integral bilinear forms coxeter transformations and coxeter polynomials of finite posets abstract linear algebra technique in the study of linear representations of finite posets is developed in the paper a concept of a quadratic wandering on a class of posets i is introduced and finite posets i are studied by means of the four integral bilinear forms b i b i b i b i z i z i z 1 1 the associated coxeter transformations and the coxeter polynomials in connection with bilinear forms of dynkin diagrams extended dynkin diagrams and irreducible root systems are also studied bilinear equivalences between some of the forms are established and equivalences with the bilinear forms of dynkin diagrams and extended dynkin diagrams are discussed a homological interpretation of the bilinear forms 1 1 is given and z bilinear equivalences between them are discussed by applying well known results of bongartz loupias and zavadskij shkabara we give several characterisations of posets i with the euler form q i x b i x x weakly positive resp with the reduced euler form q i x b i x x weakly positive and posets i with the tits form q i x b i x x weakly positive

exact mean field solutions of the asymmetric random average process we consider the asymmetric random average process arap with continuous mass variables and parallel discrete time dynamics studied recently by krug garcia and rajesh majumdar both j statist phys 99 2000 the model is defined by an arbitrary state independent fraction density function r with support on the unit interval we examine the exactness of mean field steady state mass distributions in dependence of and identify as a conjecture based on high order calculations the class of density functions yielding product measure solutions additionally the exact form of the associated mass distributions p m is derived using these results we show examplary the exactness of the mean field ansatz for monomial fraction densities r n 1 rn 2 with n 2 for verification we calculate the mass distributions p m explicitly and prove directly that product measure holds furthermore we show that even in cases where the steady state is not given by a product measure very accurate approximants can be found in the class

algebras with separating almost cyclic coherent auslander reiten components we prove that the class of artin algebras whose auslander reiten quiver admits a separating family of almost cyclic coherent components coincides with the class of generalized multicoil enlargements of concealed canonical algebras moreover the module category homological properties and the representation type of artin algebras with separating families of almost cyclic coherent auslander reiten components are described

models of stress fluctuations in granular media we investigate in detail two models describing how stresses propagate and fluctuate in granular media the first one is a scalar model where only the vertical component of the stress tensor is considered in the continuum limit this model is equivalent to a diffusion equation where the r ole of time is played by the vertical coordinate plus a randomly varying convection term we calculate the response and correlation function of this model and discuss several properties in particular related to the stress distribution function we then turn to the tensorial model where the basic starting point is a wave equation which in the absence of disorder leads to a ray like propagation of stress in the presence of disorder the rays acquire a diffusive width and the angle of propagation is shifted a striking feature is that the response function becomes negative which suggests that the contact network is mechanically unstable to very weak perturbations the stress correlation function reveals characteristic features related to the ray like propagation which are absent in the scalar description our analytical calculations are confirmed and extended by a numerical analysis of the stochastic wave equation

conserved mass models and particle systems in one dimension in this paper we study analytically a simple one dimensional model of mass transport we introduce a parameter p that interpolates between continuous time dynamics p 0 limit and discrete parallel update dynamics p 1 for each p we study the model with i both continuous and discrete masses and ii both symmetric and asymmetric transport of masses in the asymmetric continuous mass model the two limits p 1 and p 0 reduce respectively to the q model of force fluctuations in bead packs s n coppersmith et al phys rev e 53 4673 1996 and the recently studied asymmetric random average process j krug and j garcia cond mat 9909034 we calculate the steady state mass distribution function p m assuming product measure and show that it has an algebraic tail for small m p m m where the exponent depends continuously on p for the asymmetric case we find p 1 p 2 p for 0 p 1 and 1 1 and for the symmetric case p 2 p 2 8 5p p 2 for all 0 p 1 we discuss the conditions under which the product measure ansatz is exact we also calculate exactly the steady state mass mass correlation function and show that while it decouples in the asymmetric model in the symmetric case it has a nontrivial spatial oscillation with an amplitude decaying exponentially with distance

matrix product approach for the asymmetric random average process we consider the asymmetric random average process which is a one dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables first the explicit functional representations so called beta densities of all local interactions leading to steady states of product measure form are rigorously derived this also completes an outstanding proof given in a previous publication then we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz due to continuous state variables we obtain a matrix algebra in the form of a functional equation which can be solved exactly

the tits and euler forms of a tame algebra since the introduction by gabriel in 1972 of the tits quadratic form associated to finite dimensional hereditary algebras quadratic forms have played an important role in the representation theory of algebras and related categories there have been quadratic forms associated to finite dimensional algebras partially ordered sets and other objects in order to determine their representation type and the classes of indecomposable representations in the corresponding grothendieck group see for example 3 9 14 21 the class of finite dimensional algebras associative with in identity over an algebraically closed field k is divided into two disjoint classes one class consists of tame algebras for which the indecomposable modules occur in each dimension in a finite number of discrete and one parameter families the second class consist of wild algebras whose representation theory is as complicated as the classification of pairs of matrices up to simultaneous conjugation in this paper we establish properties of the tits and euler forms associated to tame simply connected algebras let a be a basic connected finite dimensional algebra over k then a has a presentation a kqa i where qa q0 q1 is the ordinary quiver of a with set of vertices q0 and set of arrows q1 and i is an admissible ideal of the path algebra kqa see 9 we shall assume that qa has no oriented cycles and hence g dim a then the euler form a zq0 z is defined by

the first cohomology group of an algebra with coefficients in a bimodule after their introduction in the 1940s cf 18 the hochschild homology and cohomology groups of an algebra with coefficients in a bimodule have played a fundamental role given an algebra and a bimodule m and viewing both and m as left modules over the enveloping algebra e op the hochschild cohomology groups h m are the groups ext m while the homology groups h m are the corre sponding tor groups cf 5 chap ix the most studied case has been that in which m and more specifically when is a split basic finite dimensional algebra over a field k in that case the algebra is partially determined by combinatorial data namely its quiver with relations and it is a natural goal to obtain information about h m resp h m in terms of those combinatorial data that was the scheme of the initial attempts made by cibils 6 and happel 17 to give explicit formulae for the dimensions of the h in terms of computations the first natural situation to look at is that in which the algebra is monomial since

longtime closeness estimates for bounded and unbounded solutions of non recurrent duffing equations with polynomial potentials abstract in this paper we consider the littlewood s problem for the second order differential equation x x 2 n 1 q t x l p t l n where the functions p t and q t do not need to be periodic using the theory of non periodic twist mappings which is developed by kunze and ortega in 3 4 5 6 7 we obtained longtime closeness results on the bounded and unbounded solutions of the equation

tame algebras and tits quadratic forms abstract we solve a long standing problem concerning the connection between the tameness of simply connected algebras and the weak nonnegativity of the associated tits integral quadratic forms and derive some consequences

module varieties over canonical algebras abstract the main purpose of this paper is the study of module varieties over the class of canonical algebras providing a rich source of examples of varieties with interesting properties our main tool is a stratification of module varieties which was recently introduced by richmond this stratification does not require a precise knowledge of the module category if it is finite then it provides a method to classify irreducible components we determine the canonical algebras for which this stratification is finite in this case we describe the algorithm for calculating the dimension of the variety and the number of irreducible components of maximal dimension for an infinite family of examples we give easy combinatorial criteria for irreducibility cohen macaulay and normality

boundedness for sublinear duffing equations with time dependent potentials in this paper we prove a sufficient and necessary condition for the boundedness of all solutions for the sublinear equation x e t x 1x p t where 0 1 p t and e t are smooth 1 periodic functions

strongly simply connected schurian algebras and multiplicative bases abstract in this paper we define concepts of crowns and quasi crowns valid in an arbitrary schurian algebra and which generalise the corresponding concepts in an incidence algebra we show first that a triangular schurian algebra is strongly simply connected if and only if it is simply connected and contains no quasi crown we then prove that the absence of quasi crowns in a triangular schurian algebra implies the existence of a multiplicative basis

model for force fluctuations in bead packs we study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials we present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile we compare our results for the force distribution function for this model including exact results for certain contact angle probability distributions with numerical simulations of force distributions in random sphere packings this model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings our model is closely related to some that have been studied in the context of self organized criticality we present evidence that in the force distribution context critical power law force distributions occur only when a parameter hidden in other interpretations is tuned our numerical mean field and exact results all indicate that for almost all contact distributions the distribution of forces decays exponentially at large forces

graphs with relations coverings and group graded algebras the paper studies the interrelationship between coverings of finite directed graphs and gradings of the path algebras associated to the directed graphs to include gradings of all basic finite dimensional algebras over an algebraically closed field a theory of coverings of graphs with relations is introduced the object of this paper is to relate group gradings on algebras to coverings of a graph which is associated to the algebra the linking of the theories allows one to relate purely algebraic questions to questions in algebraic topology group theory or combinatorics in the representation theory of artin algebras the association to each algebra of a finite directed graph called the quiver of the algebra has been a useful tool the reason that the quiver of such an algebra is of interest is that there is a natural definition of representations of the quiver so that the category of representations of the quiver satisfying certain relations is equivalent to the category of finitely generated modules over the algebra 1 gives a slight extension of these concepts to finitely generated algebras the main emphasis of the paper is to show that the theory of coverings of graphs with relations introduced by c riedtmann 9 and expanded by p gabriel 2 and the theory of group graded algebras are essentially the same although the original connection between coverings and gradings was inspired by the similarity of results for z graded artin algebras 3 4 and p gabriel s announced results 2 the context of this paper is more general and deals with all finitely generated algebras over a field we associate to each such algebra a finite directed graph which we still call a quiver of the algebra we show that for each regular covering t of a quiver t0 of an algebra a with certain prescribed restrictions we get a g grading of the algebra a where g is the automorphism group of the covering y over ro conversely given a certain type of g grading of a where g is a group we construct a regular covering y of the quiver t0 of the algebra such that g is isomorphic to the automorphism group of t over ro furthermore if y is a regular covering of t0 with automorphism group g we show that the category of representations of y satisfying a certain set of relations is equivalent to the category of finite dimensional graded g modules we

an exactly solvable dissipative transport model we introduce a class of one dimensional lattice models in which a quantity which may be thought of as an energy is either transported from one site to a neighbouring one or locally dissipated transport is controlled by a continuous bias parameter q which allows us to study symmetric as well as asymmetric cases we derive sufficient conditions for the factorization of the n body stationary distribution and give an explicit solution for the latter before briefly discussing physically relevant situations

the universal cover of an algebra without double bypass let a be a basic and connected finite dimensional algebra over a field k of characteristic zero we show that if the quiver of a has no double bypass then the fundamental group as defined in r martinez villa j a de la pena the universal cover of a quiver with relations j pure appl algebra 30 1983 277 292 of any presentation of a by quiver and relations is the quotient of the fundamental group of a privileged presentation of a then we show that the galois covering of a associated with this privileged presentation satisfies a universal property with respect to the connected galois coverings of a in a similar fashion to the universal cover of a topological space

the classifying space of a bound quiver abstract we associate to a bound quiver q i a cw complex which we denote by b q i and call the classifying space of q i we show that the fundamental group of b q i is isomorphic to the fundamental group of q i moreover we show that this construction behaves well with respect to coverings on the other hand we study the co homology groups of b q i and compare them with the simplicial and the hochschild co homology groups of the algebra a kq i more precisely we give sufficient conditions for these groups to be isomorphic this generalizes a theorem due to gerstenhaber and schack j pure appl algebra 30 1983 143 156

unboundedness in a duffing equation with polynomial potentials abstract in this paper a continuous periodic function p t is constructed such that the duffing equation d2x dt2 x2n 1 p t xl 0 with p t c0 s1 n 2 2n 1 l n 2 possesses an unbounded solution which shows that the smoothness of the coefficients of the perturbation does influence the boundedness of solutions

the coexistence of quasi periodic and blow up solutions in a class of hamiltonian systems abstract the coexistence of quasi periodic solutions and blow up phenomena in a class of higher dimensional duffing type equations is proved in this paper moreover we show that the initial point sets for both kinds of solutions are of infinite lebesgue measure in the phase space for the part of quasi periodic solutions the tool we used is the small twist theorem for higher dimensional cases

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

finite dimensional algebras with vanishing hochschild cohomology let a be a finite dimensional algebra associative with unit over an algebraically closed field k for a finitely generated bimodule x the hochschild cohomology a a i w x i groups h a x i g 0 were introduced in 10 we shall denote h a i i s h a a the vanishing of the low dimensional groups h a i f 2 has classical interpretations and plays an important role in the representaw x tion theory of algebras gernstenhaber 7 has shown some connections 2 w x 1 between h a and the deformation theory of a see also 5 h a is

algebras whose tits form weakly controls the module category an important invariant associated to a finite dimensional algebra is its tits quadratic form this invariant has been extensively used in the representation theory of algebras to determine the representation type of w x an algebra see 4 11 16 to determine the classes of indecomposable w x modules in the grothendieck group see 9 11 20 and as a tool in a wide w x range of applications see 16 21 let a s kqri be a basic finite dimensional algebra over an algebraically closed field k we will assume that q is connected and without 4 oriented cycles we denote by q s 1 n resp q the set of vertices 0 1 resp arrows of q left a modules are considered as representations of w x q satisfying the ideal i for this point of view see 12 by s we denote i the simple representation associated with the vertex i g q observe that 0 1 dim ext s s is the number of arrows from i to j in q the tits form k a i j

boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term abstract in this paper we are concerned with the sublinear reversible systems with a nonlinear damping and periodic forcing term x f x g x x 1 x p t where f x p t are odd functions p t is smooth 1 periodic function and 0 is a constant a sufficient and necessary condition for the boundedness of all solutions of the above equation is established moreover we show the existence of aubry mather sets as well

oscillatory escape in a duffing equation with a polynomial potential t x 0 v t 1 x v t x 1 a large class of such systems turns out to be near integrable at infinity asa consequence most large amplitude solutions are quasiperiodic withtwo frequencies and furthermore all solutions are bounded for all time the main distinguishing feature of this class of systems is the super quadratic behavior of the potential v for large x the near integrabilityat infinity is due to the difference in time scales between the time dependence of the potential on the one hand and the rapid oscillations ofhigh amplitude solutions on the other there has been much work on the

lagrange stability for duffing type equations abstract in this paper the duffing type equation d 2 x dt 2 x 2 n 1 p 2 n t x 2 n p 1 t x p 0 t 0 is studied where the p j s are 1 periodic it is shown that all solutions of this equation are bounded provided that the p j t 0 j n are of bounded variation in 0 1 and that the derivatives of p j t n j 2 n are lipschitzian it is also shown that there exist p j s being discontinuous everywhere such that all solutions of the equation are bounded this implies that the continuity of p j s is not necessary for the boundedness of solutions of the equation

algebras with cycle finite galois coverings we prove that the finite dimensional algebras over an algebraically closed field which admit cycle finite galois coverings with torsion free galois groups are of tame representation type and derive some consequences

lagrange stability for impulsive duffing equations abstract this work discusses the boundedness of solutions for impulsive duffing equation with time dependent polynomial potentials by kam theorem we prove that all solutions of the duffing equation with low regularity in time undergoing suitable impulses are bounded for all time and that there are many positive lebesgue measure quasi periodic solutions clustering at infinity this result extends some well known results on duffing equations to impulsive duffing equations

on the additive categories of generalized standard almost cyclic coherent auslander reiten components abstract we prove geometric and homological properties of modules in the additive categories of generalized standard almost cyclic coherent components in the auslander reiten quivers of finite dimensional algebras

cartan leray spectral sequence for galois coverings of linear categories abstract we provide a cartan leray type spectral sequence for the hochschild mitchell co homology of a galois covering of linear categories we infer results relating the galois group and hochschild cohomology in degree one

geometry of directing modules over tame algebras throughout the paper k denotes a fixed algebraically closed field by an algebra we mean a finite dimensional k algebra associative with an identity and by a module a finite dimensional left a module the class of algebras may be divided into two disjoint subclasses one class consists of tame algebras for which the indecomposable modules occur in each dimension in a finite number of discrete and a finite number of one parameter families the second class is formed by the wild algebras whose representation theory is as complicated as the study of finite dimensional vector spaces together with two noncommuting endomorphisms for which the classification up to isomorphism is a well known unsolved problem hence we can realistically hope to describe modules only for tame algebras given an algebra a and a nonnegative vector d in the grothendieck group k a of a it is an interesting task to study the 0 affine variety mod d of a modules of dimension vector d and the action a of the corresponding product g d of general linear groups for example we may ask when the variety mod d is irreducible smooth complete a intersection gorenstein cohen macaulay normal the main aim of this paper is to describe the geometry of module varieties mod d for the dimension vectors d of arbitrary directing moda w x ules over tame algebras recall that following 20 an indecomposable a module m is said to be directing if it does not belong to a cycle m a m a a m a m of nonzero nonisomorphisms between inde1 r composable a modules directing modules have played an important role

exact tracer diffusion coefficient in the asymmetric random average process we study tracer diffusion in the continuous time asymmetric random average process which is an interacting particle system on generalizing the hammersley process from the equations of motion for the particle position correlations we obtain the exact tracer diffusion coefficient which is in agreement with a recent heuristic result by krug and garcia