radical layers of representable functors i let 0 f a t4 b o c 0 be an almost split sequence then the induced sequence o g a g b g c ys 0 is exact where s gs c r c the maps a have degree 1 and y has degree 0 ii let i t i sot i be a left minimal almost split map where i is an indecomposable injective let k 03 be maximal such that im sot i c rk i if k co then the induced sequence 0 g sot i g i g i sot z is exact where the first map has degree k and the second has degree 1 if k co then the induced map g i t g z sot i is a monomorphism of degree 1 dual results hold for covariant functors x

serrin s overdetermined problem and constant mean curvature surfaces for all n 9 we find smooth entire epigraphs in rn namely smooth domains of the form x rn xn f x1 xn 1 which are not half spaces and in which a problem of the form u f u 0 in has a positive bounded solution with 0 dirichlet boundary data and constant neumann boundary data on this answers negatively for large dimensions a question by berestycki caffarelli and nirenberg in 1971 serrin proved that a bounded domain where such an overdetermined problem is solvable must be a ball in analogy to a famous result by alexandrov that states that an embedded compact surface with constant mean curvature cmc in euclidean space must be a sphere in lower dimensions we succeed in providing examples for domains whose boundary is close to large dilations of a given cmc surface where serrin s overdetermined problem is solvable

probability laws related to the jacobi theta and riemann zeta functions and brownian excursions this paper reviews known results which connect riemann s integral representations of his zeta function involving jacobi s theta function and its derivatives to some particular probability laws governing sums of independent exponential variables these laws are related to one dimensional brownian motion and to higher dimensional bessel processes we present some characterizations of these probability laws and some approximations of riemann s zeta function which are related to these laws

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

random walk polynomials and random walk measures random walk polynomials and random walk measures play a prominent role in the analysis of a class of markov chains called random walks without any reference to random walks however a random walk polynomial sequence can be defined and will be defined in this paper as a polynomial sequence pn x which is orthogonal with respect to a measure on 1 1 and which is such that the parameters alfa n in the recurrence relations pn 1 x x alfa n pn x snpn 1 x are nonnegative any measure with respect to which a random walk polynomial sequence is orthogonal is a random walk measure we collect some properties of random walk measures and polynomials and use these findings to obtain a limit theorem for random walk measures which is of interest in the study of random walks we conclude with a conjecture on random walk measures involving

on the cartan matrix of an artin algebra of global dimension two the purpose of this paper is to show that if n is an artin algebra of g obal dimension 81 dim 2 then the determinant of its cartan matrix equals i this generalizes previous results of donovan and freislich 2 igusa and todorov 4 and wilson 5 we recall that if n is an artin algebra for instance a finite dimensional algebra over a field there are finitely many nonisomorphic indecomposable projective rl modules p p p we denote by end p hom p p the length of hom p pi as an end p module then the h x n matrix c n j having knd cpi hom p p i as the i j th entry is called the cartan matrix of rl let d be now an artin algebra of finite representation typethat is having finitely many nonisomorphic indecomposable 4 modules let h u end tr hom m n be the matrix with integral entries where m n range through the set of the nonisomorphic indecomposable ii modules donovan and freislich 2 have shown that if 4 kg is a group algebra of finite representation type then det h 1 then using associated graded algebras wilson showed that det h 1 if a is a finite dimensional algebra of finite representation type over an algebraically closed field 5 io independently the same result was proved by igusa and todorov 4 without making any assumption on the ground field let p be the auslander algebra of n see 1 for further details that is r end m 0 mt m jod where m m are the nonisomorphic indecomposable n modules then it has been shown that h c t where c t denotes the cartan matrix of the auslander algebra r it is known that gl dim r 2 we recall that

a characterization of finite auslander reiten quivers a we give necessary and sufficient conditions for a finite k modulated translation quiver to be an auslander reiten quiver in terms of certain homology groups associated to the quiver section 3 b we show that whether a finite k modulated translation quiver is an auslander reiten quiver depends only on the underlying valued translation quiver and the characteristic of k and give necessary and sufficient conditions only in terms of the valued quiver and char k we also show that any valued quiver with valuations 1 n or n l n q 3 admits a modulation over any prime field sections 5 6 7 c to a valued translation quiver r we associate an unvalued translation quiver r i e all valuations are 1 and show that a finite k modulated translation quiver is an auslander reiten quiver if and only if the associated unvalued translation quiver with the trivial k modulation k prime field of k is an auslander reiten quiver section 8

on the inductive construction of galois coverings of algebras let a be a finite dimensional algebra over an algebraically closed field k in order to study the category moda of finitely generated left a modules we may assume that a is basic and connected by 8 there is a finite quiver i e oriented graph qa and a surjective homomorphism of algebras kqa a such that i ker kqa 2 where kqa denotes the path algebra associated to qa and kq a denotes the ideal of kqa generated by all arrows in qa for each pair qa i called a presentation of a we can define the fundamental group 1 qa i see 9 13 or section 1 2 below then there is surjective homomorphism of algebras f a a defined by the action of 1 qa i on a called the universal galois covering of a with respect to as in 8 we shall consider algebras as locally finite k categories galois coverings have proved to be a powerful tool for the study of the module category moda indeed a is representation finite if and only if a is locally support finite and locally representation finite in this case if chark 2 then a kq where q is a quiver without oriented cycles 4 9 14 if a is tame then a is tame 6 but the converse does not hold 11 certain a modules may be described via the push down functor f mod a moda see 5 in this paper we shall consider only triangular algebras that is algebras a kqa i such that qa has no oriented cycles in this case a vertex x in qa is said to be separating if for the indecomposable decomposition radpx m1 ms there is a decomposition into connected components q a q1 qt with t s of the induced full subquiver q a of qa with vertices those y which are not predecessors

a rigidity result for overdetermined elliptic problems in the plane let f 0 r be a locally lipschitz function and r 2 a c 1 domain whose boundary is unbounded and connected if there exists a positive bounded solution to the overdetermined elliptic problem u f u 0 in u 0 on u 1 on we prove that is a half plane in particular we obtain a partial answer to a question raised by h berestycki l caffarelli and l nirenberg in 1997

module categories with infinite radical cube zero abstract let a be an artin algebra and let mod a denote the category of finitely generated right a modules we denote by rad mod a the ideal in mod a generated by all non invertible morphisms between indecomposable modules in mod a the infinite radical rad mod a of mod a is the intersection of all powers rad i mod a i 1 of rad mod a it is known that a is representation finite if and only if rad mod a 2 0 in this paper we study the representation infinite algebras a such that rad mod a 3 0 examples of such algebras include all representation infinite tilted algebras of euclidean type

solutions to the overdetermined boundary problem for semilinear equations with position dependent nonlinearities abstract we show that a wide range of overdetermined boundary problems for semilinear equations with position dependent nonlinearities admits nontrivial solutions the result holds true both on r n and on compact riemannian manifolds as a byproduct of the proofs we also obtain some rigidity or partial symmetry results for solutions to overdetermined problems on riemannian manifolds of nonconstant curvature

bifurcating extremal domains for the first eigenvalue of the laplacian abstract we prove the existence of a smooth family of non compact domains s r n 1 n 1 bifurcating from the straight cylinder b n r for which the first eigenfunction of the laplacian with 0 dirichlet boundary condition also has constant neumann data at the boundary for each s e e the overdetermined system u u 0 in s u 0 on s u const on s has a bounded positive solution the domains s are rotationally symmetric and periodic with respect to the r axis of the cylinder they are of the form s x t r n r x 1 s cos 2 t s t o s 2 where t s t 0 o s and t 0 is a positive real number depending on n for n 2 these domains provide a smooth family of counter examples to a conjecture of berestycki caffarelli and nirenberg we also give rather precise upper and lower bounds for the bifurcation period t 0 this work improves a recent result of the second author

graded artin algebras a graded artin algebra is a graded ring which neglecting the grading is an artin algebra although this definition has the merit of brevity it does not expose some of the basic properties of graded artin algebras for instance that there is a bound on absolute values of degrees of homogeneous elements indeed a different definition is given in section 1 and the discrepancy is rectified by theory 1 4 we admit that our chief interest in graded artin algebras lies in applications to the representation theory of artin algebras see 5 1 we feel nonetheless that graded artin algebras are interesting objects of study in their own right and some of our techniques especially in sections 5 and 6 are equally applicable to arbitrary graded rings thus this paper unlike its sequel 51 is designed to be read by a general ring theoretical audience it is in addition self contained from the standpoint of knowledge concerning graded rings required the major concern of the paper is the existence of gradings on given modules over a graded artin algebra we use the term gradable when a gradation exists our transcendent result along these lines is that direct summands of finitely generated gradable modules are gradable it follows immediately see section 3 that simple modules and projective modules over a graded artin algebra are gradable also inasmuch as we do not restrict ourselves to positively graded rings endomorphism rings of graded finitely generated modules over graded artin algebras are graded artin algebras in a similar vein duality and horn

an eigenvalue decomposition for first hitting times in random walks distributions for first hitting times in random walks skip free markov chains on the non negative integers are studied their probability generating functions are expressed in terms of the eigenvalues of probability transition submatrices the study of first hitting times leads to several classes of infinitely divisible distributions closely related to the bondesson class of generalized convolutions of mixtures of exponential distributions which arises from the study of first hitting times in birth death processes some properties of these classes are derived from their characterization by pick functions

computing global dimension of endomorphism rings via ladders abstract this paper deals with computing the global dimension of endomorphism rings of maximal cohen macaulay mcm modules over commutative rings several examples are computed in particular we determine the global spectra that is the sets of all possible finite global dimensions of endomorphism rings of mcm modules of the curve singularities of type a n for all n d n for n 13 and e 6 7 8 and compute the global dimensions of leuschke s normalization chains for all ade curves as announced in 12 moreover we determine the centre of an endomorphism ring of a mcm module over any curve singularity of finite mcm type in general we describe a method for the computation of the global dimension of an endomorphism ring end r m where r is a henselian local ring using add m approximations when m 0 is a mcm module over r and r is henselian local of krull dimension 2 with a canonical module and of finite mcm type we use auslander reiten theory and iyama s ladder method to explicitly construct these approximations

the classification of special cohen macaulay modules in this paper we completely classify all the special cohen macaulay cm modules corresponding to the exceptional curves in the dual graph of the minimal resolutions of all two dimensional quotient singularities in every case we exhibit the specials explicitly in a combinatorial way our result relies on realizing the specials as those cm modules whose first ext group vanishes against the ring r thus reducing the problem to combinatorics on the ar quiver such possible ar quivers were classified by auslander and reiten we also give some general homological properties of the special cm modules and their corresponding reconstruction algebras

artin rings of global dimension two in this paper we show that a left artin ring a of global dimension at most two has loewy length at most 2 1 where n is the number of simple components of a rad a we assume that the reader is familiar with the trends but not necessarily the details of contemporary representation theory of artin rings let us record a few conventions the rings discussed here will be left artinian unless otherwise specified and will sometimes be finite dimensional algebras over an algebraically closed field henceforth denoted by k modules will be finitely generated left modules unless otherwise specified the radical of a will usually be denoted by r the loewy

the dimple in gneiting s spatial temporal covariance model gneiting 2002 proposed a nonseparable covariance model for spatial temporal data in present paper we show that in certain circumstances his model possesses a counterintuitive dimple which detracts from its modelling appeal

radial symmetry for elliptic boundary value problems on exterior domains by the alexandroff serrin method 2 14 of moving hyperplanes we obtain radial symmetry for the domain and the solutions of on an exterior domain subject to the overdetermined boundary conditions on at and in in particular the following conjecture from potential theory due to p gruber cf 11 8 is proved let or be a bounded smooth domain with a constant source distribution on and let be the induced single layer potential if is constant in then is a ball

overdetermined elliptic problems in topological disks abstract we introduce a method based on the poincare hopf index theorem to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk applications to some well known nonlinear elliptic pdes are provided our result can be seen as the analogue of hopf s uniqueness theorem for constant mean curvature spheres but for the general analytic context of overdetermined elliptic problems

the existence of covering functors for orders and consequences for stable components with oriented cycles the starting point for the covering theory for algebras of finite type over algebraically closed fields was riedtmann s paper algebren darstellungskocher uberlagerungen und zurtick 14 1 her main result from today s point of view is the existence of covering functors i e the existence of a bijection between the morphisms between indecomposable modules and purely combinatorial defined vector spaces generated by paths in a translation quiver cf 1 1 141 this bijection has recently turned out to be more and more important in the representation theory of algebras it was the first step leading to the use of auslander reiten quivers as a tool for the classification of algebras of linite type 15 81 the main purpose of this paper is to initiate an analog for classical orders over complete dedekind domains we shall formulate our results and proofs only for orders but it is always obvious that everything carries immediately over to the algebra situation let r be a complete dedekind domain with quotient field k and let n be an r order in a separable k algebra a 161 n is a subring of a with the same identity and moreover a is a full r sublattice which means that i is an r lattice and contains a k basis of a we denote by r the auslander reiten quiver of i i e vertices of r are the isomorphism classes of indecomposable n lattices and two vertices are joined by an arrow provided there exists an irreducible i map between the corresponding a lattices moreover we denote by f the universal cover of i 8 in particular the vertices of r are homotopy classes of walks in i with covering morphism f f p r 8 for each arrow x y in f we define as the space of irreducible maps irr fx fy 4 171 from fx to fy moreover for indecomposable i lattices iv n let r m n c hom m n be the ith functorial radical i e r m n ri n m where ri n is the ith power of the radical of the presentable fun or n hom n 21 292 0021 8693 85 3 00

skew ornstein uhlenbeck processes and their financial applications in this paper we investigate a special class of skew diffusions skew ornstein uhlenbeck abbr ou processes whose scale and speed densities are both piecewise functions the existence and uniqueness of solutions regarding the related stochastic differential equations abbr sdes with local time are established as well as the construction through time changes afterwards we concentrate on three computing issues including the explicit expressions of transition densities the cumulative distributions and laplace transforms of the first hitting times for skew ou processes with the hypothesis on asset dynamics two financial instances in the field of credit risk are illustrated at the end of this paper

two sided gluings of tilted algebras we study the class of algebras a satisfying the property all but at most finitely many non isomorphic indecomposable a modules are such that all their predecessors have projective dimension at most one or all their successors have injective dimension at most one such a class includes the tilted algebras d happel c ringel trans amer math soc 274 1982 399 443 the quasi tilted algebras d happel i reiten s smalo mem am math soc 120 1996 575 the shod algebras f u coelho m lanzilotta manuscripta mathematica 100 1999 1 11 the weakly shod f u coelho m lanzilotta preprint 2001 and the left and right glued algebras i assem f u coelho j pure appl algebra 96 3 1994 225 243

gauss green theorem for weakly differentiable vector fields sets of finite perimeter and balance laws we analyze a class of weakly differentiable vector fields f w r n r n with the property that f 2 l 1 and div f is a signed radon measure these fields are called bounded divergence measure fields the primary focus of our inves tigation is to introduce a suitable notion of the normal trace of any divergence measure field f over the boundary of an arbitrary set of finite perimeter that en sures the validity of the gauss green theorem to achieve this we first establish a fundamental approximation theorem which states that given a signed radon measurethat is absolutely continuous with respect to h n 1 on r n a ny set of finite perimeter can be approximated by a family of sets with smooth boundary essentially from the measure theoretic interior of the set with respect to the mea sure kk the total variation measure we employ this approximation theorem to derive the normal trace of f on the boundary of any set of finite perimeter e as the limit of the normal traces of f on the boundaries of the approximate sets with smooth boundary so that the gauss green theorem for f holds one with these results we analyze the cauchy flux that is bounded by a nonnegative radon measure over any oriented surface i e an n 1 dimensional surface that is a part of the boundary of a set of finite perimeter and thereby develop a general mathematical formulation of the physical principle of the balance law through the cauchy flux finally we apply this framework to the derivation of systems of balance laws with measure valued source terms from the formulation of the balance law this framework also allows the recovery of cauchy entropy flux through the lax entropy inequality for entropy solutions of hyperbolic con servation laws c 2008 wiley periodicals inc

a remarkable property of generalized gamma convolutions it is proved that f x is the density of a generalized gamma convolution ggc then so is c 1 cx f x provided that is a nonnegative integer some classes of ggc s are introduced

on the degree of irreducible morphisms abstract we study the degree of irreducible morphisms in generalized standard convex components of the auslander reiten quiver of an artin algebra with the property that paths with the same origin and end vertices have equal length we call the components with this last property components with length in particular we give two criteria to determine wether the degree of such an irreducible morphism f is finite or infinite one of them is given in terms of the compositions of f with non zero maps between modules in the component the other states that the left degree of an irreducible map f is finite if and only if ker f belongs to the component we apply our results to irreducible morphisms over artin algebras of finite representation type and over tame hereditary algebras

combinatorial and hypergeometric identities via the legendre polynomials a computational approach in this paper old and new combinatorial and hypergeometric identities are obtained via the legendre polynomials as one of the most commonly used orthogonal polynomials the results are tested using maple computer algebra system cas

distribution of the time to explosion for one dimensional diffusions we study the distribution of the time to explosion for one dimensional diffusions we relate this question to the computation of expectations of suitable nonnegative local martingales moreover we characterize the distribution function of the time to explosion as the minimal solution to a certain cauchy problem for an appropriate parabolic differential equation this leads to alternative characterizations of feller s criterion for explosions we discuss in detail several examples for which it is possible to obtain analytic expressions for the corresponding distribution of the time to explosion using the methodologies developed in the paper

schurian sp representation finite right peak pi rings and their indecomposable socle projective modules such that soc r is an essential right ideal in r and it is isomorphic to a direct sum of finitely many copies of p called a right peak of r here f f are local rings f f is a division ring imj is an fi fj bimodule and the multiplication in r is given by fi f bimodule maps cii imj im jm satisfying the natural associativity conditions we denote by p p p the right indecomposable row ideals of r

almost laura algebras abstract in this paper we propose a generalization for the class of laura algebras called almost laura we show that this new class of algebras retains most of the essential features of laura algebras especially concerning the important role played by the non semiregular components in their auslander reiten quivers also we study more intensively the left supported almost laura algebras showing that these are characterized by the presence of a generalized standard convex and faithful component finally we prove that almost laura algebras behave well with respect to full subcategories split by nilpotent extensions and skew group algebras

an overdetermined problem of anisotropic equations in convex cones abstract in this paper we study some overdetermined boundary value problems for anisotropic elliptic pdes in a bounded domain in a convex cone of r n by using some integral identities and maximum principle we prove the corresponding wulff shape characterizations which includes the classical serrin s overdetermined boundary value problem

entire solutions of semilinear elliptic equations in r 3 and a conjecture of de giorgi this paper is concerned with the study of bounded solutions of semilinear elliptic equations u f u in the whole space r under the assumption that u is monotone in one direction say nu in r n the goal is to establish the one dimensional character or symmetry of u namely that u only depends on one variable or equivalently that the level sets of u are hyperplanes this type of symmetry question was raised by de giorgi in who made the following conjecture we quote literally page of dg

exceptional sequences and clusters abstract we show that exceptional sequences for hereditary algebras are characterized by the fact that the product of the corresponding reflections is the inverse coxeter element in the weyl group we use this result to give a new combinatorial characterization of clusters tilting sets in the cluster category in the case where the hereditary algebra is of finite type

random walks with similar transition probabilities we consider random walks on the nonnegative integers with a possible absorbing state at 1 a random walk is called similar to a random walk x if there exist constants cij such that for the corresponding n step transition probabilities pij n ncijpij n i j 0 hold we give necessary and sufficient conditions for the similarity of two random walks both in terms of the parameters and in terms of the corresponding spectral measures which appear in the spectral representation of the n step transition probabilities developed by karlin and mcgregor

noetherianity and gelfand kirillov dimension of components abstract the category of all additive functors mod mod for a finite dimensional algebra were shown to be left noetherian if and only if is of finite representation type by m auslander here we consider the category of all additive graded functors from the category of associated graded category of mod to graded vector spaces this category decomposes into subcategories corresponding to the components of the auslander reiten quiver for a regular component we show that the corresponding graded functor category is left noetherian if and only if the section of the component is extended dynkin or infinite dynkin

geometry and topology of some overdetermined elliptic problems we study necessary conditions on the geometry and the topology of domains in r2 that support a positive solution to a classical overdetermined elliptic problem u f u 0in u 0on u constanton the ideas and tools we use come from constant mean curvature surface theory in particular we obtain a partial answer to a question posed by h berestycki l caffarelli and l nirenberg in 1997 we investigate also some boundedness properties of the solution u some of our results generalize to higher dimensions

the relationship between homological properties and representation theoretic realization of artin algebras we will study the relationship of quite different object in the theory of artin algebras namely auslander regular rings of global dimension two torsion theories categories and almost abelian categories we will apply our results to characterization problems of auslander reiten quivers 0 1 there exists a bijection between equivalence classes of krull schmidt categories c with additive generators m and morita equivalence classes of semiperfect rings which is given by c 7 c m m and the converse is given by 7 pr for the category pr of finitely generated projective modules although th is bijection itself is rather formal it will be very fruitful to study the relationship of a d below the object of this paper is to study it under the assumption that is an arti n algebra

automorphisms of representation finite algebras coverings in representation theory have been successfully used by bongartzgabriel 2 gabriel 3 green 4 riedtman 6 7 of particular importance is the study of the relations between the coverings of the auslander reiten quiver and the ordinary quiver in this direction p gabriel posed in the third international conference on representations of algebras puebla m6xico 1980 the following conjecture let g be an automorphism of an algebra a of finite representation type for each right module m denote by m g the a module with underlying group m and scalar multiplication m 2 mgl 2 if sgq s for each simple s then m g q m for each indecomposable m the aim of this note is to give a short proof of this statement the conjecture is not true for algebras of infinite representation type con

the cartan map on categories of graded modules this paper presents a technique based on elementary k theory it relies on the fact that k for a category of graded modules can be viewed as a z t t l module for some variable t in this context we will deduce a great deal of information from an explicit computation of the coordinates of the matrix of the cartan homomorphism in section 1 we begin by recalling some definitions and results that we will use throughout this paper from these we then describe our basic machinery section 2 will provide some applications of this machine we note in particular the following uses nakayama 131 proposed that if a is a finite dimensional algebra of infinite dominant dimension then a is self injective auslander and reiten 4 noticed that the following stronger statement would imply the truth of nakayama s conjecture given a finite dimensional algebra a with minimal injective resolution 0 a e e se every indecomposable injective module is isomorphic to a summand of some ei here we prove this generalized nakayama conjecture for graded algebras another application of this technique shows that the determinant of the cartan map is one for graded algebras of finite global dimension this in turn is used to show that if b is any algebra not necessarily graded with only finitely many nonisomorphic indecomposable modules m 1 m then the matrix whose ijth coordinate is dim hom mi mj has determinant one finally we give an application to the rationality of power series let f be a field and let a be a finite dimensional f algebra we will assume everywhere that a is basic that is for every simple a module s end s f this assumption is primarily to simplify notation and the arguments given could be modified to handle algebras that are not basic we will use the notation mod a for the category of finitely generated left a modules let g be a full subcategory of mod 4 and let x 55 be the free 390 0021 8693 83 3 00

on partially and globally overdetermined problems of elliptic type we consider some elliptic pdes with dirichlet and neumann data prescribed on some portion of the boundary of the domain and we obtain rigidity results that give a classication of the solution and of the domain in particular we nd mild conditions under which a partially overdetermined problem is in fact globally overdetermined this enables to use several classical results in order to classify all the domains that admit a solution of suitable general partially overdetermined problems these results may be seen as solutions of suitable inverse problems that is to say given that an overdetermined system possesses a solution we nd the shape of the admissible domains models of these type arise in several areas of mathematical physics and shape optimization

minimal model of ginzburg algebras abstract we compute the minimal model for ginzburg algebras associated to acyclic quivers q in particular we prove that there is a natural grading on the ginzburg algebra making it formal and quasi isomorphic to the preprojective algebra in non dynkin type and in dynkin type is quasi isomorphic to a twisted polynomial algebra over the preprojective with a unique higher a composition to prove these results we construct and study the minimal model of an a envelope of the derived category d b q whose higher compositions encode the triangulated structure of d b q

covering functors without groups coverings in the representation theory of algebras were introduced for the auslander reiten quiver of a representation finite algebra in ch riedtmann algebren darstellungskocher uberlagerungen und zuruch comment math helv 55 1980 199 224 and later for finite dimensional algebras in k bongartz p gabriel covering spaces in representation theory invent math 65 3 1982 331 378 p gabriel the universal cover of a representation finite algebra in proc representation theory i puebla 1980 in lecture notes in math vol 903 springer 1981 pp 68 105 r martinez villa j a de la pena the universal cover of a quiver with relations j pure appl algebra 30 3 1983 277 292 the best understood class of covering functors is that of galois covering functors f a b determined by the action of a group of automorphisms of a in this work we introduce the balanced covering functors which include the galois class and for which classical galois covering type results still hold for instance if f a b is a balanced covering functor where a and b are linear categories over an algebraically closed field and b is tame then a is tame

graded artin algebras rational series and bounds for homological dimensions is a minimal injective resolution of a then all the i are projective then n is selfinjecrive it is of interest to note that the nakayama conjecture follows in a trivial way from the finitistic dimension conjecture this one says the following let n be an artin algebra then sup proj dim m proj dimm oc is finite where m ranges over the finitely generated amodules the finitistic projective dimension has its origins in the early 1960s and was formulated from results of rosenberg and zelinsky in this paper we study the behavior or certain rational power series associated to every graded module over a graded finite dimensional algebra series which are slightly different from the usual poincare betti series it is interesting to note that rationality is enough to enable us to prove that over a graded finite dimensional algebra the linitistic projective dimension is finite over the class of finitely generated graded modules whose nonprojective syzygies have no projective summands this implies the nakayama conjecture for graded algebras see also wilson 3 also using rationality we find bounds for global dimension in terms of graded length and the number of nonisomorphic simple modules finally let a be an algebra of finite representation type having n nonisomorphic indecomposable modules we prove that every composition of more than 2n 2 nonisomorphisms of amodules is zero this is done by using the result of auslander reiten which states that every nonzero homomorphism which is not an isomorphism is a sum of compositions of irreducible morphisms

total variation cutoff in birth and death chains the cutoff phenomenon describes a case where a markov chain exhibits a sharp transition in its convergence to stationarity diaconis proc natl acad sci usa 93 4 1659 1664 1996 surveyed this phenomenon and asked how one could recognize its occurrence in families of finite ergodic markov chains peres american institute of mathematics aim research workshop palo alto http www aimath org wwn mixingtimes 2004 noted that a necessary condition for cutoff in a family of reversible chains is that the product of the mixing time and spectral gap tends to infinity and conjectured that in many settings this condition should also be sufficient diaconis and saloff coste ann appl probab 16 4 2098 2122 2006 verified this conjecture for continuous time birth and death chains started at an endpoint with convergence measured in separation it is natural to ask whether the conjecture holds for these chains in the more widely used total variation distance in this work we confirm the above conjecture for all continuous time or lazy discrete time birth and death chains with convergence measured via total variation distance namely if the product of the mixing time and spectral gap tends to infinity the chains exhibit cutoff at the maximal hitting time of the stationary distribution median with a window of at most the geometric mean between the relaxation time and mixing time in addition we show that for any lazy or continuous time birth and death chain with stationary distribution the separation 1 p t x y y is maximized when x y are the endpoints together with the above results this implies that total variation cutoff is equivalent to separation cutoff in any family of such chains

on the composite of two irreducible morphisms in radical cube abstract we study here when there are irreducible morphisms h x y and h y z between indecomposable modules such that the composite h h is a non zero morphism in r 3 x z in particular we characterize the representation finite string algebras and the tilted algebras having such irreducible morphisms

flattening results for elliptic pdes in unbounded domains with applications to overdetermined problems semilinear elliptic pdes are dealt with either in the half space or in overdetermined settings we obtain several new results and also give new proofs of celebrated theorems by exploiting some geometric analysis of level sets a geometric inequality and a pointwise gradient estimate

weighted sums of orthogonal polynomials with positive zeros we study the two sequences of polynomials which arise as denominators of the approximants of even and odd order respectively of a stieltjes fraction and which may be defined alternatively as a sequence of orthogonal polynomials with positive zeros and the associated sequence of kernel polynomials motivated by problems in the setting of birth death processes where these sequences play a major role we focus on the asymptotic behaviour of the sequences and establish convergence of certain weighted sums of the polynomials at hand

extremal domains on hadamard manifolds abstract we investigate the geometry and topology of extremal domains in a hadamard manifold i e domains that support a positive solution to an overdetermined elliptic problem oep first we study narrow properties of such domains and characterize the boundary at infinity we give an upper bound for the hausdorff dimension of its boundary at infinity and how the domain behaves at infinity this shows interesting relations with the singular yamabe problem later we focus on extremal domains in the hyperbolic space symmetry and boundedness properties will be shown in a certain sense we extend levitt rosenberg s theorem to oeps which suggests a strong relation with constant mean curvature hypersurfaces in particular we are able to prove the berestycki caffarelli nirenberg conjecture under certain assumptions either on the boundary at infinity of the extremal domain or on the oep itself also a height estimate for solutions on extremal domains in a hyperbolic space will be given

d representation finite self injective algebras abstract in this paper we initiate the study of higher dimensional auslander reiten theory of self injective algebras we give a systematic construction of weakly d representation finite self injective algebras as orbit algebras of the repetitive categories of algebras of finite global dimension satisfying a certain finiteness condition for the serre functor the condition holds in particular for all fractionally calabi yau algebras of global dimension at most d this generalizes riedtmann s classical construction of representation finite self injective algebras our method is based on an adaptation of gabriel s covering theory for k linear categories to the setting of higher dimensional auslander reiten theory applications include n fold trivial extensions and classical and higher preprojective algebras which are shown to be d representation finite in many cases we also get a complete classification of all d representation finite self injective nakayama algebras for arbitrary d

degrees of irreducible morphisms in coherent almost cyclic auslander reiten components abstract we study the finiteness of degrees of irreducible morphisms between indecomposable modules lying in coherent almost cyclic components of auslander reiten quivers of artin algebras

generalized gamma convolutions and complete monotonicity lete be the class ofpdf sf on 0 such that for eachu 0 f uv f u v is completely monotone as a function ofw v v 1 this class includes many familiarpdf s and is closed with respect to multiplication and division of independentrv s further e t wheret is the class of generalized gamma convolutions ggc introduced by o thorin moreover e coincides with the class ofpdf s of the form c cdot x beta 1 cdot mathop pi limits i 1 n 1 c i x y i all parameters positive or limits thereof the laplace transform of aggc is characterized by complete monotonicity of uv u v as a function ofw this characterization has many consequences and applications it follows that also the classt has simple multiplicative properties

ratio limits and limiting conditional distributions for discrete time birth death processes we consider discrete time birth death processes with an absorbing state and study the conditional state distribution at time n given that absorption has not occurred by that time but will occur eventually in particular we establish conditions for the convergence of these distributions to a proper distribution as n the problem turns out to be closely related to that of finding conditions for the existence of limits of ratios of n step transition probabilities as n orthogonal polynomials feature in the spectral representation for the n step transition probabilities of a birth death process and consequently play a key role in the analysis

the left and the right parts of a module category abstract in this paper we study for an artin algebra the class l a and r a which is a full subcategory of the category moda of finitely generated a modules and which consists of all indecomposable a modules whose predecessors and successors have projective dimension and injective dimension respectively at most one we consider quotient algebras of a which contain the information on these classes then define and characterize those algebras for which the class is l a is contravariantly finite and r a is covariantly finite respectively