autoregressive age period cohort models summary age period cohort analysis of vital data has received much attention recently and it is already well known that the exact linear relation of the three time factors creates a non identifiability problem previous studies have shown that the curvature terms of these factors are estimable but the linear trends are not however little attention has been paid to the possibility that the effects due to cohort and or period might change through time stochastically rather than deterministically and hence display a stochastic trend in this paper we model the cohort effects as an ar 1 process and use lung cancer mortality data from 1966 to 1990 for males in taiwan as an example the parameters are identifiable in the proposed model and the estimates are found to be stable however the assumption made in the model should be carefully considered before using our methodology

d split sequences and derived equivalences abstract in this paper we introduce the so called d split sequences and show that each d split sequence gives rise to a derived equivalence via a tilting module in particular we obtain derived equivalences from auslander reiten sequences via bb tilting modules or from n almost split sequences via n bb tilting modules and auslander reiten triangles further we recover n almost split sequences from n bb tilting modules over n auslander algebras

representation dimension and quasi hereditary algebras we study auslander s representation dimension of artin algebras which is by definition the minimal projective dimension of coherent functors on modules which are both generators and cogenerators we show the following statements 1 if an artin algebra a is stably hereditary then the representation dimension of a is at most 3 2 if two artin algebras are stably equivalent of morita type then they have the same representation dimension particularly if two self injective algebras are derived equivalent then they have the same representation dimension 3 any incidence algebra of a finite partially ordered set over a field has finite representation dimension moreover we use results on quasi hereditary algebras to show that 4 the auslander algebra of a nakayama algebra has finite representation dimension

vers une decomposition de jordan des blocs des groupes reductifs finis abstract let g be a reductive algebraic group over an algebraic closure of a prime field f p defined over f q with frobenius endomorphism f let g f be the subgroup of rational points let l be a prime number assume that l is different from p if g f is in duality with g f then by a theorem of m broue and j michel m broue j michel blocs et series de lusztig dans un groupe reductif fini j reine angew math 395 1989 56 67 for any l bloc b of g f there exists a unique g f conjugacy class s of l semi simple elements such that some irreducible representation of b is in the rational lusztig s series associated to s if s 1 b is said to be unipotent if g is not connected with identity component g define the unipotent l blocs of g f as the l blocks that cover some unipotent l bloc of g f assuming l is good for g we construct from g f and s some reductive algebraic group g s f defined over f q and a one to one map from the set of l blocks of g f with associated class s onto the set of unipotent l blocks of g s f such that if b corresponds to b then there is a significant height preserving one to one map from the set of irreducible representations irr b onto the set irr b the respective defect groups of b and b are isomorphic the associated brauer categories are equivalent one do not assume that the center of g is connected the class of s may be isolated in g

tests of spatial randomness adjusted for an inhomogeneity a general framework in many applications it is of interest to test whether a spatial point pattern is randomly generated after adjusting for an underlying spatial inhomogeneity a great variety of different test statistics have been proposed for this purpose by scientists in different fields these are reviewed in this article despite apparent dissimilarities in terms of their original formulations most of these statistics can be placed into one general framework of which they are special cases this makes it easier to see exactly how they relate to one another and also to determine which test to use for a particular application the general framework can also be used for proposing new tests by combining properties of existing tests for developing theoretical foundations for these types of test statistics for doing structured comparative evaluations and for software development

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

on the focal defect group of a block characters of height zero and lower defect group multiplicities abstract we discuss the focal subgroup of the defect group d of a p block b which we refer to as the focal defect group and denote by d 0 we note that the character group of d d 0 acts in a defect or height preserving fashion on irreducible characters in b and prove that the action on irreducible characters of height zero is semi regular we also prove that all orbits under this action have length divisible by z d d 0 z d as applications we prove that all cartan invariants for b are divisible by z d d 0 z d that if out d is a p group and d 1 then the number of irreducible characters of height zero in b is divisible by p and that if z d d 0 then the block b is of lefschetz type see r knorr g r robinson some remarks on a conjecture of alperin j london math soc 2 39 1 1989 48 60

nilpotent blocks of quasisimple groups for odd primes we investigate the nilpotent blocks of positive defect of the quasisimple groups for odd primes in particular it is shown that every nilpotent block of a quasisimple group has abelian defect groups a conjecture of puig concerning the recognition of nilpotent blocks is also shown for these groups

weighted norm inequalities for potentials with applications to schrodinger operators fourier transforms and carleson measures on donne une nouvelle caracterisation de l inegalite de trace pour des operateurs potentiel et on l utilise pour affiner des resultats sur la distribution des valeurs propres des operateurs de schrodinger

perfect generalized characters inducing the alperin mckay conjecture it is well known that the perfect isometries predicted in broue s conjecture do not always exist when the defect groups are non abelian even when the blocks have equivalent brauer categories we consider perfect generalized characters which induce bijections between the sets of irreducible characters of height zero of a block and of its brauer correspondent in the normalizer of a defect group in this way the perfect isometries predicted in broue s conjecture for blocks with abelian defect groups are generalized whilst such generalized characters do not exist in general we show that they do exist when the defect groups are non abelian trivial intersection subgroups of order p 3 as well as for 2b 2 q for q a power of two and psu 3 q for all q further we show that these blocks satisfy a generalized version of an isotypy

clustering of rare events the clustering of cases of a rare disease is considered the number of events observed for each unit is assumed to have a poisson distribution the mean of which depends upon the population size and the cluster membership of that unit here a cluster consists of those units that are homogeneous in their rate of occurrence of the rare events under study a sample of units is modeled by a mixture of poisson distributions one for each cluster the mixing parameters being the proportions of all units represented by the components of the mixture maximum likelihood and bayes approaches are employed to determine criteria for separating a sample into groups of units with homogeneous rates a likelihood ratio test for the significance of a two component mixture is presented as an example the performance of the criteria is illustrated with data on the spatial occurrence of sudden infant deaths sids in north carolina counties over a four year period the results suggest that the practice of dividing the counties into high and low risk categories on the basis of the ordered rates alone should be questioned tests based upon combinatorial methods are also presented to examine the significance of the number of contiguous counties among those with high rates

on the number of characters in a block wc arc concerned here with the following question of brauer 11 given a y block b with defect group d of a finite group g is it true that b contains at most d irreducible characters in their famous paper 2 brauer and feit showed that k b our results are somewhat technical to state bu wc do obtain that c kh b ldj2 1 and that this inequality is strict unless perhaps l is cyclic among other results of a similar nature our results may be compared to some results of brauer 11 though they are of a somewhat different nature

spatial modeling of regional variables abstract in this article accumulated sudden infant death syndrome sids data from 1974 1978 and 1979 1984 for the counties of north carolina are analyzed after a spatial exploratory data analysis markov random field models are fit to the data the spatial trend is meant to capture the large scale variation in the data and the variance and spatial dependence are meant to capture the small scale variation the trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location both models are fit and compared the results give an excellent illustration of a phenomenon already well known in time series that autocorrelation in data can be due to an undiscovered explanatory variable indeed for 1974 1978 we confirm a dependence of sids rate on proportion of nonwhite babies born along with insignificant spatial correlation without this regressor variable however the spatial correlation is significant in 1979 1984 perhaps due to reporting bias o

on singular equivalences of morita type abstract stable equivalences of morita type preserve many interesting properties and are proved to be the appropriate concept for studying equivalences between stable categories recently the singularity category attained much attraction and xiao wu chen and long gang sun gave an appropriate definition of singular equivalence of morita type we shall show that under some conditions singular equivalences of morita type have some biadjoint functor properties and preserve positive degree hochschild homology

computer assisted analysis of mixtures c a man statistical algorithms summary this paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity i e observations stemming from different subpopulations in a univariate sample the case with unknown number of population subgroups as well as the case with known number of population subgroups with emphasis on the first is considered in the computer package c a man computer assisted mixture analysis it includes an algorithmic menu with choices of the em algorithm the vertex exchange algorithm a combination of both as well as the vertex direction method to ensure reliable convergence a steplength menu is provided for the three latter methods each achieving monotonicity for the direction of choice c a man has the option to work with restricted support size that is the case when the number of components is known a priori in the latter case the em algorithm is used applications of mixture modelling in medical problems are discussed

on the finitistic dimension conjecture iii related to the pair eae a let a be an artin algebra and e an idempotent element in a in this paper we use co homological conditions on a to control the finitistic dimension of eae such a consideration is of particular interest for understanding the finitistic dimension conjecture let us denote the finitistic dimension and global dimension of a by fin dim a and gl dim a respectively suppose gl dim a 4 then fin dim eae if one of the following conditions holds 1 a aea has representation dimension at most 3 2 a 3 a is an a aea module 3 proj dim sa 3 for all simple a aea modules s this result can be considered as a first step to the question of whether gl dim a 4 implies fin dim eae moreover we show the following let a be an arbitrary artin algebra and e an idempotent element of a such that the syzygy dimension or the gorenstein dimension of the eae module ae is finite if fin dim a then fin dim eae

on p blocks with abelian defect groups and inertial index 2 or 3 ii abstract let g be a finite group and b be a p block of g with an abelian defect group and inertial index 2 or 3 in this paper we determine some generalized decomposition numbers of the block b

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 centres of 3 blocks of the ree groups g22 q abstract let g g 2 2 q be the simple ree group with q 3 2 k 1 and k a positive integer we show that the centre of the principal block z k g e 0 where k is an algebraically closed field of characteristic 3 is not isomorphic to the centre of the brauer corresponding block z k n g p where n g p is the normaliser in g of a sylow 3 subgroup

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

2 blocks with minimal nonabelian defect groups abstract we study numerical invariants of 2 blocks with minimal nonabelian defect groups these groups were classified by redei see redei 1947 41 if the defect group is also metacyclic then the block invariants are known see sambale 43 in the remaining cases there are only two infinite families of interesting defect groups in all other cases the blocks are nilpotent we prove brauer s k b conjecture and olsson s conjecture for all 2 blocks with minimal nonabelian defect groups for one of the two families we also show that alperin s weight conjecture and dade s conjecture are satisfied this paper is a part of the author s phd thesis

gluing of idempotents radical embeddings and two classes of stable equivalences abstract stable equivalences are studied between any finite dimensional algebra a with a simple projective module and a simple injective module and an algebra b obtained from a by gluing the corresponding idempotents of a this extends results by martinez villa stable equivalences modulo projectives are compared to stable equivalences modulo semisimples and in either situation a characterization is given for a radical embedding to induce such a stable equivalence

relative stable equivalences of morita type in the representation theory of finite groups the stable equivalence of morita type plays a prominent role however except for self injective algebras one does not know much on existence of such equivalences between arbitrary algebras moreover this notion seems to be not general enough to be preserved by classical algebraic constructions in the paper there is introduced a notion of relative stable equivalence of morita type such an equivalence appears in the context of stable equivalence of morita type as is showed in theorem 0 1

constructions of stable equivalences of morita type for finite dimensional algebras ii suppose k is a field let a and b be two finite dimensional k algebras such that there is a stable equivalence of morita type between a and b in this paper we prove that 1 if a and b are representation finite then their auslander algebras are stably equivalent of morita type 2 the n th hochschild homology groups of a and b are isomorphic for all n 1 a new proof is also provided for hochschild cohomology groups of self injective algebras under a stable equivalence of morita type

generalized perfect isometries in some groups of lie rank one abstract in a recent paper b kulshammer j b olsson and g r robinson introduced notions of generalized blocks and generalized perfect isometries and studied them in the case of the symmetric group s n it is the purpose of this paper to investigate some families of groups of lie rank one exhibiting generalized perfect isometries where there are none in the sense given by m broue and thus proving a weaker analogue of one of broue s conjectures in these cases

on the finitistic dimension conjecture ii related to finite global dimension abstract in this paper we study the finitistic dimensions of artin algebras by establishing a relationship between the global dimensions of the given algebras on the one hand and the finitistic dimensions of their subalgebras on the other hand this is a continuation of the project in j pure appl algebra 193 2004 287 305 for an artin algebra a we denote by gl dim a fin dim a and rep dim a the global dimension finitistic dimension and representation dimension of a respectively the jacobson radical of a is denoted by rad a the main results in the paper are as follows let b be a subalgebra of an artin algebra a such that rad b is a left ideal in a then 1 if gl dim a 4 and rad a rad b a then fin dim b 2 if rep dim a 3 then fin dim b the results are applied to pullbacks of algebras over semi simple algebras moreover we have also the following dual statement 3 let b a be a surjective homomorphism between two algebras b and a suppose that the kernel of is contained in the socle of the right b module b b if gl dim a 4 or rep dim a 3 then fin dim b finally we provide a class of algebras with representation dimension at most three 4 if a is stably hereditary and rad b is an ideal in a then rep dim b 3

cartan matrices and brauerʼs k b conjecture ii abstract this paper continues sambale 2011 28 we show that the methods developed there also work for odd primes in particular we prove brauer s k b conjecture for defect groups which contain a central cyclic subgroup of index at most 9 as a consequence the k b conjecture holds for 3 blocks of defect at most 3 in the second part of the paper we illustrate the limits of our methods by considering an example then we use the work of kessar koshitani and linckelmann 13 and thus the classification to show that the k b conjecture is satisfied for 2 blocks of defect 5 except for the extraspecial defect group d 8 d 8 as a byproduct we also obtain the block invariants of 2 blocks with minimal nonmetacyclic defect groups some proofs rely on computer computations with gap the gap group 2008 10

weighted nonlinear potential theory the potential theoretic idea of the thinness of a set at a given point is extended to the weighted nonlinear potential theoretic setting the weights representing in general singularities degeneracies and conditions on these weights are given that guarantee when two such notions are equivalent at the given point when applied to questions of boundary regularity for solutions to degenerate elliptic second order partial differential equations in bounded domains this result relates the boundary wiener criterion for one operator to that of another and in the linear case gives conditions for boundary regular points to be the same for various operators the methods also yield two weight norm inequalities for riesz potentials j llq p 1 p q oo which at least in the first order case a 1 have found some use in a number of places in analysis

higman ideal stable hochschild homology and auslander reiten conjecture let a and b be two finite dimensional algebras over an algebraically closed field related to each other by a stable equivalence of morita type we prove that a and b have the same number of isomorphism classes of simple modules if and only if their 0 degree hochschild homology groups hh0 a and hh0 b have the same dimension the first of these two equivalent conditions is claimed by the auslander reiten conjecture for symmetric algebras we will show that the auslander reiten conjecture is equivalent to other dimension equalities involving the centers and the projective centers of a and b this motivates our detailed study of the projective center which now appears to contain the main obstruction to proving the auslander reiten conjecture for symmetric algebras as a by product we get several new invariants of stable equivalences of morita type