assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

cauchy problems of the gauged sigma model we study the gauged sigma model in r1 1 the existence of the global smooth solution will be proved furthermore we show that the global weak solutions exist in rn 1 n 2 3

asymptotic behaviors of governing equation of gauged sigma model for heisenberg ferromagnet abstract in this note we study weak solutions of equation 0 1 u 4 e u 1 e u 4 i 1 n p i 4 j 1 m q j in r 2 where p i i 1 n resp q j j 1 m are dirac masses concentrated at the points p i i 1 n resp q j j 1 m and n m 1 eq 0 1 represents a governing equation of gauged sigma model for heisenberg ferromagnet we show that it has a sequence of solutions u having behaviors as ln x o 1 at infinity with a free parameter 2 2 n m and our concern in this paper is to study the asymptotic behavior of b as approaching the extremal values 2 and 2 n m

exceptional components of wild hereditary algebras this paper studies regular components of wild hereditary algebras it is clear that the existence of extremely many maps in the infinite radical of the module category causes algebras to be wild whereas the dimension of the horn spaces of maps from indecomposable preprojective modules or to indecomposable preinjective modules can be calculated by linear methods via the euler bilinearform these methods give only poor information if we pass to regular modules so it is natural to study as a first step maps between regular modules which are in the same regular component v and we see in 4 7 that this is a way to get information about the maps between arbitrary regular modules there is another less obvious reason for the study of single components if a and b are connected wild hereditary algebras then by 9 via tilting modules there can be constructed bijections between the regular components of the auslander reiten quivers t a and t b in order to find finally properties of these bijections we have to study properties of components proposition 6 3 points in that direction if g is a regular component in t a with a wild hereditary we denote by the quasi rank rk of v the smallest integer n such that rad x r x 0 for all n 2 n and all xe we call a component v exceptional if there is an indecomposable quasi simple module xe such that hom x yx 0 but hom x z r 1 0 for some r 0 in section 4 we show that there are only finitely many exceptional components in t a and that the existence of those components has strict consequences for the algebra a that is for its ordinary quiver 9 a in section 5 we present the numerical invariants of the most important exceptional components in the last section we give applications to tilting theory the applications are chosen under the aspect that the notion of the quasi rank of a regular component might be a pendant to the period of a tube in the tame case 184 0021 8693 92 5 00

on algebras of generalized standard semiregular type abstract we study the structure of artin algebras whose auslander reiten quiver consists of generalized standard semiregular components

l bounds for maxwell gauged equations in r1 1 and their applications abstract by making use of local energy conservation we estimate the l norm of the first derivative of the solution to the maxwell gauged o 3 sigma model in r 1 1 as an application of the bound we obtain the growth of the h 2 norm of the solution quadratic polynomial growth is obtained by improving exponential growth a similar idea can be applied to the maxwell klein gordon equations in r 1 1

wild canonical algebras canonical algebras p depending on a weight sequence p p1 pt of positive integers and a parameter sequence 3 t of pairwise distinct non zero elements from the base eld k were introduced and studied in 23 the nite dimensional representation theory mod is completely controlled by the category coh x of coherent sheaves on a non singular weighted projective line x x p since the derived categories d mod and d coh x are equivalent as triangulated categories 9 the curve x attached to has virtual genus gx 1 2 t 2 p t i 1 p pi where p l c m p1 pt the complexity of the classi cation problem for coh x and hence for mod is essentially determined by gx for gxi1 the algebra is concealed of extended dynkin type accordingly the classi cation problem for coh x and mod is equivalent to the classi cation of indecomposable modules over a tame hereditary algebra cf 18 9 or according to 10 to the classi cation problem for cohen macaulay modules over a simple surface singularity for gx 1 the algebra is of tubular type its representation theory is known from 23 while the classi cation problem for coh x 9 20 relates to atiyah s classi cation 1 of vector bundles over an elliptic curve very little was known on mod or coh x if gx 1 in this case 0 r is the one point extension of a wild hereditary algebra 0 accordingly the category mod 0 embeds into coh x as a full exact and extension closed subcategory implying that the classi cation problems for coh x and mod are wild from now on we assume gx 1 combining the sheaf theory 9 with the spectral investigation of wild hereditary algebras 6 we obtain a fairly complete picture on the structure of auslander reiten components for mod the asymptotic behaviour of the auslander reiten translations and

existence of solutions to the self dual equations in the maxwell gauged o 3 sigma model abstract in this paper we prove the existence of solutions in the self dual maxwell gauged o 3 sigma model by the super and subsolution method the supersolutions are explicitly constructed and the subsolutions are given in different ways according to the parameter representing the decay rates of solutions at infinity when has noncritical values we obtain subsolutions by solving laplace equations on weighted sobolev spaces if is the critical number we find the subsolutions via induction and shooting arguments

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

piecewise hereditary one point extensions abstract it is shown that a one point extension of a wild hereditary algebra with a regular module is piecewise hereditary if and only if the one point extension with some auslander reiten translate of the module is quasitilted the auslander reiten structure of such piecewise hereditary one point extensions is investigated

uniqueness and solution structure of nonlinear equations arising from the chern simons gauged o 3 sigma models abstract in this paper we study radially symmetric solutions of nonlinear equations arising from the chern simons gauged o 3 sigma models there are three types of solutions according to the boundary conditions topological solutions nontopological solutions of type i and ii we classify radially symmetric nontopological solutions of type i and ii by the decay rates at infinity in particular we provide a complete picture of the graph of which gives uniqueness and structure of solutions

triangle singularities ade chains and weighted projective lines abstract we study the singularity category of the triangle singularity f x a y b z c or s k x y z f attached to the weighted projective line x given by the weight triple a b c by investigating the stable category vect x of vector bundles on x obtained from the category of vector bundles by factoring out all the line bundles we show that vect x is fractional calabi yau whose cy dimension is a function of the euler characteristic of x and establish the existence of a tilting object having the shape of an a 1 b 1 c 1 cuboid the weight types 2 a b yield an explanation of happel seidel symmetry for a class of important nakayama algebras further the weight sequence 2 3 p corresponds to an ade chain the e n chain extrapolating the exceptional dynkin cases e 6 e 7 and e 8 to a whole sequence of triangulated categories

classification of solutions of elliptic equations arising from a gravitational o 3 gauge field model abstract in this paper we study an elliptic equation arising from the self dual maxwell gauged o 3 sigma model coupled with gravity when the parameter equals 1 and there is only one singular source we consider radially symmetric solutions there appear three important constants a positive parameter a representing a scaled gravitational constant a nonnegative integer n 1 representing the total string number and a nonnegative integer n 2 representing the total anti string number the values of the products a n 1 a n 2 0 play a crucial role in classifying radial solutions by using the decay rates of solutions at infinity we provide a complete classification of solutions for all possible values of a n 1 and a n 2 this improves previously known results

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

selfinjective algebras with hereditary stable slice abstract we determine the structure of all finite dimensional selfinjective algebras over a field whose auslander reiten quiver admits a hereditary stable slice

perpendicular categories with applications to representations and sheaves this paper is concerned with the omnipresence of the formation of the subcategories right left perpendicular to a subcategory of objects in an abelian category we encounter these subcategories in various contexts the formation of quotient categories with respect to localizing subcategories cf section 2 the deletion of vertices and shrinking of arrows see 37 in the representation theory of finite dimensional algebras cf section 5 the comparison of the representation theories of different extended dynkin quivers cf section 10 the theory of tilting cf sections 4 and 6 the study of homological epimorphisms of rings cf section 4 the passage from graded modules to coherent sheaves on a possibly weighted projective variety or scheme cf section 7 and 21 the study of maximal cohen macaulay modules over surface singularities cf sections the comparison of weighted projective lines for different weight sequences cf section 9 the formation of affine and local algebras attached to path algebras of extended dynkin quivers canonical algebras and weighted projective lines cf section 11 and 21 and the concept of universal localization in 40 formation of the perpendicular category has many aspects in common with localization and allows one to dispose of localization techniques in situations not accessible to any of the classical concepts of localization this applies in particular to applications in the domain of finite dimensional algebras and their representations several applications of the methods presented in this paper are already in existence partly published or appearing in print in the near future see for instance 40 39 4 45 26 49 46 and have show the versatility of the notion of a perpendicular category it seems that right perpendicular categories first appeared as the subcategories of so called closed objects in the process of the formation of the quotient cateogory of an abelian category with respect to a localizing serre subcategory see 18 47 34 another natural occurrence is encountered in commutative algebra forming the possibly infinitely generated modules of depth 2 cf section 7 the concept and some of the central applications were first presented in a talk given by the first author at the honnef meeting in january 1985 we also note that the perfectly matching nomination perpendicular category was coined by a schofield who discovered independently the usefulness of this concept in dealing with hereditary algebras see 39 cf also section 7 the authors further acknowledge the support of the deutsche forschungsgemeinschaft spp darstellungstheorie von endlichen gruppen und endlichdimensionalen algebren throughout this paper rings are associative with unit and modules are unitary right modules mod r respectively mod r denotes the category of all respectively all finitely presented right r modules

a necessary and sufficient condition for the existence of multisolitons in a self dual gauged sigma model this paper presents a resolution of the gaugedo 3 sigma model proposed by b j schroers in which the matter field o mapsr2 intos2 while the vector gauge potential gives rise to a magnetic field it is shown that for each natural numbern there are solutions to saturate the classical energy lower bounde 4 n for the field configurations in the topological family deg o n if and only ifn 1 furthermore the solutions obtained depend on at least 4n 3 continuous parameters the associated magnetic flux can assume its value in an open interval and the decay rates of the field strengths may be specified in a suitable range these solutions are multisolitons represented byn prescribed lumps of the magnetic field simulatingn identical particles in equilibrium and are governed by a nonlinear elliptic equation with both vortex and anti vortex source terms

estimation of a stationary markov chain this article addresses the issue of empirical bayes estimation procedures for the transition probability matrix of a single stationary markov chain the distribution of the frequency count matrix is obtained by relying heavily on the whittle distributions and on the natural conjugate priors thence empirical bayes estimates are obtained and the limiting distribution is derived

existence of topological multi string solutions in abelian gauge field theories in this paper we consider a general form of self dual equations arising from abelian gauge field theories coupled with the einstein equations by applying the super subsolution method we prove that topological multi string solutions exist for any coupling constant which improves previously known results we provide two examples for application the self dual einstein maxwell higgs model and the gravitational maxwell gauged o 3 sigma model

nontopological solutions in the self dual maxwell chern simons gauged o 3 sigma model abstract in this paper we prove the existence of nontopological solutions in the self dual maxwell chern simons gauged o 3 sigma model in the plane if the scaling parameter is small enough the reduced equation can be regarded as a perturbation of the liouville equation then we use the generalized implicit function theorem to prove the existence of solutions with nontopological boundary conditions using this result we show the existence of symmetrically topological solutions and nontopological solutions for the original self dual equations whose magnetic fluxes are slightly bigger than the critical value moreover we also compute the topological charge and the degree of the spin vectors

tilting classes over wild hereditary algebras in this paper we investigate tilting classes over connected hereditary algebras of in nite representation type and in particular over connected wild hereditary algebras thecase when the generating tilting module is nitely generated was studied in 13 in 17 lukas proved several facts important for our general setting in the present terminology heshowed that given a wild hereditary algebra

constructing tilting modules we investigate the structure of infinite dimensional tilting modules over hereditary artin algebras for connected algebras of infinite representation type with grothendieck group of rank n we prove that for each 0 i n 1 there is an infinite dimensional tilting module t i with exactly i pairwise non isomorphic indecomposable finite dimensional direct summands we also show that any stone is a direct summand in a tilting module in the final section we give explicit constructions of infinite dimensional tilting modules over iterated one point extensions

multivortex solutions in the chern simons gauged o 3 sigma model on a doubly periodic domain abstract we establish the existence and uniqueness results for multivortex solutions of an elliptic equation arising from the self dual chern simons gauged o 3 sigma model with a symmetric potential on a flat 2 torus we prove that if the parameter e 0 is small then the elliptic governing equation admits a maximal solution we also study the asymptotic behavior of the maximal solutions as e 0 by using this asymptotic behavior we establish the uniqueness results for solutions which tend to a e as e 0 under suitable conditions on the dirac measure

local and global solutions of chern simons gauged o 3 sigma equations in one space dimension we study an initial value problem of the chern simons gauged o 3 sigma model in one space dimension the global existence of solutions to the model is proved for high regularity initial data moreover we study low regularity local well posedness observing null forms of the system and applying bilinear estimates for wave sobolev space hs as a by product a finite energy global solution is constructed

on the perpendicular category of a partial tilting module abstract the perpendicular category of a partial tilting module is studied in particular that of a regular module over a hereditary algebra preferably of wild representation type the results are used to establish the existence of a unique preprojective component for a large class of tilted algebras

the structure and homological properties of generalized standard auslander reiten components abstract we describe the structure and homological properties of arbitrary generalized standard auslander reiten components of artin algebras in particular we prove that for all but finitely many indecomposable modules in such components the euler characteristic is defined and nonnegative further we provide a handy criterion for an infinite auslander reiten component of an artin algebra to be generalized standard we solve also the long standing open problem concerning the structure of artin algebras admitting a separating family of auslander reiten components