B and B, Trunfio declared, and the researcher presenting the clips looked relieved.
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S&P affirmed BIDV's respective B+ and B long-term and short-term issuer credit ratings this month.
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It's sort of like the transitive property of equality — if A=B and B=C then A=C.
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Find out how to book on Llety Cynin's website, or send the b-and-b a message on Facebook.
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According to MMA Math—the argument that A beats C, because A beat B, and B beat C—the answer is yes.
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David Nanney, the founder of the Haines John Muir Association and operator of the Chilkat Eagle B and B, collected me at the ferry terminal.
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All are widely known and respected, offering products and services used by billions of people in both the B-to-B and B-to-C spaces.
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Then it had been the cheapest B. and B. I could find, hunks of bread and cheese eaten in the street, bottles of rough red passed from mouth to mouth.
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When I pitched it to Pete he said, "Well, you'd have to change A to B and B to C and C to D." And we developed it a little bit.
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This nonsense charms my brain just because A connects to B and B to C. I want this big thing in my brain that makes sense out of everything, I guess!
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To turn this into a maths problem: if A must equal B and B must equal C then A must equal C. At some point, this fudge will have to be resolved.
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Nonetheless, Wonder Woman has also proven to be a crowd pleaser (an A on CinemaScore, 76 percent on Metacritic) compared to both DC films (B+ and B on CinemaScore, 40 and 23 percent on Metacritic).
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It honors the women's flintiness and fear as C swears not to become B and B hopes not to become A. In doing so, it slips Beckettian existentialism through the commercial barricades by disguising it as comfortable mainstream entertainment.
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To celebrate the 20th anniversary of J.K. Rowling's first book, Harry Potter and the Philosopher's Stone — and the 10th anniversary of Harry Potter and the Deathly Hallows, the series' final book — the b-and-b is pulling out all the stops.
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And it says that if one system is in equilibrium with another — A with B, and B with C — then A must be in equilibrium with C. The foundation of thermodynamics is this equilibrium relation, which sets up the meaning of temperature.
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VRs SB and GB The affirmation of SB's and GB's VRs at, respectively, 'b' and 'b-' reflects that the moderate improvements in their credit profiles expected when the ratings were previously reviewed have largely taken place, mainly as a result of recapitalisation/clean-up undertaken by VEB in 33717-3371495Q3371956.
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However, in Fitch's view the sale may take longer or not happen at all due to VEB's sale price expectations, generally low investor interest in banking assets and weaknesses in the banks' stand-alone profiles, which are reflected in low Viability Ratings (VRs) of 'b' and 'b-' for SB and GB, respectively.
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The transitive property of inequality states that for any real numbers a, b, c: : If a ≤ b and b ≤ c, then a ≤ c. If either of the premises is a strict inequality, then the conclusion is a strict inequality: : If a ≤ b and b < c, then a < c. : If a < b and b ≤ c, then a < c.
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Upstairs, there is also a restaurant and coffee company, Hangar B and B-Side, respectively, serving breakfast and lunch.
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New York: Appleton-Century-Crofts.Ferster, Charles B., and B. F. Skinner. 1957. Schedules of Reinforcement. New York: Appleton-Century-Crofts.
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Small nuclear ribonucleoprotein-associated proteins B and B' is a protein that in humans is encoded by the SNRPB gene.
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174, figure 184. A two-pole, four-coil Gramme ring. The coils of A and A' sum together, as do the coils of B and B', producing two pulses of power 90° out of phase with each other. When coils A and A' are at maximum output, coils B and B' are at zero output.
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This coda plays with the semitonal relationship between B and B, and briefly returns to the first theme before dying away.
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The relations ≤ and ≥ are each other's converse, meaning that for any real numbers a and b: : a ≤ b and b ≥ a are equivalent.
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Another consequence of the above equivalence is that "integrality" is transitive, in the following sense. Let C be a ring containing B and c \in C. If c is integral over B and B integral over A, then c is integral over A. In particular, if C is itself integral over B and B is integral over A, then C is also integral over A.
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B- and B+ are attached to two batteries in this case. The light will be shown through the LED light when all of these are connected.
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The product of two quaternions can be found in the article on quaternions. Note, in this case, that a \cdot b and b \cdot a are in general different.
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An example of the former is the mother relation. If A is the mother of B, and B the mother of C, then A can't be the mother of C.
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There are no a and b such that a < b and b < a.Introduction to Set Theory, Third Edition, Revised and Expanded: Hrbacek, Jech. This form of asymmetry is an asymmetrical relation.
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In mathematics, a total order, simple order, linear order, connex order, or full order is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation. A set paired with a total order is called a chain, a totally ordered set, a simply ordered set, a linearly ordered set, or a loset. Formally, a binary relation \leq is a total order on a set X if the following statements hold for all a, b and c in X: ; Antisymmetry: If a \leq b and b \leq a then a = b; ; Transitivity: If a \leq b and b \leq c then a \leq c; ; Connexity: a \leq b or b \leq a. Antisymmetry eliminates uncertain cases when both a precedes b and b precedes a.
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B-And-B is a British television sitcom starring Bernard Braden, his wife Barbara Kelly and their daughter Kim Braden. It was written by Michael Pertwee, and aired for a pilot and one series in 1968.
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Shears was awarded a CERN fellowship to conduct research on the Large Electron–Positron Collider (LEP). In 1995 she conducted a project: A Measurement of the B"+ and B"0 Meson Lifetimes and Lifetime Ratio Using the OPAL Detector at LEP.
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An example of transitive inference would be when a child is presented with the information "A" is greater than "B" and "B" is greater than "C". This child may have difficulty here understanding that "A" is also greater than "C".
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This chromosome can differentiate the social organisation of a colony carrying one of two variants of a supergene (B and b) which contains more than 600 genes. The social chromosome has often been compared to sexual chromosomes because they share similar genetic features and they define colony phenotype in a similar way. For example, colonies exclusively carrying the B variant of this chromosome accept single BB queens, but colonies with both B and b variants will accept multiple Bb queens only. Differences in another single gene can also determine whether the colony will have single or multiple queens.
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The Hollywood Reporter stated that "while climactic battles are violent, they never really thrill," concluding that "fans of The Raid [Evans' previous film series] should look elsewhere for their thrills." Collider and The A.V. Club gave Apostle more favorable reviews with a B and B minus respectively.
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There is a transitive effect that permeates through the system. If colony A interacts with colony B, and B with C, then C affects A through B. Therefore, if the competitive Lotka–Volterra equations are to be used for modeling such a system, they must incorporate this spatial structure.
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Writing for Anime News Network, Sam Leach awarded the first two Reverie episodes a "B-" and "B" rating; Leach praised the character interactions, but described the lengthy flashback sequences as "disposable" and argued that at times the anime's pacing was not sympathetic to the manga material it adapted.
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A horizon that combines the characteristics of two horizons is indicated with both capital letters, the dominant one written first. Example: AB and BA. If distinct parts have properties of two kinds of horizons, the horizon symbols are combined using a slash (/). Example: A/B and B/A.
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A horizon that combines the characteristics of two master horizons is indicated with both capital letters, the dominant one written first. Example: AB and BA. If discrete, intermingled bodies of two master horizons occur together, the horizon symbols are combined using a slash (/). Example: A/B and B/A.
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The following conditions are equivalent for a poset P: #P is a disjoint union of zigzag posets. #If a ≤ b ≤ c in P, either a = b or b = c. #< \circ < = \emptyset, i.e. it is never the case that a < b and b < c, so that < is vacuously transitive.
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A (non-strict) partial order is a binary relation ≤ over a set P which is reflexive, antisymmetric, and transitive. That is, for all a, b, and c in P, it must satisfy the three following clauses: # a ≤ a (reflexivity) # if a ≤ b and b ≤ a, then a = b (antisymmetry) # if a ≤ b and b ≤ c, then a ≤ c (transitivity) A set with a partial order is called a partially ordered set. Those are the very basic axioms that every kind of order has to satisfy. Other axioms that exist for other definitions of orders on a set P include: # For every a and b in P, a ≤ b or b ≤ a (total order).
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A transitive tournament on 8 vertices. A tournament in which ((a \rightarrow b) and (b \rightarrow c)) \Rightarrow (a \rightarrow c) is called transitive. In other words, in a transitive tournament, the vertices may be (strictly) totally ordered by the edge relation, and the edge relation is the same as reachability.
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Consider a triangle with sides of lengths a, b, and c in decreasing order. Define the "scalenity" of the triangle to be the smaller of the two ratios a/b and b/c. The scalenity is always less than and can be made as close as desired to .American Mathematical Monthly, pp.
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To tally the votes, consider each voter's preferences. For example, if a voter states "A > B > C" (A is better than B, and B is better than C), the tally should add one for A in A vs. B, one for A in A vs. C, and one for B in B vs.
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A chocolate Oriental Shorthair kitten. The browning gene B/b/bl codes for TYRP1, an enzyme involved in the metabolic pathway for eumelanin pigment production. Its dominant form, B, will produce black eumelanin. It has two recessive variants, b(chocolate), and bl(cinnamon), with bl being recessive to both B and b.
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Sorting a set of unlabelled weights by weight using only a balance scale requires a comparison sort algorithm. A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator forms a total preorder over the data, with: # if a ≤ b and b ≤ c then a ≤ c (transitivity) # for all a and b, a ≤ b or b ≤ a (connexity). It is possible that both a ≤ b and b ≤ a; in this case either may come first in the sorted list.
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Feldman wanted Charles Boyer and Gertrude Lawrence to star.Tierney, Boyer Figure in Feldman Film, Plans; Donlevy in India Deal Schallert, Edwin. Los Angeles Times 16 Apr 1949: 11.RANDOM NOTES ABOUT PEOPLE AND PICTURES: Jed Harris to Direct Film--Of Bogart And Bacall--Sequel to 'Iwo Jima' B AND B: SEQUEL: BONANZA: By A.H. WEILER.
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He teamed with Thunderbolt Patterson to feud with Arn and Ole Anderson. In late 1985, he started helping Jimmy Valiant in his war against Paul Jones and his "Army". He formed a team with Valiant called the "B and B Connection" ("Boogie Woogie" and "Bull"). He had some matches against Abdullah the Butcher and The Barbarian.
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The peripheral stalk differs in subunit composition between mitochondrial, chloroplast and bacterial F-ATPases. In bacterial and chloroplast F-ATPases, the peripheral stalk is composed of one copy of the delta subunit (homologous to OSCP in mitochondria), and two copies of subunit b in bacteria, or one copy each of subunits b and b' in chloroplasts and photosynthetic bacteria.
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Another article may contain terms B and C. Linking A to B and B to C creates a co-occurrence network of these three terms. Rules to define co-occurrence within a text corpus can be set according to desired criteria. For example, a more stringent criteria for co-occurrence may require a pair of terms to appear in the same sentence.
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Note however that the existence of f (such that the diagram commutes) has to be assumed from the start; two objects B and B′ that simply have isomorphic sub- and factor objects need not themselves be isomorphic (for example, in the category of abelian groups, B could be the cyclic group of order four and B′ the Klein four-group).
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In case of intransitivity given A beats B and B beats C, A does not automatically beat C. On the contrary, it might even be the case that C beats A, like in rock-paper- scissors. Intransitive relations can be assessed within the properties of game elements instead of just defining the outcome. This helps to create variety and prevent dominant strategies.
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A general formula that works for both alligation "alternate" and alligation "medial" is the following: Aa + Bb = Cc. In this formula, A is the volume of ingredient A and a is its mixture coefficient (i.e. a= 3%); B is volume of ingredient B and b is its mixture coefficient; and C is the desired volume C, and c is its mixture coefficient.
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Both forms of music are diatonic, but use notes that are additional to the 12 semitones of western music. In Turkish folk music, for example, some scales include a note roughly halfway between B and B flat. The scales of Turkish folk music are associated with different regions, and can be known by different names depending on the region, such as: Beşiri, Garip, Kerem, Misket, and Müstezad.
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A horizon that combines the characteristics of two master horizons is indicated with both capital letters, the dominant one written first. Example: AB and BA. If discrete, intermingled bodies of two master horizons occur together, the horizon symbols are combined using a slash (/). Example: A/B and B/A. The master horizon symbols may be followed by the lowercase letters indicating subordinate characteristics (see below).
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A lattice is sometimes called weakly semimodular if it satisfies the following condition due to Garrett Birkhoff: ;Birkhoff's condition: If a ∧ b <: a and a ∧ b <: b, :then a <: a ∨ b and b <: a ∨ b. Every semimodular lattice is weakly semimodular. The converse is true for lattices of finite length, and more generally for upper continuous (meets distribute over joins of chains) relatively atomic lattices.
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Let r and s be two ultraparallel lines. From any two distinct points A and C on s draw AB and CB' perpendicular to r with B and B' on r. If it happens that AB = CB', then the desired common perpendicular joins the midpoints of AC and BB' (by the symmetry of the Saccheri quadrilateral ACB'B). If not, we may suppose AB < CB' without loss of generality.
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Children in this stage commonly experience difficulties with figuring out logic in their heads. For example, a child will understand that "A is more than B" and "B is more than C". However, when asked "is A more than C?", the child might not be able to logically figure the question out mentally. Two other important processes in the concrete operational stage are logic and the elimination of egocentrism.
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The Sierpiński arrowhead curve is a fractal curve similar in appearance and identical in limit to the Sierpiński triangle. Evolution of Sierpiński arrowhead curve The Sierpiński arrowhead curve draws an equilateral triangle with triangular holes at equal intervals. It can be described with two substituting production rules: (A → B-A-B) and (B → A+B+A). A and B recur and at the bottom do the same thing — draw a line.
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Corridor B-1 travels from KY 10 to the north end of the Portsmouth Bypass. In Kentucky, it follows US 23 and US 23 Truck; after crossing the two-lane Carl Perkins Bridge into Ohio, it uses current and planned SR 852—a western bypass of Portsmouth—and US 23\. Corridors B and B-1 both end near Lucasville, where Corridor C continues north along US 23 to Columbus.
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A descendant of Guinness brewing family, he was a son of Henry Grattan Guinness, Irish Protestant missionary, originally from Dublin, who worked around the world for 15 years, and his wife Fanny, née Fitzgerald. He was educated at the High School, Launceston, Tasmania; and Leys School, Cambridge. B. A. 1891. Enrolling into Caius college in 1888 to study medicine, he received his M. B. and B. C. there in 1896.
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With the adoption of articulated G key action operated by the bell key mechanisms, more leverage from the table keys became necessary. Enlarged key tables considerably increased the leverage of the B and B keys although the left-to-right push was more severe owing to the larger arc radius of the larger keys. Some increase in leverage was possible with the C key, although its position in the table limited its design options.
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Blakley et al. have described how the technique used by BioFabric, which they refer to as a cartographic representation, can be used to compare the networks A and B by juxtaposing the edges in (A ∖ B), (A ∩ B), and (B ∖ A), a technique that is evocative of a Venn Diagram. Rossi and Magnani. have developed ranked sociograms, which is a BioFabric-like presentation where the node ordering is based upon a ranking metric.
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The terms are evaluated and compared in order. The operation has short-circuit semantics, meaning that evaluation is guaranteed to stop as soon as a verdict is clear: if `a < b` is false, `c` is never evaluated as the expression cannot possibly be true anymore. For expressions without side effects, `a < b < c` is equivalent to `a < b and b < c`. However, there is a substantial difference when the expressions have side effects.
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In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field. More precisely, Abhyankar's lemma states that if A, B, C are local fields such that A and B are finite extensions of C, with ramification indices a and b, and B is tamely ramified over C and b divides a, then the compositum AB is an unramified extension of A.
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The segment AB is the set of points P such that [APB]. The interval AB is the segment AB and its end points A and B. The ray A/B (read as "the ray from A away from B") is the set of points P such that [PAB]. The line AB is the interval AB and the two rays A/B and B/A. Points on the line AB are said to be collinear.
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In mitochondria, the peripheral stalk is composed of one copy each of subunits OSCP (oligomycin sensitivity conferral protein), F6, b and d. There is no homologue of subunit F6 in bacterial or chloroplast F-ATPase, whose peripheral stalks are composed of one copy of the delta subunit (homologous to OSCP), and two copies of subunit b in bacteria, or one copy each of subunits b and b' in chloroplasts and photosynthetic bacteria.
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A stimulus can have different functions depending on contextual cues. However a stimulus function can change based on the arbitrary relations with that stimulus. For example, this relational frame: A is more than B and B is more than C. For now the stimulus functions of these letters are rather neutral. But as soon as C would be labeled 'as very valuable' and 'nice to have', then A would become more attractive than C, based on the relations.
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It usually had ten strings in a repetitive open C tuning, of which the highest eight are paired in four courses (duplicated strings), :C E GG cc ee gg. The English guitar may have influenced the development and tuning of the Russian guitar, which has seven strings tuned to open G in thirds (G'-B, B-D, g-b, and b-d') with two fourths (D'-G', and D-g): :D', G', B, D, g, b, d'.
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Pringle was born in Clones, County Monaghan, son of John Pringle; he was a first cousin of James Pringle KC, MP. Educated at Campbell College, Belfast, he entered the School of Physic in Trinity College, Dublin. He proved to be a brilliant student, winning a number of awards. He took his B.A. in 1902 and his M. B. and B. Ch. the following year. Two years later he became a fellow of the Royal College of Surgeons in Ireland.
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In mathematics, a partial equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) R on a set X is a binary relation that is symmetric and transitive. In other words, it holds for all a, b, c \in X that: # if a R b, then b R a (symmetry) # if a R b and b R c, then a R c (transitivity) If R is also reflexive, then R is an equivalence relation.
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The set of Wadge degrees ordered by the Wadge order is called the Wadge hierarchy. Properties of Wadge degrees include their consistency with measures of complexity stated in terms of definability. For example, if A ≤W B and B is a countable intersection of open sets, then so is A. The same works for all levels of the Borel hierarchy and the difference hierarchy. The Wadge hierarchy plays an important role in models of the axiom of determinacy.
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Temkin has shown, however, that if we apply one set of criteria for making certain comparisons, and another set for making others, then the Axiom of Transitivity will either fail, or fail to apply, across the different comparisons. In particular, if it is FSV that is relevant when comparing A with B, and B with C, and if it is instead SSV that is relevant when comparing A with C, then it will not be surprising if A is better than B, and B better than C, in terms of the criteria that are relevant for making those comparisons, but A is not better than C, in terms of the criteria that are relevant for making that comparison. Thus, Temkin has provided a plausible and powerful explanation of how failures of transitivity can arise when comparing various outcomes, in virtue of the different factors that can be relevant in comparing different outcomes. Temkin has shown that the same logic that applies when comparing distributions of benefits and burdens across populations also applies when comparing such distributions within a single life.
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Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of petal colour in a pea plant. The letters B and b represent alleles for colour and the pictures show the resultant flowers. A genotype is an organism’s complete set of heritable genes, or genes that can be passed down from parents to offspring. These genes help encode the characteristics that are physically expressed (phenotype) in an organism, such as hair color, height, etc.
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Sports ratings systems use a variety of methods for rating teams, but the most prevalent method is called a power rating. The power rating of a team is a calculation of the team's strength relative to other teams in the same league or division. The basic idea is to maximize the amount of transitive relations in a given data set due to game outcomes. For example, if A defeats B and B defeats C, then one can safely say that A>B>C.
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Consider some set P and a binary relation ≤ on P. Then ≤ is a preorder, or quasiorder, if it is reflexive and transitive; i.e., for all a, b and c in P, we have that: : a ≤ a (reflexivity) : if a ≤ b and b ≤ c then a ≤ c (transitivity) A set that is equipped with a preorder is called a preordered set (or proset).For "proset", see e.g. . If a preorder is also antisymmetric, that is, and implies , then it is a partial order.
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P4HB has four thioredoxin domains (a, b, b’, and a’), with two CGHC active sites in the a and a’ domains. In both the reduced and oxidized state, these domains are arranged as a horseshoe shape. In reduced P4HB, domains a, b, and b' are in the same plane, while domain a' twists out at an ∼45° angle. When oxidized, the four domains stay in the same plane, and the distance between the active sites is larger than that in the reduced state.
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The protein encoded by this gene is one of several nuclear proteins that are found in common among U1, U2, U4/U6, and U5 small ribonucleoprotein particles (snRNPs). These snRNPs are involved in pre-mRNA splicing, and the encoded protein may also play a role in pre-mRNA splicing or snRNP structure. Autoantibodies from patients with systemic lupus erythematosus frequently recognize epitopes on the encoded protein. Two transcript variants encoding different isoforms (B and B') have been found for this gene.
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Capital Intelligence (CI), Credit Analysis & Ratings on August 11, 2020 announced that it has affirmed the Long-Term Foreign Currency Rating (LT FCR) and Short-Term Foreign Currency Rating (ST FCR) of Export Development Bank of Iran (EDBI) at 'B' and 'B', respectively. At the same time, CI Ratings has affirmed EDBI's Bank Standalone Rating (BSR) of 'b', Core Financial Strength (CFS) rating of 'b' and Extraordinary Support Level (ESL) of Moderate. The Outlook for the LT FCR and BSR remains Negative.
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Ultimately Dingle re-focused his criticism to claim that special relativity was logically inconsistent: "The theory [special relativity] unavoidably requires that A works more slowly than B and B more slowly than A — which it requires no super-intelligence to see is impossible."Dingle, Science at the Crossroads, p. 17. Hence he asserted that the well-known reciprocity of the Lorentz transformation is self-evidently impossible.Commentary on the Dingle Dispute in the journal Nature, 1967, reproduced in Dingle's 1972 book Science at the Crossroads.
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B is also a musical note. In English-speaking countries, it represents Si, the 12th note of a chromatic scale built on C. In Central Europe and Scandinavia, "B" is used to denote B-flat and the 12th note of the chromatic scale is denoted "H". Archaic forms of 'b', the b quadratum (square b, ) and b rotundum (round b, ) are used in musical notation as the symbols for natural and flat, respectively. In Contracted (grade 2) English braille, 'b' stands for "but" when in isolation.
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There are views of Maria Island from parts of Orford and nearby Spring Beach. Sanda House. the oldest house in Orford operates as a B and B with numerous other accommodation available. In February 2007 an artificial reef and dive site was created from the scuttling of the ship the Troy D in the Mercury Passage approximately 1 km off Maria Island, to further bolster the area's reputation as a premier location for scuba diving, thanks to its unpolluted water and abundant sea life.
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JAP V-twin with Bosch magneto ignition and B and B carburetor. Transmission was through a metal-to-metal disc clutch, then by Renold chain to the gearbox offering two forward speeds, with the gear always in mesh and selected by substantial dog-clutches. There was then Renold chain back to the back axle, which was remarkably strong with double radius rods, and a massive differential. It was stated that the engine could be started from the driver's seat, though the mechanism was not explained.
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The culpability of the person does not depend on whether the person intended to kill or was recklessly indifferent. Under NSW law is also guilty of murder if the act causing death was done with the intent to cause grievous bodily harm. Grievous bodily harm includes any permanent or serious disfiguring, death of a foetus or causing a person to contract a grievous bodily disease. Definitions. If A intentionally inflicts grievous bodily harm on B and B dies, then A is guilty of B's murder.
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ARP spoofing is often used by developers to debug IP traffic between two hosts when a switch is in use: if host A and host B are communicating through an Ethernet switch, their traffic would normally be invisible to a third monitoring host M. The developer configures A to have M's MAC address for B, and B to have M's MAC address for A; and also configures M to forward packets. M can now monitor the traffic, exactly as in a man-in-the-middle attack.
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This was the official language of the deterministic track of the 4th IPC in 2004. It introduced derived predicates (to model the dependency of given facts from other facts, e.g. if A is reachable from B, and B is reachable from C, then A is reachable from C (transitivity)), and timed initial literals (to model exogenous events occurring at given time independently from plan-execution). Eventually PDDL2.2 extended the language with a few important elements, but wasn't a radical evolution compared to PDDL2.1 after PDDL1.2.
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The seventh note was not part of the medieval hexachord and does not occur in this melody, and it was originally called "si" from "Sancte Ioannes" (Johannes). In the nineteenth century, Sarah Glover, an English music teacher, renamed "si" to "ti" so that every syllable might be notated by its initial letter. But this was not adopted in countries using fixed-do systems: in Romance languages "si" is used alike for B and B flat, and no separate syllable is required for sharp "sol".
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Triadic closure is a concept in social network theory, first suggested by German sociologist Georg Simmel in his 1908 book Soziologie [Sociology: Investigations on the Forms of Sociation].Georg Simmel, originator of the concept: "Facebook" article at the New York Times website. Retrieved on December 21, 2007. Triadic closure is the property among three nodes A, B, and C (representing people, for instance), that if the connections A-B and B-C exist, there is a tendency for the new connection A-C to be formed.
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At a more technical level, various versions of the Kaldor–Hicks criteria lack desirable formal properties. For instance, Tibor Scitovsky demonstrated that the Kaldor criterion alone is not antisymmetric: it's possible to have a situation where an outcome A is an improvement (according to the Kaldor criterion) over outcome B, but B is also an improvement over A. The combined Kaldor–Hicks criterion does not have this problem, but it can be non-transitive (though A may be an improvement over B, and B over C, A is not thereby an improvement over C).
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The B B Chemical Company is an historic office and industrial building at 784 Memorial Drive in Cambridge, Massachusetts. It was built in 1937 for the Boston Blacking Company, an adhesive manufacturer whose most famous brand name was Bostik, to a design by Coolidge, Shepley, Bulfinch & Abbott, and is a prominent local example of Streamline Moderne architecture. From 1979 to 1996, it served as the headquarters of the Polaroid Corporation. The building was added to the National Register of Historic Places in 1982 under the incorrect name "B and B Chemical Company".
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"Fire Rehabilitation Work Begins on B and B Complex", Local Area News Release, Deschutes National Forest, United states Forest Service, United States Department of Agriculture, Sisters, Oregon, 2 October 2003. Crew rehabilitating a fire line in September 2003Shortly after the fire, smokejumpers and professional timber fallers cut hazard snags along Forest Service roads. Approximately 950 fire-killed trees were removed, allowing survey teams and rehabilitation crews to safely conduct their work. The next stage of the recovery work focused on high and moderate severity burn areas where there was an increased risk of runoff damage.
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With the card B/W there is always a 50% chance W being on top, thus in 50% of the cases card B/W is drawn, the draw affects neither numerator nor denominator and effectively does not count (this is also true for all times W/W is drawn, so that card might as well be removed from the set altogether). Conclusively, the cards B/B and B/W are not of equal chances, because in the 50% of the cases B/W is drawn, this card is simply "disqualified".
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During this three-year feud, Valiant received help from Héctor Guerrero and "Raging Bull" Manny Fernandez. Although Jimmy Valiant would lose a Loser Leaves Town Tuxedo Street Fight to Paul Jones at Starrcade 1984 in Greensboro, North Carolina the feud with Paul Jones stable continued, which would come to include Abdullah The Butcher. In 1985, Valiant and Ragin' Bull Manny Fernandez formed a team called B and B Connection ("Boogie Woogie" and "Bull"). In the spring of 1986 Pez Whatley turned on Valiant, cutting off his pony tail, later joining Jones' Army as Shaska Whatley.
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On May 2014, state budget cuts resulted in closing of the neighboring B and B High School in Baileyville, Kansas. Those students were transferred to Nemaha Valley High School. This prompted a school renaming the preceding year, with students in grades 7 through 11 at Baileyville, students in grades K through 11 in Nemaha Valley, and students in Saints Peter and Paul Catholic School voting to change the name to Nemaha Central. The mascot was renamed the Thunder, and the new school colors were purple and Columbia blue.
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Insertion on internal nodes is more complex than on external nodes. Say that the internal node is node A and that node B is the child of A. (If the insertion is to insert a right child, then B is the right child of A, and similarly with a left child insertion or mid child.) A assigns its child to the new node and the new node assigns its parent to A. Then the new node assigns its child to B and B assigns its parent as the new node.
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Kelly made regular appearances on her husband's show, Bedtime with Braden, in 1950. The next year (1951) she got equal billing with Braden in An Evening at Home with Bernard Braden and Barbara Kelly. She continued to star in her husband's shows throughout the 1950s and 1960s, and in 1968 appeared in the sitcom B-And-B, along with her husband and daughter. In the early 1950s, Kelly appeared in a few films including The Desert Hawk, A Tale of Five Cities, Castle in the Air, and Love in Pawn.
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"Some People" received adequate to good reviews. Gonzalez missed Kurt's usual charisma and thought the performance "a bit lackluster", and Benigno called it "kind of a boring cover". It received their lowest grades of the show, "B" and "B−", respectively. Kubicek stated, "Kurt has a unique voice that sounds positively beautiful with the right melodic song, but this is a terrible song for his style", and Vanity Fair Brett Berk added, after he gave it two out of five stars, that it was "not the best showcase of Kurt's talents".
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A rational number can be defined as the quotient of two integers (as long as the denominator is non-zero). A more detailed definition goes as follows: : A real number r is rational, if and only if it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational. Or more formally: : Given a real number r, r is rational if and only if there exists integers a and b such that r = \tfrac a b and b eq 0.
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The usual form of the CHSH inequality is where a and a′ are detector settings on side A, b and b′ on side B, the four combinations being tested in separate subexperiments. The terms E(a, b) etc. are the quantum correlations of the particle pairs, where the quantum correlation is defined to be the expectation value of the product of the "outcomes" of the experiment, i.e. the statistical average of A(a)·B(b), where A and B are the separate outcomes, using the coding +1 for the '+' channel and −1 for the '−' channel.
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Around 1800 in France terminal crooks were invented, which proved to be extremely popular. These instruments used a separate crook for each key, and the crooks maintained a fairly uniform distance between the mouthpiece and the body of the instrument. Horn players typically needed at least eight crooks, for B-alto, A, G, F, E, E, D, and C. After about 1828, an additional crook in A-alto was also included. Although crooks for low B and B were also occasionally made, these keys were usually reached by adding couplers to the C crook.
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He proposed that determinism is logically inconsistent: the determinist claims that because A caused B, and B caused C, that A is the true cause of C. Applied to a case of the human will, a determinist would argue that the will does not have causal power and that something outside the will causes the will to act as it does. But this argument merely assumes what it sets out to prove: viz. that the human will is part of the causal chain. Secondly, Kant remarks that free will is inherently unknowable.
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Suppose B is larger than A, but it is not discernible without an extremely sensitive scale. Further suppose C is larger than B, but this also is not discernible without an extremely sensitive scale. However, the difference in sizes between apples A and C is large enough that you can discern that C is larger than A without a sensitive scale. In psychophysical terms, the size difference between A and C is above the just noticeable difference ('jnd') while the size differences between A and B and B and C are below the jnd.
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In this section, R is an integral domain. Given elements a and b of R, one says that a divides b, or that a is a divisor of b, or that b is a multiple of a, if there exists an element x in R such that ax = b. The units of R are the elements that divide 1; these are precisely the invertible elements in R. Units divide all other elements. If a divides b and b divides a, then a and b are associated elements or associates.
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So, when the chromosomes go on to meiosis II and separate, some of the daughter cells receive daughter chromosomes with recombined alleles. Due to this genetic recombination, the offspring have a different set of alleles and genes than their parents do. In the diagram, genes B and b are crossed over with each other, making the resulting recombinants after meiosis Ab, AB, ab, and aB. Thomas Hunt Morgan's illustration of crossing over (1916) A double crossing over Chromosomal crossover, or crossing over, is the exchange of genetic material during sexual reproduction between two homologous chromosomes' non-sister chromatids that results in recombinant chromosomes.
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Cantor wanted the second paper to include a proof of the continuum hypothesis, but had to settle for expositing his theory of well-ordered sets and ordinal numbers. Cantor attempts to prove that if A and B are sets with A equivalent to a subset of B and B equivalent to a subset of A, then A and B are equivalent. Ernst Schröder had stated this theorem a bit earlier, but his proof, as well as Cantor's, was flawed. Felix Bernstein supplied a correct proof in his 1898 PhD thesis; hence the name Cantor–Bernstein–Schröder theorem.
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Because the development of note names took place within the framework of modes, in the German-speaking world B-flat was named 'B' and B-natural was named 'H'. The most common musical cryptogram is the B-A-C-H motif, which was used by Johann Sebastian Bach himself, by his contemporaries and by many later composers. Other note names were derived by sound, for example E-flat, 'Es' in German, could represent 'S' and A-flat the digraph 'As'. Composers less fortunate than Bach usually seem to have chosen to ignore non-musical letters in generating their motifs.
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With the C.G. Conn 6M and 10M saxophones, the low C, B, and B key touches were mounted angled strongly off the radius of the action. The G key touch was mounted on a horizontal pivot and on the same plane as the bell key touches. That layout mitigated the cross-push issue considerably and compared favorably to those of competitors King, Buescher, Martin, and, at its introduction, Selmer. With the 26M and 30M "Connqueror" saxophones, Conn mounted all of the left cluster touches on horizontal pivots and moved the cluster closer to the left hand stack keys.
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Schedeen consistently had kind words for Norton's "clean, expressive pencils".Schedeen, Jesse. "Fear Itself: Youth in Revolt #3 Review". IGN. July 6, 2011"Fear Itself: Youth in Revolt #4 Review". IGN. August 24, 2011Schedeen, Jesse. "Fear Itself: Youth in Revolt #5 Review". IGN. September 24, 2011 Dean Stell of Weekly Comic Book Review gave a "B" and "B+" to the first two issues, pleased with McKeever's ability to write younger characters, in particular Thor Girl, Cloud 9 and Ultragirl, and utilizing B-list and C-list characters, which he felt added depth to the main series.
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The notation a < b < c stands for "a < b and b < c", from which, by the transitivity property above, it also follows that a < c. By the above laws, one can add or subtract the same number to all three terms, or multiply or divide all three terms by same nonzero number and reverse all inequalities if that number is negative. Hence, for example, a < b + e < c is equivalent to a − e < b < c − e. This notation can be generalized to any number of terms: for instance, a1 ≤ a2 ≤ ... ≤ an means that ai ≤ ai+1 for i = 1, 2, ..., n − 1.
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The minimum in i(G) is taken over less elements (only the independent sets are considered), so γ(G) ≤ i(G) for all graphs G. The inequality can be strict - there are graphs G for which γ(G) < i(G). For example, let G be the double star graph consisting of vertices x1, ..., xp, a, b, y1, ..., yq, where p, q > 1. The edges of G are defined as follows: each xi is adjacent to a, a is adjacent to b, and b is adjacent to each bj. Then γ(G) = 2 since {a, b} is a smallest dominating set.
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Augmented octave on C. In modern Western tonal music theory an augmented octave is the sum of a perfect octave and an augmented unison or chromatic semitone. It is the interval between two notes, with the same note letter on staff positions an octave apart, whose alterations cause them, in ordinary equal temperament, to be thirteen semitones apart. In other words, it is a perfect octave which has been widened by a half-step, such as B and B or C and C; it is a compound augmented unison. It is the enharmonic equivalent of a minor ninth.
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Hierarchical linear models (or multilevel regression) organizes the data into a hierarchy of regressions, for example where A is regressed on B, and B is regressed on C. It is often used where the variables of interest have a natural hierarchical structure such as in educational statistics, where students are nested in classrooms, classrooms are nested in schools, and schools are nested in some administrative grouping, such as a school district. The response variable might be a measure of student achievement such as a test score, and different covariates would be collected at the classroom, school, and school district levels.
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An ordinal scale arises from the ordering or ranking objects, so that A is greater than B, B is greater than C, and so on. Many psychological experiments yield numbers of this sort; for example, a participant might be able to rank odors such that A is more pleasant than B, and B is more pleasant than C, but these rankings ("1, 2, 3 ...") would not tell by how much each odor differed from another. Some statistics can be computed from ordinal measures – for example, median, percentile, and order correlation – but others, such as standard deviation, cannot properly be used.
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It is an unlikely situation for all voters to have dichotomous preferences when there are more than a few voters. Having dichotomous preferences means that a voter has bi-level preferences for the candidates. All of the candidates are divided into two groups such that the voter is indifferent between any two candidates in the same group and any candidate in the top-level group is preferred to any candidate in the bottom-level group. A voter that has strict preferences between three candidates—prefers A to B and B to C—does not have dichotomous preferences.
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In situations where A trusts B and B trusts C, transitivity concerns the extent to which A trusts C. Without transitivity, trust metrics are unlikely to be used to reason about trust in more complex relationships. The intuition behind transitivity follows everyday experience of 'friends of a friend' (FOAF), the foundation of social networks. However, the attempt to attribute exact formal semantics to transitivity reveals problems, related to the notion of a trust scope or context. For example,Josang, A., and Pope, S. (2005) Semantic Constraints for Trust Transitivity Second Asia-Pacific Conference on Conceptual Modelling (APCCM2005).
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The process of inserting a node into a binary tree Insertion on internal nodes is slightly more complex than on leaf nodes. Say that the internal node is node A and that node B is the child of A. (If the insertion is to insert a right child, then B is the right child of A, and similarly with a left child insertion.) A assigns its child to the new node and the new node assigns its parent to A. Then the new node assigns its child to B and B assigns its parent as the new node.
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The phrase "to Strawberry" for example begins with a somewhat dissonant G melody note against a prevailing F minor key, then uses the semi-tone dissonance B and B notes (the natural and sharpened 11th degrees against the Fm chord) until the consonant F note is reached on "Fields". The same series of mostly dissonant melody notes cover the phrase "nothing is real" against the prevailing F7 chord (in A key). A half-measure complicates the metre of the verses, as well as the fact that the vocals begin in the middle of the first measure. The first verse comes after the chorus and is eight measures long.
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Every topological space is a dense subset of itself. For a set X equipped with the discrete topology, the whole space is the only dense subset. Every non- empty subset of a set X equipped with the trivial topology is dense, and every topology for which every non-empty subset is dense must be trivial. Denseness is transitive: Given three subsets A, B and C of a topological space X with such that A is dense in B and B is dense in C (in the respective subspace topology) then A is also dense in C. The image of a dense subset under a surjective continuous function is again dense.
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It is more symmetrical to use the (A,B) notation for Dedekind cuts, but each of A and B does determine the other. It can be a simplification, in terms of notation if nothing more, to concentrate on one "half" — say, the lower one — and call any downward closed set A without greatest element a "Dedekind cut". If the ordered set S is complete, then, for every Dedekind cut (A, B) of S, the set B must have a minimal element b, hence we must have that A is the interval (−∞, b), and B the interval [b, +∞). In this case, we say that b is represented by the cut (A,B).
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After B-And-B, Kelly had few television roles although she did appear in episodes of Hawaii Five-O, Pearl, the 1977 film Lust of a Eunuch and an episode of Magnum, P.I. in 1981. In 1983 she took part in a revival of What's My Line? This ran for three years, although Kelly, who thought that the original show was never the same after the death of Gilbert Harding in 1960, felt that the revival did not match it either. During the 1970s, the Bradens ran Adanac Productions, a company they had set up 20 years before which specialised in presentations at business conferences.
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By participating in the election the two voters supporting A changed the winner from A to B. In fact, the voters can turn the defeat in direct pairwise comparison of A against B into a victory. But in this example, the relation between A and B does not depend on the direct comparison, since the paths A > D > B and B > C > A are stronger. The additional voters diminish D > B, the weakest link of the A > D > B path, while giving a boost to B > C, the weakest link of the path B > C > A. Thus, the Schulze method fails the Participation criterion.
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Upon the album's release, We're an American Band became the band's best received album by critics, so far. Robert Christgau gave the album a B-, his highest rating for a Grand Funk Railroad album at the time (although Shinin' On (1974) and Grand Funk Hits (1976) would receive a B and B+, respectively). A modern review of the album by William Ruhlmann for Allmusic stated that the album was a departure from the band's usual material, which was mostly due to Todd Rundgren's production and Don Brewer's increase in lead vocal work. Ruhlmann also said that the album sounded more professional than their previous ones.
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This is the most common way of specifying a note in speech or in written text in English or German. In some European countries H is used instead of B, and B is used instead of B. Western letter pitch notation has the virtue of identifying discrete pitches, but among its disadvantages are its occasional inability to represent pitches or inflections lying outside those theoretically derived, or (leaving aside chordal and tablature notations) representing the relationship between pitches—e.g., it does not indicate the difference between a whole step and a half step, knowledge of which was so critical to Medieval and Renaissance performers and theorists.
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Elucidating complex signaling pathway phosphorylation events can be difficult. In cellular signaling pathways, protein A phosphorylates protein B, and B phosphorylates C. However, in another signaling pathway, protein D phosphorylates A, or phosphorylates protein C. Global approaches such as phosphoproteomics, the study of phosphorylated proteins, which is a sub-branch of proteomics, combined with mass spectrometry-based proteomics, have been utilised to identify and quantify dynamic changes in phosphorylated proteins over time. These techniques are becoming increasingly important for the systematic analysis of complex phosphorylation networks. They have been successfully used to identify dynamic changes in the phosphorylation status of more than 6000 sites after stimulation with epidermal growth factor.
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The Holdrian comma has been employed mainly in Turkish music theory by Kemal Ilerici, and by the Turkish composer Erol Sayan. The name of this comma is Holder koması in Turkish. For instance, the Rast makam (similar to the Western major scale, or more precisely to the justly-tuned major scale) may be considered in terms of Holdrian commas: 500px, where denotes a Holdrian comma flat, while in contrast, the Nihavend makam (similar to the Western minor scale): 500px, where denotes a five-comma flat, has medium seconds between d–e, e–f, g–a, a–b, and b–c', a medium second being somewhere in between 8 and 9 commas.
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Alternatively, you can only use pairs of stations and by comparing all pairs with each other determine which station most likely is the one with the break. If there is a break in 1950 in pair A&B and B&C, but not in A&C, the break is likely in station B; with more pairs such an inference can be made with more certainty. If there are multiple breaks in a time series, the number of combinations easily becomes very large and it is becomes impossible to try them all. For example, in case of five breaks (k=5) in 100 years of annual data (n=100), the number of combinations is about 1005=1010 or 10 billion.
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In terms of the implicative form of a 2-CNF formula, this rule amounts to finding two implications \lnot a\Rightarrow b and b\Rightarrow \lnot c, and inferring by transitivity a third implication \lnot a\Rightarrow \lnot c. Krom writes that a formula is consistent if repeated application of this inference rule cannot generate both the clauses (x\lor x) and (\lnot x\lor\lnot x), for any variable x. As he proves, a 2-CNF formula is satisfiable if and only if it is consistent. For, if a formula is not consistent, it is not possible to satisfy both of the two clauses (x\lor x) and (\lnot x\lor\lnot x) simultaneously.
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The opening bars of the Hammerklavier sonata The first movement opens with a series of fortissimo B-major chords, which form much of the basis of the first subject. After the first subject is spun out for a while, the opening set of fortissimo chords are stated again, this time followed by a similar rhythm on the unexpected chord of D major. This ushers in the more lyrical second subject in the submediant (that is, a minor third below the tonic), G major. A third and final musical subject appears after this, which exemplifies the fundamental opposition of B and B in this movement through its chromatic alterations of the third scale degree.
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The free group with two generators a and b consists of all finite strings that can be formed from the four symbols a, a−1, b and b−1 such that no a appears directly next to an a−1 and no b appears directly next to a b−1. Two such strings can be concatenated and converted into a string of this type by repeatedly replacing the "forbidden" substrings with the empty string. For instance: "abab−1a−1" concatenated with "abab−1a" yields "abab−1a−1abab−1a", which gets reduced to "abaab−1a". One can check that the set of those strings with this operation forms a group with neutral element the empty string ε := "".
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Small holes in cell membranes, called ion channels, are selective to specific ions and determine the membrane resistance. The concentration of ions in a liquid (e.g., in an aqueous solution) depends on the degree of dissociation of the dissolved substance, characterized by a dissociation coefficient \alpha, which is the ratio of the concentration of ions N to the concentration of molecules of the dissolved substance N_0: : N = \alpha N_0. The specific electrical conductivity (\sigma) of a solution is equal to: : \sigma = q\left(b^+ + b^-\right)\alpha N_0, where q: module of the ion charge, b^+ and b^-: mobility of positively and negatively charged ions, N_0: concentration of molecules of the dissolved substance, \alpha: the coefficient of dissociation.
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Benigno and Stack praised the choreography of "Make 'Em Laugh", but both graded it lower than "Forget You", at a "B" and "B+" respectively. Futterman called the recreation an "impressive feat", but likened it to hallucinatory Britney Spears covers in the episode "Britney/Brittany" in that it "stands alone better than it fits into the plot." Vick was critical of the performance, observing that Glee covers from musicals often introduce classic songs to viewers with a modern twist, an element which was absent in "Make 'Em Laugh". The Chicago cover also left some critics wanting, and Futterman, The Wall Street Journal Raymund Flandez and The Atlantic Patrick Burns all found its choreography lacking.
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Imagine that A commits a wrong against B and B sues in respect of that wrong. A will certainly be liable to pay compensation to B. If B seeks compensation then the court award will be measured by reference to the loss that B has suffered as a result of A's wrongful act. However, in certain circumstances it will be open to B to seek restitution rather than compensation. It will be in his interest to do so if the profit that A made by his wrongful act is greater than the loss suffered by B. Whether or not a claimant can seek restitution for a wrong depends to a large extent on the particular wrong in question.
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They illustrate what happens over time as populations genetically diverge, specifically because they represent, in living populations, what normally happens over time between long-deceased ancestor populations and living populations, in which the intermediates have become extinct. The evolutionary biologist Richard Dawkins remarks that ring species "are only showing us in the spatial dimension something that must always happen in the time dimension". Formally, the issue is that interfertility (ability to interbreed) is not a transitive relation; if A breeds with B, and B breeds with C, it does not mean that A breeds with C, and therefore does not define an equivalence relation. A ring species is a species with a counterexample to the transitivity of interbreeding.
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Liquid democracy, or direct democracy with delegable proxy, would allow citizens to choose a proxy to vote on their behalf while retaining the right to cast their own vote on legislation. The voting and the appointment of proxies could be done electronically. Taking this further, the proxies could form proxy chains, in which if A appoints B and B appoints C, and neither A nor B vote on a proposed bill but C does, C's vote will count for all three of them. Citizens could also rank their proxies in order of preference, so that if their first choice proxy fails to vote, their vote can be cast by their second-choice proxy.
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Consider now what happens if both the link from A to C and the link from B to C vanish at the same time (this can happen if node C has crashed). A believes that C is still reachable through B, and B believes that C is reachable through A. In a simple reachability protocol, such as EGP, the routing loop will persist forever. In a naive distance vector protocol, such as the routing information protocol, the loop will persist until the metrics for C reach infinity (the maximum number of routers that a packet can traverse in RIP is 15. The value 16 is considered infinity and the packet is discarded).
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The Universal Second Processor Unit was an adapter for BBC Master internal co-processor boards, to allow them to be used as external co-processors. It comprised a power supply, interface logic and a connector that matched the internal co- processor connector built into the BBC Master main board. This allowed the BBC B and B+ to use the Turbo board (4 MHz 65C102 with 64 KB of RAM) and the Master 512 board (10 MHz 80186 with 512 kKB of RAM), by fitting them into this expansion unit. It also allowed the BBC Master to have two internal co- processor boards connected, only one of which could be enabled through software.
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Raney's next release, Playing by Heart, a novella, was published by Barbour Books in 2003. The plot relied on a bed-and-breakfast for its setting, and was conceived the previous autumn when Deborah retreated to write at such a B and B while on a tight deadline. Playing by Heart again earned ACFW Book of the Year honors (2004), was a 2004 Christy Award Finalist, and recognized with the National Readers Choice Award for Best Novella (2003). Since then, Raney has written or contributed to more than thirty-five other books, most notably her Clayburn Novels series and Hanover Falls Novels series from Howard, an imprint of Simon & Schuster, and her Chicory Inn Novels series from Abingdon Press.
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Paid is where the business pays the social media site to have their advertisement show up on the users screen without the user giving permission. These are usually either on the side of the screen or can be “sponsored” depending on what the business pays. According to Xie, and Lee (2015) paid and unpaid advertisements have equal effect on consumers’ willingness to purchase the certain brand. As an example of how tourism companies are using social media NZ Rental Cars follows travels Instagram posts and re-blogs them onto their site to showcase NZ places to visit and attract customers. A more recent change in the tourism industry is the rise of “Air B and B” (Air BnB, n.
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A necessary and sufficient condition for a Heyting algebra to be subdirectly irreducible is for there to be a greatest element strictly below 1. The witnessing pair is that element and 1, and identifying any other pair a, b of elements identifies both a→b and b→a with 1 thereby collapsing everything above those two implications to 1. Hence every finite chain of two or more elements as a Heyting algebra is subdirectly irreducible. By Jónsson's Lemma, subdirectly irreducible algebras of a congruence-distributive variety generated by a finite set of finite algebras are no larger than the generating algebras, since the quotients and subalgebras of an algebra A are never larger than A itself.
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Posets are an object of study in the mathematical discipline of order theory. They belong to the class of binary relations but they have three additional properties: reflexivity, anti- symmetry and transitivity. Ontological dependency is a special poset because it is a binary relation, every thing is ontologically dependent on itself for its existence, two things that are mutually ontologically dependent must be the same thing and if a depends on b and b depends on c then a depends on c. The last of these properties - the transitive property of posets - was exploited by Helmut Hasse to give us the Hasse diagram - a diagram of incredible power, simplicity and if drawn well elegant as well.
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The instrument is most usually (nowadays) tuned in the key of D, a tradition begun by the Taylor brothers, famous pipe makers in Philadelphia in the late 19th century (Canon Goodman played a Taylor set). Up to then, most pipes were what would be termed as "flat sets" in other keys, such as C, C, B and B, tunings which were largely incompatible with playing with other instruments. The chanter length determines the overall tuning; accompanying pieces of the instrument, such as drones and regulators, are tuned to the same key as the chanter. Chanters of around in length produce a bottom note on or near D4 (D above middle C) where A4 = 440 Hz, i.e.
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Then O is a subset of Z, Z is a subset of R, and (hence) O is a subset of R, where in all cases subset may even be read as proper subset. Not all sets are comparable in this way. For example, it is not the case either that R is a subset of P nor that P is a subset of R. It follows immediately from the definition of equality of sets above that, given two sets A and B, A = B if and only if A ⊆ B and B ⊆ A. In fact this is often given as the definition of equality. Usually when trying to prove that two sets are equal, one aims to show these two inclusions.
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The Anglo-Saxon Chronicle records that King Æthelstan married his sister to Sihtric Cáech (died 927), king of Northumbria, and that the nuptials were celebrated at the Mercian royal centre at Tamworth on 30 January 926.Anglo-Saxon Chronicle (MSS B and B, Mercian register) 924; (D) 924-5 for 925-6. William notes that she was Ecgwynn's daughter, but was unable to discover her name in any of the sources available to him. It is only later sources which offer suggestions, whose value remains uncertain. Roger of Wendover (died 1236) and Matthew Paris (died 1259) thought that she was the St Edith (Eadgyth) who according to the Old English saints' list known as Secgan, was buried at the nunnery of Polesworth (Warwickshire), not far from Tamworth.
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R. L. Shafer of IGN rated the episode a 7/10 in a joint review with its predecessor. He deemed the episode "only moderately funny, save for the hilarious final image of Beavis and Butt-Head lounging in the bathroom", and commented how he only found one line funny in their music video review. He concluded that it was "funny and filled with nostalgia, but not quite as consistent as the first three episodes". For The A.V. Club, Kenny Herzog gave the episode and its predecessor an A-, writing that they "make a great tandem, collectively striking just the right chords of satire, idiocy, classic B And B-isms and a little bit of Judge’s blackened anger" and praising their commentary on the music video.
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An active repeater is a powered piece of equipment essentially comprising a receiving antenna, a receiver, a transmitter and a transmitting antenna. If the ends of the NLOS link are at positions A and C, the repeater is located at position B where links A-B and B-C are in fact LOS. The active repeater may simply amplify the received signal and re-transmit it un-altered at either the same frequency or a different frequency. The former case is simpler and cheaper but requires good isolation between two antennas to avoid feedback, however it does mean that the end of the NLOS link at A or C does not require to change the receive frequency from that used for a LOS link.
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Implementations of programming languages with subtyping fall into two general classes: inclusive implementations, in which the representation of any value of type A also represents the same value at type B if A<:B, and coercive implementations, in which a value of type A can be automatically converted into one of type B. The subtyping induced by subclassing in an object-oriented language is usually inclusive; subtyping relations that relate integers and floating-point numbers, which are represented differently, are usually coercive. In almost all type systems that define a subtyping relation, it is reflexive (meaning A<:A for any type A) and transitive (meaning that if A<:B and B<:C then A<:C). This makes it a preorder on types.
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However, from as early as the time of Hucbald the Hypolydian mode—even more than the corresponding authentic mode, the Lydian—was characterized by the predominance of B instead of B as the fourth degree above the final . The melodic centering on F and A, as well as the use of B instead of B, is illustrated in the accompanying example from the Requiem Mass introit, "Requiem aeternam". Finer distinctions among the scale degree are sometimes made, with the D below the final called the "mediant", the lowest note, C, the "participant" (a tone functioning as an auxiliary to the mediant), the G, B, and B the "conceded modulations" (subsidiary degrees), and the lowest C, the final, F, and (rarely) the D the "absolute initials" .
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Combinatorial mutual entailment refers to deriving relations between two stimuli, given the relations of those two stimuli with a third stimulus: Given the relation, A to B and B to C, the relations A to C and C to A can be derived. To go on with the examples above: Joyce is standing in front of Peter and Peter is standing in front of Lucy. The relations trained in this example are: stimulus A in front of B and stimulus B in front of C. With this it can be derived that Joyce is standing in front of Lucy and Lucy is standing behind Joyce. The derived relations are A is in front of C and C is behind A. John is older than Jared and Jared is older than Jacob.
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The B' and B-I alleles are considered to be epialleles because they are identical at the DNA sequence level but differ in the level of DNA methylation, siRNA production, and chromosomal interactions within the nucleus. Additionally, plants defective in components of the RNA-directed DNA-methylation pathway show an increased expression of b1 in B' individuals similar to that of B-I, however, once these components are restored, the plant reverts to the low expression state. Although spontaneous conversion from B-I to B' has been observed, a reversion from B' to B-I (green to purple) has never been observed over 50 years and thousands of plants in both greenhouse and field experiments. Examples of environmentally induced transgenerational epigenetic inheritance in plants has also been reported.
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B-flat tuning. B tuning, or A tuning, is a method of guitar tuning (and stringed instruments per se) in which all strings on a six-stringed instrument, most often guitar, are tuned down by 3 steps. For example, standard guitar tuning is E A D G B E. B♭ tuning starts by tuning the lowest string on a guitar E, to B♭ and then tuning all strings down in the same interval of 3 steps down. Strings on a guitar tuned to B♭ are B♭ E♭ A♭ D♭ F B♭ Seven-string guitars achieve B and B♭ tuning because they have a lower B string below the E string, which is the lowest string on a conventional guitar.
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Note that two alternatives a, b can satisfy a R b and b R a. If this is the case, we say R is indifferent to a, b. Each individual x in X will have an idiosyncratic ranking Rx of the alternatives in A. A profile is any function P that associate to each individual x a ranking of alternatives Px; a profile is thus a function from X to rankings of A. An arbitration scheme (or constitution or voting scheme) is a way of producing a ranking Rsoc for the whole society from any profile P. Thus an arbitration scheme is itself a function P → Rsoc. Though any argument about politics is in a sense a political argument, an effective political argument is one that can actually change the social preference ranking.
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Preset keys on a Hammond organ are reverse-colored and sit to the left of the manuals In addition to drawbars, many Hammond tonewheel organ models also include presets, which make predefined drawbar combinations available at the press of a button. Console organs have one octave of reverse colored keys (naturals are black, sharps and flats are white) to the left of each manual, with each key activating a preset; the far left key (C), also known as the cancel key, de-activates all presets, and results in no sound coming from that manual. The two right-most preset keys (B and B) activate the corresponding set of drawbars for that manual, while the other preset keys produce preselected drawbar settings that are internally wired into the preset panel.
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ATP synthase delta subunit is a subunit of bacterial and chloroplast F-ATPase/synthase. It is known as OSCP (oligomycin sensitivity conferral protein) in mitochondrial ATPase (note that in mitochondria there is a different delta subunit, ATP synthase delta/epsilon subunit). The OSCP/delta subunit appears to be part of the peripheral stalk that holds the F1 complex alpha3beta3 catalytic core stationary against the torque of the rotating central stalk, and links subunit A of the FO complex with the F1 complex. In mitochondria, the peripheral stalk consists of OSCP, as well as FO components F6, B and D. In bacteria and chloroplasts the peripheral stalks have different subunit compositions: delta and two copies of FO component B (bacteria), or delta and FO components B and B' (chloroplasts).
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A molecule may, of course, possess more than one set of magnetically inequivalent nuclei, related or not by additional symmetry elements that do not affect each. Most commonly, two chemically inequivalent pairs of hydrogen nuclei (protons) are involved, although other magnetically active nuclei will also show this phenomenon, and the spin system is often labelled an AA′BB′ system. Additional coupling partners may also be present, but it is the two A/A′ and B/B′ signals (at different chemical shifts) that are said to show magnetic inequivalence between the symmetry-related A and A′ (or B and B′) pairs at the same chemical shift. If the chemical shift difference (νA−νB) is large compared to the largest coupling constant, the spin system may be designated AA′XX′.
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In computer science, an interchangeability algorithm is a technique used to more efficiently solve constraint satisfaction problems (CSP). A CSP is a mathematical problem in which objects, represented by variables, are subject to constraints on the values of those variables; the goal in a CSP is to assign values to the variables that are consistent with the constraints. If two variables A and B in a CSP may be swapped for each other (that is, A is replaced by B and B is replaced by A) without changing the nature of the problem or its solutions, then A and B are interchangeable variables. Interchangeable variables represent a symmetry of the CSP and by exploiting that symmetry, the search space for solutions to a CSP problem may be reduced.
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In economic theory, the money pump argument is a thought experiment intended to show that rational behavior requires transitive preferences: If one prefers A to B and B to C, then one should not prefer C to A. Standard economic theory assumes that preferences are transitive. However, many people have argued that intransitive preferences are quite common, and often observed in real world settings. A cognitive bias is called the focusing effect: people focus on one characteristic which stands out in order to make decisions In choosing potential mates, candidate A is more beautiful/handsome than candidate B. B is wealthier then C. C is far better attuned on a personal level than A – the hearts meet. Then choices could be intransitive because instead of evaluating the whole package, people focus on one characteristic which distinguishes between two candidates to make decisions.
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An Example network Consider the network to the right, where a route has to be computed from router-A to the router-C satisfying bandwidth constrained of x- units, and link cost for each link is based on hop-count (i.e., 1). If x = 50 units then CSPF will give path A → B → C. If x = 55 units then CSPF will give path A → D → E → C. If x = 90 units then CSPF will give path A → D → E → F → C. In all of these cases OSPF and IS-IS will result in path A → B → C. However, if the link costs in this topology are different, CSPF may accordingly determine a different path. For example, suppose that as before, hop count is used as link cost for all links but A → B and B → C, for which the cost is 4.
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In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask how much better it is or how good it is. All of the theory of consumer decision-making under conditions of certainty can be, and typically is, expressed in terms of ordinal utility. For example, suppose George tells us that "I prefer A to B and B to C". George's preferences can be represented by a function u such that: :u(A)=9, u(B)=8, u(C)=1 But critics of cardinal utility claim the only meaningful message of this function is the order u(A)>u(B)>u(C); the actual numbers are meaningless.
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Semiorders generalize strict weak orderings, but do not assume transitivity of incomparability.. A strict weak order that is trichotomous is called a strict total order.. The total preorder which is the inverse of its complement is in this case a total order. For a strict weak order "<" another associated reflexive relation is its reflexive closure, a (non-strict) partial order "≤". The two associated reflexive relations differ with regard to different a and b for which neither a < b nor b < a: in the total preorder corresponding to a strict weak order we get a \lesssim b and b \lesssim a, while in the partial order given by the reflexive closure we get neither a ≤ b nor b ≤ a. For strict total orders these two associated reflexive relations are the same: the corresponding (non-strict) total order.
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A well-known comparison is that of Kenneth Kister, who gave a qualitative and quantitative comparison of Collier's Encyclopedia with the Encyclopædia Britannica and the Encyclopedia Americana. For the quantitative analysis, ten articles were selected at random (circumcision, Charles Drew, Galileo, Philip Glass, heart disease, IQ, panda bear, sexual harassment, Shroud of Turin and Uzbekistan) and letter grades (A–D, F) were awarded in four categories: coverage, accuracy, clarity, and recency. In all four categories and for all three encyclopaedias, the four average grades fell between B− and B+, chiefly because not one encyclopaedia had an article on sexual harassment in 1994. In the accuracy category, Collier's received one D and seven As. Encyclopedia Americana received eight As, and the Britannica received one D and eight As; thus, Collier's received an average score of 92% for accuracy to Americanas 95% and Britannicas 92%.
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Four separate subexperiments are conducted, corresponding to the four terms E(a, b) in the test statistic S (equation (2) shown below). The settings a, a′, b and b′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively -- the "Bell test angles" -- these being the ones for which the quantum mechanical formula gives the greatest violation of the inequality. For each selected value of a and b, the numbers of coincidences in each category (N++, N−−, N+− and N−+) are recorded. The experimental estimate for E(a, b) is then calculated as: (1) E = (N++ \+ N−− − N+− − N−+)/(N++ \+ N−− \+ N+− \+ N−+). Once all four E’s have been estimated, an experimental estimate of the test statistic (2) S = E(a, b) − E(a, b′) + E(a′, b) + E(a′, b′) can be found.
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However, if the three links connecting the three outer nodes of the diagram to the center node are interpreted as representing a non-transitive quasi-equivalence relation (where the statement "A is equivalent to C" does not follow from the two statements "A is equivalent to B" and "B is equivalent to C"), then the diagram is fully logically coherent and non-self-contradictory. So the medieval Shield of the Trinity diagram could be considered to contain some implicit kernel of the idea of alternative logical systems. Unlike some other logical or mathematical constructs sometimes offered as analogies for the Trinity (such as the Venn diagram and the cube viewed by inhabitants of a two-dimensional plane), the Shield of the Trinity does not too easily lend itself to interpretations that are non-orthodox from the traditional mainstream Christian point of view.
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Similar considerations apply to languages with final obstruent devoicing, in which the isolation form undergoes loss of voicing contrast, but other forms may not. If the grammar of a language is assumed to have two rules, rule A and rule B, with A ordered before B, a given derivation may cause the application of rule A to create the environment for rule B to apply, which was not present before the application of rule A. Both rules then are in a feeding relationship. If rule A is ordered before B in the derivation in which rule A destroys the environment to which rule B applies, both rules are in a bleeding order. If A is ordered before B, and B creates an environment in which A could have applied, B is then said to counterfeed A, and the relationship is counterfeeding.
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The latter is a hill located south of the town, topped with a huge cross. many activities are available such as: Boat tours for fishing, whale watching, snorkeling, mountain tours and sightseeing are available, as well as walking and nature tours. Taboga Island has small hotels and restaurants Calaloo Beach Fishbar & Grill on Playa Honda just 2 minutes from the pier, Agua Sol Villa, located on the water with a private beach entry from the hotels ocean deck; palm beach hotel, B and B Hotel Cerrito Tropical and Restaurant; Mundi's; Hotel Vereda Tropical, Taboga Palace, the espectacular Villa Caprichosa Boutique Hotel (@villa_caprichosa) and La Dolce Vita Restaurant by the famous American-Italian designer Diane Burn. Tours such as mountain tours, historical walking tours, whale watching, boat tours, bird watching,snorkelin,fishing, paddleboarding, gear rental, beach locker rentals and daypasses can be organized through Taboga Tour Center.
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IGN rated the episode a 7/10, commenting "The short is pretty darn funny, especially when Beavis and Butt-head find themselves the subject of their own documentary – an idea Mr. Van Driessen comes up with. Like many of the other shorts, the climax isn't quite as funny as the buildup, but watching B&B; get fat and lurch around a fast food restaurant proves rather amusing. Now, I can't help but wonder how they end up losing the weight. Perhaps they just popped in the music video for 'It's So Cold in the D' (from last week's ep.) and danced the fat away". For The A.V. Club, Kenny Herzog gave the episode and its successor an A-, writing that they "make a great tandem, collectively striking just the right chords of satire, idiocy, classic B And B-isms and a little bit of Judge’s blackened anger".
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" In another incident which took place at Unaon, near Kanpur, a few years later; when the Ustad came to know that his patron was spending beyond his means to host the concert of the Ustad to celebrate the 'sacred threading ceremony' of his son, Faiyaz Khan accepted only the fare for his return journey and blessed the child with a gold ring purchased from the local goldsmith during his afternoon stroll the day before. Faiyaz Khan was a great composer who composed several bandishes using the pen-name 'Prem Piya'. According to SwarGanga Music Foundation website, "Failing health due to a bout of typhoid in 1945 followed by tuberculosis restricted him to lower his pitch to "B" and "B Flat", though in his prime, he always sang in "C Sharp" and "C". The available recordings of the Ustad are almost entirely from his later years.
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The earliest designs of keyboards were based heavily on the notes used in Gregorian chant (the seven diatonic notes plus B-flat) and as such would often include B and B both as diatonic "white notes," with the B at the leftmost side of the keyboard and the B at the rightmost. Thus, an octave would have eight "white keys" and only four "black keys." The emphasis on these eight notes would continue for a few centuries after the "seven and five" system was adopted, in the form of the short octave: the eight aforementioned notes were arranged at the leftmost side of the keyboard, compressed in the keys between E and C (at the time, accidentals that low were very uncommon and thus not needed). During the sixteenth century, when instruments were often tuned in meantone temperament, some harpsichords were constructed with the G and E keys split into two.
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Consider an election consisting of five voters and three alternatives, in which three voters prefer A to B and B to C, while two of the voters prefer B to C and C to A. The fact that A is preferred by three of the five voters to all other alternatives makes it a Condorcet Winner. However the Borda count awards 2 points for 1st choice, 1 point for second and 0 points for third. Thus, from three voters who prefer A, A receives 6 points (3 x 2), and 0 points from the other two voters, for a total of 6 points. B receives 3 points (3 x 1) from the three voters who prefer A to B to C, and 4 points (2 x 2) from the other two voters who prefer B to C to A. With 7 points, B is the Borda winner.
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In the expanded form of value, the equation process between quantities of different commodities is simply continued serially, so that their values relative to each other are established, and they can all be expressed in some or other commodity-equivalent. The expanded value-form expression really represents only an extension of the simple value form, where products alternate as relative and equivalent forms in order to be equated to each other. Marx argues that, as such, the expanded form of value is practically inadequate, because to express what any commodity is worth might now require the calculation of a whole "chain" of comparisons, i.e. What this means is, that if A is normally traded for B, and B is normally traded for C, then to find out how much A is worth in terms of C, we first have to convert the amounts into B (and maybe many more intermediate steps).
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Peano defined the notion of "function" in a manner somewhat similar to Frege, but without the precision."...Peano intends to cover much more ground than Frege does in his Begriffsschrift and his subsequent works, but he does not till that ground to any depth comparable to what Frege does in his self-allotted field", First Peano defines the sign "K means class, or aggregate of objects", the objects of which satisfy three simple equality-conditions, a = a, (a = b) = (b = a), IF ((a = b) AND (b = c)) THEN (a = c). He then introduces φ, "a sign or an aggregate of signs such that if x is an object of the class s, the expression φx denotes a new object". Peano adds two conditions on these new objects: First, that the three equality-conditions hold for the objects φx; secondly, that "if x and y are objects of class s and if x = y, we assume it is possible to deduce φx = φy".
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Kister in 1994 gave a qualitative and quantitative comparison of Collier's Encyclopedia with two comparable encyclopaedias, Encyclopædia Britannica and the Encyclopedia Americana. For the quantitative analysis, ten articles were selected at random (circumcision, Charles Drew, Galileo, Philip Glass, heart disease, IQ, panda bear, sexual harassment, Shroud of Turin and Uzbekistan) and letter grades (A–D, F) were awarded in four categories: coverage, accuracy, clarity, and recency. In all four categories and for all three encyclopaedias, the four average grades fell between B− and B+, chiefly because not one encyclopaedia had an article on sexual harassment in 1994. In the accuracy category, Collier's received one D and seven As. Encyclopedia Americana received eight As, and the Britannica received one D and eight As; thus, Collier's received an average score of 92% for accuracy to Americana's 95% and Britannica’s 92%. In the timeliness category, Collier's averaged an 85% to Americana 90% and Britannica’ 86%.
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Knowing that if A>B and B>C, then A>C, is another type of evidence for intelligence, and it can be applied in the context of dominance hierarchies. In a study with the cichlid Astatotilapia burtoni, eight observer fish could watch individual A beat individual B, then B over C, C over D, and D over E. The observer fish were then given a choice of associating with either B or D (both of which they had seen win once and lose once). All eight observer fish spent more time next to D. Fish in this species prefer to associate with more dominant individuals, so the preference for D showed that the observers had worked out that B was superior to C, and C to D, and therefore D was dominant to B.Grosenick, L., Clement, T.S., and Fernald, R.D. (2007) Fish can infer social rank by observation alone. Nature 445: 429-432.
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Dynamic and detail complexity are both important to understand but are usually best approached through different modeling methods. Third, the System Dynamics method, unlike other modeling approaches, shows reciprocal feedback relationships between variables instead of simple one-way causality. Most statistical models are based on one- way causal relationship between a set of independent variables and a dependent variable. For example, component failures could be correlated with various conditions on the production line. System Dynamics models, such as those underlying LPM, include two way causality in which a variable “a” has a causal effect on variable “b” and “b” feeds back to affect “a”. For example, end-item failures reduce the number of planes’ available flying hours. A fleet’s fewer available flying hours increases the required number of hours flown per plane which increases end-item failures. The interaction between failures and hours flown creates a self-reinforcing relationship that is called a positive feedback loop.
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One says that a is a two-sided divisor of b if it is both a left divisor and a right divisor of b; in this case, it is not necessarily true that (using the previous notation) x=y, only that both some x and some y which each individually satisfy the previous equations in R exist in R. When R is commutative, a left divisor, a right divisor and a two-sided divisor coincide, so in this context one says that a is a divisor of b, or that b is a multiple of a, and one writes a \mid b . Elements a and b of an integral domain are associates if both a \mid b and b \mid a . The associate relationship is an equivalence relation on R, and hence divides R into disjoint equivalence classes. Notes: These definitions make sense in any magma R, but they are used primarily when this magma is the multiplicative monoid of a ring.
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Syncopations and cross-accents are characteristic of his rhythmic idiom, giving ictus to his otherwise seamless, enduring lines. Harmonically, Gombert's compositions stressed the traditional modal framework as a baseline, but especially in dense textures of six or more voices, he wrote polymodal sections wherein a subset of voices would sing the lowered pitches of F or B while another subset would sing the raised pitches of F or B: a D major and D minor chord or a G major and a G minor chord might be simultaneously sounded . Melodic motion in one voice that, to retain melodic and harmonic coherence with the other voices, employed musica ficta, or an extended set of pitches from the basic modal framework, was very prominent in his musical stylings. The false relations, usually between an F and an F or a B and B, create a dissonance that Gombert employed for emotional effect while adhering to traditional rules of counterpoint.
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This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition. This is also the reason that the zeroth law of thermodynamics is stated explicitly. If three physical systems, A, B, and C are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, A can heat B and B can heat C and C can heat A. In non-equilibrium situations, cycles of flow are possible. It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement.
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January 2008: Trading loss incident (Kerviel Fraud) On January 24, 2008, the bank announced that a single futures trader at the bank had fraudulently lost the bank €4.9 billion (an equivalent of US$7.2 billion), the largest such loss in history. The company did not name the trader, but other sources identified him as Jérôme Kerviel, a relatively junior futures trader who allegedly orchestrated a series of bogus transactions that spiraled out of control amid turbulent markets in 2007 and early 2008. Partly due to the loss, that same day two credit rating agencies reduced the bank's long term debt ratings: from AA to AA- by Fitch; and from Aa1/B to Aa2/B- by Moody's (B and B- indicate the bank's financial strength ratings).Ratings for Société GénéraleSociete Generale Uncovers Massive Fraud, Emma Vandore, Associated Press Executives said the trader acted alone and that he may not have benefited directly from the fraudulent deals. The bank announced it will be immediately seeking 5.5 billion euros in financing.
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Consider a circle within the ball, containing the point at the center of the ball. Using an argument like that used to prove the Claim, one can see that the full circle is equidecomposable with the circle minus the point at the ball's center. (Basically, a countable set of points on the circle can be rotated to give itself plus one more point.) Note that this involves the rotation about a point other than the origin, so the Banach–Tarski paradox involves isometries of Euclidean 3-space rather than just SO(3). Use is made of the fact that if A ~ B and B ~ C, then A ~ C. The decomposition of A into C can be done using number of pieces equal to the product of the numbers needed for taking A into B and for taking B into C. The proof sketched above requires 2 × 4 × 2 + 8 = 24 pieces - a factor of 2 to remove fixed points, a factor 4 from step 1, a factor 2 to recreate fixed points, and 8 for the center point of the second ball.
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Given two sets A and B, A is a subset of B if every element of A is also an element of B. In particular, each set B is a subset of itself; a subset of B that is not equal to B is called a proper subset. If A is a subset of B, then one can also say that B is a superset of A, that A is contained in B, or that B contains A. In symbols, A ⊆ B means that A is a subset of B, and B ⊇ A means that B is a superset of A. Some authors use the symbols ⊂ and ⊃ for subsets, and others use these symbols only for proper subsets. For clarity, one can explicitly use the symbols ⊊ and ⊋ to indicate non-equality. As an illustration, let R be the set of real numbers, let Z be the set of integers, let O be the set of odd integers, and let P be the set of current or former U.S. Presidents.
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Subsequent to the development of the Shoe Doctrine, states have enacted so-called long-arm statutes, by which courts in a state can serve process and thus exercise jurisdiction over a party located outside the state. The doctrine of International Shoe applies only in cases where there is no presence in the forum state. For example, if A committed a tort in State X. He is sued by B and B serves him with process just before he leaves State X before the flight was took off, the service would be valid and State X would have jurisdiction over A. If A did not comply with the final judgement passed by the courts of State X, B could enforce that judgement in the state where A resides under the full faith and credit clause of the US Constitution. There was one case where a defendant was served while the airplane was in the air over the forum State, and the federal district court held that this was valid service, since at law the territory of a state includes the airspace above the State.
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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.
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