weak liftings of dg modules abstract this paper contains a weak lifting result for differential graded dg modules that is a generalization of auslander ding and solberg s weak lifting for modules and yoshino s weak lifting for complexes

cheeger muller theorem on manifolds with cusps we prove equality between the renormalized ray singer analytic torsion and the intersection r torsion on a witt manifold with cusps up to an error term determined explicitly by the betti numbers of the cross section of the cusp and the intersection r torsion of a model cone in the first step of the proof we compute explicitly the renormalized ray singer analytic torsion of a model cusp in general dimension and without the witt condition in the second step we establish a gluing formula for renormalized ray singer analytic torsion on a general class of non compact manifolds in any dimension that includes witt manifolds with cusps but also scattering manifolds with asymptotically conical ends in the final step a cheeger muller theorem on cusps follows by a combination of the previous explicit computation and the gluing formula

zeta determinants of sturm liouville operators with quadratic potentials at infinity abstract we consider sturm liouville operators on a half line a a 0 with potentials that are growing at most quadratically at infinity such operators arise naturally in the analysis of hyperbolic manifolds or more generally manifolds with cusps we establish existence and a formula for the associated zeta determinant in terms of the wronski determinant of a fundamental system of solutions adapted to the boundary conditions despite being the natural objects in the context of hyperbolic geometry spectral geometry of such operators has only recently been studied in the context of analytic torsion

fuzzy closure spaces abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems but many results can be extended to what are called fuzzy closure spaces or fcs s for short the notions of a subspace a sum and a product are extended to fcs s the hereditary additivity and productivity behaviour of compactness in fcs s is investigated and some weak forms of compactness and fuzzy continuous functions in fcs s are introduced the interaction between fuzzy proximity spaces and fcs s is investigated a necessary background is included for completeness

topological modification of a fuzzy closure space abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems and many results can be extended to what are called fuzzy closure spaces fuzzy closure spaces have been introduced in 6 as a generalization of closure spaces 1 in the present paper we introduce the concept of topological modification of a fuzzy closure operator we prove that the topological modification of a fuzzy closure operator u on x is the finest topological fuzzy closure operator on x coarser than u the interaction between the concepts of a subspace and the topological modification of a fuzzy closure operator is also examined

pseudo closure operators in fuzzy topological spaces abstract the concept of a pseudo closure operator s of an fts x has been introduced in 6 in this paper we give an axiomatic characterization of pseudo closure operators also we give a necessary and sufficient condition on an fts x so that is the unique fuzzy topology which induces s at the end of the paper we give a characterization of fts s of structure a 6 in terms of pseudo closure operators

fuzzy cores and their extensions abstract we introduce core theory simultaneously for general topology and for fuzzy topology a fuzzy core on a set x is an operator from a subfamily of i x into i x subject to certain conditions we identify all the extension of a fuzzy core fuzzy cech closure operators and to fuzzy kuratowski operators the main purpose of this theory is to characterize as we do here some properties of functions as being equivalent to their continuity with respect to certain fuzzy topologies on their domains and codomains we nominate three existing theories as special instances of core theory one is from general topology and is strongly related to applications the theory of the scott topology on a partially set the other two theories are from fuzzy topology klein s theory of closure operators and the mashhour et al theory of pseudo closure operators

on the determinant of one dimensional elliptic boundary value problems we discuss the regularized determinant of elliptic boundary value problems on a line segment our framework is applicable for separated and non separated boundary conditions

semi dualizing complexes and their auslander categories let r be a commutative noetherian ring we study r modules and complexes of such with excellent duality properties while their common properties are strong enough to admit a rich theory we count among them such potentially diverse objects as dualizing complexes for r on one side and on the other the ring itself in several ways these two examples constitute the extremes and their well understood properties serve as guidelines for our study however also the employment in recent studies of ring homomorphisms of complexes lying between these extremes is incentive

uniform annihilators of local cohomology of excellent rings abstract the main purpose of this paper is to give an affirmative answer to a conjecture of huneke c huneke uniform bounds in noetherian rings invent math 107 1992 203 223 conjecture 2 13

regular singular sturm liouville operators and their zeta determinants abstract we consider sturm liouville operators on the line segment 0 1 with general regular singular potentials and separated boundary conditions we establish existence and a formula for the associated zeta determinant in terms of the wronski determinant of a fundamental system of solutions adapted to the boundary conditions this generalizes the earlier work of the first author treating general regular singular potentials but only the dirichlet boundary conditions at the singular end and the recent results by kirsten loya park for general separated boundary conditions but only special regular singular potentials

spectral geometry of singular riemannian spaces on considere la trace du noyau de la chaleur et l application de la methode de l equation de la chaleur au theoreme d indice pour la caracteristique d euler et des complexes signatures

fuzzy topologies with specified level properties abstract recently the author and p wuyts have studied the problem of defining fuzzy topologies when one is given the family of closure operators or the family of level topologies this paper is concerned with the relationship between these two problems when the family of topologies is a chain with the lt property there is a natural family of closure operators that generates the wuyts maximum i e the largest fuzzy topology with the given level topologies as a corollary it is shown that the fuzzy neighborhood spaces are precisely the pseudo regular spaces in general the relationship between the two problems is weak for example given an lt family of topologies and an l ftp family of semi closure operators there is a fuzzy topology associated with both if and only if the 0 level closure generates the 0 level topology and the closure of a set is always closed in the level topology lastly it is shown that when a function s domain has a wuyts maximum as its topology fuzzy continuity is equivalent to level continuity

on product fuzzy topological spaces abstract we provide complete answers to the following three questions in fuzzy topology when is the fuzzy closure operator finitely productive on a given family of fuzzy topological spaces which need not be fully stratified when is the fuzzy interior operator finitely productive on such a family when are the coordinate projections open maps from arbitrary products of members of such a family the answer to the first question is the harder one to establish the second and the third question turn out to have same answer

liftings and quasi liftings of dg modules abstract we prove lifting results for dg modules that are akin to auslander ding and solberg s famous lifting results for modules

generating fuzzy topologies with semi closure operators let x be an l fuzzy topological space for a e l 1 and a x x ec a a if and only if g fuzzy open and g x a imply there is a e a with g a 0 under certain restrictions on a which are always satisfied if l is linearly ordered c a is a semi closure operator this paper contains necessary and sufficient conditions under which a collection of semi closure operators generates a fuzzy topology in general such a collection does not generate a unique topology the class of topologies generated is shown to be closed under suprema and its largest member is characterized the topology for the fuzzy unit interval is characterized among those generated by its a closure operators

dixmier traces and residues on weak operator ideals we develop the theory of modulated operators in general principal ideals of compact operators for laplacian modulated operators we establish connes trace formula in its local euclidean model and a global version thereof it expresses dixmier traces in terms of the vector valued wodzicki residue we demonstrate the applicability of our main results in the context of log classical pseudo differential operators studied by lesch and a class of operators naturally appearing in noncommutative geometry c 2020 elsevier inc all rights reserved

regularizing infinite sums of zeta determinants we present a new multiparameter resolvent trace expansion for elliptic operators polyhomogeneous in both the resolvent and auxiliary variables for elliptic operators on closed manifolds the expansion is a simple consequence of the parameter dependent pseudodifferential calculus as an additional nontrivial toy example we treat here sturm liouville operators with separated boundary conditions as an application we give a new formula in terms of regularized sums for the zeta determinant of an infinite direct sum of sturm liouville operators the laplace beltrami operator on a surface of revolution decomposes into an infinite direct sum of sturm louville operators parametrized by the eigenvalues of the laplacian on the cross section mathbb s 1 we apply the polyhomogeneous expansion to equate the zeta determinant of the laplace beltrami operator as a regularized sum of zeta determinants of the sturm liouville operators plus a locally computable term from the polyhomogeneous resolvent trace asymptotics this approach provides a completely new method for summing up zeta functions of operators and computing the meromorphic extension of that infinite sum to s 0 we expect our method to extend to a much larger class of operators

pseudo closure operators in fuzzy neighbourhood base spaces abstract fuzzy neighbourhood base spaces and dual fuzzy neighbourhood spaces are two special types of fuzzy topological spaces they were introduced by morsi as useful tools for the theory explanation and application of lowen s fuzzy neighbourhood systems the notion of the pseudoclosure operator of a fuzzy topological space was introduced by mashhour et al as a tool in establishing a necessary and sufficient condition for the productivity of fuzzy kuratowski operators pseudo closure operators carry partial information about the fuzzy closure operators of their respective spaces we establish relationships between the pseudo closure operators of fuzzy neighbourhood base spaces their fuzzy closure operators and their level topologies we provide counterexamples to disprove other nonvalid relationships we also study some categorical aspects of the operation of taking the pseudo closure operators of fuzzy topological spaces

ring homomorphisms and finite gorenstein dimension the local structure of homomorphisms of commutative noetherian rings is investigated from the point of view of dualizing complexes a concept of finite gorenstein dimension which substantially weakens the notion of finite flat dimension is introduced for homomorphisms it is shown to impose structural constraints due to a remarkable equivalence of subcategories of the derived category of all modules an essential part of this study is the development of relative notions of dualizing complexes and bass numbers it is proved that the bass numbers of local homomorphisms are rigid extending a known result for local rings quasi gorenstein homomorphisms are introduced as local homomorphisms that base change a dualizing complex for the source ring into one for the target they are shown to have the stability properties of the gorenstein homomorphism that they generalize 1991 mathematics subject classification primary 13h10 13d23 14e40 secondary 13c15

descent via koszul extensions abstract let r be a commutative noetherian local ring with completion r we apply differential graded dg algebra techniques to study descent of modules and complexes from r to r where r is either the henselization of r or a pointed etale neighborhood of r we extend a given r complex to a dg module over a koszul complex we describe this dg module equationally and apply artin approximation to descend it to r this descent result for koszul extensions has several applications when r is excellent we use it to descend the dualizing complex from r to a pointed etale neighborhood of r this yields a new version of p roberts theorem on uniform annihilation of homology modules of perfect complexes as another application we prove that the auslander condition on uniform vanishing of cohomology ascends to r when r is excellent henselian and cohen macaulay