rational singularities and almost split sequences the main aim of this paper is to relate almost split sequences to singularity theory by showing that the mckay quiver built from the finite dimen sional representations of a finite subgroup g of gl 2 c where c is the complex numbers is isomorphic to the ar quiver of the reflexive modules of the quotient singularity associated with g over the past decade almost split sequences have been playing an increasingly important role in the representation theories of finite dimensional algebras and classical orders see 5 and 3 8 for basic existence theorems in these contexts while they have been known for some time to exist in higher dimensional situations 3 it has not been at all clear how they related to singularity theory if at all the main aim of this paper is to relate almost split sequences to singularity theory by showing that the mckay quiver built from the fimte dimensional complex represen tations of a finite subgroup g of gl 2 c where c is the complex numbers is isomorphic to the ar quiver of the reflexive modules over the quotient singularity r associated with g as in the case of finite dimensional algebras the ar quiver of reflexive r modules is defined in terms of the almost split sequences of reflexive r modules in the case g c sl 2 c mckay observed that the underlying graph of the mckay quiver with the trivial module removed is isomorphic to the desingulariza tion graph of the associated singularity various explanations of this phenomenon have been given by knorrer gonzalez sprinberg verdier 6 and artin verdier 1 which along the way have established most explicitly in 1 a natural one to one correspondence between the indecomposable reflexive r modules and the nodes of the desingularization graph but why the almost split sequences describe the edge of the desingularization graph still remains to be explained an effort has been made to make this paper as self contained as possible in particular no prior knowledge of almost split sequences is required before describing the contents of the six sections of this paper we fix some notation throughout this paper g is a finite group k an algebraically closed field of characteristic not dividing the order of g and v a two dimensional k representation of g setting s k x y the k algebra of formal power series the two dimen sional representation v gives a linear action of g on s as a group of k algebra automorphisms we denote by s g the skew group ring given by this action

incompressible limit of the degenerate quantum compressible navier stokes equations with general initial data abstract in this paper we study the incompressible limit of the degenerate quantum compressible navier stokes equations in a periodic domain t 3 and the whole space r 3 with general initial data in the periodic case by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity we prove rigorously that the gradient part of the weak solutions velocity of the degenerate quantum compressible navier stokes equations converge to the strong solution of the incompressible navier stokes equations our results improve considerably the ones obtained by yang ju and yang 25 where only the well prepared initial data case is considered while for the whole space case thanks to the strichartz s estimates of linear wave equations we can obtain the convergence of the weak solutions of the degenerate quantum compressible navier stokes equations to the strong solution of the incompressible navier stokes euler equations with a linear damping term moreover the convergence rates are also given

lp zd estimates for discrete operators of radon type maximal functions and vector valued estimates abstract we prove l p z d bounds for p 1 of discrete maximal functions corresponding to averaging operators and truncated singular integrals of radon type and their applications to pointwise ergodic theory our new approach is based on a unified analysis of both types of operators and also yields an extension to the vector valued form of these results

harmonic analysis on nilpotent groups and singular integrals ii singular kernels supported on submanifolds on etudie des operateurs de convolution singuliers sur des groupes de lie nilpotents generaux et plus specifiquement des operateurs dont les noyaux ont pour supports des varietes de faible dimension et qui peuvent aussi contenir des facteurs polynomiaux exponentiels oscillatoires

local rings of finite cohen macaulay type abstract let r m be a local cohen macaulay ring whose m adic completion r has an isolated singularity we verify the following conjecture of f o schreyer r has finite cohen macaulay type if and only if r has finite cohen macaulay type we also show that the hypersurface k x 0 x d f has finite cohen macaulay type if and only if k s x 0 x d f has finite cohen macaulay type where k s is the separable closure of the field k

vanishing capillarity limit of the compressible non isentropic navier stokes korteweg system to navier stokes system abstract in this paper we consider the three dimensional compressible nonisentropic fluid model of korteweg type we mainly present the vanishing capillarity limit of smooth solution to the initial value problem based on the uniform estimates with respect to the capillary coefficient we show the unique smooth solutions of the three dimensional korteweg model converges globally in time to the smooth solution of the three dimensional compressible nonisentropic navier stokes system as tends to zero also we give the convergence rate estimates in h 2 norm with respect to

classifying thick subcategories of the stable category of cohen macaulay modules abstract various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics in this paper as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p group due to benson carlson and rickard we consider classifying thick subcategories of the stable category of cohen macaulay modules over a gorenstein local ring the main result of this paper yields a complete classification of the thick subcategories of the stable category of cohen macaulay modules over a local hypersurface in terms of specialization closed subsets of the prime ideal spectrum of the ring which are contained in its singular locus

non commutative crepant resolution of minimal nilpotent orbit closures of type a and mukai flops abstract in this article we construct a non commutative crepant resolution nccr of a minimal nilpotent orbit closure b 1 of type a and study relations between an nccr and crepant resolutions y and y of b 1 more precisely we show that the nccr is isomorphic to the path algebra of the double beilinson quiver with certain relations and we reconstruct the crepant resolutions y and y of b 1 as moduli spaces of representations of the quiver we also study the kawamata namikawa s derived equivalence between crepant resolutions y and y of b 1 in terms of an nccr we also show that the p twist on the derived category of y corresponds to a certain operation of the nccr which we call multi mutation and that a multi mutation is a composition of iyama wemyss s mutations

existence of global weak solutions for a 2d viscous shallow water equations and convergence to the quasi geostrophic model we consider a two dimensional viscous shallow water model with friction term existence of global weak solutions is obtained and convergence to the strong solution of the viscous quasi geostrophic equation with free surface term is proven in the well prepared case the ill prepared data case is also discussed

singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation abstract a short time existence theorem is proven for the initial boundary value problem for a class of quasilinear symmetric hyperbolic systems containing a constant coefficient spatial operator multiplied by a large parameter solutions u are shown to remain bounded independently of for a time independent of provided that u 0 and u l 0 are bounded independently of and certain structural conditions are satisfied this result is applied to the quasigeostrophic approximation of the shallow water equations and the constant pressure approximation in combustion and solutions for these cases are shown to converge to solutions of limiting equations as

tilting and cluster tilting for quotient singularities we shall show that the stable categories of graded cohen macaulay modules over quotient singularities have tilting objects in particular these categories are triangle equivalent to derived categories of finite dimensional algebras our method is based on higher dimensional auslander reiten theory which gives cluster tilting objects in the stable categories of ungraded cohen macaulay modules

observations on the f signature of local rings of characteristic p abstract let r m k be a d dimensional noetherian reduced local ring of prime characteristic p such that r 1 p e are finite over r for all e n i e r is f finite consider the sequence a e q r d e 0 in which r log p k k p q p e and a e is the maximal rank of free r modules appearing as direct summands of r module r 1 q denote by s r and s r the liminf and limsup respectively of the above sequence as e if s r s r then the limit denoted by s r is called the f signature of r it turns out that the f signature can be defined in a way that is independent of the module finite property of r 1 q over r we show that 1 if s r 1 1 d p d then r is regular 2 if r is excellent such that r p is gorenstein for every p spec r m then s r exists 3 if r m s n is a local flat ring homomorphism then s r s s and if furthermore s m s is gorenstein s s s r s s m s

maximal orders in unramified central simple algebras this is the author s version of a work that was accepted for publication in journal of algebra changes resulting from the publishing process such as peer review editing corrections structural formatting and other quality control mechanisms may not be reflected in this document changes may have been made to this work since it was submitted for publication a definitive version was subsequently published in journal of algebra 2016 452 94 105 doi 10 1016 j jalgebra 2015 12 006

incompressible limit of a compressible micropolar fluid model with general initial data abstract in this paper we consider the incompressible limit of a compressible micropolar fluid model with general initial data in the whole space r 3 it is proved that as the mach number goes to zero the weak solutions of the compressible micropolar fluids converge to the strong solution of the ideal incompressible micropolar fluids as long as the latter exists moreover the rate of convergence is also obtained

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

picard groups for derived module categories we introduce in this paper a generalization of picard groups to derived cat egories of algebras we study general properties of those groups and we construct braid group actions on these groups for particular classes of algebras

global well posedness and long time dynamics for a higher order quasi geostrophic type equation abstract in this paper we study a higher order viscous quasi geostrophic type equation this equation was derived in 11 as the limit dynamics of a singularly perturbed navier stokes korteweg system with coriolis force when the mach rossby and weber numbers go to zero at the same rate the scope of the present paper is twofold first of all we investigate well posedness of such a model on the whole space r 2 we prove that it is well posed in h s for any s 3 globally in time interestingly enough we show that this equation owns two levels of energy estimates for which one gets existence and uniqueness of weak solutions with different regularities namely h 3 and h 4 regularities this fact can be viewed as a remainder of the so called bd entropy structure of the original system in the second part of the paper we investigate the long time behavior of these solutions we show that they converge to the solution of the corresponding linear parabolic type equation with same initial datum and external force our proof is based on dispersive estimates both for the solutions to the linear and non linear problems

effective velocity in compressible navier stokes equations with third order derivatives abstract a formulation of certain barotropic compressible navier stokes equations with third order derivatives as a viscous euler system is proposed by using an effective velocity variable the equations model for instance viscous korteweg or quantum navier stokes flows the formulation in the new variable allows for the derivation of an entropy identity which is known as the bd bresch desjardins entropy equation as a consequence of this estimate a new global in time existence result for the one dimensional quantum navier stokes equations with strictly positive particle densities is proved

singular derived categories of factorial terminalizations and maximal modification algebras abstract let x be a gorenstein normal 3 fold satisfying elf with local rings which are at worst isolated hypersurface e g terminal singularities by using the singular derived category d sg x and its idempotent completion d sg x we give necessary and sufficient categorical conditions for x to be q factorial and complete locally q factorial respectively we then relate this information to maximal modification algebras mmas introduced in 20 by showing that if an algebra is derived equivalent to x as above then x is q factorial if and only if is an mma thus all rings derived equivalent to q factorial terminalizations in dimension three are mmas as an application we extend some of the algebraic results in 6 and 14 using geometric arguments

discrete analogues in harmonic analysis i l 2 estimates for singular radon transforms this paper studies the discrete analogues of singular radon transforms we prove the 2 boundedness for those operators that are quasi translation invariant the approach used is related to the circle method of hardy and littlewood and requires multi dimensional extensions of weyl sums and gauss sums as well as variants that replace scalar sums by operator sums 1 introduction the purpose of this paper is to study discrete analogues of singular radon transforms their analysis will involve considerations originating in analytic number theory related to the circle method of hardy and littlewood and necessitates an extension of the notion of weyl sums and gauss sums this will require that we pass from the usual setting of scalar valued sums to certain operator analogues of these sums

singular and maximal radon transforms analysis and geometry part 2 geometric theory 8 curvature introduction 8 1 three notions of curvature 8 2 theorems 8 3 examples 9 curvature some details 9 1 the exponential representation 9 2 diffeomorphism invariance 9 3 curvature condition cy 9 4 two lemmas 9 5 double fibration formulation 10 equivalence of curvature conditions 10 1 invariant submanifolds and deficient lie algebras 10 2 vanishing jacobians 10 3 construction of invariant submanifolds

the mckay correspondence as an equivalence of derived categories the classical mckay correspondence relates representations of a finite subgroup g sl 2 c to the cohomology of the well known minimal resolution of the kleinian singularity c2 g gonzalez sprinberg and verdier 10 interpreted the mckay correspondence as an isomorphism on k theory observing that the representation ring of g is equal to the g equivariant k theory of c2 more precisely they identify a basis of the k theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of g

higher nakayama algebras i construction we introduce higher dimensional analogues of the nakayama algebras from the viewpoint of iyama s higher auslander reiten theory more precisely for each nakayama algebra a and each positive intege

existence and asymptotic behavior of multi dimensional quantum hydrodynamic model for semiconductors this paper is devoted to the study of the existence and the time asymptotic of multi dimensional quantum hydrodynamic equations for the electron particle density the current density and the electrostatic potential in spatial periodic domain the equations are formally analogous to classical hydrodynamics but differ in the momentum equation which is forced by an additional nonlinear dispersion term due to the quantum bohm potential and are used in the modelling of quantum effects on semiconductor devices we prove the local in time existence of the solutions in the case of the general nonconvex pressure density relation and large and regular initial data furthermore we propose a subsonic type stability condition related to one of the classical hydrodynamical equations when this condition is satisfied the local in time solutions exist globally in time and converge time exponentially toward the corresponding steady state since for this problem classical methods like for instance the friedrichs theory for symmetric hyperbolic systems cannot be used we investigate via an iterative procedure an extended system which incorporates the one under investigation as a special case in particular the dispersive terms appear in the form of a fourth order wave type equation

examples of non commutative crepant resolutions of cohen macaulay normal domains abstract let a be a cohen macaulay normal domain a non commutative crepant resolution nccr of a is an a algebra of the form end a m where m is a reflexive a module is maximal cohen macaulay as an a module and gldim p dim a p for all primes p of a we give bountiful examples of equi characteristic cohen macaulay normal local domains and mixed characteristic cohen macaulay normal local domains having nccr we also give plentiful examples of affine cohen macaulay normal domains having nccr

decent intersection and tor rigidity for modules over local hypersurfaces first published in transactions of the american mathematical society in 2013 published by the american mathematical society also available electronically from http www ams org journals tran 2013 365 06 s0002 9947 2012 05574 7 home html

three dimensional flops and noncommutative rings limburgs univ ctr dept math b 3590 diepenbeek belgium van den bergh m limburgs univ ctr dept math univ campus b 3590 diepenbeek belgium vdbergh luc ac be

gorenstein and totally reflexive orders abstract in this paper we study orders over cohen macaulay rings we discuss the properties needed for these orders to give noncommutative crepant resolutions of the base rings namely we want algebraic analogs of birationality nonsingularity and crepancy while some definitions have been made we discuss an alternate definition and obstructions to the existence of such objects we then give necessary and sufficient conditions for an order to have certain desirable homological properties we examine examples of rings satisfying these properties to prove that certain endomorphism rings over abelian quotient singularities have infinite global dimension

ascent of finite cohen macaulay type in 1987 f o schreyer conjectured that a local ring r has finite cohen macaulay type if and only if the completion r has finite cohen macaulay type we prove the conjecture for excellent cohen macaulay local rings and also show by example that it can fail in general

characterization of completions of unique factorization domains it is shown that a complete local ring is the completion of a unique factorization domain if and only if it is a field a discrete valuation ring or it has depth at least two and no element of its prime ring is a zerodivisor it is also shown that the normal chain conjecture is false and that there exist local noncatenary ufds

low dimensional orders of finite representation type in this paper we study noncommutative surface singularities arising from orders the singularities we study are mild in the sense that they have finite representation type or equivalently are log terminal in the sense of the mori minimal model program for orders chan and ingalls in invent math 161 2 427 452 2005 these were classified independently by artin in terms of ramification data and reiten van den bergh in terms of their ar quivers the first main goal of this paper is to connect these two classifications by going through the finite subgroups g subset mathrm gl 2 explicitly computing h 2 g k and then matching these up with artin s list of ramification data and reiten van den bergh s ar quivers this provides a semi independent proof of their classifications and extends the study of canonical orders in chan et al proc lond math soc 3 98 1 83 115 2009 to the case of log terminal orders a secondary goal of this paper is to study noncommutative analogues of plane curves which arise as follows let b k zeta llbracket x y rrbracket be the skew power series ring where zeta is a root of unity or more generally a terminal order over a complete local ring we consider rings of the form a b f where f in z b which we interpret to be the ring of functions on a noncommutative plane curve we classify those noncommutative plane curves which are of finite representation type and compute their ar quivers

flops and equivalences of derived categories for threefolds with only terminal gorenstein singularities the main purpose of this paper is to show that bridgeland s moduli space of perverse point sheaves for certain flopping contractions gives the flops and the fourier mukai transform given by the birational correspondence of the flop is an equivalence between bounded derived categories

ell p mathbb z boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems we establish the first pointwise ergodic theorems along thin sets of prime numbers a set with zero density with respect to the primes for instance we will be able to achieve this with the piatetski shapiro primes our methods will be robust enough to solve the ternary goldbach problem for some thin sets of primes

finite gorenstein representation type implies simple singularity let r be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive r modules we prove that if this set is finite then either it has exactly one element represented by the rank 1 free module or r is gorenstein and an isolated singularity if r is complete then it is even a simple hypersurface singularity the crux of our proof is to argue that if the residue field has a totally reflexive cover then r is gorenstein or every totally reflexive r module is free

a nilpotent roth theorem let t and s be invertible measure preserving transformations of a probability measure space x we prove that if the group generated by t and s is nilpotent then lim n ras infty frac 1 n sum n 1 n u t n x v s n x exists in l 2 norm for any u v l x we also show that for a with a 0 one has lim n ras infty frac 1 n sum n 1 n mu a cap t n a cap s n a 0 by the way of contrast we bring examples showing that if measure preserving transformations t s generate a solvable group then i the above limits do not have to exist ii the double recurrence property fails that is for some a a 0 one may have a t n a s n a 0 for all n finally we show that when t and s generate a nilpotent group of class c lim n ras infty frac 1 n sum n 1 n u t n x v s n x int ud mu int vd mu in l 2 x for all u v l x if and only if t s is ergodic on x x and the group generated by t 1 s t 2 s 2 t c s c acts ergodically on x

discrete fractional integral operators with binary quadratic forms as phase polynomials abstract we give estimates on discrete fractional integral operators along binary quadratic forms these operators have been studied for 30 years starting with the investigations of arkhipov and oskolkov but efforts have concentrated on cases where the phase polynomial is translation invariant or quasi translation invariant this work presents the first results for operators with neither translation invariant nor quasi translation invariant phase polynomials

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

contraction algebra and singularity of three dimensional flopping contraction donovan and wemyss duke math j 165 8 1397 1474 2016 introduced the contraction algebra of flopping curves in threefold they conjectured that the contraction algebra determines the formal neighborhood of the underlying singularity of the contraction in this paper we prove that the contraction algebra together with its natural a infty structure constructed in hua and toda int math res not rnw333 2017 determine the formal neighborhood of the singularity

highly rotating viscous compressible fluids in presence of capillarity effects we study here a singular limit problem for a navier stokes korteweg system with coriolis force in the domain mathbb r 2 times 0 1 and for general ill prepared initial data taking the mach and the rossby numbers proportional to a small parameter varepsilon rightarrow 0 we perform the incompressible and high rotation limits simultaneously moreover we consider both the constant and vanishing capillarity regimes in this last case the limit problem is identified as a 2 d incompressible navier stokes equation in the variables orthogonal to the rotation axis if the capillarity is constant instead the limit equation slightly changes keeping however a similar structure due to the presence of an additional surface tension term in the vanishing capillarity regime various rates at which the capillarity coefficient goes to 0 are considered in general this produces an anisotropic scaling in the system the proof of the results is based on suitable applications of the rage theorem combined with microlocal symmetrization arguments

on the noncommutative bondal orlov conjecture let r be a normal equi codimensional cohen macaulay ring of dimension d 2 with a canonical module r we give a sufficient criterion that establishes a derived equivalence between the noncommutative crepant resolutions of r when d 3 this criterion is always satisfied and so all noncommutative crepant resolutions of r are derived equivalent our method is based on cluster tilting theory for commutative algebras developed by iyama and wemyss 2010

discrete radon transforms and applications to ergodic theory we prove lp boundedness of certain non translation invariant discrete maximal radon transforms and discrete singular radon transforms we also prove maximal pointwise and lp ergodic theorems for certain families of non commuting operators

low mach number limit of viscous compressible flows in the whole space this paper is devoted to the low mach number limit of weak solutions to the compressible navier stokes equations for isentropic fluids in the whole space r d d 2 or 3 this problem was investigated by p l lions and n masmoudi we present here a different approach based upon strichartz s estimates for the linear wave equation in the inviscid case which improves the convergence result and simplifies the proof we prove that the velocity field is strongly compact and converges to a global weak solution of the incompressible navier stokes equations

mutations vs seiberg duality abstract for a quiver with potential derksen weyman and zelevinsky defined in h derksen j weyman a zelevinsky quivers with potentials and their representations i mutations arxiv 0704 0649v2 math ra a combinatorial transformation mutations mukhopadhyay and ray on the other hand tell us how to compute seiberg dual quivers for some quivers with potentials through a tilting procedure thus obtaining derived equivalent algebras in this text we compare mutations with the concept of seiberg duality given by s mukhopadhyay k ray seiberg duality as derived equivalence for some quiver gauge theories arxiv hep th 0309191v2 concluding that for a certain class of potentials the good ones mutations coincide with seiberg duality therefore giving derived equivalences

asymptotic limit for rotational quantum compressible navier stokes equations with multiple scales abstract in this paper we consider the degenerate quantum compressible navier stokes equations giving rise to a variety of mathematical problems in many areas we study the asymptotic limit for the rotational compressible navier stokes equations with quantum term and the ill prepared initial data

a mckay correspondence for reflection groups we construct a noncommutative desingularization of the discriminant of a finite reflection group g as a quotient of the skew group ring a s g if g is generated by order 2 reflections then this quotient identifies with the endomorphism ring of the reflection arrangement a g viewed as a module over the coordinate ring sg of the discriminant of g this yields in particular a correspondence between the nontrivial irreducible representations of g to certain maximal cohen macaulay modules over the coordinate ring sg these maximal cohen macaulay modules are precisely the nonisomorphic direct summands of the coordinate ring of the reflection arrangement a g viewed as a module over sg we identify some of the corresponding matrix factorizations namely the so called logarithmic co residues of the discriminant

classifying resolving subcategories over a cohen macaulay local ring let r be a cohen macaulay local ring denote by modr the category of finitely generated r modules in this paper we consider the classification problem of resolving subcategories of modr in terms of specialization closed subsets of specr we give a classification of the resolving subcategories closed under tensor products and transposes under restrictive hypotheses we also give better classification results

discrete maximal functions in higher dimensions and applications to ergodic theory we establish a higher dimensional counterpart of bourgain s pointwise ergodic theorem along an arbitrary integer valued polynomial mapping we achieve this by proving variational estimates v r on l p spaces for all 1

higher dimensional auslander reiten theory on maximal orthogonal subcategories abstract we introduce the concept of maximal n 1 orthogonal subcategories over artin algebras and orders and develop n 1 dimensional auslander reiten theory on them we give the n auslander reiten translation and the n auslander reiten duality then show the existence of n almost split sequences and n fundamental sequences we give some examples

maximal modifications and auslander reiten duality for non isolated singularities we first generalize classical auslander reiten duality for isolated singularities to cover singularities with a one dimensional singular locus we then define the notion of ct modules for non isolated singularities and we show that these are intimately related to noncommutative crepant resolutions nccrs when r has isolated singularities ct modules recover the classical notion of cluster tilting modules but in general the two concepts differ then wanting to generalize the notion of nccrs to cover partial resolutions of operatorname spec r in the main body of this paper we introduce a theory of modifying and maximal modifying modules under mild assumptions all the corresponding endomorphism algebras of the maximal modifying modules for three dimensional gorenstein rings are shown to be derived equivalent we then develop a theory of mutation for modifying modules which is similar but different to mutations arising in cluster tilting theory our mutation works in arbitrary dimension and in dimension three the behavior of our mutation strongly depends on whether a certain factor algebra is artinian

harmonic analysis on nilpotent groups and singular integrals i oscillatory integrals abstract this paper is devoted to the study of the operator given by where k is a standard calderon zygmund kernel and p is a real polynomial on r n r n we show t is bounded on lp to itself when 1

two theorems about maximal cohen macaulay modules this paper contains two theorems concerning the theory of maximal cohen macaulay modules the first theorem proves that certain ext groups between maximal cohen macaulay modules m and n must have finite length provided only finitely many isomorphism classes of maximal cohen macaulay modules exist having ranks up to the sum of the ranks of m and n this has several corollaries in particular it proves that a cohen macaulay local ring of finite cohen macaulay type has an isolated singularity a well known theorem of auslander gives the same conclusion but requires that the ring be henselian other corollaries of our result include statements concerning when a ring is gorenstein or a complete intersection on the punctured spectrum and the recent theorem of leuschke and wiegand that the completion of an excellent cohen macaulay local ring of finite cohen macaulay type is again of finite cohen macaulay type the second theorem proves that a complete local gorenstein domain of positive characteristic p and dimension d is f rational if and only if the number of copies of r splitting out of r 1 p e divided by p de has a positive limit this result generalizes work of smith and van den bergh we call this limit the f signature of the ring and give some of its properties

computation of depth in c x abstract we show that depth i 1 for each ideal i of c x this gives a positive answer to a conjecture in azarpanah et al 2019 3 the present article is in fact an attempt to complete the aforementioned paper using the above fact the depth of some ideals of c x such as principal ideals the ideals o p p x and prime ideals are determined in the sense that when they are 0 and when they are 1 we have generalized proposition 2 9 in that paper and we have shown that depth c x f is at most 1 for each principal ideal f in c x and it is exactly 1 if and only if int x z f contains at least one non almost p point also we prove that for each non essential principal ideal f depth c x f 1 or equivalently depth ann f 1 if and only if the set of non almost p points of x is dense in x finally it has been shown that depth o p 1 for each p x if and only if x contains at least two non almost p points and topological spaces x are characterized for which depth i 1 for each essential ideal of c x

an asymptotic limit of a navier stokes system with capillary effects a combined incompressible and vanishing capillarity limit in the barotropic compressible navier stokes equations for smooth solutions is proved the equations are considered on the two dimensional torus with well prepared initial data the momentum equation contains a rotational term originating from a coriolis force a general korteweg type tensor modeling capillary effects and a density dependent viscosity the limiting model is the viscous quasi geostrophic equation for the rotated velocity potential the proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms