electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate we consider a two dimensional problem of scattering of a time harmonic electromagnetic plane wave by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate the magnetic permeability is assumed to be a fixed positive constant in the media the material properties of the media are characterized completely by an index of refraction which is a bounded measurable function in the layer and a positive constant above the layer corresponding to a homogeneous dielectric medium in this paper we only examine the tm transverse magnetic polarization case a radiation condition is introduced and equivalence with a second kind lippmann schwinger type integral equation is shown with additional assumptions on the index of refraction in the layer uniqueness of solution is proved existence of solution is then established by employing a form of fredholm alternative using a general result on the solvability of integral equations on unbounded domains published earlier by chandler wilde and zhang an approximate analytic solution for the case of a thin inhomogeneous layer is obtained from the integral equation formulation and is used to show that if the index of refraction is appropriately chosen the scattered field can grow with distance from the plate

precovers and orthogonality in the stable module category abstract we show that any module admits a presentation as the quotient of a gorenstein projective module by a submodule which is itself right orthogonal with respect to the standard ext 1 pairing to the class of gorenstein projective modules of type fp for that purpose we use the concept of orthogonality in the stable module category and examine the orthogonal pair which is induced therein by the class of completely finitary gorenstein projective modules

cohen macaulay modules co torsion pairs and virtually gorenstein algebras abstract we use torsion pairs in stable categories and cotorsion pairs in modules categories to study in general infinitely generated cohen macaulay modules and a generalization of modules of finite projective or injective dimension over an artin algebra we concentrate our investigation to the study of virtually gorenstein algebras which provide a common generalization of gorenstein algebras and algebras of finite representation or cohen macaulay type this class of algebras on the one hand has rich homological structure and satisfies several representation torsion theoretic finiteness conditions and on the other hand it is closed under various operations for instance derived equivalences and stable equivalences of morita type in addition virtual gorensteinness provides a useful tool for the study of the gorenstein symmetry conjecture and modified versions of the telescope conjecture for module or stable categories

quantifying the effect of the surrogate marker by information gain statistical validation of a surrogate marker has been studied for more than a decade recently alonso et al 2004 biometrics 60 724 728 proposed a quantity called the likelihood reduction factor lrf to evaluate the validity of a surrogate marker however as pointed out in the present article the lrf may not correctly validate a surrogate marker therefore a new quantity the proportion of information gain pig using the kullback leibler information is proposed simulations show that under some model assumptions the pig precisely reflects the role of a surrogate marker

proper resolutions and gorenstein categories abstract let a be an abelian category and c an additive full subcategory of a we provide a method to construct a proper c resolution resp coproper c coresolution of one term in a short exact sequence in a from that of the other two terms by using these constructions we answer affirmatively an open question on the stability of the gorenstein category g c posed by sather wagstaff sharif and white and also prove that g c is closed under direct summands in addition we obtain some criteria for computing the c dimension and the g c dimension of an object in a

a categorification of biclosed sets of strings abstract we consider a closure space known as biclosed sets of strings of a gentle algebra of finite representation type palu pilaud and plamondon proved that the collection of all biclosed sets of strings forms a lattice and moreover that this lattice is congruence uniform many interesting examples of finite congruence uniform lattices may be represented as the lattice of torsion classes of an associative algebra we introduce a generalization the lattice of torsion shadows and we prove that the lattice of biclosed sets of strings is isomorphic to a lattice of torsion shadows when every indecomposable module over the gentle algebra is a brick finite congruence uniform lattices admit an alternate partial order known as the core label order in many cases the core label order of a congruence uniform lattice is isomorphic to a lattice of wide subcategories of an associative algebra analogous to torsion shadows we introduce wide shadows and prove that the core label order of the lattice of biclosed sets is isomorphic to a lattice of wide shadows

on the derivation of boundary integral equations for scattering by an infinite two dimensional rough surface a plane acoustic wave is incident upon an infinite rough impenetrable surface s the aim is to find the scattered field by deriving a boundary integral equation over s using green s theorem and the free space green s function this requires careful consideration of certain integrals over a large hemisphere of radius r it is known that these integrals vanish as r if the scattered field satisfies the sommerfeld radiation condition but that is not the case here reflected plane waves must be present it is shown that the well known helmholtz integral equation is not valid in all circumstances for example it is not valid when the scattered field includes plane waves propagating away from s along the axis of the hemisphere in particular it is not valid for the simplest possible problem of a plane wave at normal incidence to an infinite flat plane some suggestions for modified integral equations are discussed

acoustic scattering by mildly rough unbounded surfaces in three dimensions for a nonlocally perturbed half space we consider the scattering of time harmonic acoustic waves a second kind boundary integral equation formulation is proposed for the sound soft case based on a standard ansatz as a combined single and double layer potential but replacing the usual fundamental solution of the helmholtz equation with an appropriate half space green s function due to the unboundedness of the surface the integral operators are noncompact in contrast to the two dimensional case the integral operators are also strongly singular due to the slow decay at infinity of the fundamental solution of the three dimensional helmholtz equation in the case when the surface is sufficiently smooth lyapunov we show that the integral operators are nevertheless bounded as operators on l 2 gamma and on l 2 gamma cap bc gamma and that the operators depend continuously in norm on the wave number and on gamma we further show that for emph mild roughness i e a surface gamma which d

on the solvability of second kind integral equations on the real line abstract this paper considers general second kind integral equations of the form s r k s t t dt s in operator form k k where the functions k and are assumed known with y the space of bounded continuous functions on r and k such that the mapping s k s from r to l1 r is bounded and continuous the function y is the solution to be determined conditions on a set w bc r l1 r are obtained such that a generalised fredholm alternative holds if w satisfies these conditions and i k k is injective for all k w then i k k is also surjective for all k w and moreover the inverse operators i k k 1 on y are uniformly bounded for k w the approximation of the kernel in the integral equation by a sequence kn converging in a weak sense to k is also considered and results on stability and convergence are obtained these general theorems are used to establish results for two special classes of kernels k s t s t z t and k s t s t s t t where l1 r z l r and bc r 0 r kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces the general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period

the left and right parts of the module category of crossed product group algebras let g be a finite group k be a field with characteristic not dividing the order of g a nd b e at wistedkg module algebra such that g or g for short exists as a crossed product algebra in this paper we study the relationship between the class l g or r g which consists of all finitely generated indecomposable g modules whose predecessors or successors have projective dimension or injective dimension at most one and the class l or r then we study those properties which rely on the left or right part of that are preserved under the extension of crossed product group algebra g

the classification of uniserial sl 2 v m modules and a new interpretation of the racah wigner 6j symbol abstract all lie algebras and representations will be assumed to be finite dimensional over the complex numbers let v m be the irreducible sl 2 module with highest weight m 1 and consider the perfect lie algebra g sl 2 v m recall that a g module is uniserial when its submodules form a chain in this paper we classify all uniserial g modules the main family of uniserial g modules is actually constructed in greater generality for the perfect lie algebra g s v where s is a semisimple lie algebra and v is the irreducible s module with highest weight 0 the fact that the members of this family are but for a few exceptions of lengths 2 3 and 4 the only uniserial sl 2 v m modules depends in an essential manner on the determination of certain non trivial zeros of racah wigner 6j symbol

standardly stratified algebras and tilting abstract the concept of the characteristic tilting module and of the ringel dual for quasi hereditary algebras is generalized for the setting of standardly stratified algebras

tilting categories with applications to stratifying systems abstract in the study of standardly stratified algebras and stratifying systems we find an object which is either a tilting module or one whose properties strongly remind us of a tilting module this tilting module appeared already in dlab and ringel s work on quasi hereditary algebras see v dlab c m ringel the module theoretical approach to quasi hereditary algebras in repr theory and related topics in london math soc lecture note ser 168 1992 200 224 and c m ringel the category of modules with good filtrations over a quasi hereditary algebra has almost split sequences math z 208 1991 209 223 also this tilting module appears on the work on standardly stratified algebras of i agoston d happel e lukacs and l unger and in the paper of m i platzeck and i reiten see i agoston d happel e lukacs l unger standardly stratified algebras and tilting j algebra 226 2000 144 160 and m i platzeck i reiten modules of finite projective dimension for standardly stratified algebras comm algebra 29 3 2001 973 986 inspired by them we introduce the notion of tilting category in order to give a unified approach of these situations for stratifying systems to do so we use the ideas of m auslander o buchweitz and i reiten related to approximation theory see m auslander r o buchweitz the homological theory of maximal cohen macaulay approximations mem soc math fr n s 38 1989 5 37 m auslander i reiten applications of contravariantly finite subcategories adv math 86 1991 111 152

a well posed integral equation formulation for three dimensional rough surface scattering we consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft rough surface recently a brakhage werner type integral equation formulation of this problem has been proposed based on an ansatz as a combined single and double layer potential but replacing the usual fundamental solution of the helmholtz equation with an appropriate half space green s function moreover it has been shown in the three dimensional case that thi si ntegral equation is uniquely solvable in the space l 2 g when the scattering surface g does not differ too much from a plane in this paper we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope moreover we construct explicit bounds on the inverse of the associated boundary integral operator as a function of the wave number the parameter coupling the single and double layer potentials and the maximum surface slope these bounds show that the norm of the inverse operator is bounded uniformly in the wave number k f orko0 if the coupling parameter h is chosen proportional to the wave number in the case when g is a plane we show that the choice hzk 2 is nearly optimal in terms of minimizing the condition number

optimal filtrations on representations of finite dimensional algebras we present a representation theoretic description of the non empty strata in the hesselink stratification of the nullcone of representations of quivers we use this stratification to define optimal filtrations on representations of finite dimensional algebras as an application we investigate the isomorphism problem for uniserial representations 1 optimal filtrations 1 1 let a be a finite dimensional algebra over an algebraically closed field k in this paper we want to parameterize isomorphism classes of finite dimensional amodules having a specific jordan holder sequence in particular we want to relate the recent results of k bongartz and b huisgen zimmermann 3 4 1 on uniserial modules to the hesselink stratification of nullcones by morita theory we may reduce to the case that a is a basic algebra that is all simple a modules are one dimensional in this case we can write a as the quotient of the path algebra of a quiver and relate finite dimensional a modules to representations of this quiver 1 2 a quiver q is a directed graph on a finite set of vertices vl vn let aij be the number of directed arrows from vi to vj or loops if v vj the euler form of q is the bilinear form x z x zn z determined by the matrix x xij i j c mn z with entries xij 6ij aij clearly x encodes the structure of the directed graph q a representation v of a quiver q of dimension vector a al an e nn assigns to every arrow vi vj in q a matrix v q e majixi k the set of all a dimensional representations form an affine space

an efficient algorithm for electromagnetic scattering from rough surfaces using a single integral equation and multilevel sparse matrix canonical grid method an efficient algorithm for wave scattering from two dimensional lossy rough surfaces is proposed it entails the use of a single magnetic field integral equation smfie in conjunction with a multilevel sparse matrix canonical grid msmcg method the rao wilton glisson rwg triangular discretization is adopted to better model the rough surface than the pulse basis functions used in the well established smcg method using the smfie formulation only one unknown per interior edge of the triangular mesh approximating the rough surface is required and the iterative solution to the moment equation converges more rapidly than that of the conventional coupled equations for dielectric rough surfaces the msmcg method extends the applicability of the smcg method to rougher surfaces parallel implementation of the proposed method enables us to model dielectric surfaces up to a few thousand square wavelengths simulation results are presented as bistatic scattering coefficients for gaussian randomly rough surfaces

scattering by infinite one dimensional rough surfaces we consider the dirichlet boundary value problem for the helmholtz equation in a non locally perturbed half plane this problem models time harmonic electromagnetic scattering by a one dimensional infinite rough perfectly conducting surface the same problem arises in acoustic scattering by a sound soft surface chandler wilde and zhang have suggested a radiation condition for this problem a generalization of the rayleigh expansion condition for diffraction gratings and uniqueness of solution has been established recently an integral equation formulation of the problem has also been proposed and in the special case when the whole boundary is both lyapunov and a small perturbation of a flat boundary the unique solvability of this integral equation has been shown by chandler wilde and ross by operator perturbation arguments in this paper we study the general case with no limit on surface amplitudes or slopes and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers as an important corollary we prove that for a variety of incident fields including the incident plane wave the dirichlet boundary value problem for the scattered field has a unique solution

standard stratifications of ei categories and alperin s weight conjecture abstract we characterize the finite ei categories whose representations are standardly stratified with respect to the natural preorder on the simple representations the orbit category of a finite group with respect to any set of subgroups is always such a category taking the subgroups to be the p subgroups of the group we reformulate alperin s weight conjecture in terms of the standard and proper costandard representations of the orbit category we do this using the properties of the ringel dual construction and a theorem of dlab which have elsewhere been described for standardly stratified algebras where there is a partial order on the simple modules we indicate that these results hold in the generality of an algebra whose simple modules are preordered rather than partially ordered

syzygy modules for quasi k gorenstein rings abstract let be a right quasi k gorenstein ring for each dth syzygy module m in mod where 0 d k 1 we obtain an exact sequence 0 b m p c 0 in mod with the properties that it is dual exact p is projective c is a d 1 st syzygy module b is a dth syzygy of ext op d 1 tr m and the right projective dimension of b is less than or equal to d 1 we then give some applications of such an exact sequence as follows 1 we obtain a chain of epimorphisms concerning m and by dualizing it we then get the spherical filtration of auslander and bridger for m 2 we get auslander and bridger s approximation theorem for each reflexive module in mod op 3 we show that for any 0 d k 1 each dth syzygy module in mod has an evans griffith presentation as an immediate consequence of 3 we have that if is a commutative noetherian ring with finite self injective dimension then for any non negative integer d each dth syzygy module in mod has an evans griffith presentation which generalizes an evans and griffith s result to much more general setting

criteria for the validation of surrogate endpoints in randomized experiments the validation of surrogate endpoints has been studied by prentice 1989 statistics in medicine 8 431 440 and freedman graubard and schatzkin 1992 statistics in medicine 11 167 178 we extended their proposals in the cases where the surrogate and the final endpoints are both binary or normally distributed letting t and s be random variables that denote the true and surrogate endpoint respectively and z be an indicator variable for treatment prentice s criteria are fulfilled if z has a significant effect on t and on s if s has a significant effect on t and if z has no effect on t given s freedman relaxed the latter criterion by estimating pe the proportion of the effect of z on t that is explained by s and by requiring that the lower confidence limit of pe be larger than some proportion say 0 5 or 0 75 this condition can only be verified if the treatment has a massively significant effect on the true endpoint a rare situation we argue that two other quantities must be considered in the validation of a surrogate endpoint re the effect of z on t relative to that of z on s and gamma z the association between s and t after adjustment for z a surrogate is said to be perfect at the individual level when there is a perfect association between the surrogate and the final endpoint after adjustment for treatment a surrogate is said to be perfect at the population level if re is 1 a perfect surrogate fulfills both conditions in which case s and t are identical up to a deterministic transformation fieller s theorem is used for the estimation of pe re and their respective confidence intervals logistic regression models and the global odds ratio model studied by dale 1986 biometrics 42 909 917 are used for binary endpoints linear models are employed for continuous endpoints in order to be of practical value the validation of surrogate endpoints is shown to require large numbers of observations

singular equivalence of morita type with level abstract we generalize the notion of stable equivalence of morita type and define what is called singular equivalence of morita type with level such an equivalence induces an equivalence between singular categories we will also prove that a derived equivalence of standard type induces a singular equivalence of morita type with level

on the representation dimension of finite dimensional algebras the importance of the representation finite artin algebras for the whole representation theory of artin algebras is well understood and there is much literature on the subject see 1 6 12 these are artin algebras such that every indecomposable module is finitely generated and every module is a direct sum of indecomposable modules moreover there is a bijective correspondence between the class of representation finite artin algebras and that of artin algebras with global dimension of at most 2 and with dominant dimension of at least 2 this result was established by auslander in 1 motivated by this correspondence auslander introduced the concept of representation dimension for artin algebras to study the connection of arbitrary artin algebras with representation finite artin algebras it is hoped that this notion gives a reasonable way of measuring how far an artin algebra is from being representation finite type 1 p 134 representation dimension is a morita invariant of artin algebras and its definition involves homological dimensions and modules which are both generators and cogenerators unfortunately little seems to be known about representation dimension so there are a lot of essential questions on this invariant dealing with the computation and estimation of the representation dimension of an artin algebra there are a few cases known auslander proved that the representation dimension of an artin algebra is two if and

tilting modules over an algebra by igusa smalo and todorov abstract the finiteness of the little finitistic dimension of an artin algebra r is known to be equivalent to the existence of a tilting r module t such that t p where p is the category of all finitely presented r modules of finite projective dimension moreover t can be taken finitely generated if and only if p is contravariantly finite in this paper we describe explicitly the structure of t for the ist algebra a finite dimensional algebra with p not contravariantly finite we also characterize the indecomposable modules in p and all tilting classes over this algebra

estimating the proportion of treatment effect explained by a surrogate marker in this paper we measure the extent to which a biological marker is a surrogate endpoint for a clinical event by the proportional reduction in the regression coefficient for the treatment indicator due to the inclusion of the marker in the cox regression model we estimate this proportion by applying the partial likelihood function to two cox models postulated on the same failure time variable we show that the resultant estimator is asymptotically normal with a simple variance estimator one can construct confidence intervals for the proportion by using the direct normal approximation to the point estimator or by using fieller s theorem extensive simulation studies demonstrate that the proposed methods are appropriate for practical use we provide applications to hiv aids clinical trials

non periodic acoustic and electromagnetic scattering from periodic structures in 3d abstract scattering of non periodic waves from unbounded structures is difficult to treat as one typically formulates the problem in an unbounded domain covering the unbounded periodic structure the floquet bloch transform reduces the latter problem to a family of decoupled periodic scattering problems this reduction is in particular interesting from the point of view of numerical computations we analyze a corresponding fully discrete numerical solution algorithm for three dimensional scattering problems in acoustics and electromagnetics proving in particular convergence rates under suitable assumptions on the geometry and the material coefficients a crucial part of our analysis relies on the continuous dependence of the family of solutions to the quasiperiodic scattering problems on the quasiperiodicity the latter part is actually more difficult to establish than for corresponding two dimensional problems we further provide a numerical example in 3d acoustics that illustrates feasibility of the proposed algorithm

representation dimensions of triangular matrix algebras abstract let a be a finite dimensional hereditary algebra over an algebraically closed field k t 2 a a 0 a a be the triangular matrix algebra we prove that rep dim t 2 a is at most three if a is dynkin type and rep dim t 2 a is at most four if a is not dynkin type let a 1 a 0 da a be the duplicated algebra of a let t be a tilting a module and t t p be a tilting a 1 module we show that end a 1 t is representation finite if and only if the full subcategory x a y a f x a mod a y a 1 f t a add a of mod t 2 a is of finite type where is the auslander reiten translation and f t a is the torsion free class of mod a associated with t moreover we also prove that rep dim end a 1 t is at most three if a is dynkin type

algebras with irreducible module varieties i abstract we call a finite dimensional k algebra a geometrically irreducible if for all d 0 all connected components of the affine scheme of d dimensional a modules are irreducible we show that the geometrically irreducible algebras without loops this includes all algebras of finite global dimension are the hereditary algebras we also show that truncated polynomial rings are the only geometrically irreducible local algebras finally we formulate a conjectural classification of all geometrically irreducible algebras

almost split sequences in subcategories let r be a commutative artin ring and let i be an r algebra which is a finitely generated r module in 5 auslander and reiten introduced the notion of an almost split sequence in mod a the category of finitely generated modules over a and the existence and uniqueness of such short exact sequences were established there the theory of almost split sequences developed further and similar results for certain subcategories of mod i were proved by bautista and martinez 8 and roggenkamp 9 the main purpose of this paper is to develop a more general theory for subcategories of mod i having almost split sequences which has the previous examples as special cases notions closely related to that of almost split sequences are those of minimal left and right almost split morphisms these notions were introduced in 61 for mod i and further developed in 7 for subcategories of mod ii this paper is based upon 7 and we therefore use the same notations and conventions as used there we now give some definitions and then proceed to describe the content of the paper section by section let c be a subcategory of mod ii then a morphism g b c in c is said to be a right almost split morphism in c if i g is not a splittable epimorphism and ii whenever there is a nonsplittable epimorphism h c c in c there exists an h c b such that gh h dually a morphismfi a f b in c is said to be left almost split if i f is not a splittable monomorphism and ii whenever there is a nonsplittable monomorphism h a a there exists an h b a such that h f h we say that c has right almost split morphisms if for all indecomposable objects

on uniserial modules in the auslander reiten quiver abstract this article begins the study of irreducible maps involving finite dimensional uniserial modules over finite dimensional associative algebras we work on the classification of irreducible maps between two uniserials over triangular algebras and give estimates for the number of middle terms of an almost split sequence with a uniserial end term

singular equivalence and the fg condition abstract we show that singular equivalences of morita type with level between finite dimensional gorenstein algebras over a field preserve the fg condition

endomorphism algebras of tilting modules over m replicated algebras abstract let a be a finite dimensional hereditary algebra over an algebraically closed field k and let a m be the m replicated algebra of a in this paper we investigate the structure properties of the endomorphism algebras of tilting modules of a m and prove that all the endomorphism algebras of tilting modules of a m can be realized as the iterated endomorphism algebras of bb tilting modules that is for each pair of basic tilting a m modules t 1 and t 2 there exists a series of finite dimensional algebras 0 1 s which are the endomorphism algebras of some basic tilting a m modules and for each i there is a bb tilting i module m i such that 0 end a m t 1 i end i 1 m i 1 for 1 i s and end a m t 2 end s m s

gorenstein projective modules and symmetric recollements we introduce compatible bimodules if m is a compatible a b bimodule then the gorenstein projective modules over algebra am0b are explicitly described and if is gorenstein then this description implies that m is compatible as an application if m is compatible then there is a left recollement of the stable category gp and if is gorenstein and ma is projective then there is a symmetric recollement of the singularity category dsgb

monte carlo simulations of large scale problems of random rough surface scattering and applications to grazing incidence with the bmia canonical grid method scattering of a te incident wave from a perfectly conducting one dimensional random rough surface is studied with the banded matrix iterative approach canonical grid bmia cag method the bmia cag is an improvement over the previous bmia the key idea of bmia cag is that outside the near field interaction the rest of the interactions can be translated to a canonical grid by taylor series expansion the use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast fourier transform for nonnear field interaction the method can be used for monte carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface we illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns the method is also applied to study scattering from random rough surfaces at near grazing incidence the numerical examples illustrate the importance of using a large surface length for some backscattering problems

the transpose of modules relative to subcategories abstract let r be a left noetherian ring and s a right noetherian ring and let x be a subcategory of finitely generated left r modules and b s r a finite r s bimodule as a generalization of the auslander transpose replacing a projective presentation by an x presentation and the functor hom r r by the functor hom r b we introduce the x b transpose of an r module m admitting an x presentation for a suitable subcategory x some useful properties of x b transposes are obtained it is shown that the x b transpose shares many nice properties with the auslander transpose some known results are obtained as corollaries

enright s completions and injectively copresented modules let 21 be a finite dimensional simple lie algebra over the complex numbers it is shown that a module is complete or relatively complete in the sense of enright if and only if it is injectively copresented by certain injective modules in the bgg category o let a be the finite dimensional algebra associated to a block of o then the corresponding block of the category of complete modules is equivalent to the category of eae modules for a suitable choice of the idempotent e using this equivalence a very easy proof is given for deodhar s theorem also proved by bouaziz that completion functors satisfy braid relations the algebra eae is left properly and standardly stratified it satisfies a double centralizer property similar to soergel s combinatorial description of o its simple objects their characters and their multiplicities in projective or standard objects are determined

derived equivalences induced by big cotilting modules abstract we prove that given a grothendieck category g with a tilting object of finite projective dimension the induced triangle equivalence sends an injective cogenerator of g to a big cotilting module moreover every big cotilting module can be constructed like that in an essentially unique way we also prove that the triangle equivalence is at the base of an equivalence of derivators which in turn is induced by a quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes

partial tilting and cotilting bimodules abstract let r and s be arbitrary associative rings the purpose of this paper is to study the equivalences induced by hom r v v s and their derived functors and the dualities induced by hom r w hom s w and their derived functors with v s r partial tilting bimodule and w s r partial cotilting bimodule without any finiteness condition

maximal rigid subcategories and cluster tilting subcategories in 2 cy categories abstract let c be a connected hom finite 2 cy triangulated category we prove that if t is a functorially finite maximal rigid subcategory of c without loops in its quiver then t is cluster tilting in particular this gives a positive answer to a conjecture proposed in 5

three results on frobenius categories this paper consists of three results on frobenius categories 1 we give sufficient conditions on when a factor category of a frobenius category is still a frobenius category 2 we show that any frobenius category is equivalent to an extension closed exact subcategory of the frobenius category formed by cohen macaulay modules over some additive category this is an analogue of gabriel quillen s embedding theorem for frobenius categories 3 we show that under certain conditions an exact category with enough projective and enough injective objects allows a natural new exact structure with which the given category becomes a frobenius category several applications of the results are discussed

double centralizer properties dominant dimension and tilting modules double centralizer properties play a central role in many parts of algebraic lie theory soergel s double centralizer theorem relates the principal block of the bernstein gelfand gelfand category o of a semisimple complex lie algebra with the coinvariant algebra i e the cohomology algebra of the corresponding flag manifold schur weyl duality relates the representation theories of general linear and symmetric groups in defining characteristic or via the quantized version in nondefining characteristic in this paper we exhibit algebraic structures behind these double centralizer properties we show that the finite dimensional algebras relevant in this context have dominant dimension at least two with respect to some projective injective or tilting modules general arguments which combine methods from ring theory qf 3 rings and dominant dimension with tools from representation theory approximations tilting modules then imply the validity of these double centralizer properties as well as new ones in contrast to the traditional proofs e g by the fundamental theorems of invariant theory no computations are necessary

on arkhipov s and enright s functors we give a description of arkhipov s and joseph s and deodhar mathieu s versions of enright s endofunctors on the category open image in new window associated with a fixed triangular decomposition of a complex finite dimensional semi simple lie algebra in terms of co approximation functors with respect to suitably chosen injective resp projective modules we establish some new connections between these functors for example we show that arkhipov s and joseph s functors are adjoint to each other we also give several proofs of braid relations for arkhipov s and enright s functors

an approach to the finitistic dimension conjecture abstract let r be a finite dimensional k algebra over an algebraically closed field k and modr be the category of all finitely generated left r modules for a given full subcategory x of modr we denote by pfd x the projective finitistic dimension of x that is pfd x sup pd x x x and pd x it was conjectured by h bass in the 60 s that the projective finitistic dimension pfd r pfd mod r has to be finite since then much work has been done toward the proof of this conjecture recently k igusa and g todorov defined in k igusa g todorov on the finitistic global dimension conjecture for artin algebras in representations of algebras and related topics in fields inst commun vol 45 amer math soc providence ri 2005 pp 201 204 a function mod r n which turned out to be useful to prove that pfd r is finite for some classes of algebras in order to have a different approach to the finitistic dimension conjecture we propose to consider a class of full subcategories of modr instead of a class of algebras that is we suggest to take the class of categories f of filtered r modules for all stratifying systems in modr we prove that the finitistic dimension conjecture holds for the categories of filtered modules for stratifying systems with one or two and some cases of three modules of infinite projective dimension

from triangulated categories to module categories via localisation we show that the category of finite dimensional modules over the endomorphism algebra of a rigid object in a hom finite triangulated category is equivalent to the gabriel zisman localisation of the category with respect to a certain class of maps this generalises the 2 calabi yau tilting theorem of keller reiten in which the module category is obtained as a factor category to the rigid case

tilting modules of finite projective dimension tilting modules are well known and are useful in the representation theory of artinian algebras 2 4 6 11 the purpose of this paper is to define tilting modules of finite projective dimension and prove some fundamental results a unital left a module a t over a ring a is said to be a tilting module of projective dimension 0 is an integer if it satisfies the following three conditions 1 a t has a projective resolution

representation theoretic properties of balanced big cohen macaulay modules let r mathfrak m k be a complete cohen macaulay local ring in this paper we assign a numerical invariant for any balanced big cohen macaulay module called underline mathsf h length among other results it is proved that for a given balanced big cohen macaulay r module m with an mathfrak m primary cohomological annihilator if there is a bound on the underline mathsf h length of all modules appearing in mathsf cm support of m then it is fully decomposable i e it is a direct sum of finitely generated modules while the first brauer thrall conjecture fails in general by a counterexample of dieterich dealing with multiplicities to measure the size of maximal cohen macaulay modules our formalism establishes the validity of the conjecture for complete cohen macaulay local rings in addition the pure semisimplicity of a subcategory of balanced big cohen macaulay modules is settled namely it is shown that r is of finite mathsf cm type if and only if r is an isolated singularity and the category of all fully decomposable balanced big cohen macaulay modules is closed under kernels of epimorphisms finally we examine the mentioned results in the context of cohen macaulay artin algebras admitting a dualizing bimodule omega as defined by auslander and reiten it will turn out that omega gorenstein projective modules with bounded mathsf cm support are fully decomposable in particular a cohen macaulay algebra lambda is of finite mathsf cm type if and only if every omega gorenstein projective module is of finite mathsf cm type which generalizes a result of chen for gorenstein algebras our main tool in the proof of results is gabriel roiter co measure an invariant assigned to modules of finite length and defined by gabriel and ringel this in fact provides an application of the gabriel roiter co measure in the category of maximal cohen macaulay modules

the structure of preenvelopes with respect to maximal cohen macaulay modules abstract this paper studies the structure of special preenvelopes and envelopes with respect to maximal cohen macaulay modules we investigate the structure of them in terms of their kernels and cokernels moreover using this result we also study the structure of special proper coresolutions with respect to maximal cohen macaulay modules over a henselian cohen macaulay local ring

reconstruction of path algebras from their posets of tilting modules let a k be the path algebra of a finite quiver without orientedcycles the set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set we will show here that t a uniquely determines if has no multiple arrows and no isolated vertices

an auslander buchweitz approximation approach to pre silting subcategories in triangulated categories abstract we apply the auslander buchweitz approximation triangles to study pre silting subcategories in a triangulated catego ry t an auslander reiten type correspondence between the class of silting subcategories of t and that of certain covariantly finite subcategories of t is established we introduce a relation on presilting subcategories of t which can be used to obtain another silting subcategory from a given one we also give a bazzoni s characterization for two presilting subcategories satisfying such a relation the results can be used to improve the auslander reiten type correspondence and bazzoni s characterization for small silting complexes established by wei

generalized tilting modules with finite injective dimension let r be a left noetherian ring s be a right noetherian ring and r be a generalized tilting module with s end r we mainly consider the conditions such that l id r 1 in this paper and obtain some characterizations for this inequality further when l id r and r id s are finite we provide the conditions such that r and s are injective as a direct application we get some necessary and sufficient conditions for a gorenstein ring to be a qf ring

a note on abelian quotient categories abstract let c be a triangulated category with a serre functor s and x a non zero contravariantly finite rigid subcategory of c then x is cluster tilting if and only if the quotient category c x is abelian and s x x 2 as an application this result generalizes the work by beligiannis

on galois coverings and tilting modules abstract let a be a basic connected finite dimensional algebra over an algebraically closed field k let t be a basic tilting a module with arbitrary finite projective dimension for a fixed group g we compare the set of isoclasses of connected galois coverings of a with group g and the set of isoclasses of connected galois coverings of end a t with group g using the hasse diagram k a see d happel l unger on a partial order of tilting modules algebr represent theory 8 2 2005 147 156 and c riedtmann a schofield on a simplicial complex associated with tilting modules comment math helv 66 1 1991 70 78 of basic tilting a modules we give sufficient conditions on t under which there is a bijection between these two sets these conditions are always verified when a is of finite representation type then we apply these results to study when the simple connectedness of a implies the one of end a t see i assem e n marcos j a de la pena the simple connectedness of a tame tilted algebra j algebra 237 2 2001 647 656 finally using an argument due to w crawley boevey we prove that the type of any simply connected tilted algebra is a tree and that its first hochschild cohomology group vanishes

on modules with trivial self extensions throughout this note all rings will be self basic connected artin algebras over a fixed commutative local artin ring k and all modules will be finitely generated homomorphisms will be written on the opposite side of the scalars by mod a resp a mod we denote the category of all right resp left a modules for an artin algebra a the ordinary duality functor is denoted by d mod a 2 a mod i e d hom f with the minimal injective cogenerator i over k we are interested in the bimodules bta with the following properties

approximations and the little finitistic dimension of artinian rings let r be a ring and let simp r be a representative set of all simple right r modules denote by p the class of all modules which are finitely generated and have finite projective dimension the little finitistic dimension of r is defined by fdim r sup proj dim m m p let a b be the complete cotorsion theory cogenerated by p for each s simp r let fs xs s be a special a precover of s we prove that fdim r max proj dim xs s simp r provided that r is right artinian as a corollary we extend to right artinian rings the well known auslander reiten sufficient condition for finiteness of the little finitistic dimension

selforthogonal modules with finite injective dimension ii let be a left and right artin ring and a faithfully balanced selforthogonal bimodule we give a sufficient condition that the injective dimension of is finite implies that of is also finite

homological domino effects and the first finitistic dimension conjecture counterexamples to the first finitistic dimension conjecture are constructed in fact for any fieldk and any integerm 2 there exist finite dimensionalk algebras such that the little finitistic dimension of ism while the big finitistic dimension ism 1 our examples are monomial relation algebras within this class of algebras the big and little finitistic dimensions cannot differ by more than 1 the analysis of the examples is based on a sharp picture of arbitrary second syzygies over monomial relation algebras

totally reflexive extensions and modules abstract we introduce the notion of totally reflexive extension of rings it unifies gorenstein orders and frobenius extensions we prove that for a totally reflexive extension a module over the extension ring is totally reflexive if and only if its underlying module over the base ring is totally reflexive

an entropy based nonparametric test for the validation of surrogate endpoints we present a nonparametric test to validate surrogate endpoints based on measure of divergence and random permutation this test is a proposal to directly verify the prentice statistical definition of surrogacy the test does not impose distributional assumptions on the endpoints and it is robust to model misspecification our simulation study shows that the proposed nonparametric test outperforms the practical test of the prentice criterion in terms of both robustness of size and power we also evaluate the performance of three leading methods that attempt to quantify the effect of surrogate endpoints the proposed method is applied to validate magnetic resonance imaging lesions as the surrogate endpoint for clinical relapses in a multiple sclerosis trial copyright 2012 john wiley sons ltd

auslander type conditions and cotorsion pairs we study the properties of rings satisfying auslander type conditions if an artin algebra satisfies the auslander condition that is is an gorenstein artin algebra then we construct two kinds of subcategories which form functorially finite cotorsion pairs

wakamatsu tilting modules abstract we study a generalization of tilting modules to modules of possibly infinite projective dimension introduced by wakamatsu in j algebra 114 1988 106 114 in particular we characterize these modules in terms of suitable subcategories of finitely generated modules and in terms of cotorsion theories

gorenstein defect categories of triangular matrix algebras abstract we apply the technique of recollement to study the gorenstein defect categories of triangular matrix algebras first we construct a left recollement of gorenstein defect categories for a triangular matrix algebra under some conditions using it we give a categorical interpretation of the gorenstein properties of the triangular matrix algebras obtained by x w chen b l xiong and p zhang respectively second under some additional conditions a recollement of gorenstein defect categories for a triangular matrix algebra is constructed as an application for a special kind of triangular matrix algebras which are called simple gluing algebras we describe their singularity categories and gorenstein defect categories

the time harmonic maxwell equations in a doubly periodic structure abstract consider the diffraction of a beam of particles in r 3 when the dielectric coefficient is a constant e1 above a surface s and a different constant e2 below s and the magnetic permeability is constant throughout r 3 s is assumed to be a doubly periodic surface say z f x y with f x ml1 y nl2 f x y for integers m n the existence and uniqueness of a solution satisfying a radiation condition at infinity is reduced to a system of fredholm equations thus for all but a discrete set of e s there exists a unique solution

information gain and a general measure of correlation summary given a parametric model of dependence between two random quantities x and y the notion of information gain can be used to define a measure of correlation this definition of correlation generalizes both the usual product moment correlation coeffi cient for the bivariate normal model and the multiple correlation coefficient in the standard linear regression model the use of this information based correlation in a descriptive statistical analysis is examined and several examples are given if the dependence between two random quantities x and y is modelled parametri cally then the concept of information gain can be used to define a measure of correlation this correlation coefficient can appear in two possible contexts depending on whether one models the joint distribution of x and y or just the conditional distribution of y given x an important motivating feature for this information based correlation coefficient is the fact that it generalizes both the usual product moment correlation coefficient for the bivariate normal model and the usual multiple correlation coefficient for the standard multiple regression model with normal errors our intuition is well developed for these usual correlation coefficients and hopefully our intuition will still be applicable for the information based correlation in more general modelling situations of parametric dependence further since our correlation coefficient is based on information gain we might hope to extend our intuition to interpret the information gain in any statistical modelling situation where we want to assess how much better a more complicated model is than a simpler model the concept of information gain for general statistical models is described in 2 this concept is then used to define an information based measure of correlation the joint case is covered in 3 and the conditional case in 4 estimation of the correlation coefficient is carried out by estimating the corresponding information gain see 5 7 the use of information gain for the purpose of model choice in a descriptive statistical analysis is discussed in 8 and a comparison between our approach and akaike s information criterion is given in 9 some examples of the use of this information based correlation are given in 10 and 11

on algebras of finite cohen macaulay type abstract we study artin algebras and commutative noetherian complete local rings r in connection with the following decomposition property of gorenstein projective modules any gorenstein projective module is a direct sum of finitely generated modules we show that the class of algebras enjoying coincides with the class of virtually gorenstein algebras of finite cohen macaulay type introduced in beligiannis and reiten 2007 27 beligiannis 2005 24 thus we solve the problem stated in chen 2008 33 this is proved by characterizing when a resolving subcategory is of finite representation type in terms of decomposition properties of its closure under filtered colimits thus generalizing a classical result of auslander 1976 9 and ringel and tachikawa 1974 63 in the commutative case if r admits a non free finitely generated gorenstein projective module then we show that r is of finite cohen macaulay type iff r is gorenstein and satisfies we also generalize a result of yoshino 2005 68 by characterizing when finitely generated modules without extensions with the ring are gorenstein projective finally we study the stable relative auslander algebra of a virtually gorenstein algebra of finite cohen macaulay type and under the presence of a cluster tilting object we give descriptions of the stable category of gorenstein projective modules in terms of the cluster category associated to the quiver of the stable relative auslander algebra in this setting we show that the cluster category is invariant under derived equivalences

boundary integral equation methods for the scattering problem by an unbounded sound soft rough surface with tapered wave incidence in this paper we consider the scattering problem of tapered acoustic wave by an unbounded sound soft surface the scattering problem is modeled as a boundary value problem governed by the helmholtz equation with dirichlet boundary condition although the tapered wave is often introduced to realize asymptotic truncation for unbounded rough surface the standard helmholtz integral equations which derive for the scattering of plane waves by an arbitrary bounded obstacle are often used to generate benchmark numerical solutions different from the scattering of plane waves by an arbitrary bounded obstacle we use the angular spectrum representation radiation condition to replace the sommerfeld radiation condition and derive a boundary integral equation for studying the scattering problem then we study the integral equation by the truncation method whereby the integral equation posed on an unbounded region is approximated by an integral equation on a bounded region some properties of the integral equation in an energy space with weights are proved then the collocation method is used to solve the integral equation on a bounded region and its convergence is also obtained a rigorous derivation of bie is presented for studying the scattering problem some properties of the integral equation in an energy space with weights are proved the convergence of the numerical method is also obtained

convergence and numerics of a multisection method for scattering by three dimensional rough surfaces we introduce a novel multisection method for the solution of integral equations on unbounded domains the method is applied to the rough surface scattering problem in three dimensions in particular to a brakhage werner type integral equation for acoustic scattering by an unbounded rough surface with dirichlet boundary condition where the fundamental solution is replaced by some appropriate half space green s function the basic idea of the multisection method is to solve an integral equation a varphi f by approximately solving the equation p varrho a p tau varphi p varrho f for some positive constants varrho tau here p varrho is a projection operator that truncates a function to a ball with radius varrho 0 for a very general class of operators a for which the brakhage werner equation from acoustic scattering is a particular example we will show existence of approximate solutions to the multisection equation and show that approximate solutions to the multisection equation approximate the true solution varphi 0 of the operator equation a varphi f finally we describe a numerical implementation of the multisection algorithm and provide numerical examples for the case of rough surface scattering in three dimensions

on the finitistic dimension conjecture of artin algebras abstract let a be an artin algebra and e be an idempotent element of a we prove that if a has representation dimension at most three then the finitistic dimension of eae is finite and deduce that if quasi hereditary algebras have representation dimensions at most three then the finitistic dimension conjecture holds