongs. It may help to understand the concept 'count-as-one' if it is associated with the concept of 'terming': a multiple is not one, but it is referred to with 'multiple': one word. To count a set as one is to mention that set. How the being of terms such as 'multiple' does not contradict the non-being of the one can be understood by considering the multiple nature of terminology: for there to be a term without there also being a system of terminology, within which the difference between terms gives context and meaning to any one term, is impossible.

With her following books Geluksbrenger (Lucky Charm, 2008), gestamelde werken (work in stuttering, 2012), and verdere bijzonderheden (further particulars, 2017) Hirs playfully develops her mature writing style, based on simultaneaous multiplicities of meaning, possibilities of reading. In 2017 the Berlin-based Kookbooks published her multilingual compendium gestammelte werke, containing original poems in Dutch, German, English and Spanish by the poet, and translations into more than ten languages by Daniela Seel, Henri Deluy, Diego Puls, Kim Andringa, Jelica Novakovic, Donald Gardner, Daniel Cunin, among others. In 2014 her poetry collection in Serbian translation život mogućnosti appeared with Biblioteka Prevodi in Banja Luka, Bosnia & Herzegovina. In 2019 her poetry collection in Spanish translation ahora es una rosa was published by Yauguru, Uruguay. Hirs' work was selected for De 100 beste gedichten van 2008, and 2012, and appeared in poetry collections, and literary magazines in Belgium, Germany, France, Mexico, and the Netherlands. The musical poetry of Geluksbrenger is constructed along the line of a ‘counterpoint’.

If the polar line of C with respect to a point Q is a line L, then Q is said to be a pole of L. A given line has (n−1)2 poles (counting multiplicities etc.) where n is the degree of C. To see this, pick two points P and Q on L. The locus of points whose polar lines pass through P is the first polar of P and this is a curve of degree n−1. Similarly, the locus of points whose polar lines pass through Q is the first polar of Q and this is also a curve of degree n−1. The polar line of a point is L if and only if it contains both P and Q, so the poles of L are exactly the points of intersection of the two first polars. By Bézout's theorem these curves have (n−1)2 points of intersection and these are the poles of L.Basset p.

Descartes' rule of signs asserts that the difference between the number of sign variations in the sequence of the coefficients of a polynomial and the number of its positive real roots is a nonnegative even integer. It results that if this number of sign variations is zero, then the polynomial does not have any positive real roots, and, if this number is one, then the polynomial has a unique positive real root, which is a single root. Unfortunately the converse is not true, that is, a polynomial which has either no positive real root or as a single positive simple root may have a number of sign variations greater than 1. This has been generalized by Budan's theorem (1807), into a similar result for the real roots in a half-open interval : If is a polynomial, and is the difference between of the numbers of sign variations of the sequences of the coefficients of and , then minus the number of real roots in the interval, counted with their multiplicities, is a nonnegative even integer.