a new method of the high temperature series expansion we formulate a new method of performing high temperature series expansions for the spin half heisenberg model or more generally for su n heisenberg model with arbitrary n the new method is a novel extension of the well established finite cluster method our method emphasizes hidden combinatorial aspects of the high temperature series expansion and solves the long standing problem of how to efficiently calculate correlation functions of operators acting at widely separated sites series coefficients are expressed in terms of cumulants which are shown to have the property that all deviations from the lowest order nonzero cumulant can be expressed in terms of a particular kind of moment expansion these quasi moments can be written in terms of corresponding quasi cumulants which enable us to calculate higher order terms in the high temperature series expansion we also present a new technique for obtaining the low order contributions to specific heat from finite clusters

an approximate approach of global optimization for polynomial programming problems abstract many methods for solving polynomial programming problems can only find locally optimal solutions this paper proposes a method for finding the approximately globally optimal solutions of polynomial programs representing a bounded continuous variable x i as the addition of a discrete variable d i and a small variable i a polynomial term x i x i can be expanded as the sum of d i x j d j i and i j a procedure is then developed to fully linearize d i x j and d j e i and to approximately linearize i j with an error below a pre specified tolerance this linearization procedure can also be extended to higher order polynomial programs several polynomial programming examples in the literature are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a pre specified error

connectedness at infinity of complete kahler manifolds one of the main purposes of this paper is to prove that on a complete k ahler manifold of dimension m if the holomorphic bisectional curvature is bounded from below by 1 and the minimum spectrum lambda 1 m ge m 2 then it must either be connected at infinity or isometric to bbb r times n with a specialized metric with n being compact generalizations to complete k ahler manifolds satisfying a weighted poincar e inequality are also being considered

symmetric green s functions on complete manifolds on demontre d une facon constructive que l operateur de laplace admet une fonction de green symetrique g x y sur une variete de riemann complete

on stability and the convergence of the kahler ricci flow assuming uniform bounds for the curvature the exponential convergence of the kahler ricci flow is established under two con ditions which are a form of stability the mabuchi energy is bound ed from below and the dimension of the space of holomorphic vector fields in an orbit of the diffeomorphism group cannot jump up in the limit

mixed integer bilinear programming problems this paper addresses a class of problems called mixed integer bilinear programming problems these problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued and they arise in various production location allocation and distribution application contexts we first identify some special cases of this problem which are relatively more readily solvable even though their continuous relaxations are still nonconvex for the more general case we employ a linearization technique and design a composite lagrangian relaxation implicit enumeration cutting plane algorithm extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm

poisson equation poincare lelong equation and curvature decay on complete kahler manifolds in the first part of this work the poisson equation on complete noncompact manifolds with nonnegative ricci curvature is studied sufficient and necessary conditions for the existence of solutions with certain growth rates are obtained sharp estimates on the solutions are also derived in the second part these results are applied to the study of curvature decay on complete kahler manifolds in particular the poincare lelong equation on complete noncompact kahler manifolds with nonnegative holomorphic bisectional curvature is studied several applications are then derived which include the steinness of the complete kahler manifolds with nonnegative curvature and the flatness of a class of complete kahler manifolds satisfying a curvature pinching condition liouville type results for plurisubharmonic functions are also obtained 0 introduction in this paper we will discuss the poisson equation on complete noncompact manifolds and derive some applications on kahler manifolds let mm be a complete noncompact kahler manifold where m 2 is the complex dimension assume m has nonnegative holomorphic bisectional curvature and has maximal volume growth such that the scalar curvature decays like r 2 where r is the distance from a fixed point then it was proved in 20 by mok siu yau that one can solve the following poincare lelong equation 0 1 1 u received november 25 2000 and in revised form june 28 2001 the first author was partially supported by nsf grant dms9970284 usa the second author was partially supported by nsf of china project 10001001 and the third author was partially supported by earmarked grant of hong kong cuhk4217 99p

rotational symmetry of conical kahler ricci solitons we show that expanding kahler ricci solitons which have positive holomorphic bisectional curvature and are c 2 asymptotic to a conical kahler manifold at infinity must be the u n rotationally symmetric expanding solitons constructed by cao

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

kahler manifolds with real holomorphic vector fields for a kahler manifold endowed with a weighted measure e f dv the associated weighted hodge laplacian delta f maps the space of p q forms to itself if and only if the 1 0 part of the gradient vector field nabla f is holomorphic we use this fact to prove that for such f a finite energy f harmonic function must be pluriharmonic motivated by this result we verify that the same also holds true for f harmonic maps into a strongly negatively curved manifold furthermore we demonstrate that such f harmonic maps must be constant if f has an isolated minimum point in particular this implies that for a compact kahler manifold admitting such a function there is no nontrivial homomorphism from its first fundamental group into that of a strongly negatively curved manifold

on tightening the relaxations of miller tucker zemlin formulations for asymmetric traveling salesman problems this paper is concerned with applying thereformulation linearization technique rlt to derive tighter relaxations for theasymmetric traveling salesman problem atsp formulation that is based on themiller tucker zemlin mtz subtour elimination constraints the mtz constraints yield a compact representation for the traveling salesman problem tsp and their use is particularly attractive in various routing and scheduling contexts that have an embedded atsp structure however it is well recognized that these constraints yield weak relaxations and with this motivation desrochers and laporte 1991 have lifted the mtz constraints into facets of the underlying atsp polytope we show that a novel application of the rlt process from a nonstandard mtz representation of the atsp reveals a new formulation of this problem that is compact and yet theoretically as well as computationally dominates the lifted mtz formulation of desrochers and laporte this approach is also extended to derive tight formulations for theprecedence constrained asymmetric traveling salesman problem pcatsp based on the mtz subtour elimination constraints additional classes of valid inequalities are also developed for both these versions of the atsp and further ideas for developing tighter representations are suggested for future investigations

linearization strategies for a class of zero one mixed integer programming problems this paper is concerned with a new linearization strategy for a class of zero one mixed integer programming problems that contains quadratic cross product terms between continuous and binary variables and between the binary variables themselves this linearization scheme provides an equivalent mixed integer linear programming problem which yields a tighter continuous relaxation than that obtainable via the alternative linearization techniques available in the literature moreover the proposed technique provides a unifying framework in the sense that all the alternate methods lead to formulations that are accessible through appropriate surrogates of the constraints of the new linearized formulation extensions to various other types of mixed integer nonlinear programming problems are also discussed

a maximally superintegrable system on an n dimensional space of nonconstant curvature abstract we present a novel hamiltonian system in n dimensions which admits the maximal number 2 n 1 of functionally independent quadratic first integrals this system turns out to be the first example of a maximally superintegrable hamiltonian on an n dimensional riemannian space of nonconstant curvature and it can be interpreted as the intrinsic smorodinsky winternitz system on such a space moreover we provide three different complete sets of integrals in involution and solve the equations of motion in closed form

polynomial growth harmonic functions on connected sums of complete riemannian manifolds let m be a connected sum of complete riemannian manifolds satisfying the volume doubling condition and the poincare inequality we prove that the space of polynomial growth harmonic functions on m is finite dimensional whenever m has finitely many ends and satisfies the finite covering condition on each end this result directly generalizes that of tam and it also partially generalizes that of colding and minicozzi ii

poisson equation on complete manifolds abstract we develop heat kernel and green s function estimates for manifolds with positive bottom spectrum the results are then used to establish existence and sharp estimates of the solution to the poisson equation on such manifolds with ricci curvature bounded below as an application we show that the curvature of a steady gradient ricci soliton must decay exponentially if it decays faster than linear and the potential function is bounded above

a note on the existence of positive green s function abstract it is an important problem to determine when a complete noncompact riemannian manifold admits a positive green s function in this regard one tries to seek geometric assumptions which are stable with respect to uniform perturbations of the metric in this note we obtained some results in this direction generalizing some earlier results of li and tam

complete manifolds with positive spectrum ii in this paper we continued our investigation of complete manifolds whose spectrum of the laplacian has an optimal positive lower bound in particular we proved a splitting type theorem for n dimensional manifolds that have a finite volume end this can be viewed as a study of the equality case of a theorem of cheng

martin compactification of a complete surface with negative curvature in this paper we consider the martin compactification associated with the operator mathcal l delta 1 of a complete non compact surface sigma 2 with negative curvature in particular we investigate positive eigenfunctions with eigenvalue one of the laplace operator delta of sigma 2 and prove a uniqueness result such eigenfunctions are unique up to a positive multiplicative constant if they vanish on the part of the geometric boundary s infty sigma 2 of sigma 2 where the curvature is bounded above by a negative constant and satisfy some growth estimate on the other part of s infty sigma 2 where the curvature approaches zero this uniqueness result plays an essential role in our recent paper cao and he infinitesimal rigidity of steady gradient ricci soliton in dimension three arxiv 1412 2714 2014 preprint in which we prove an infinitesimal rigidity theorem for deformations of certain three dimensional collapsed gradient steady ricci soliton with a non trivial killing vector field

reduction of symmetric semidefinite programs using the regular ast representation we consider semidefinite programming problems on which a permutation group is acting we describe a general technique to reduce the size of such problems exploiting the symmetry the technique is based on a low order matrix representation of the commutant centralizer ring of the matrix algebra generated by the permutation matrices we apply it to extending a method of de klerk et al that gives a semidefinite programming lower bound to the crossing number of complete bipartite graphs it implies that cr k 8 n 2 9299n 2 6n cr k 9 n 3 8676n 2 8n and for any m 9 lim n to infty frac rm cr k m n z m n geq 0 8594 frac m m 1 where z m n is the zarankiewicz number lfloor frac 1 4 m 1 2 rfloor lfloor frac 1 4 n 1 2 rfloor which is the conjectured value of cr k m n here the best factor previously known was 0 8303 instead of 0 8594

on green functions of second order elliptic operators on riemannian manifolds the critical case abstract let p be a second order linear elliptic operator with real coefficients which is defined on a noncompact and connected riemannian manifold m it is well known that the equation p u 0 in m admits a positive supersolution which is not a solution if and only if p admits a unique positive minimal green function on m and in this case p is said to be subcritical in m if p does not admit a positive green function but admits a global positive super solution then such a solution is called a ground state of p in m and p is said to be critical in m we prove for a critical operator p in m the existence of a green function which is dominated above by the ground state of p away from the singularity moreover in a certain class of green functions such a green function is unique up to an addition of a product of the ground states of p and p under some further assumptions we describe the behavior at infinity of such a green function this result extends and sharpens the celebrated result of p li and l f tam concerning the existence of a symmetric green function for the laplace beltrami operator on a smooth and complete riemannian manifold m

cohomologie l 2 des varietes qale we give a topological interpretation of the space of l 2 harmonis forms of some qale manifolds introduced by d joyce we introduce a analytical criterium which make possible the used of mayer vietoris sequence

global optimization of nonconvex factorable programming problems in this paper we consider a special class of nonconvex programming problems for which the objective function and constraints are defined in terms of general nonconvex factorable functions we propose a branch and bound approach based on linear programming relaxations generated through various approximation schemes that utilize for example the mean value theorem and chebyshev interpolation polynomials coordinated with a reformulation linearization technique rlt a suitable partitioning process is proposed that induces convergence to a global optimum the algorithm has been implemented in c and some preliminary computational results are reported on a set of fifteen engineering process control and design test problems from various sources in the literature the results indicate that the proposed procedure generates tight relaxations even via the initial node linear program itself furthermore for nine of these fifteen problems the application of a local search method that is initialized at the lp relaxation solution produced the actual global optimum at the initial node of the enumeration tree moreover for two test cases the global optimum found improves upon the solutions previously reported in the source literature

sparse sos relaxations for minimizing functions that are summations of small polynomials this paper discusses how to find the global minimum of functions that are summations of small polynomials small means involving a small number of variables some sparse sum of squares sos techniques are proposed we compare their computational complexity and lower bounds with prior sos relaxations under certain conditions we also discuss how to extract the global minimizers from these sparse relaxations the proposed methods are especially useful in solving sparse polynomial system and nonlinear least squares problems numerical experiments are presented which show that the proposed methods significantly improve the computational performance of prior methods for solving these problems lastly we present applications of this sparsity technique in solving polynomial systems derived from nonlinear differential equations and sensor network localization

the kahler ricci flow with positive bisectional curvature we show that the kahler ricci flow on a manifold with positive first chern class converges to a kahler einstein metric assuming positive bisectional curvature and certain stability conditions

matrix li yau hamilton estimates for the heat equation on kahler manifolds in l y peter li and s t yau developed the fundamental gradient estimate which is now widely called the li yau estimate for any positive solution u x t of the heat equation on a riemannian manifold m n dimrm and showed how the classical harnack inequality can be derived from their gradient estimate when m is complete and of nonnegative ricci curvature the li yau estimate is sharp later in h2 richard hamilton extended the li yau estimate to the full matrix version of the hessian estimate of u under the stronger assumptions that m is ricci parallel and of nonnegative sectional curvature in this paper we consider positive solutions to the heat equation

an accelerated covering relaxation algorithm for solving 0 1 positive polynomial programs the purpose of this note is to present an accelerated algorithm for solving 0 1 positive polynomial pp problems like our covering relaxation algorithm management science 1979 the accelerated algorithm is a cutting plane method which uses the linear set covering problem as a relaxation for pp however a unique and novel feature of the accelerated algorithm is that it attempts to generate cutting planes from heuristic solutions to the set covering problem whenever possible computational results reveal that this strategy of generating cutting planes has led to a significant reduction in the computational time required to solve a pp problem

ricci flow under local almost non negative curvature conditions abstract we find a local solution to the ricci flow equation under a negative lower bound for many known curvature conditions under a non collapsing assumption the flow exists for a uniform amount of time during which the curvature stays bounded below by a controllable negative number the curvature conditions we consider include 2 non negative and weakly pic 1 cases of which the results are new we complete the discussion of the almost preservation problem by bamler cabezas rivas wilking and the 2 non negative case generalizes a result in 3d by simon topping to higher dimensions as an application we use the local ricci flow to smooth a metric space which is the limit of a sequence of manifolds with the almost non negative curvature conditions and show that this limit space is bi holder homeomorphic to a smooth manifold

projective manifolds whose tangent bundles are numerically effective in 1979 mori mo proved the so called hartshorne frankel conjecture every projective n dimensional manifold with ample tangent bundle is isomorphic to the complex projective space p a differential geometric analogon assuming the existence of a k ihler metric on x with positive holomorphic bisectional curvature is independently due to siu yau sy thus it seems natural to classify projective manifolds x whose tangent bundle tx satisfy a degenerate condition of ampleness numerical effectivity abbreviated by nef this means that the tautological quotient line bundle d 1 on f tx is numerically effective i e c 0

a matrix li yau hamilton estimate for kahler ricci flow in this paper we prove a new matrix li yau hamilton lyh estimate for kahler ricci flow on manifolds with nonnegative bisectional curvature the form of this new lyh estimate is obtained by the interpolation consideration originated in ch by chow this new inequality is shown to be connected with perelman s entropy formula through a family of differential equalities in the rest of the paper we show several applications of this new estimate and its corresponding estimate for linear heat equation these include a sharp heat kernel comparison theorem generalizing the earlier result of li and tian lt a manifold version of stoll s theorem st on the characterization of algebraic divisors and a localized monotonicity formula for analytic subvarieties which sharpens the bishop volume comparison theorem motivated by the connection between the heat kernel estimate and the reduced volume monotonicity of perelman p we prove a sharp lower bound heat kernel estimate for the time dependent heat equation which is in a certain sense dual to perelman s monotonicity of the reduced volume as an application of this new monotonicity formula we show that the blow down limit of a certain type long time solution is a gradient expanding soliton we also illustrate the connection between the new lyh estimate and the hessian comparison theorem of fin on the forward reduced distance local monotonicity formulae on entropy and forward reduced volume are also derived

a polyhedral branch and cut approach to global optimization a variety of nonlinear including semidefinite relaxations have been developed in recent years for nonconvex optimization problems their potential can be realized only if they can be solved with sufficient speed and reliability unfortunately state of the art nonlinear programming codes are significantly slower and numerically unstable compared to linear programming software in this paper we facilitate the reliable use of nonlinear convex relaxations in global optimization via a polyhedral branch and cut approach our algorithm exploits convexity either identified automatically or supplied through a suitable modeling language construct in order to generate polyhedral cutting planes and relaxations for multivariate nonconvex problems we prove that if the convexity of a univariate or multivariate function is apparent by decomposing it into convex subexpressions our relaxation constructor automatically exploits this convexity in a manner that is much superior to developing polyhedral outer approximators for the original function the convexity of functional expressions that are composed to form nonconvex expressions is also automatically exploited root node relaxations are computed for 87 problems from globallib and minlplib and detailed computational results are presented for globally solving 26 of these problems with baron 7 2 which implements the proposed techniques the use of cutting planes for these problems reduces root node relaxation gaps by up to 100 and expedites the solution process often by several orders of magnitude

sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative ricci curvature in this paper we consider complete noncompact riemannian manifolds m g with nonnegative ricci curvature and euclidean volume growth of dimension n ge 3 for every bounded open subset omega subset m with smooth boundary we prove that begin aligned int limits partial omega left frac mathrm h n 1 right n 1 mathrm d sigma ge mathrm avr g big mathbb s n 1 big end aligned where mathrm h is the mean curvature of partial omega and mathrm avr g is the asymptotic volume ratio of m g moreover the equality holds true if and only if m setminus omega g is isometric to a truncated cone over partial omega an optimal version of huisken s isoperimetric inequality for 3 manifolds is obtained using this result finally exploiting a natural extension of our techniques to the case of parabolic manifolds we also deduce an enhanced version of kasue s non existence result for closed minimal hypersurfaces in manifolds with nonnegative ricci curvature

frankel conjecture and sasaki geometry abstract we classify simply connected compact sasaki manifolds of dimension 2 n 1 with positive transverse bisectional curvature in particular the kahler cone corresponding to such manifolds must be bi holomorphic to c n 1 0 as an application we recover the theorem of mori and siu yau on the frankel conjecture and extend it to certain orbifold version the main idea is to deform such sasaki manifolds to the standard round sphere in two steps both fixing the complex structure on the kahler cone first we deform the metric along the sasaki ricci flow and obtain a limit sasaki ricci soliton with positive transverse bisectional curvature then by varying the reeb vector field which essentially decreases the volume functional we deform the sasaki ricci soliton to a sasaki einstein metric with positive transverse bisectional curvature i e a round sphere the second deformation is only possible when one treats simultaneously regular and irregular sasaki manifolds even if the manifold one starts with is regular quasi regular i e kahler manifolds orbifolds

a probabilistic approach to martin boundaries for manifolds with ends we use martingale methods and coupling arguments to prove results of li and tam 1987 and donnelly 1986 characterizing positive and bounded harmonic functions respectively on certain manifolds with ends

exploiting special structure in semidefinite programming a survey of theory and applications abstract semidefinite programming sdp may be seen as a generalization of linear programming lp in particular one may extend interior point algorithms for lp to sdp but it has proven much more difficult to exploit structure in the sdp data during computation we survey three types of special structures in sdp data 1 a common chordal sparsity pattern of all the data matrices this structure arises in applications in graph theory and may also be used to deal with more general sparsity patterns in a heuristic way 2 low rank of all the data matrices this structure is common in sdp relaxations of combinatorial optimization problems and sdp approximations of polynomial optimization problems 3 the situation where the data matrices are invariant under the action of a permutation group or more generally where the data matrices belong to a low dimensional matrix algebra such problems arise in truss topology optimization particle physics coding theory computational geometry and graph theory we will give an overview of existing techniques to exploit these structures in the data most of the paper will be devoted to the third situation since it has received the least attention in the literature so far

a dynamic inequality generation scheme for polynomial programming hierarchies of semidefinite programs have been used to approximate or even solve polynomial programs this approach rapidly becomes computationally expensive and is often tractable only for problems of small size in this paper we propose a dynamic inequality generation scheme to generate valid polynomial inequalities for general polynomial programs when used iteratively this scheme improves the bounds without incurring an exponential growth in the size of the relaxation as a result the proposed scheme is in principle scalable to large general polynomial programming problems when all the variables of the problem are non negative or when all the variables are binary the general algorithm is specialized to a more efficient algorithm in the case of binary polynomial programs we show special cases for which the proposed scheme converges to the global optimal solution we also present several examples illustrating the computational behavior of the scheme and provide comparisons with lasserre s approach and for the binary linear case with the lift and project method of balas ceria and cornuejols

the structure of operators in effective particle conserving models for many particle systems defined on lattices we investigate the global structure of effective hamiltonians and observables obtained by means of a suitable basis transformation we study transformations which lead to effective hamiltonians conserving the number of excitations the same transformation must be used to obtain effective observables the analysis of the structure shows that effective operators give rise to a simple and intuitive perspective on the initial problem the systematic calculation of n particle irreducible quantities becomes possible constituting a significant progress details on how to implement the approach perturbatively for a large class of systems are presented

lie algebraic curvature conditions preserved by the hermitian curvature flow the purpose of this paper is to prove that the hermitian curvature flow hcf on an hermitian manifold m g j preserves many natural curvature positivity conditions following ideas of wilking j reine angew math 679 223 247 2013 for an text ad gl t 1 0 m invariant subset s subset text end t 1 0 m and a nice function f text end t 1 0 m rightarrow mathbb r we construct a convex set of curvature operators c s f which is invariant under the hcf varying s and f we prove that the hcf preserves griffiths positivity dual nakano positivity positivity of holomorphic orthogonal bisectional curvature lower bounds on the second scalar curvature as an application we prove that stationary periodic solutions to the hcf can exist only on manifolds m with the trivial canonical bundle on the universal cover widetilde m

on manifolds with nonnegative curvature on totally isotropic 2 planes we prove that a compact orientable 2n dimensional riemannian manifold with second betti number nonzero nonnegative curvature on totally isotropic 2 planes and satisfying a positivity type condition at one point is necessarily kahler with second betti number 1 using the methods of siu and yau we prove that if the positivity condition is satisfied at every point then the manifold is biholomorphic to complex projective space

univariate parameterization for global optimization of mixed integer polynomial problems abstract this paper presents a new relaxation technique to globally optimize mixed integer polynomial programming problems that arise in many engineering and management contexts using a bilinear term as the basic building block the underlying idea involves the discretization of one of the variables up to a chosen accuracy level teles j p castro p m matos h a 2013 multiparametric disaggregation technique for global optimization of polynomial programming problems j glob optim 55 227 251 by means of a radix based numeric representation system coupled with a residual variable to effectively make its domain continuous binary variables are added to the formulation to choose the appropriate digit for each position together with new sets of continuous variables and constraints leading to the transformation of the original mixed integer non linear problem into a larger one of the mixed integer linear programming type the new underestimation approach can be made as tight as desired and is shown capable of providing considerably better lower bounds than a widely used global optimization solver for a specific class of design problems involving bilinear terms

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

harmonic maps from noncompact riemannian manifolds with non negative ricci curvature outside a compact set in this paper we prove the uniqueness and existence of harmonic maps of finite energy from a complete noncompact riemannian manifold m g with sobolev constant s2 m 0 and ricci curvature ric m 0 outside some compact subset into a complete manifold of nonpositive curvature or a regular ball in particular we prove the uniqueness and existence of bounded harmonic functions on m g

mott transition and sign problem for a model of lattice fermions we consider a model of spinless fermions on the square latticez2 with an interaction potential of strengthu 0 at distance one and strengthj at distance two in the largeu limit t j u wheret is the hopping amplitude as the chemical potential is varied ift t 0 we find three different phases corresponding to full half and zero filling fractions we study the system at low temperaturet 0 by a method involving a canonical transformation and a functional integral representation ift 0 we locate the phase boundaries of the mott metal insulator transition for all j u with upper and lower bounds show that mean field theory is valid ifj 0 we have only one sided bounds for the phase boundaries and we can t validate mean field theory in casej 0 we introduce a new resummation scheme for low temperature expansions which yields finite and convergent perturbation series and permits us to study issues like the sign problem our algorithm gives an optimal canonical transformation for the functional integral such that the expectation of the sign observables is exp c cdot t cdot ve frac beta 2 wherev is the volume and t 1

ricci flow on kahler einstein manifolds this is the continuation of our earlier article 10 for any kahler einstein surfaces with positive scalar curvature if the initial metric has positive bisectional curvature then we have proved see 10 that the kahler ricci flow converges exponentially to a unique kahler einstein metric in the end this partially answers a long standing problem in ricci flow on a compact kahler einstein manifold does the kahler ricci flow converge to a kahler einstein metric if the initial metric has positive bisectional curvature in this article we give a complete affirmative answer to this problem

an exact penalty function approach for nonlinear integer programming problems abstract nonlinear integer programming problems with bounded feasible sets are considered it is shown how the number of constraints in such problems can be reduced with the aid of an exact penalty function approach this approach can be used to construct an equivalent unconstrained problem or a problem with a constraint set which makes it easier to solve the application of this approach to various nonlinear integer programming problems is discussed

minimizing polynomials via sum of squares over the gradient ideal a method is proposed for finding the global minimum of a multivariate polynomial via sum of squares sos relaxation over its gradient variety that variety consists of all points where the gradient is zero and it need not be finite a polynomial which is nonnegative on its gradient variety is shown to be sos modulo its gradient ideal provided the gradient ideal is radical or the polynomial is strictly positive on the real gradient variety this opens up the possibility of solving previously intractable polynomial optimization problems the related problem of constrained minimization is also considered and numerical examples are discussed experiments show that our method using the gradient variety outperforms prior sos methods

kahler manifolds with almost nonnegative ricci curvature in this paper the authors prove that if a complete kahler manifold with almost nonnegative ricci curvature has at least three ends then it must holomorphically factor through a parabolic riemann surface 0 introduction in ll l2 the first author studied the structure of com plete kahler manifolds with nonnegative sectional curvature near infinity a man ifold is said to have nonnegative sectional curvature near infinity if there exists a compact subset d such that the sectional curvature is nonnegative on m d in one of the theorems he showed that if such a manifold has more than one end then each end must be isometrically and holomorphically a fiber bundle over some riemann surface moreover the fibers are all totally geodesic and isometric to a compact kahler manifold with nonnegative sectional curvature and the riemann surface is a complete surface with boundary of nonnegative gaussian curvature it turned out that there was a gap in the part of the argu ment in which the author constructed a proper holomorphic function by using a proper pluri harmonic function this fact was pointed out by napier and the second author in n r where they showed by way of an example that a flat complete kahler manifold that has only 2 ends might not holomorphically fac tor through a riemann surface in their paper they also proved a holomorphic factorization theorem for complete kahler manifolds that either have bounded geometry or admit a pluri subharmonic exhaustion function and have at least 3 ends this argument of napier ramachandran provided a complete proof of the isometric holomorphic factorization of li for when the manifold has at least 3 ends in this paper we would like to combine some of the arguments used in ll l2 l t3 l y and n r to prove a holomorphic factorization theorem theorem for complete kahler manifolds with almost nonnegative ricci curva ture and at least 3 ends we say that a complete riemannian manifold m has

constrained matrix li yau hamilton estimates on kahler manifolds we derive a family of constrained matrix li yau hamilton estimates on kahler manifolds as a result we first get a constrained matrix li yau hamilton estimate for heat equation on a kahler manifold with fixed kahler metric secondly we get such estimate for forward conjugate heat equation on kahler manifolds with time dependent kahler metrics evolving under the kahler ricci flow

critical points of green s functions on complete manifolds we prove that the number of critical points of a li tam green s function on a complete open riemannian surface of finite type admits a topological upper bound given by the first betti number of the surface in higher dimensions we show that there are no topological upper bounds on the number of critical points by constructing for each nonnegative integer n a riemannian manifold diffeomorphic to r n n 3 whose minimal green s function has at least n non degenerate critical points variations on the method of proof of the latter result yield contractible n manifolds whose minimal green s functions have level sets diffeomorphic to any fixed codimension 1 compact submanifold of r n

sparsity in sums of squares of polynomials representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and semidefinite programming sdp relaxation of polynomial optimization problems we discuss effective methods to obtain a simpler representation of a sparse polynomial as a sum of squares of sparse polynomials by eliminating redundancy

large scale behavior of kernels of schrodinger operators in this paper we study the asymptotic behavior of solutions to schrodinger equations on manifolds with nonnegative ricci curvature and euclidean volume growth as a first application we get a sharp asymptotic estimate on the green s function for the laplacian which sharpens results of li and yau next we establish a definite gap in the possible rates of decay of exterior harmonic functions on these manifolds when the manifold also has quadratic curvature decay we get supremum estimates on the c 2 norm of the green s function this has function theoretic implications for these manifolds we then give a generalization to manifolds with nonnegative ricci curvature outside a compact set finally we study schrodinger operators where the potential decays quadratically at infinity in this setting we obtain a geometric version at infinity of a classical theorem of bers

sharp differential estimates of li yau hamilton type for positive p p forms on kahler manifolds in this paper we study the heat equation of hodge laplacian deformation of p p forms on a kahler manifold after identifying the condition and establishing that the positivity of a p p form solution is preserved under such an invariant condition we prove the sharp differential harnack in the sense of liyau hamilton estimates for the positive solutions of the hodge laplacian heat equation we also prove a nonlinear version coupled with the kahler ricci flow and some interpolating matrix differential harnack type estimates for both the kahler ricci flow and the ricci flow 2011 wiley periodicals inc

heat kernel on smooth metric measure spaces and applications we derive a harnack inequality for positive solutions of the f heat equation and gaussian upper and lower bound estimates for the f heat kernel on complete smooth metric measure spaces with bakry emery ricci curvature bounded below both upper and lower bound estimates are sharp when the bakry emery ricci curvature is nonnegative the main argument is the de giorgi nash moser theory as applications we prove an l f 1 liouville theorem for f subharmonic functions and an l f 1 uniqueness theorem for f heat equations when f has at most linear growth we also obtain eigenvalues estimates and f green s function estimates for the f laplace operator

on the boundary behavior of kahler einstein metrics on log canonical pairs in this paper we study the boundary behavior of the negatively curved kahler einstein metric attached to a log canonical pair x d such that k x d is ample in the case where x is smooth and d has simple normal crossings support but possibly negative coefficients we provide a very precise estimate on the potential of the ke metric near the boundary d in the more general singular case d being assumed effective though we show that the ke metric has mixed cone and cusp singularities near d on the snc locus of the pair as a corollary we derive the behavior in codimension one of the ke metric of a stable variety

a tight linearization and an algorithm for zero one quadratic programming problems this paper is concerned with the solution of linearly constrained zero one quadratic programming problems problems of this kind arise in numerous economic location decision and strategic planning situations including capital budgeting facility location quadratic assignment media selection and dynamic set covering a new linearization technique is presented for this problem which is demonstrated to yield a tighter continuous or linear programming relaxation than is available through other methods an implicit enumeration algorithm which uses lagrangian relaxation benders cutting planes and local explorations is designed to exploit the strength of this linearization computational experience is provided to demonstrate the usefulness of the proposed linearization and algorithm

sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity unconstrained and inequality constrained sparse polynomial optimization problems pops are considered a correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a pop based on this graph sets of the supports for sums of squares sos polynomials that lead to efficient sos and semidefinite program sdp relaxations are obtained numerical results from various test problems are included to show the improved performance of the sos and sdp relaxations

perturbation expansions for quantum many body systems a systematic method for developing high order zero temperature perturbation expansions for quantum many body systems is presented the models discussed explicitly are spin models with a variety of interactions in one and two dimensions the wide applicability of the method is illustrated by expansions around hamiltonians with ordered and disordered ground states namely ising and dimerized models computer implementation of this method is discussed in great detail some previously unpublished series are tabulated

hamiltonian systems admitting a runge lenz vector and an optimal extension of bertrand s theorem to curved manifolds bertrand s theorem asserts that any spherically symmetric natural hamiltonian system in euclidean 3 space which possesses stable circular orbits and whose bounded trajectories are all periodic is either a harmonic oscillator or a kepler system in this paper we extend this classical result to curved spaces by proving that any hamiltonian on a spherically symmetric riemannian 3 manifold which satisfies the same conditions as in bertrand s theorem is superintegrable and given by an intrinsic oscillator or kepler system as a byproduct we obtain a wide panoply of new superintegrable hamiltonian systems the demonstration relies on perlick s classification of bertrand spacetimes and on the construction of a suitable globally defined generalization of the runge lenz vector

polynomial programming lp relaxations also converge we consider the global minimization of a multivariate polynomial on a compact semialgebraic set using a result of krivine j analyse math 12 1964 pp 307 326 c r acad sci paris 258 1964 pp 3417 3418 it is shown that lp relaxations based on products of the original constraints in the spirit of the reformulation linearization technique procedure of sherali and adams converge to the global optimum this extends to compact semialgebraic sets previous results known for polytopes and 0 1 programs the asymptotic behavior of the lp relaxations is also analyzed and it is shown that in important cases finite convergence cannot occur