equivariant stable homotopy and segal s burnside ring conjecture analogous results were proved later for ko in the generality of compact lie groups by atiyah and segal 8 and for kfq the algebraic k theory spectrum associated to the finite field fq by rector 29 using quillen s 26 computation of it kfq in each case the answer involves an appropriate completed representation ring of g and the cohomology theory in question is constructed from the permutative category of finite dimensional vector spaces over a field see 31 if one considers cohomology theories constructed from other permutative categories one expects to find analogous computations in terms of a completed representation ring of g in the given category appropriately defined in particular stable cohomotopy ts is constructed from the category of finite sets 31 and for this category the analogue of the representation ring is a well known object the burnside ring a g 13 a g is a commutative ring with augmentation so one may speak of a g the completed burnside ring moreover there is

coupling and hydrodynamic limit for the inclusion process we show propagation of local equilibrium for the symmetric inclusion process sip after diffusive rescaling of space and time as well as the local equilibrium property of the non equilibrium steady state in the boundary driven sip the main tool is self duality and a coupling between n sip particles and n independent random walkers

linking first occurrence polynomials over f2 by steenrod operations abstract it is proved that for every irreducible representation l of the full matrix semigroup mn f 2 the first occurrence of l as a composition factor in the polynomial algebra p f 2 x1 xn is linked by a steenrod operation to the first occurrence of l as a submodule in p this steenrod operation is given explicitly as the image of an admissible monomial in the steenrod squares sqr under the canonical anti automorphism of the mod 2 steenrod algebra a the first occurrences of both kinds are also linked to higher degree occurrences of l by elements of the milnor basis of a

duality in interacting particle systems and boson representation in the context of markov processes we show a new scheme to derive dual processes and a duality function based on a boson representation this scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators for some stochastic processes duality relations have been known which connect continuous time markov processes with discrete state space and those with continuous state space we clarify that using a generating function approach and the doi peliti method a birth death process or discrete random walk model is naturally connected to a differential equation with continuous variables which would be interpreted as a dual markov process the key point in the derivation is to use bosonic coherent states as a bra state instead of a conventional projection state as examples we apply the scheme to a simple birth coagulation process and a brownian momentum process the generator of the brownian momentum process is written by elements of the su 1 1 algebra and using a boson realization of su 1 1 we show that the same scheme is available

equilibrium fluctuations for a system of harmonic oscillators with conservative noise we investigate the harmonic chain forced by a multiplicative noise the evolution is given by an infinite system of stochastic differential equations total energy and deformation are preserved the conservation of momentum is destroyed by the noise gaussian product measures are the extremal stationary states of this model equilibrium fluctuations of the conserved fields at a diffusive scaling are described by a couple of generalized ornstein uhlenbeck processes

determinism and non determinism in pdl abstract the main purpose of this paper is to consider a variant of propositional dynamic logic pdl in which the natural program concepts while do od and if then else fi are basic and in which is the only non deterministic program concept dropping leads to the known system strict propositional dynamic logic spdl the main result of this paper is that spdl is weaker than pdl it is pointed out however that by extending spdl by propositional assignments a system called propositional program logic ppl is obtained which has the same expressive power as pdl

a generalized asymmetric exclusion process with uq sl2 stochastic duality we study a new process which we call asep q j where particles move asymmetrically on a one dimensional integer lattice with a bias determined by q 0 1 and where at most 2 j n particles per site are allowed the process is constructed from a 2 j 1 dimensional representation of a quantum hamiltonian with uq sl2 invariance by applying a suitable ground state transformation after showing basic properties of the process asep q j we prove self duality with several selfduality functions constructed from the symmetries of the quantum hamiltonian by making use of the self duality property we compute the first q exponential moment of the current for step initial conditions both a shock or a rarefaction fan as well as when the process is started from a homogeneous product measure

extended duality relations between birth death processes and partial differential equations duality relations between continuous state and discrete state stochastic processes with continuous time have already been studied and used in various research fields we propose extended duality relations which enable us to derive discrete state stochastic processes from arbitrary diffusion type partial differential equations the derivation is based on the doi peliti formalism and it will be clarified that additional states for the discrete state stochastic processes must be considered in some cases

the composition factors of fp x1 x2 x3 as a gl 3 p module let gl n p denote the general linear group over the prime field fp and let sd denote the right gl n p module consisting of all homogeneous polynomials of degree d in n variables x1 x2 x over f we wish to determine the simple composition factors of sd unfortunately satisfactory models for all the simple gl n p modules themselves are not known there are p p 1 of these simple modules up to isomorphism and all of them are known to occur in the symmetric algebra s cf sd the general problem is therefore a very difficult one in our present state of knowledge the purpose of this paper is to offer a solution to this problem in the case n 3 this extends the work of david carlisle who calculated in his manchester thesis 2 the occurrences of all the l dimensional modules and developed a method for dealing with the general case let us begin with some general remarks about the problem the case n 1 is trivial as s d detd the dth power of the determinant representation the case n 2 is also easily disposed of for instance by glover 9 the simple modules are the tensor products of the sd for d 1 and d p the module s is not simple for example the pth power sf of the natural module is a proper submodule of 411 0021 8693192 3 00

structure of the condensed phase in the inclusion process we establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum occupation number we make use of size biased sampling to study the structure of the condensed phase which can extend over more than one lattice site and exhibit an interesting hierarchical structure characterized by the poisson dirichlet distribution while this approach is established in other areas including population genetics or random permutations we show that it also provides a powerful tool to analyse homogeneous condensation in stochastic particle systems with stationary product distributions we discuss the main mechanisms beyond inclusion processes that lead to the interesting structure of the condensed phase and the connection to other generic particle systems our results are exact and we present monte carlo simulation data and recursive numerics for partition functions to illustrate the main points

conservative interacting particles system with anomalous rate of ergodicity we analyse certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures furthermore we show that convergence rate to equilibrium is exponential this result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence the system in question is stochastic rather than deterministic

non abelian symmetries of stochastic processes derivation of correlation functions for random vertex models and disordered interacting particle systems we consider systems of particles hopping stochastically on d dimensional lattices with space dependent probabilities we map the master equation onto an evolution equation in a fock space where the dynamics are given by a quantum hamiltonian continuous time or a transfer matrix discrete time using non abelian symmetries of these operators we derive duality relations expressing the time evolution of a given initial configuration in terms of correlation functions of simpler dual processes particularly simple results are obtained for the time evolution of the density profile as a special case we show that for any su 2 symmetric system the two point and three point density correlation functions in the n particle steady state can be computed from the probability distribution of a single particle moving in the same environment we apply our results to various models among them partial exclusion a simple diffusion reaction system and the two dimensional six vertex model with space dependent vertex weights for a random distribution of the vertex weights one obtains a version of the random barrier model describing diffusion of particles in disordered media we derive exact expressions for the averaged two point density correlation functions in the presence of weak correlated disorder

duality and exact correlations for a model of heat conduction we study a model of heat conduction with stochastic diffusion of energy we obtain a dual particle process which describes the evolution of all the correlation functions an exact expression for the covariance of the energy exhibits long range correlations in the presence of a current we discuss the formal connection of this model with the simple symmetric exclusion process

self duality for the two component asymmetric simple exclusion process we study a two component asymmetric simple exclusion process asep that is equivalent to the asep with second class particles we prove self duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra uq x1d524 x1d529 3 we construct all invariant measures in explicit form and discuss some of their properties we also prove a sum rule for the duality functions

entropy of open lattice systems we investigate the behavior of the gibbs shannon entropy of the stationary nonequilibrium measure describing a one dimensional lattice gas of l sites with symmetric exclusion dynamics and in contact with particle reservoirs at different densities in the hydrodynamic scaling limit l the leading order o l behavior of this entropy has been shown by bahadoran to be that of a product measure corresponding to strict local equilibrium we compute the first correction which is o 1 the computation uses a formal expansion of the entropy in terms of truncated correlation functions for this system the k th such correlation is shown to be o l k 1 this entropy correction depends only on the scaled truncated pair correlation which describes the covariance of the density field it coincides in the large l limit with the corresponding correction obtained from a gaussian measure with the same covariance

the propositional dynamic logic of deterministic well structured programs abstract we consider a restricted propositional dynamic logic strict deterministic propositional dynamic logic sdpdl which is appropriate for reasoning about deterministic well structured programs in contrast to pdl for which the validity problem is known to be complete in deterministic exponential time the validity problem for sdpdl is shown to be polynomial space complete we also show that sdpdl is less expressive than pdl and give a complete axiomatization for it the results rely on structure theorems for models of satisfiable sdpdl formulas and the proofs give insight into the effects of nondeterminism on intractability and expressiveness in program logics

subalgebras of the steenrod algebra and the action of matrices on truncated polynomial algebras let a t be the subalgebra of the steenrod algebra generated by sqi i 2t we determine which a module indecomposable summands of f2 x1 xn are free over a t by first showing this to be equivalent to the group theoretic question of determining which irreducible modular representations of mn f2 or gln f2 occur as composition factors in the truncated polynomial algebra f2 x1 xn x12 xn2 the second question is then answered

nonequilibrium dynamics of a stochastic model of anomalous heat transport we study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic langevin heat baths the noise amounts to random collisions between nearest neighbour oscillators that exchange their momenta in a recent paper lepri et al 2009 j phys a math theor 42 025001 we have studied the stationary state of this system with fixed boundary conditions finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic continuum limit in this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state starting from the exact equations governing the evolution of the correlation matrix we identify and adiabatically eliminate the fast variables arriving at a continuity equation for the temperature profile t y t complemented by an ordinary equation that accounts for the evolution in the bulk altogether we find that the evolution of t y t is the result of fractional diffusion

nonequilibrium measures which exhibit a temperature gradient study of a model we give some rules to define measures which could describe heat flow in homogeneous crystals we then study a particular model which is explicitly solvable the one dimensional nearest neighborhood ising model we analyze two cases in the first one the spins at the two boundaries interact with reservoirs at different temperatures in the thermodynamical limit the measure we introduce converges locally to gibbs measures and a temperature profile is so derived we obtain an explicit expression for the thermal conductivity coefficient which depends on the temperature in the second case we study the asymptotic behavior starting from an initial state in which each half of the space is at a different temperature we find again a temperature profile which asymptotically obeys the heat equation with the thermal conductivity coefficient previously derived from a mathematical point of view the analysis of the invariant measure is made possible by studying a time reversed process related to a graphical representation of an associated process this provides us with an explicit formula for then fold correlation function and we study the limiting behavior using both this representation for proving an exchangeability result and a donsker type spacetime renormalization procedure

the bar complex of an e infinity algebra the standard reduced bar complex b a of a differential graded algebra a inherits a natural commutative algebra structure if a is a commutative algebra we address an extension of this construction in the context of e infinity algebras we prove that the bar complex of any e infinity algebra can be equipped with the structure of an e infinity algebra so that the bar construction defines a functor from e infinity algebras to e infinity algebras we prove the homotopy uniqueness of such natural e infinity structures on the bar construction we apply our construction to cochain complexes of topological spaces which are instances of e infinity algebras we prove that the n th iterated bar complexes of the cochain algebra of a space x is equivalent to the cochain complex of the n fold iterated loop space of x under reasonable connectedness completeness and finiteness assumptions on x

correlation inequalities for interacting particle systems with duality we prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other a process which we call here the symmetric inclusion process sip or repel each other a generalized version of the well known symmetric exclusion process as an application new correlation inequalities are obtained for the sip as well as for some interacting diffusions which are used as models of heat conduction the so called brownian momentum process and the brownian energy process these inequalities are counterparts of the inequalities in the opposite direction for the symmetric exclusion process showing that the sip is a natural bosonic analogue of the symmetric exclusion process which is fermionic finally we consider a boundary driven version of the sip for which we prove duality and then obtain correlation inequalities

large deviations for a stochastic model of heat flow we investigate a one dimensional chain of 2n harmonic oscillators in which neighboring sites have their energies redistributed randomly the sites n and n are in contact with thermal reservoirs at different temperature and kipnis et al j statist phys 27 65 74 1982 proved that this model satisfies fourier s law and that in the hydrodynamical scaling limit when n the stationary state has a linear energy density profile bar theta u u 1 1 we derive the large deviation function s u for the probability of finding in the stationary state a profile u different from bar theta u the function s has striking similarities to but also large differences from the corresponding one of the symmetric exclusion process like the latter it is nonlocal and satisfies a variational equation unlike the latter it is not convex and the gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state we also briefly discuss more general models and find the features common in these two and other models whose s is known

modular representations of gl 3 fp symmetric squares and mod p cohomology of gl 3 z abstract we prove certain cases of nonabelian reciprocity between mod p galois representations and hecke eigenclasses in the mod p cohomology of gl 3 z using the symmetric square liftings from gl 2 and congruences on hecke eigenvalues we need to develop some modular representation theory for gl 3 z p in some cases we also need to invoke certain computer calculations to finish the proof

on dualities for ssep and asep with open boundary conditions duality relations for simple exclusion processes with general open boundaries are discussed it is shown that a combination of spin operators and bosonic operators enables us to have a unified discussion about duality relations with open boundaries as for the symmetric simple exclusion process ssep more general results than those from previous studies are obtained it is clarified that not only the absorbing sites but also additional sites called copying sites are needed for the boundaries in the dual process for the ssep the role of the copying sites is to conserve information about the particle states on the boundary sites similar discussions are applied to the asymmetric simple exclusion process asep in which the q analogues are employed and it is clarified that the asep with open boundaries has a complicated dual process on the boundaries

foncteurs polynomiaux stricts et modules instables sur l algebre de steenrod resume soient u f et p respectivement les categories des modules instables sur l algebre de steenrod modulo p sans bockstein des representations generiques des groupes lineaires generaux h w henn j lannes and l schwartz 1993 1 n j kuhn 1994 2 et des foncteurs polynomiaux stricts a la friedlander and suslin 1997 3 un foncteur f u f est construit dans h w henn j lannes and l schwartz 1993 1 utilisant le foncteur de lannes en degre 0 on construit dans cet article un foncteur m p u exact et commutant au produit tensoriel et a la torsion de frobenius qui constitute un relevement du foncteur oubli o p f m f o

characterizations of spectra with injective cohomology which satisfy the brown gitler property we work in the stable homotopy category ofp complete connective spectra having mod p homology of nite type h x means cohomology with z p coecients and is a left module over the steenrod algebraa a spectrum z is called spacelike if it is a wedge summand of a suspension spectrum and a spectrum x satises the brown gitler property if the natural map x z homa h z h x is onto for all spacelike z it is known that there exist spectra t n satisfying the brown gitler prop erty and with h t n isomorphic to the injective envelope of h s n i n the categoryu of unstablea modules call a spectrum x standard if it is a wedge of spectra of the form l t n where l is a stable wedge summand of the classifying space of some elementary abelian p group such spectra haveu injective cohomology and allu injectives appear in this way working directly with the two properties of t n stated above we clarify and extend earlier work by many people on brown gitler spectra our main theorem is that if x is a spectrum withu injective cohomology the following conditions are equivalent a there exists a spectrum y whose cohomology is a reducedu injective and a map x y that is epic in cohomology b there exists a spacelike spectrum z a nd am apx z that is epic in cohomology c 11 x x is monic in cohomology d x satises the brown gitler property e x is spacelike f x is standard m2uis reduced if it has no nontrivial submodule which is a suspension as an application we prove that the snaith summands of 2 s 3 are brown gitler spectra a new result for the most interesting summands at odd primes another application combines the theorem with the second author s work on the whitehead conjecture of independent interest enroute to proving that b implies c we prove that the homology suspension has the following property if an n connected space x admits a map to an n fold suspension that is monic in mod p homol ogy then nn x x is onto in mod p homology

weyl modules and the mod 2 steenrod algebra abstract this paper continues our study of the action of the mod 2 steenrod algebra a 2 on the polynomial algebra p n f 2 t 1 t n we obtain further partial results on the hit problem of f p peterson which asks for a minimal generating set for p n as an a 2 module we also study the structure of the quotient by the hit elements as a graded representation of the finite general linear group g n gl n f 2 i e as a module over the finite group algebra f 2 g n these results were obtained in previous work of the authors for the special case of the steinberg module for g n by extending the scalars to f 2 the algebraic closure of f 2 we obtain commuting actions of a 2 and g n on p n f 2 t 1 t n while this makes no essential difference to the representation theory of g n or to the hit problem it allows us to treat the action of g n on p n as the restriction of that of the algebraic group g n gl n f 2 in particular we make use of tilting modules for g n to show that for every irreducible representation l of g n a minimal set of a 2 generators of p n must contain a copy of the corresponding dual weyl module

deligne lusztig characters of the finite general linear groups and eigenvectors of lannes t functor abstract the eigenvalue conjecture of lionel schwartz states that the induced action of lannes t functor on the grothendieck ring of reduced injective unstable modules over the mod p steenrod algebra is diagonalizable over q with eigenvalues the powers of p while some proofs have been given for the conjecture none of them could shed light on the problem of determining the eigenvectors of t the aim of this paper is to compute at the same time eigenvalues and eigenvectors of t by making use of the deligne lusztig characters of the finite general linear groups based on this computation some remarks and conjectures about the multiplicative structure of the grothendieck ring and the poincare series of eigenvectors will be also given

lannes t functor on summands of h b z p s let h be the mod p cohomology of the classifying space b z p thought of as an object in the category u of unstable modules over the steenrod algebra lannes constructed a functor t u u which is left adjoint to the functor a a h in this paper we evaluate t on the indecomposable u summands of h s the tensor product of s copies of h our formula involves the composition factors of certain tensor products of irreducible representations of the semigroup ring f p m s s z p

propositional dynamic logic with local assignment we propose an extension of propositional dynamic logic which allows a new kind of program terms local assignments to propositional variables they are very close to the known array assignments in dynamic logic beacuse they allow us to change the truth values of predicate variables in this logic many notions like equivalence of programs looping and finitely branching are expressible on a propositional level in fact we show that the resulting logic is equivalent in expressive power to first order logic augmented by a device to express transitive closures in other words it is modulo extra predicate symbols equivalent to first order dynamic logic not suprisingly therefore the validity problem for this extension is 11 complete

the morava k theories of some classifying spaces let p be a finite abelian p group with classifying space bp we compute in representation theoretic terms the morava k theories of the stable wedge summands of bp in particular we obtain a simple and purely group theoretic description of the rank of k s bg for any finite group g with an abelian p sylow subgroup a minimal amount of topology quickly reduces the problem to an algebraic one of analyzing truncated polynomial algebras as modular representations of the semigroup m 1 z p 1 main results for a fixed prime p there exists a sequence of cohomology theories k 1 k 2 with k s periodic with period 2 ps 1 these are the morava k theories 13 and generalize ordinary complex k theory in the sense that k 1 is one of the p 1 isomorphic summands of k z p recently it has been becoming clear that they play a central role in homotopy theory see for example the work of m hopkins and j smith 6 k s has further computational virtues k s x is always a free module over the coefficient ring k s and there is a kunneth isomorphism a major outstanding problem is to find good models for the spaces representing these theories related to this is the question of finding for finite groups g a group theoretic description for the rings k s bg analogous to atiyah s isomorphism 2 r g k bg the author together with j harris recently analyzed stable wedge decompositions of classifying spaces of abelian p groups 5 in this paper we compute in representation theoretic terms the morava k theories of the resulting wedge summands as a consequence we obtain a very simple and purely group theoretic description of the rank of k s bg for any finite group g with an abelian p sylow subgroup to state our results we establish some notation it is convenient to let k o be rational cohomology we let k s x always denote the reduced sth morava k theory of x if x is a space or spectrum we let k5 x equal the rank of k s x as a k s module and by abuse of notation we let ks g ks bg for a finite group g bg is the union of bg with a disjoint basepoint received bv the editors may 27 1986 1980 marhemat7es subject cl lssific ltion primary 55n22 secondary 20g05 research partially supported by the sloan foundation and the nsf t1987 american mathematical society 0002 9947 87 1 00 25 per page

fluctuations in driven systems abstract the lecture notes give an introduction to some aspects of fluctuations in driven systems first a particularly straightforward derivation of fluctuation theorems and their relation to linear response will be given being particularly simple the derivation gives clear limitations on the regime of validity of the theorems second an introduction to systems in local thermal equilibrium in time and space will be given to this end two building blocks will be studied one a system which is driven by some cyclically changing external potential the other consisting of two systems at different temperatures which are equilibrating both building blocks display an interesting time evolution for example the statistical properties of fluctuations of the energy in driven isolated systems generally fall into two types of distinct behaviors following this a systematic approach for describing more complicated systems will be outlined by studying other setups specifically driven dissipative systems and systems driven by two external baths at different temperatures the formalism will be used to elucidate in a minimal model the origin and sign of correlation in a boundary driven system

homotopy fixed point methods for lie groups and finite loop spaces a loop space x is by definition a triple x bx e in which x is a space bx is a connected pointed space and e x qbx is a homotopy equivalence from x to the space qbx of based loops in bx we will say that a loop space x is finite if the integral homology h x z is finitely generated as a graded abelian group i e if x appears at least homologically to be a finite complex in this paper we prove the following theorem

on the cohomology of elementary abelian groups the structure of the bp cohomology of elementary abelian p groups is studied obtaining a presentation expressed in terms of bp cohomology and mod p singular cohomology using the milnor derivations the arguments are based on a result on multi koszul complexes which is related to margolis s criterion for freeness of a graded module over an exterior algebra

orthogonal stochastic duality functions from lie algebra representations we obtain stochastic duality functions for specific markov processes using representation theory of lie algebras the duality functions come from the kernel of a unitary intertwiner between representations which provides generalized orthogonality relations for the duality functions in particular we consider representations of the heisenberg algebra and mathfrak su 1 1 both cases lead to orthogonal self duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes

on the p adic completions of nonnilpotent spaces this paper deals with the p adic completion f p x developed by bousfield kan for a space x and prime p a space x is called f p good when the map x f p x is a mod p homology equivalence and called f p bad otherwise general examples of f p good spaces are established beyond the usual nilpotent or virtually nilpotent ones these include the polycyclic by finite spaces however the wedge of a circle with a sphere of positive dimension is shown to be f p bad this provides the first example of an f p bad space of finite type and implies that the p profinite completion of a free group on two generators must have nontrivial higher mod p homology as a discrete group

a proof of schwartz s conjecture about the eigenvalues of lannes t functor abstract this paper gives an algebraic proof of a conjecture due to lionel schwartz which asserts that the linear operator induced by lannes t functor on the grothendieck group k n red generated by indecomposable summands of the mod p cohomology of a rank n elementary abelian p group is diagonalizable over q with eigenvalues 1 p p n and with multiplicities p n p n 1 p n 1 p n 2 p 1 1 respectively using work of harris and shank we first reduce this to an algebraic question involving the grothendieck ring g 0 m n p of modules over the semigroup ring f p end f p n showing that the induced action of t on k n red corresponds to the multiplication by an explicit element in the second step we establish the separability of the algebra c g 0 m n p from which the diagonalizability and the computation of the eigenvalues and their multiplicities follow easily the arguments use ingredients from the theory of brauer characters of finite groups

negative dependence and the geometry of polynomials we introduce the class of strongly rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter this class covers important models such as determinantal measures e g product measures and uniform random spanning tree measures and distributions for symmetric exclusion processes we show that strongly rayleigh measures enjoy all virtues of negative dependence and we also prove a series of conjectures due to liggett pemantle and wagner respectively moreover we extend lyons recent results on determinantal measures and we construct counterexamples to several conjectures of pemantle and wagner on negative dependence and ultra log concave rank sequences

decidability of finite probabilistic propositional dynamic logics abstract this paper deals with various versions of finite propositional probabilistic dynamic logic we present probabilistic propositional dynamic logic with simple probabilistic estimations and almost regular program language besides the logics previously introduced in the literature we present some natural variations and extensions of these logics we investigate the un decidability of these logics and give a complete picture of decidability and undecidability some of these logics have the finite model property and therefore if they are undecidable they are exactly 10 we show that allowing nesting and probabilistic choice often leads to undecidability

propositional dynamic logic of looping and converse is elementarily decidable propositional dynamic logic is a formal system for reasoning about the before after behavior of regular program schemes an extension of propositional dynamic logic which includes both an infinite looping construct and a converse or backtracking construct is considered and it is proved that the satisfiability problem for this logic is elementarily decidable in order to establish this result deterministic two way automata on infinite trees are defined and it is shown how they can be simulated by nondeterministic one way automata the satisfiability problem for propositional dynamic logic of looping and converse is then reduced to the emptiness problem for these two way automata

rational homotopy of the homotopy fixed point sets of circle actions in this paper when g is the circle s 1 and m is a g space we study the rational homotopy type of the fixed point set m g the homotopy fixed point set m hg and the natural injection m g m hg c 2009 elsevier inc all rights reserved

heat flow in an exactly solvable model a chain of one dimensional oscillators is considered they are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors the total energy is kept constant except for the interactions of the extremal oscillators with reservoirs at different temperatures the stationary measures are obtained when the chain is finite the thermodynamic limit is then considered approach to the gibbs distribution is proven and a linear temperature profile is obtained

new formulation of restricted growth processes we present a new formulation of a class of growth models those which evolve according to an exclusion process this formulation is based upon a transformation of the probability distribution function which involves grassmann variables this method is very general and enables one to derive an exact stochastic differential equation for the model of interest we describe this method using the traffic model as an example

condensation in stochastic particle systems with stationary product measures we study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities we review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit this leads to strengthened results on weak convergence for subcritical systems and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions extending previous results which focused on attractive and finite systems we use relative entropy techniques which provide simple proofs making use of general versions of local limit theorems for independent random variables

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

the structure ofī λnin generic representation theory abstract this paper pursues a study of the category f of functors between f 2 vector spaces it is proved that the objects i n occur in short exact sequences k n i n k n 1 where each k n is a non finite functor which has the property that every proper sub functor is finite moreover every sub functor of i n either contains k n or is finite