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Topic: H-theorem

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Theorem - Wikipedia, the free encyclopedia A theorem has two parts, stated in a formal language – a set of assumptions, and a conclusion that can be derived from the given assumptions according to the inference rules of the formal system comprising the formal language. Informally speaking, most such theorems are not of any particular interest; 'theorem' used in this sense is a technical term indicating that a derivation exists and has none of the subjective connotations of importance as when the term is used in general mathematics. Proving theorems is a central activity of mathematicians. en.wikipedia.org /wiki/Theorem   (488 words)

Search Results for theorem* I: The Casorati- Weierstrass theorem, Historia Mathematica 5 (2) (1978), 139-166. I Bulmer-Thomas, Guldin's theorem - or Pappus's?, Isis 75 (277) (1984), 348-352. D K Faddeev and A I Skopin, Proof of a theorem of Kawada (Russian), Dokl. www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=theorem*&CONTEXT=1   (8556 words)

Arrow's impossibility theorem - Wikipedia, the free encyclopedia Arrow's theorem says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social welfare function that satisfies all these conditions at once. The Gibbard-Satterthwaite theorem, an attempt at weakening the conditions of Arrow's paradox, replaces the IIA criterion with a criterion of non-manipulability, only to reveal the same impossibility. So, what Arrow's theorem really shows is that voting is a non-trivial game, and that game theory should be used to predict the outcome of most voting mechanisms. en.wikipedia.org /wiki/Arrow's_impossibility_theorem   (1737 words)

The Mathematics of Fermat's Last Theorem Theorem B is even harder still, and it is the theorem of which Andrew Wiles first claimed a proof in 1993, thus proving FLT as well. Theorem B certainly seems, to one unfamiliar with the territory, to be quite technical and abstruse. Theorem B and more general forms of the Taniyama-Shimura Conjecture can be viewed in yet another way to affirm that there is a very significant relationship between modular functions and elliptic curves. www.mbay.net /~cgd/flt/fltmain.htm   (2364 words)

Notes on the attached paper Theorem 2 follows naturally and in a standard mathematical manner from theorem 4/6, and if needed I can revise and re-write any part of that proof to satisfy any objections. The main problem is that just because the function f in theorem 4 is a quotient of polynomials, this does not imply that the functions you break it into in theorem 4 are also quotients of polynomials. He stated that even if theorem 4 has been proven, nothing such as theorem 2 could follow from it, because one could never be sure all possibilities have been eliminated. www.infiniteseriestheorem.org   (1268 words)

Bayes' Theorem In this guise Bayes's theorem is particularly useful for inferring causes from their effects since it is often fairly easy to discern the probability of an effect given the presence or absence of a putative cause. Though a mathematical triviality, the Theorem's central insight — that a hypothesis is supported by any body of data it renders probable — lies at the heart of all subjectivist approaches to epistemology, statistics, and inductive logic. Indeed, the Theorem's central insight — that a hypothesis is confirmed by any body data that its truth renders probable — is the cornerstone of all subjectivist methodology. plato.stanford.edu /entries/bayes-theorem   (7490 words)

PlanetMath: Cauchy integral theorem Cauchy's theorem is an essential stepping stone in the theory of complex analysis. This is version 10 of Cauchy integral theorem, born on 2002-08-01, modified 2005-07-09. The proof of Green's theorem, however, involves an interchange of order in a double integral, and this can only be justified if the integrand, which involves the real and imaginary parts of planetmath.org /encyclopedia/GoursatsTheorem.html   (390 words)

The Pythagorean Theorem According to the Pythagorean Theorem, the sum of the areas of the two red squares, squares A and B, is equal to the area of the blue square, square C. The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. The next proof of the Pythagorean Theorem that I will present is one that can be taught and proved using puzzles. jwilson.coe.uga.edu /emt669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html   (2131 words)

Bell's Theorem What is actually found [in the experimental tests of Bell's theorem] is that the behavior of the two [electrons] is correlated in a way that is rather similar to that of the two television images of the fish, as described earlier. The same theorem can be applied to measurements of the polarisation of light, which is equivalent to measuring the spin of photon pairs. Sometimes people have trouble with the theorem because we will be doing a variation of a technique called proof by negation. www.upscale.utoronto.ca /GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html   (6569 words)

Pick's Theorem: An Interactive Activity Polygons covered by the theorem have their vertices located at nodes of a square grid or lattice whose nodes are spaced at distance 1 from their immediate neighbors. The theorem gives an elegant formula for the area of simple lattice polygons, where "simple", as usual, only means the absence of self-intersection. With Pick's theorem one may determine area of a (polygonal) portion of a map. www.cut-the-knot.org /ctk/Pick.shtml   (803 words)

Pythagoras' Theorem Use Pythagoras' theorem to show that, in a right-angled triangle, the area of the semicircle on the hypotenuse is the sum of the areas of the semicircles on the other two sides. The converse of Pythagoras' theorem is the statement: In this case, the converse is true, and you can use Pythagoras' theorem to prove so. thejuniverse.org /Mathdesign/widgets/Pythagoras   (516 words)

Theorem Solutions - Leading Suppliers of CAD/CAM/CAE Data Translators, Converters and Viewers Theorem also provides on-line CAD Data Translation Services to enable customers with a small volume of translation requirements to receive the benefits of CADverter technology whilst managing overall project costs. The Theorem CADverter family is the widest range of direct CAD translators available from any single source. Theorem Solutions is recognised as one of the world leaders in CAD/CAM product data exchange, offering application programs for Direct Database conversion and for International Standards-based conversion methods (STEP). www.theorem.co.uk   (261 words)

Bayes theorem definition - Medical Dictionary definitions of popular medical terms Bayes' theorem is employed in clinical epidemiology to determine the probability of a particular disease in a group of people with a specific characteristic on the basis of the overall rate of that disease and of the likelihood of that specific characteristic in healthy and diseased individuals, respectively. In technical terms, in Bayes' theorem the impact of new data on the merit of competing scientific hypotheses is compared by computing for each hypothesis the product of the antecedent plausibility and the likelihood of the current data given that particular hypothesis and rescaling them so that their total is unity. A common application of Bayes' theorem is in clinical decision making where it is used to estimate the probability of a particular diagnosis given the appearance of specific signs, symptoms, or test outcomes. www.medterms.com /script/main/art.asp?articlekey=10301   (348 words)

Math Forum: Ask Dr. Math FAQ: Pythagorean Theorem The applications that use the Pythagorean theorem include computing the distance between points on a plane; converting between polar and rectangular coordinates; computing perimeters, surface areas and volumes of various geometric shapes; and calculating maxima and minima of perimeters, or surface areas and volumes of various geometric shapes. The Pythagorean theorem is used any time we have a right triangle, we know the length of two sides, and we want to find the third side. One of the most common applications of the Pythagorean theorem is in the distance formula. mathforum.org /dr.math/faq/faq.pythagorean.html   (657 words)

Computing Papers on Theorem Some of the principal Theorems include the existence of a universal program, the unsolvability of the halting problem (there does not exist a mechanical means of checking for infinite loops in the executions of programs), and Rice`s Theorem. The sweeping conclusion of Rice`s Theorem is the impossibility of algorithmically analyzing computer programs to determine in which cases a given property is possessed by the function computed by the program. Unfortunately, after G¨del announced his famed incompleteness Theorem in o 1931 stating that it is impossible to have a formalism that can help us to reach all truths and only truths, we nally realized that we had gone a long way in ghting a battle that was impossible to win. computing.breinestorm.net /Theorem   (3065 words)

Remainder Theorem Lesson This is because the tool is presented as a theorem with a proof, which you probably don't feel ready for at this stage in your studies. First off, even though the Remainder Theorem refers to the polynomial and to long division and to restating the polynomial in terms of a quotient, a divisor, and a remainder, that's not actually what you're meant to be doing. The Remainder Theorem is useful for evaluating polynomials at a given value of www.purplemath.com /modules/remaindr.htm   (549 words)

Pythagorean Theorem To begin, the Pythagorean theorem states that the square on the hypotenuse of a right triangle has an area equal to the combined areas of the squares on the other two sides. With the Pythagorean theorem being such a popular topic, it is no wonder high school students study the theorem. The Pythagorean theorem was a mathematical fact that the Babylonians knew and used. www.ms.uky.edu /~lee/ma502/pythag/pythag.htm   (488 words)

Theorem : THX The THX collaborations between Theorem and like-minded artists from around the globe are now available as a compilation-CD from Minus. th.m-nus.com   (20 words)

Gödel's Incompleteness Theorem All the limitative theorems of mathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally. Gödel's Theorem has been used to argue that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths... I am reminded of Gödel's second theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent. www.miskatonic.org /godel.html   (1155 words)

The Theorem - Offical Site The Theorem is a breakthrough and controversial new book by Douglas M. Arone, which chronicles the exciting discovery of the possible answers to and the origins of most behaviors and disorders that define the psychology human. The Theorem is a truly international work; one of the endorsees is the highly admired and well-known Japanese scholar, Dr. Hiroshi Motoyama.The Theorem is a controversial womb based theory of human behavior. At its best, The Theorem may one day be considered one of the most important books in the history of human thought, likely the very answers mankind has been seeking since his beginning. www.thetheorem.com   (518 words)

PlanetMath: Ramsey's theorem This is version 14 of Ramsey's theorem, born on 2003-08-20, modified 2006-01-11. The original version of Ramsey's theorem states that for every positive integers Cross-references: combination, matching, fixed, even, terms, open, upper bounds, between, Calculus, coloring, expectation, sum, random variable, size, lower bounds, minimal, argument, QED, bounded, classes, partition, cliques, contains, graph, theorem, induction, colors, vertices, complete graph, edges, integers, positive, states planetmath.org /encyclopedia/RamseysTheorem2.html   (366 words)

Frege's Logic, Theorem, and Foundations for Arithmetic Theorem 5 now follows from the Lemma on Successors and the fact that successors of natural numbers are natural numbers. Frege's Theorem is an elegant derivation of the basic laws of arithmetic which can be carried out independently of the portion of Frege's system which led to inconsistency. In any statement of the form …Fx… (in which the variable F is free) which is derivable as a theorem of logic, we may substitute any open formula φ(x) (with the free variable x) for all the occurrences of the atomic formula Fx in …Fx…. plato.stanford.edu /entries/frege-logic   (15095 words)

Pythagorean Theorem and its many proofs The theorem is of fundamental importance in the Euclidean Geometry where it serves as a basis for the definition of distance between two points. It generalizes the Pythagorean Theorem in two ways: the triangle ABC is not required to be right-angled and the shapes built on its sides are arbitrary parallelograms instead of squares. The invocation of the Power of a Point theorem may be regarded as a shortcut to the argument in proof #39. www.cut-the-knot.org /pythagoras/index.shtml   (7547 words)

Godel's Theorems The reason they escape the conclusion of the first incompleteness theorem is their inadequacy, they can't encode and computably deal with finite sequences. In general, diagonalization shows that a set of objects (sequences, programs, provable theorems, true facts) either can't be listed, computed or defined in a nice way or else a simple-to-construct diagonal or self-referential object is not one of the set's objects. We'll start with Cantor's uncountability theorem and end with Godel's incompleteness theorems on truth and provability. www.math.hawaii.edu /~dale/godel/godel.html   (2115 words)

Fermat's little theorem Translation: "There is a fundamental theorem holding in every finite group, usually called Fermat's little Theorem because Fermat was the first to have proved a very special part of it." So at least in German, this seems to have been a term in common use, in 1913. So this little bit of detective work reveals that the term "little Fermat theorem" probably first appeared sometime between 1936 and 1939 and was in common usage by 1945. 145 you will find: 'Fermat states a result of which an important theorem, now known as the "little Fermat theorem," is a consequence.' This indicates to me that someone had coined the term "little Fermat theorem" by the time Uspensky and Heaslet published their book in 1939. www.spd.dcu.ie /johnbcos/fermat's_little_theorem.htm   (1565 words)

Pythagorean Theorem Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in southern Italy. The figure at the left contains a proof of the theorem, because the area of the big, outer, green square is equal to the sum of the areas of the four red triangles and the little, inner white square: It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and the theory of Hilbert space. scidiv.bcc.ctc.edu /Math/Pythagoras.html   (191 words)

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