positive solutions for higher order multi point boundary value problems with nonhomogeneous boundary conditions abstract we study nth order boundary value problems with a nonlinear term f t x subject to nonhomogeneous multi point boundary conditions criteria for the existence of positive solutions of such problems are established conditions are determined by the relationship between the behavior of f t x x near 0 and when compared with the smallest positive characteristic value of an associated linear integral operator this work improves and extends some recent results in the literature for the second order problems the results are illustrated with examples

positive solutions to a second order three point boundary value problem abstract the existence nonexistence and multiplicity of nonnegative solutions are established for the three point boundary value problem u t p t f u t 0 u 0 0 u 1 u where 0 1 0 1 and is a nonnegative parameter under appropriate hypotheses the key idea is that the problem of finding a nonnegative solution is transformed into the problem of finding a fixed point of a completely continuous operator the arguments involve the schauder fixed point the method of upper and lower solutions for three point boundary value problems and the leray schauder degree theory

generalized kahler potentials from supergravity we consider supersymmetric mathcal n 2 solutions with non vanishing ns three form building on worldsheet results we reduce the problem to a single generalized monge ampere equation on the generalized kahler potential k recently interpreted geometrically by lindstrom rocek von unge and zabzine one input in the procedure is a holomorphic function w that can be thought of as the effective superpotential for a d3 brane probe the procedure is hence likely to be useful for finding gravity duals to field theories with non vanishing abelian superpotential such as leigh strassler theories we indeed show that a purely ns precursor of the lunin maldacena dual to the deformed mathcal n 4 super yang mills falls in our class

a polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed we prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d dimensional euclidean space previously such algorithms were known for dimensions d 1 2 3 and 4 only

generalized complex geometry generalized complex geometry encompasses complex and symplectic ge ometry as its extremal special cases we explore the basic properties of this geometry including its enhanced symmetry group elliptic deforma tion theory relation to poisson geometry and local structure theory we also dene and study generalized complex branes which interpolate be tween at bundles on lagrangian submanifolds and holomorphic bundles on complex submanifolds

rapidly mixing markov chains for sampling contingency tables with a constant number of rows we consider the problem of sampling almost uniformly from the set of contingency tables with given row and column sums when the number of rows is a constant cryan and dyer j comput system sci 67 2003 pp 291 310 have recently given a fully polynomial randomized approximation scheme fpras for the related counting problem which employs markov chain methods indirectly they leave open the question as to whether a natural markov chain on such tables mixes rapidly here we show that the 2 x 2 heat bath markov chain is rapidly mixing we prove this by considering first a heat bath chain operating on a larger window using techniques developed by morris random walks in convex sets ph d thesis department of statistics university of california berkeley ca 2000 and morris and sinclair siam j comput 34 2004 pp 195 226 for the multidimensional knapsack problem we show that this chain mixes rapidly we then apply the comparison method of diaconis and saloff coste ann appl probab 3 1993 pp 696 730 to show that the 2 x 2 chain is also rapidly mixing

superstrings and topological strings at large n we embed the large n chern simons topological string duality in ordinary superstrings this corresponds to a large n duality between generalized gauge systems with n 1 supersymmetry in four dimensions and superstrings propagating on noncompact calabi yau manifolds with certain fluxes turned on we also show that in a particular limit of the n 1 gauge theory system certain superpotential terms in the n 1 system including deformations if spacetime is noncommutative are captured to all orders in 1 n by the amplitudes of noncritical bosonic strings propagating on a circle with self dual radius we also consider d brane anti d brane system wrapped over vanishing cycles of compact calabi yau manifolds and argue that at large n they induce a shift in the background to a topologically distinct calabi yau which we identify as the ground state system of the brane anti brane system

positive solutions for a three point boundary value problem the second order three point boundary value problem x t 2x t h t f t x t t 0 1 x 0 0 x x 1 is considered under some conditions concerning the first eigenvalue of the relevant linear operator where 0 1 is a constant h t is allowed to be singular at t 0 and t 1 the existence of positive solutions is studied by means of fixed point index theory

generalized complex manifolds and supersymmetry we find a worldsheet realization of generalized complex geometry a notion introduced recently by hitchin which interpolates between complex and symplectic manifolds the two dimensional model we construct is a supersymmetric relative of the poisson sigma model used in the context of deformation quantization

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

dirac sigma models we introduce a new topological sigma model whose fields are bundle maps from the tangent bundle of a 2 dimensional world sheet to a dirac subbundle of an exact courant algebroid over a target manifold it generalizes simultaneously the twisted poisson sigma model as well as the g g wzw model the equations of motion are satisfied iff the corresponding classical field is a lie algebroid morphism the dirac sigma model has an inherently topological part as well as a kinetic term which uses a metric on worldsheet and target the latter contribution serves as a kind of regulator for the theory while at least classically the gauge invariant content turns out to be independent of any additional structure in the twisted poisson case one may drop the kinetic term altogether obtaining the wz poisson sigma model in general however it is compulsory for establishing the morphism property

mirror symmetric su 3 structure manifolds with ns fluxes when string theory is compactified on a six dimensional manifold with a nontrivial ns flux turned on mirror symmetry exchanges the flux with a purely geometrical composite ns form associated with lack of integrability of the complex structure on the mirror side considering a general class of t3 fibered geometries admitting su 3 structure we find an exchange of pure spinors e ij and in dual geometries under fiberwise t duality and study the transformations of the ns flux and the components of intrinsic torsion a complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with ns flux

on positive solutions of an m point nonhomogeneous singular boundary value problem abstract this paper is concerned with the existence nonexistence and multiplicity of positive solutions for the following second order m point nonhomogeneous singular boundary value problem u t a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 k i u i b where b 0 k i 0 i 1 2 m 2 0 1 2 m 2 1 i 1 m 2 k i i 1 a t may be singular at t 0 and or t 1 we show that under suitable conditions there exists a positive number b such that the above problem has at least two positive solutions for 0 b b at least one positive solution for b b and no solution for b b by using the krasnosel skii guo fixed point theorem the upper lower solutions method and topological degree theory

algebraic unimodular counting we study algebraic algorithms for expressing the number of non negative integer solutions to a unimodular system of linear equations as a function of the right hand side our methods include todd classes of toric varieties via grobner bases and rational generating functions as in barvinok s algorithm we report polyhedral and computational results for two special cases counting contingency tables and kostant s partition function

multi point boundary value problems of second order differential equations i abstract we study the nonlinear boundary value problem with nonhomogeneous multi point boundary condition u f t u u 0 t 0 1 u 0 i 1 m a i u t i 1 u 1 i 1 m b i u t i 2 sufficient conditions are found for the existence of solutions of the problem based on the existence of lower and upper solutions with certain relations using one of the results under some assumptions we obtain explicit ranges of values of 1 and 2 with which the problem has a solution has a positive solution and has no solution respectively furthermore we prove that the whole plane for 1 and 2 can be divided into two disjoint connected regions e and n such that the problem has a solution for 1 2 e and has no solution for 1 2 n

the complexity of three way statistical tables multiway tables with specified marginals arise in a variety of applications in statistics and operations research we provide a comprehensive complexity classification of three fundamental computational problems on tables existence counting and entry security one outcome of our work is that each of the following problems is intractable already for slim 3 tables with constant number 3 of rows 1 deciding existence of 3 tables with specified 2 marginals 2 counting all 3 tables with specified 2 marginals 3 deciding whether a specified value is attained in a specified entry by at least one of the 3 tables having the same 2 marginals as a given table this implies that a characterization of feasible marginals for such slim tables sought by much recent research is unlikely to exist another consequence of our study is a systematic efficient way of embedding the set of 3 tables satisfying any given 1 marginals and entry upper bounds in a set of slim 3 tables satisfying suitable 2 marginals with no entry bounds this provides a valuable tool for studying multi index transportation problems and multi index transportation polytopes remarkably it enables us to automatically recover a famous example due to vlach of a real feasible integer infeasible collection of 2 marginals for 3 tables of smallest possible size 3 4 6

optimal existence criteria for symmetric positive solutions to a three point boundary value problem abstract in this paper we shall consider the following second order three point boundary value problem u t a t f t u t 0 0 t 1 u 0 u 1 u where 0 1 0 1 2 a l 1 0 1 is nonnegative and symmetric on 0 1 f 0 1 0 0 satisfies caratheodory conditions and f u is symmetric on 0 1 for all u 0 by using fixed point index theorems we get some optimal existence criteria for the existence of one or two symmetric solutions which involve the principal eigenvalue of a related linear operator

positive solutions for second order m point boundary value problems by using the schauder fixed point theorem and analysis method we establish the existence of solutions for the m point boundary value problem u t a t f u 0 u 0 0 u 1 i 1m 2kiu i b where b ki 0 i 1 2 m 2 0 b

twenty combinatorial examples of asymptotics derived from multivariate generating functions let a bf r bf r in mathbb n d be a d dimensional array of numbers for which the generating function f bf z sum bf r a bf r bf z bf r is meromorphic in a neighborhood of the origin for example f may be a rational multivariate generating function we discuss recent results that allow the effective computation of asymptotic expansions for the coefficients of f our purpose is to illustrate the use of these techniques on a variety of problems of combinatorial interest the survey begins by summarizing previous work on the asymptotics of univariate and multivariate generating functions next we describe the morse theoretic underpinnings of some new asymptotic techniques we then quote and summarize these results in such a way that only elementary analyses are needed to check hypotheses and carry out computations the remainder of the survey focuses on combinatorial applications such as enumeration of words with forbidden substrings edges and cycles in graphs polyominoes and descents in permutations after the individual examples we discuss three broad classes of examples namely functions derived via the transfer matrix method those derived via the kernel method and those derived via the method of lagrange inversion these methods have the property that generating functions derived from them are amenable to our asymptotic analyses and we describe further machinery that facilitates computations for these classes of examples

existence of positive solutions to n point nonhomogeneous boundary value problem in this paper we are concerned with the existence of positive solutions to a n point nonhomogeneous boundary value problem by using the krasnoselskii s fixed point theorem in banach spaces some sufficient conditions guaranteeing the existence of positive solution is established for the n point nonhomogeneous boundary value problem

a path integral approach to the kontsevich quantization formula we give a quantum field theory interpretation of kontsevich s deformation quantization formula for poisson manifolds we show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory its batalin vilkovisky quantization yields a superconformal field theory the associativity of the star product and more generally the formality conjecture can then be understood by field theory methods as an application we compute the center of the deformed algebra in terms of the center of the poisson algebra

exact sampling and counting for fixed margin matrices the uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two way tables binary or nonnegative integer due to the difficulty of sampling from this distribution many approximate methods have been developed we will show that by exploiting certain symmetries exact sampling and counting is in fact possible in many nontrivial real world cases we illustrate with real datasets including ecological co occurrence matrices and contingency tables

on barvinok s algorithm for counting lattice points in fixed dimension we describe a simplification of a recent polynomial time algorithm of a i barvinok for counting the number of lattice points in a polyhedron in fixed dimension in particular we show that only very elementary properties of exponential sums are needed to develop a polynomial time algorithm

positive solutions for nonhomogeneous m point boundary value problems let a c 0 1 b c 0 1 0 let d r and d 0 let 1 t be the unique solution of the linear boundary value problem u t a t u t b t u t 0 t 0 1 u 0 0 u 1 1 we study the existence of positive solutions for the m point boundary value problem u a t u t b t u h t f u 0 u 0 0 u 1 i 1m 2 iu ei d where i 0 1 and i 0 for i 1 m 2 are given constants satisfying i 1m 2 ix 1 d

monotone positive solutions of second order multi point boundary value problems abstract in this paper by using guo krasnosel skii fixed point theorem and schauder s fixed point theorem we establish sufficient conditions for the existence and nonexistence of monotone increasing positive solution for a class of second order differential equation with multi point nonhomogeneous boundary conditions