invariant manifolds for impulsive equations and nonuniform polynomial dichotomies for impulsive differential equations in banach spaces we construct stable and unstable invariant manifolds for sufficiently small perturbations of a polynomial dichotomy we also consider the general case of nonuniform polynomial dichotomies moreover we introduce the notions of polynomial lyapunov exponent and of regularity coefficient for a linear impulsive differential equation and we show that when the lyapunov exponent never vanishes the linear equation admits a nonuniform polynomial dichotomy

exit problems associated with affine reflection groups we obtain a formula for the distribution of the first exit time of brownian motion from the alcove of an affine weyl group in most cases the formula is expressed compactly in terms of pfaffians expected exit times are derived in the type widetilde a case the results extend to other markov processes we also give formulas for the real eigenfunctions of the dirichlet and neumann laplacians on alcoves observing that the hot spots conjecture of j rauch is true for alcoves

the classification of automorphism groups of rational elliptic surfaces with section abstract in this paper we give a classification of regular automorphism groups of relatively minimal rational elliptic surfaces with section over the field c which have non constant j maps the automorphism group aut b of such a surface b is the semi direct product of its mordell weil group mw b and the subgroup aut b of the automorphisms preserving the zero section of the rational elliptic surface b the configuration of singular fibers on the surface determines the mordell weil group as has been shown by oguiso and shioda 1991 and aut b also depends on the singular fibers the classification of automorphism groups in this paper gives the group aut b in terms of the configuration of singular fibers on the surface in general aut b is a finite group of order less than or equal to 24 which is a z 2 z extension of either z n z z 2 z z 2 z d n the dihedral group of order 2n or a 4 the alternating group of order 12 the configuration of singular fibers does not determine the group aut b uniquely however we list explicitly all the possible groups aut b and the configurations of singular fibers for which each group occurs

configurations of kodaira fibers on rational elliptic surfaces i n t r o d u c t i o n l legend 6 the list 7 i d i s c r i m i n a n t cons ide ra t i ons 14 if po l a r s of p lane curves 16 ili in t r ins ic g e o m e t r y on g e n u s two curves 19 iv ell iptic qua r t i c s 25 v r a t i o n a l qua r t i c s 30 the reduc ib le case 43 to r s ion g r o u p s of ra t iona l elliptic surfaces 43 epi logue 46 references 46

on partition identities of capparelli and primc abstract we show that up to multiplication by a factor 1 c q q the weighted words version of capparelli s identity is a particular case of the weighted words version of primc s identity we prove this first using recurrences and then bijectively we also give finite versions of both identities

a solution to an open problem for wave equations with generalized wentzell boundary conditions in this paper we solve an open problem put forward by a favini g r goldstein j a goldstein and s romanelli concerning the mixed problem for wave equations with generalized wentzell boundary conditions as a consequence we also develop the previous wellposedness result regarding the mixed problem for heat equations with generalized wentzell boundary conditions

classes of representable disjoint np pairs for a propositional proof system p we introduce the complexity class dnpp p of all disjoint np pairs for which the disjointness of the pair is efficiently provable in the proof system p we exhibit structural properties of proof systems which make canonical np pairs associated with these proof systems hard or complete for dnpp p moreover we demonstrate that non equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for dnpp p and the reductions between the canonical pairs exist

schur s partition theorem companions refinements and generalizations schur s partition theorem asserts the equality s n s1 n where s n is the number of partitions of n into distinct parts 1 2 mod 3 and si n is the number of partitions of n into parts with minimal difference 3 and no consecutive multiples of 3 using a computer search andrews found a companion result s n s2 n where s2 n is the number of partitions of n whose parts e satisfy e1 e i 3 2 or 5 according as e 1 2 or 3 mod 3 by means of a new technique called the method of weighted words a combinatorial as well as a generating function proof of both these theorems are given simultaneously it is shown that si n and s2 n are only two of six companion partition functions sj n j 1 2 6 all equal to s n a three parameter refinement and generalization of these results is obtained

a nonterminating 8 φ 7 summation for the root system c r using multiple q integrals and a determinant evaluation we establish a nonterminating 8 7 summation for the root system cr we also give some important specializations explicitly

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

log canonical models of elliptic surfaces abstract we classify the log canonical models of elliptic surface pairs f x c s f a where f x c is an elliptic fibration s is a section and f a is a weighted sum of marked fibers in particular we show how the log canonical models depend on the choice of the weights we describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes in addition we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers this is the first step in constructing compactifications of moduli spaces of elliptic surfaces using the minimal model program

robust nonuniform dichotomies and parameter dependence abstract we establish the robustness of linear cocycles with an exponential dichotomy under sufficiently small lipschitz perturbations in the sense that the existence of an exponential dichotomy for a given cocycle persists under these perturbations we consider cocycles in banach spaces as well as the general case of nonuniform exponential dichotomies and also the general case of an exponential behavior e c n given by an arbitrary sequence n including the usual exponential behavior n n as a very special case moreover we show that the projections of the exponential dichotomies obtained from the perturbation vary continuously with the parameter and in fact that they are locally lipschitz on finite dimensional parameters

false theta functions and companions to capparelli s identities abstract capparelli conjectured two modular identities for partitions whose parts satisfy certain gap conditions which were motivated by the calculation of characters for the standard modules of certain affine lie algebras and by vertex operator theory these identities were subsequently proved and refined by andrews who related them to jacobi theta functions and also by alladi andrews gordon capparelli and tamba xie in this paper we prove two new companions to capparelli s identities where the evaluations are expressed in terms of jacobi theta functions and false theta functions

double centralizing theorems for the alternating groups let v n be the n fold tensor product of a vector space v following i schur we consider the action of the symmetric group sn on v n by permuting coordinates in the super z2 graded case v v0 v1 a sign is added these actions give rise to the corresponding schur algebras s sn v here s sn v is compared with s an v the schur algebra corresponding to the alternating subgroup an sn while in the classical signless case these two schur algebras are the same for n large enough it is proved that in the super case where dim v0 dim v1 s an v is isomorphic to the cross product algebra s an v s sn v z2

coding the principal character formula for affine kac moody lie algebras in this paper an algorithm for computing the principal character for affine lie algebras is discussed and presented the principal characters discovered using this program are given and or proven results include level 2 and 3 character formulas in a2n 1 2 and the sole existence of the rogers ramanujan products in a1 1 a2 1 a2 2 c3 1 f4 1 g2 1 a7 2

zeros of jones polynomials for families of knots and links abstract we calculate jones polynomials v l t for several families of alternating knots and links by computing the tutte polynomials t g x y for the associated graphs g and then obtaining v l t as a special case of the tutte polynomial for each of these families we determine the zeros of the jones polynomial including the accumulation set in the limit of infinitely many crossings a discussion is also given of the calculation of jones polynomials for non alternating links

modular invariant of quantum tori the quantum modular invariant j qt of 2r is defined as a discontin uous pgl2 z invariant multi valued map using the distance to the nearest integer function k k for 2 q it is shown that j qt 1 and for quadratic irrationalities pari gp experiments suggest that j qt is a finite set in the case of the golden mean we produce explicit formulas involving weighted versions of the rogers ramanujan functions for the experimental supremum and infimum we then define a universal modular invariant j a mod c as a continuous and single valued map of ultrasolenoids such that 1 the classical modular invariant is a quotient of the re striction of j to a subsolenoid mod cl a mod fibering over the classical moduli space of elliptic curves and 2 the quantum modular invariant is a quotient of the restric tion of j to a subsolenoid mod qt a mod fibering over the moduli space of elliptic curves equipped with a kronecker foliation

the construction of numerically calabi yau orders on projective surfaces abstract in this paper we construct a vast collection of maximal numerically calabi yau orders utilising a noncommutative analogue of the well known commutative cyclic covering trick such orders play an integral role in the mori program for orders on projective surfaces and although we know a substantial amount about them there are relatively few known examples

scheduling with and or precedence constraints in many scheduling applications it is required that the processing of some job be postponed until some other job which can be chosen from a pregiven set of alternatives has been completed the traditional concept of precedence constraints fails to model such restrictions therefore the concept has been generalized to so called and or precedence constraints which can cope with this kind of requirement in the context of traditional precedence constraints feasibility transitivity and the computation of earliest start times for jobs are fundamental well studied problems the purpose of this paper is to provide efficient algorithms for these tasks for the more general model of and or precedence constraints we show that feasibility as well as many questions related to transitivity can be solved by applying essentially the same linear time algorithm in order to compute earliest start times we propose two polynomial time algorithms to cope with different classes of time distances between jobs

invariant measures and regularity properties of perturbed ornstein uhlenbeck semigroups abstract this paper deals with perturbations of the ornstein uhlenbeck operator on l 2 spaces with respect to a gaussian measure we perturb the generator of the ornstein uhlenbeck semigroup by a certain unbounded non linear drift and show various properties of the perturbed semigroup such as compactness and positivity strong feller property existence and uniqueness of an invariant measure are discussed as well

combining hook length formulas and bg ranks for partitions via the littlewood decomposition recently the first author has studied hook length formulas for partitions in a systematic manner in the present paper we show that most of those hook length formulas can be generalized and include more variables via the littlewood decomposition which maps each partition to its t core and t quotient in the case t 2 we ob tain new formulas by combining hook lengths and bg ranks introduced by berkovich and garvan as applications we list several multivari able generalizations of classical and new hook length formulas including the nekrasov okounkov the han carde loubert potechin sanborn the bessenrodt bacher manivel the okada panova and the stanley panova formulas summary

trace representation of some generalized cyclotomic sequences of length pq this paper contributes to trace representation of some generalized cyclotomic sequences of length pq p qprime which are defined by ding and helleseth from the relations between these sequences and the legendre sequence we firstly confirm the defining pairs of these sequences of arbitrary order then we obtain their trace representation from which we give their linear complexity using key s method it can be seen that bai et al s conclusion is a special case of our result when the order is two finally an example is given to illustrate the validity of our result

flows on hypergraphs we consider the capacitated minimum cost flow problem on directed hypergraphs we define spanning hypertrees so generalizing the spanning tree of a standard graph and show that like in the standard and in the generalized minimum cost flow problems a correspondence exists between bases and spanning hypertrees then we show that like for the network simplex algorithms for the standard and for the generalized minimum cost flow problems most of the computations performed at each pivot operation have direct hypergraph interpretations

effectivity of brauer manin obstructions we study brauer manin obstructions to the hasse principle and to weak approximation with special regard to effectivity questions

grobner geometry of vertex decompositions and of flagged tableaux we relate a classic algebro geometric degeneration technique dating at least to hodge 1941 to the notion of vertex decompositions of simplicial com plexes the good case is when the degeneration is reduced and we call this a geometric vertex decomposition our main example in this paper is the family of vexillary matrix schubert vari eties whose ideals are also known as one sided ladder determinantal ideals us ing a diagonal term order to specify the grobner degeneration we show that these have geometric vertex decompositions into simpler varieties of the same type from this together with the combinatorics of the pipe dreams of fomin kirillov 1996 we derive a new formula for the numerators of their multigraded hilbert series the double grothendieck polynomials in terms of flagged set valued tableaux this unifies work of wachs 1985 on flagged tableaux and buch 2002 on set valued tableaux giving geometric meaning to both this work focuses on diagonal term orders giving results complementary to those of knutson miller 2004 where it was shown that the generating minors form a grobner basis for any antidiagonal term order and any matrix schubert va riety we show here that under a diagonal term order the only matrix schubert varieties for which these minors form grobner bases are the vexillary ones reach ing an end toward which the ladder determinantal literature had been building contents

automorphisms of elliptic surfaces inducing the identity in cohomology abstract we give a numerical classification for pairs s g consisting of complex nonsingular projective surfaces s of kodaira dimension one and subgroups g of automorphisms of s inducing trivial actions on h 2 s q

lattices on simplicial partitions which are not simply connected in this paper d 1 pencil lattices on simplicial partitions in r d which are not simply connected are studied it is shown how the fact that a partition is not simply connected can be used to increase the flexibility of a lattice a local modification algorithm is developed also to deal with slight partition topology changes that may appear afterwards a lattice has already been constructed

twelve points on the projective line branched covers and rational elliptic fibrations the following divisors in the space rm sym 12 mathbb p 1 of twelve points on mathbb p 1 are actually the same mathcal a the possible locus of the twelve nodal fibers in a rational elliptic fibration i e a pencil of plane cubic curves mathcal b degree 12 binary forms that can be expressed as a cube plus a square mathcal c the locus of the twelve tangents to a smooth plane quartic from a general point of the plane mathcal d the branch locus of a degree 4 map from a hyperelliptic genus 3 curve to mathbb p 1 mathcal e the branch locus of a degree 3 map from a genus 4 curve to mathbb p 1 induced by a theta characteristic and several more the corresponding moduli spaces are smooth but they are not all isomorphic some are finite etale covers of others we describe the web of interconnections among these spaces and give monodromy rationality and prym related consequences enumerative consequences include i the degree of this locus is 3762 e g there are 3762 rational elliptic fibrations with nodes above 11 given general points of the base ii if c rightarrow mathbb p 1 is a cover as in mathcal d then there are 135 different such covers branched at the same points iii the general set of 12 tangent lines that arise in mathcal c turn up in 120 essentially different ways some parts of this story are well known and some other parts were known classically to zeuthen zariski coble mumford and others the unified picture is surprisingly intricate and connects many beautiful constructions including recillas trigonal construction and shioda s e 8 mordell weil lattice

dynamic maintenance of directed hypergraphs abstract in this paper we are concerned with the on line maintenance of directed hypergraphs a generalization of directed graphs previously introduced in the literature in particular we show how to maintain efficiently information about hyperpaths while new hyperarcs are inserted we present a data structure which allows us to check whether there exists a hyperpath between an arbitrarily given pair of nodes in constant time and to return such a hyperpath in a time which is linear in its size the total time required to maintain the data structure during the insertion of new hyperarcs is o mn where m is the total size of the description of the hyperarcs and n is the number of nodes this generalizes a previous result known for directed graphs and has applications in several areas of computer science such as rewriting systems database schemes logic programming and problem solving an extension of these results to hyperpaths between sets of nodes is also presented

a new four parameter q series identity and its partition implications we prove a new four parameter q hypergeometric series identity from which the three parameter identity for the gollnitz theorem due to alladi andrews and gordon follows as a special case by setting one of the parameters equal to 0 the new identity is equivalent to a four parameter partition theorem which extends the deep theorem of gollnitz and thereby settles a problem raised by andrews thirty years ago some consequences including a quadruple product extension of jacobi s triple product identity and prospects of future research are briefly discussed

annihilating fields of standard modules for affine lie algebras given an affine kac moody lie algebra tilde mathfrak g sigma of arbitrary type we determine certain minimal sets of annihilating fields of standard tilde mathfrak g sigma modules we then use these sets in order to obtain a characterization of standard tilde mathfrak g sigma modules in terms of irreducible loop tilde mathfrak g sigma modules which proves to be a useful tool for combinatorial constructions of bases for standard tilde mathfrak g sigma modules

generation of localization in a discrete chain with periodic boundary conditions numerical and analytical results we study the generation of localization in a discrete chain composed of n subsystems and periodic boundary conditions strongly localized motions are studied that is time periodic motions where nearly all of the energy is spatially confined to a single subsystem for varying n numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in phase spatially extended solution however in the limit as n rightarrow infty the bifurcation point tends to infinity and a smooth transition from localization to nonlocalization occurs we then present an analytic technique to complement the numerical results it is based on the matching local asymptotic expansions of a solution branch using pade approximants this leads to global analytic representations of the considered solutions valid over the entire range of the control parameter

hypernetworks in a directed hypergraph abstract recently novel distributed approaches to the formation of collaborative networked organizations have been proposed some of them make use of logical formal structures i e hypernetworks and hyperpaths based on concepts related to directed hypergraphs in order to formally represent competitive inter cluster and collaborative intra cluster relationships in this paper we introduce the concepts of the s hypernetwork the structure consisting of all hyperpaths from a node s to any node in a directed hypergraph the s d hypernetwork the structure consisting of all hyperpaths from a node s to a node d in a directed hypergraph moreover we present characterization theorems for both structures a polynomial algorithm to determine the s hypernetwork and some conditions under which the problem of finding the s d hypernetwork is solvable in polynomial time

a systematic method for constructing discrete painleve equations in the degeneration cascade of the e8 group we present a systematic and quite elementary method for constructing discrete painleve equations in the degeneration cascade for e8 1 starting from the invariant for the autonomous limit of the e8 1 equation one wishes to study the method relies on choosing simple homographies that will cast this invariant into certain judiciously chosen canonical forms these new invariants lead to mappings the deautonomisations of which allow us to build up the entire degeneration cascade of the original mapping we explain the method on three examples two symmetric mappings and an asymmetric one and we discuss the link between our results and the known geometric structure of these mappings

max horn sat and the minimum cut problem in directed hypergraphs in this paper we consider the maximum horn satisfiability problem which is reduced to the problem of finding a minimum cardinality cut on a directed hypergraph for the latter problem we propose different ip formulations related to three different definitions of hyperpath weight we investigate the properties of their linear relaxations showing that they define a hierarchy the weakest relaxation is shown to be equivalent to the relaxation of a well known ip formulation of max horn sat and to a max flow problem on hypergraphs the tightest relaxation which is a disjunctive programming problem is shown to have integer optimum the intermediate relaxation consists in a set covering problem with a possible exponential number of constraints this latter relaxation provides an approximation of the convex hull of the integer solutions which as proven by the experimental results given is much tighter than the one known in the literature 1998 the mathematical programming society inc published by elsevier science b v

the complexity of weighted boolean csp with mixed signs we give a complexity dichotomy for the problem of computing the partition function of a weighted boolean constraint satisfaction problem such a problem is parameterized by a set c of rational valued functions which generalize constraints each function assigns a weight to every assignment to a set of boolean variables our dichotomy extends previous work in which the weight functions were restricted to being non negative we represent a weight function as a product of the form 1 sg where the polynomial s determines the sign of the weight and the non negative function g determines its magnitude we show that the problem of computing the partition function the sum of the weights of all possible variable assignments is in polynomial time if either every function in c can be defined by a pure affine magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of product type with a linear sign polynomial in all other cases computing the partition function is fp p complete

density of rational points on del pezzo surfaces of degree one we state conditions under which the set s k of k rational points on a del pezzo surface s of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is zariski dense for example it suffices to require that the elliptic fibration s p 1 induced by the anticanonical map has a nodal fiber over a k rational point of p 1 it also suffices to require the existence of a point in s k that does not lie on six exceptional curves of s and that has order 3 on its fiber of the elliptic fibration this allows us to show that within a parameter space for del pezzo surfaces of degree 1 over r the set of surfaces s defined over q for which the set s q is zariski dense is dense with respect to the real analytic topology we also include conditions that may be satisfied for every del pezzo surface s and that can be verified with a finite computation for any del pezzo surface s that does satisfy them c 2014 elsevier inc all rights reserved

combinatorial bases of basic modules for affine lie algebras cn 1 lepowsky and wilson initiated the approach to combinatorial rogers ramanujan type identities via vertex operator constructions of standard i e integrable highest weight representations of affine kac moody lie algebras meurman and primc developed further this approach for sl 2 c by using vertex operator algebras and verma modules in this paper we use the same method to construct combinatorial bases of basic modules for affine lie algebras of type cn 1 and as a consequence we obtain a series of rogers ramanujan type identities a major new insight is a combinatorial parametrization of leading terms of defining relations for level one standard modules for affine lie algebra of type cn 1

a construction of the level 3 modules for the affine lie algebra and a new combinatorial identity of the rogers ramanujan type amer math soc 348 1996 pp 481 501

new combinatorial interpretations of ramanujan s partition congruences mod 5 7 and 11 soit p n le nombre de partitions non restreintes de n on donne de nouvelles interpretations combinatoires des congruences p 5n 4 p 7n 5 et p 11n 6 0 mod 5 7 et 11 respectivement

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

arithmetic of del pezzo surfaces of degree 4 and vertical brauer groups we show that brauer classes of a locally solvable degree 4 del pezzo surface x are vertical for some projection away from a plane g x p 1 i e that every brauer class is obtained by pullback from an element of br k p 1 as a consequence we prove that a brauer class obstructs the existence of a k rational point if and only if all k fibers of g fail to be locally solvable or in other words if and only if x is covered by curves that each have no adelic points using work of wittenberg we deduce that for certain quartic del pezzo surfaces with nontrivial brauer group the algebraic brauer manin obstruction is sufficient to explain all failures of the hasse principle conditional on schinzel s hypothesis and the finiteness of tate shafarevich groups the proof of the main theorem is constructive and gives a simple and practical algorithm distinct from that in 5 for computing all classes in the brauer group of x modulo constant algebras c 2014 elsevier inc all rights reserved

the brauer manin obstruction on del pezzo surfaces of degree 2 this paper explores the computation of the brauer manin obstruction on del pezzo surfaces of degree 2 with examples coming from the class of semi diagonal del pezzo surfaces of degree 2 it is conjectured that the failure of the hasse principle for a broad class of varieties including del pezzo surfaces can always be explained by a nontrivial brauer manin obstruction we provide computational evidence in support of this conjecture for semi diagonal del pezzo surfaces of degree 2 in addition we determine the complete list of the possibilities for the finite abelian group h k picx where x is a del pezzo surface of any degree thus completing a computation which had been previously carried out in various special cases only

the x ray transform and its inversion for the series expansion basis functions in three dimensional tomography a formula for the three dimensional x ray transform and an expression for its inversion have been derived the spherical harmonics and the rotation matrices in terms of euler angles are used in the generalized fourier series expansion some properties of the transformed fourier components are discussed

gainfree leontief substitution flow problems leontief substitution systems have been studied by economists and operations researchers for many years we show how such linear systems are naturally viewed asleontief substitution flow problems on directed hypergraphs and that important solution properties follow from structural characteristics of the hypergraphs we give a strongly polynomial non simplex algorithm for leontief substitution flow problems that satisfy againfree property leading to acyclic extreme solutions integrality conditions follow easily from this algorithm another structural property support disjoint reachability leads to necessary and sufficient conditions for extreme solutions to be binary in a survey of applications we show how the leontief flow paradigm links polyhedral combinatorics expert systems mixed integer model formulation and some problems in graph optimization

an improved sectional anosov closing lemma we prove that all nonwandering points of a sectional anosov flow on a compact 3 manifold can be approximated by periodic points or by points for which the omega limit set is a singularity this improves the closing lemma in morales mich math j 56 1 29 53 2008 we also describe a sectional anosov flow for which the recurrent points are not dense in the nonwandering set

on the arithmetic of del pezzo surfaces of degree 2 we study the arithmetic of certain del pezzo surfaces of degree 2 we produce examples of brauer manin obstruction to the hasse principle coming from 2 and 4 torsion elements in the brauer group

auction algorithms for shortest hyperpath problems the auction reduction algorithm is a strongly polynomial version of the auction method for the shortest path problem in this paper we extend the auction reduction algorithm to different types of shortest hyperpath problems in directed hypergraphs the results of preliminary computational experiences show that the auction reduction method is comparable to other known methods for specific classes of hypergraphs

a simply connected surface of general type with p g 0 and k 2 2 in this paper we construct a simply connected minimal complex surface of general type with pg 0 and k2 2 using a rational blow down surgery and a gorenstein smoothing theory

partition identities involving gaps and weights we obtain interesting new identities connecting the famous partition functions of euler gauss lebesgue rogers ramanujan and others by attaching weights to the gaps between parts the weights are in general multiplicative some identities involve powers of 2 as weights and yield combinatorial information about some remarkable partition congruences modulo powers of 2

weak approximation on del pezzo surfaces of degree 1 we study del pezzo surfaces of degree 1 of the form w2 z3 ax6 by6in the weighted projective space where k is a perfect field of characteristic not 2 or 3 and a bk over a number field we exhibit an infinite family of minimal counterexamples to weak approximation amongst these surfaces via a brauer manin obstruction

n point pade approximants to real valued stieltjes series with nonzero radii of convergence abstract by employing special continued fractions to two stieltjes series with nonzero radii of convergence we extend the inequalities for one point pade approximants reported by baker 1975 corollory 17 1 to the case of two point pade approximants we prove that some convergents of the continued fractions form a monotone sequences of upper and lower bounds converging uniformly to stieltjes function x1 x on compact subsets of r where r is a radius of convergence of an expansion of x f1 x at x 0 for an illustration of theoretical results we provide nontrivial numerical examples as an application to real physical problems second order pade approximants bounds on the effective conductivity of a square array of cylinders are evaluated

log fano varieties over function fields of curves consider a smooth log fano variety over the function field of a curve suppose that the boundary has positive normal bundle choose an integral model over the curve then integral points are zariski dense after removing an explicit finite set of points on the base curve

on the q analogues of some transformations of nearly poised hypergeometric series a number of transformation formulas for very well poised basic hypergeometric series have been obtained which in the limit q 1 approach the known transformation formulas for nearly poised ordinary hypergeometric series

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets

exponents of nonnegative matrix pairs the notions of primitivity and exponent of a square nonnegative matrix a are classical a is primitive provided there is a nonnegative integer k such that a k is entrywise positive and in the case a is primitive the exponent of a is the smallest such k fornasini and valcher have extended the notion of primitivity to pairs a b of square nonnegative matrices of the same order the pair a b is primitive provided there exist nonnegative integers h and k such that the sum of all products formed by words consisting of ha s and kb s is entrywise positive this paper defines the exponent of a nonnegative matrix pair to be the smallest value of h k over all such h and k it is then shown that the largest exponent of a primitive pair of n by n nonnegative matrices lies in the interval n 3 5n 2 2 3n 3 2n 2 2n 2 in addition the exponent of a pair of nonnegative matrices is related to properties of an associated twodimensional dynamical system 2001 elsevier science inc all rights reserved

optimal bounds for t singularities in stable surfaces abstract we explicitly bound t singularities on normal projective surfaces w with one singularity and k w ample this bound depends only on k w 2 and it is optimal when w is not rational we classify and realize surfaces attaining the bound for each nonnegative kodaira dimension of the minimal resolution of w this answers effectiveness of bounds see 1 2 17 for those surfaces