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# Topic: Existence theorem

 Nonconstructive proof - Wikipedia, the free encyclopedia In mathematics, a nonconstructive proof, is a mathematical proof that purports to demonstrate the existence of something, but which does not say how to construct it. The term "pure existence proof" is often used as a synonym for "nonconstructive proof", although this is not strictly accurate, as both constructive and nonconstructive proofs can be used to prove existence. Another example of a nonconstructive theorem is John Nash's proof, using the strategy-stealing argument, that the game of Hex is a first-player win. en.wikipedia.org /wiki/Nonconstructive_proof   (354 words)

 PlanetMath: Cauchy-Kowalewski theorem   (Site not responding. Last check: 2007-10-07) The Cauchy-Kowalewski theorem is a local existence theorem -- it only asserts that a solution exists in a neighborhood of the point, not in all space. A peculiar feature of this theorem is that the type of the differential equation (whether it is elliptic, parabolic, or hyperbolic) is irrelevant. This is version 8 of Cauchy-Kowalewski theorem, born on 2004-09-19, modified 2005-02-12. planetmath.org /encyclopedia/CauchyKovalevskayaTheorem.html   (288 words)

 [No title] Several of the fundamental theorems present diffficulties from the constructive point of view, for example the fundamental existence theorem that says every Jordan curve in three-space bounds a surface whose area is minimum among surfaces with the given boundary. For example, the theorem that a uniformly continuous function on [0,1] has a minimum is not constructive, because the minimum can shift from near x = 1/4 to near x = 3/4 suddenly as a parameter passes through a critical value. This condition is stated as the main theorem of [15], since it is nicer to state a theorem with purely geometric conditions, rather than the ugly hypothesis that no relative minimum of area has a boundary branch point. www.cs.sjsu.edu /~beeson/Papers/minsurf.html   (2320 words)

 mp_arc 00-38   (Site not responding. Last check: 2007-10-07) We prove a global existence theorem for a class of deterministic infinite-dimensional Hamiltonian systems in which a Vlasov gas is coupled to a finite-dimensional Hamiltonian system. The later is the motion of the rigid and macroscopic boundary. Our existence result shows that if the gas density is initially a smooth function on the phase space, the boundary moves continuously. rene.ma.utexas.edu /mp_arc-bin/mpa?yn=00-38   (120 words)

 An Existence Theorem for The Logic of Decision* In this paper I discuss some of the mathematics behind an often quoted existence theorem from Richard Jeffreyâ€™s The Logic of Decision (Jeffrey 1990) in order to pose several new questions about the meaning and value of that mathematics for decision theory. When I looked at those theorems again I saw pieces that those philosophers may have overlooked. The existence theorem in the previous section is not satisfactory for decision theory. www.cs.umb.edu /~eb/jeffrey/PSA99.html   (686 words)

 Stony Brook Math Calendar The existence problem for periodic orbits is one of the most central questions in Hamiltonian dynamical systems. The almost existence theorem asserts that almost all regular levels of a proper smooth Hamiltonian carry periodic orbits. For instance, the almost existence theorem, whenever it can be established, implies the Weinstein conjecture, one of the most influential conjectures in Hamiltonian dynamics and symplectic topology. www.math.sunysb.edu /~calendar/scott.php?LocationID=9&Date=2005-10-01   (573 words)

 Existence Theorems For Inclusions Of The Type . . . (ResearchIndex)   (Site not responding. Last check: 2007-10-07) Abstract: For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chiefly using Ky Fan's fixed point principle. The main result of the paper improves Theorem 1 in [16] as well as Theorem 2.2 of [3]. 1 An existence theorem for inclusions of the type \Psi(u)(t) 2.. citeseer.ist.psu.edu /366455.html   (351 words)

 Fermat's Last Theorem Pythagoras, a Greek philosopher, around the 5th Century BC generalized the theorem which states that in a right triangle the area of the square of the hypotenuse is the sum of the areas of the squares of the other two sides. Cursory reading of a few books on the subject has not revealed any conjecture or a theorem on the "even" or "balanced" case, where the number of summands is equal to the power of z. In any case, proving the existence conjecture for each n is probably too time-consuming, and computers might help us prove existence up to a very large number. www.public.iastate.edu /~kchoi/fermat.htm   (1628 words)

 Andreu Mas-Colell The story begins in 1974, when Andreu Mas-Colell proved the existence of a competitive equilibrium after dropping the famous axioms of completeness and transitivity of consumer preferences. Indeed, his 1986 proof of existence of a Walrasian equilibrium in a rather generic infinite-dimensional economy has been hailed as definitive (although his introduction of "uniform properness" has been an issue of concern ever since). Mas-Colell is also renowned for his work on relating game theory to Walrasian G.E. - notably, in the relationship of the bargaining set with competitive equilibrium (1989) and exploring the relationship between Walrasian and Nash equilibria (1981, 1983). cepa.newschool.edu /~het/profiles/andreu.htm   (934 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. Given that the proof of Frege's Theorem makes no appeal to Basic Law V, some philosophers have argued Frege's best strategy for achieving his goal is to replace Basic Law V with Hume's Principle and argue that Hume's Principle is an analytic principle of logic. plato.stanford.edu /entries/frege-logic   (15095 words)

 A generalization of Hasminskii's theorem on existence of invariant measures for locally integrable drifts - Bogachev, ...   (Site not responding. Last check: 2007-10-07) Bogachev V.I., Rockner M., A generalization of Hasminskii's theorem on existence of invariant measures for locally integrable drifts, SFB 343 Preprint N 98{ 072 (1998); Theory Probab. 7 Existence of invariant measures of diffusions on an abstract.. 1 Existence of invariant measures for diffusions with singular.. citeseer.ist.psu.edu /bogachev98generalization.html   (714 words)

 The Role of Reverse Mathematics Reverse Mathematics is a highly developed research program whose purpose is to investigate the role of strong set existence axioms in ordinary mathematics. The usual pattern of mathematical reasoning is to deduce a theorem from some axioms. This might be called ``forward mathematics.'' But in order to establish that the axioms are needed for a proof of the theorem, one must reverse the process and deduce the axioms from the theorem. www.math.psu.edu /simpson/papers/hilbert/node5.html   (729 words)

 Example 2 By this we can see that our existence theorem is closely coupled to the initial value specified in the problem and that the differential equation might not have a solution for just any initial condition. However, this does not violate the theorem, because the theorem was not applicable in the first place due to the problem with the partial derivative for the specified initial condition. The solution should align itself with the vector field showing that for this selection of the initial conditions and the size of the box we have one solution as is indicated by the uniqueness theorem. www.utpb.edu /scimath/WKFIELD/mod3/examp2.htm   (886 words)

 D:\Goza\wakefield\mod3\3.txt The application of the existence and especially the uniqueness concepts serve as important checks on the results of numerical solutions. Therefore, before applying the theorem we must always check to be certain that the conditions are indeed satisfied. It had to be abandoned due to interval of existence of our numerically generated solution. www.utpb.edu /scimath/WKFIELD/mod3/Safety3.htm   (3616 words)

 Talboito.com » Probability   (Site not responding. Last check: 2007-10-07) Via Calpundit we learn about an Ohio risk assessor who claims to have proven that the probability for the existence of God stands at about 67%. Stephen Unwin used Bayes’ Theorem to calculate the conditional probability of God’s existence. Bayes’ theorem adjusts a given probability in the face of observed evidence. www.talboito.com /category/science/probability   (328 words)

 Math 341 Notes - Muncaster The theorem asserts that the Picard iterates converge uniformly. This is a very strong type of convergence and it gives you extra properties of the limit functions, i.e. The proof of the theorem involves an estimate of the degree to which the Picard iterates approximate the unique solution of (*). www.math.uiuc.edu /~muncast/courses/math341f97/wk13/m341f97wk13.html   (556 words)

 Existence of Solutions   (Site not responding. Last check: 2007-10-07) The following is a general existence theorem for solutions to constrained optimization problems. To apply Theorem 2.3, we need weakly sequentially compact lower level sets. The Eberlein-Smulian theorem [9] states that a subset of a Banach space is weakly compact if and only if it is weakly sequentially compact, and thus we see that the lower level sets of www.cecm.sfu.ca /~malimber/Copper/subsection3_2_2.html   (235 words)

 On a Local Existence Theorem for a Simplified One-Dimensional Hydrodynamic Model for Semiconductor Devices On a Local Existence Theorem for a Simplified One-Dimensional Hydrodynamic Model for Semiconductor Devices:SIAM Journal on Mathematical Analysis Vol. A simplified hydrodynamic model for semiconductor devices, where the energy equation is replaced by a pressure-density relationship, is studied. The local existence of a smooth solution of the Euler-Poisson equations is then obtained by using a known result for the quasilinear wave equation. epubs.siam.org /sam-bin/dbq/article/22459   (134 words)

 [No title]   (Site not responding. Last check: 2007-10-07) Aug 31: extensibility; sufficient cond's for global existence; flow; continuity/differentiability of flow. Proof of stability theorem; Defn and examples of omega-limit set Hwk: 14c hard deadline tomorrow. Oct 21: lemma on invariant hypersurfaces; the implicit function theorem seen in action. www.math.utk.edu /~denzler/M531-Fa2004/oldclassdiary.html   (370 words)

 Cornell Math - Basic Courses for Graduate Students   (Site not responding. Last check: 2007-10-07) Continuous and differentiable functions: continuous functions, uniform continuity, monotone functions, derivatives of functions, intermediate and mean value theorems, product and chain rules, inverse function theorem, higher derivatives, Taylor series Riemann integral: existence, fundamental theorem of calculus, integration by parts, change of variable formula Ordinary differential equations: existence and uniqueness of solutions. www.math.cornell.edu /~www/Graduate/basic_courses.html   (452 words)

 Topics in Combinatorics (MIT 18.318) The topics will include some rather standard ones (Dehn-Sommerville equations, Helly Theorem, Cauchy and Steinitz theorems) as well as some less standard ones (Alexandrov and Minkowski existence theorems, Koebe Theorem, Sabitov's proof of the The Bellows Conjecture, nonoverlapping unfoldings). For Helly Theorem, various extensions and generalizations see classical survey article Danzer, Grunbaum, and Klee, Helly Theorem and its relatives (1963). For modern approach and Kapovich and Millson's theorem see their original article; see also King's followup. www-math.mit.edu /~pak/courses/318.htm   (571 words)

 One-dimensional flow of a compressible viscous micropolar fluid: a global existence theorem   (Site not responding. Last check: 2007-10-07) One-dimensional flow of a compressible viscous micropolar fluid: a global existence theorem The proof is based on a local existence theorem, obtained in the previous paper. Micropolar fluid, viscousity, compressibility, boundary value problem, global existence. www.math.hr /glasnik/vol_33/no2_06.html   (84 words)

 Math Forum - Ask Dr. Math Archives: Pythagorean Theorem Proofs   (Site not responding. Last check: 2007-10-07) I've decided to do a project with some connections to the Pythagorean theorem, but the project requires innovative ideas. Proving the Pythagorean Theorem: A Traditional and a Modern Approach A friend of mine is irked because of constant use of the Pythagorean theorem, which he has not seen proven. mathforum.org /library/drmath/sets/select/dm_pythag.html   (217 words)

 Fixed Point Theory and Applications   (Site not responding. Last check: 2007-10-07) We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. [4] A. Cellina, A theorem on the approximation of compact multivalued mappings, Atti Accad. www.hindawi.com /journals/fpta/volume-2004/S1687182004406056.html   (251 words)

 Published Articles Some remarks about continuity properties of local Maxwellians and on existence theorem for the BGK model of the Boltzmann equation, Averaging techniques for the transport operator and an existence theorem for the BGK equation in kinetic theory, A note on kinetic models for chemical reactions: comparisons and existence results, (with M. Groppi), submitted for publication. www.csun.edu /~hcmth008/publications/list/node2.html   (664 words)

 ARNO show document   (Site not responding. Last check: 2007-10-07) Another well-known condition for the existence of a zero point follows from Ky Fan's coincidence theorem, which says that if for every point the intersection of the image with the tangent cone of X at the point is non-empty, the mapping must have a zero point. In this paper we extend all these existence results by giving a general zero point existence theorem, of which the two results are obtained as special cases. We also discuss what kind of solutions may exist when no further conditions are stated on the mapping 0. arno.uvt.nl /show.cgi?did=118505   (260 words)

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