derivations of the parabolic subalgebras of the general linear lie algebra over a commutative ring let r be an arbitrary commutative ring with identity gl n r the general linear lie algebra over r the aim of this paper is to give an explicit description of the derivation algebras of the parabolic subalgebras of gl n r

lie triple derivations of tuhf algebras we study lie triple derivations of tuhf algebras it is shown that if l is a continuous lie triple derivation of a tuhf algebra t then there exists an associative derivation d of t such that l d where is a linear map of t into its center which annihilates brackets of operators

a nonlinear analytic approach to the splitting theorem of jacobs de leeuw glicksberg abstract in this paper we study nonlinear analytic methods for linear contractive semigroups in banach spaces and apply them to the splitting theorem of jacobs de leeuw glicksberg using these results we obtain the extension of lin s proposition for a group of linear operators to a semigroup

commutativity preserving linear maps and lie automorphisms of triangular matrix algebras abstract in this article we classify linear maps from the algebra t n of n upper triangular matrices into itself satisfying ab ba 0 if and only if ab ba 0 in particular we show that for n 2 any such map is either the sum of an algebra automorphism and a map into the centre or the sum of the negative of an algebra anti automorphism and a map into the centre as a consequence lie automorphisms of the algebra t n are also classified

random products of contractions in banach spaces we show that the random product of a finite number of w contractions converges weakly in all smooth reflexive banach spaces if one of the contractions is compact then the convergence is uniform let x 1 be a real banach space and t x x a linear operator recall that t is called a contraction if i tvi i v i for all vectors v in x we say that a contraction t satisfies condition w if whenever v is bounded and ivni itvni 0 it follows that the weak limn o vn tvn 0 the algebraic semigroup s generated by a possibly infinite set of contractions will be said to satisfy condition w if for any bounded sequence of vectors vn c x and a sequence of words wn from s such that i v n wnvni 0 the weak limn oo vn wnvn 0 now let t1 t2 be a sequence of contractions that satisfy condition w and let r be a self mapping of the set of natural numbers a random product of these contractions is the sequence sn n 1 2 defined by sn tr n tr n 1 tro 1 our purpose in this paper is to study the convergence properties of such products such a study is not only of intrinsic interest but is also motivated by applications to the numerical solution of partial differential equations 2 14 and linear inequalities 19 approximation theory 16 9 and computer tomography 18 11 we begin by noting several properties of contractions which satisfy condition w we shall call such contractions w contractions for short we then consider the algebraic semigroup generated by a finite number of w contractions and establish a weak convergence theorem for random products of these contractions in all smooth reflexive banach spaces theorem 1 this seems to be the first such result outside hilbert space it includes the hilbert space theorem due to amemiya and ando 1 we continue with a weak convergence result for semigroups generated by an infinite sequence of contractions theorem 2 finally we obtain a uniform convergence theorem for random received by the editors october 24 1988 and in revised form april 4 1989 1980 mathematics subject classification 1985 revision primary 47a05 secondary 47b05 65j10

linear preservers on upper triangular operator matrix algebras abstract in this paper we obtain several characterizations of rank preserving linear maps and completely rank nonincreasing linear maps on upper triangular hilbert space operator matrix algebras and apply them to get some algebraic results we show that every automorphism of an upper triangular operator matrix algebra is inner and every weakly continuous surjective local automorphism is in fact an automorphism a weakly continuous linear bijection on an upper triangular operator matrix algebra is idempotent preserving if and only if it is a jordan homomorphism and in turn if and only if it is an automorphism or an anti automorphism as an application we also obtain a result concerning the asymptotic joint similarity of matrix tuples

linear transformations on symmetric matrices that preserve commutativity it is shown that if a nonsingular linear transformation t on the space of n square real symmetric matrices preserves the commutativity where n 3 then t a qaqt q a in for all symmetric matricesa for some scalar orthogonal matrix q and linear functional q

stochastic lattice gas model for a predator prey system we propose a stochastic lattice gas model to describe the dynamics of two animal species population one being a predator and the other a prey this model comprehends the mechanisms of the lotka volterra model our analysis was performed by using a dynamical mean field approximation and computer simulations our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators for the sets of parameters used in our computer simulations these oscillations occur at a local level mean field results predict synchronized collective oscillations

invertible linear maps on borel subalgebras preserving zero lie products abstract let g be a simple lie algebra of rank l over an algebraically closed field of characteristic zero b a borel subalgebra of g an invertible linear map on b is said preserving zero lie products in both directions if for x y b x y 0 if and only if x y 0 in this paper it is shown that an invertible linear map on b preserving zero lie products in both directions if and only if it is a composition of an inner automorphism a graph automorphism a scalar multiplication map and a diagonal automorphism which extends the main result in 8 from a linear solvable lie algebra to far more general cases

generalized lie derivations on skew elements of prime algebras with involution we characterize generalized lie derivations on skew elements of prime algebras a with involution provided that a does not satisfy polynomial identities of low degree the analogous result for matrix algebras is also described

jordan isomorphisms of triangular matrix algebras over a connected commutative ring abstract let c be a 2 torsionfree commutative ring with identity 1 and let t r c r 2 be the algebra of all upper triangular r r r 2 matrices over c then c contains no idempotents except 0 and 1 if and only if every jordan isomorphism of t r c onto an arbitrary algebra over c is either an isomorphism or an anti isomorphism

lie triple derivations of nest algebras abstract let n be a nest on a complex separable hilbert space h and n be the associated nest algebra in this paper we prove that every lie triple derivation from n into itself is of the form x xt tx h x i where t n and h is a linear mapping from n into c such that h a b c 0 for all a b c n

a note on algebra automorphisms of strictly upper triangular matrices over commutative rings abstract in this note we explicitly describe the automorphism group of the r algebra of strictly upper triangular n n matrices over an arbitrary commutative ring

isotropic majority vote model on a square lattice the stationary critical properties of the isotropic majority vote model on a square lattice are calculated by monte carlo simulations and finite size analysis the critical exponents and are found to be the same as those of the ising model and the critical noise parameter is found to beqc 0 075 0 001

reduction techniques for strongly graded rings and finite representation type abstract we present reduction techniques for studying the category of lattices over strongly graded orders in particular we apply these techniques in order to reduce the problem of classifying those strongly graded orders with finite representation type to the case where the coefficient ring is a maximal order in a division ring

iterative convergence to cesaro means for continuous pseudocontractive mappings abstract let f be a fixed strongly pseudocontractive mapping and t be a continuous pseudocontractive mapping with f t 0 the sequence z m is iteratively defined as follows z m t m f z m 1 t m 1 m 1 j 0 m t j z m m 0 where t m 0 1 satisfies the condition lim m t m 0 we prove that z m converges strongly to the unique solution p to some variational inequality in f t our results develop and complement the corresponding ones by matsushita daishi kuroiwa j math anal appl 294 2004 206 214 and shioji takahashi arch math 72 1999 354 359 and moore nnoli j math anal appl 260 2001 269 278 and su li appl math comput 181 2006 332 341 and song chen appl math comput 186 2007 1120 1128 and wangkeeree appl math comput 201 2008 239 249

automorphisms and derivations of upper triangular matrix rings abstract kezlan proved that for a commutative ring c every c automorphism of the ring of upper triangular matrices over c is inner we generalize this result to rings in which all idempotents are central moreover we show that for a semiprime ring a and central subring c every c automorphism of the ring of upper triangular matrices over c is the composite of an inner automorphism and an automorphism induced from a c automorphism of a by the method of proof we re prove results of s p coelho and c p milies and of mathis stating that a derivation of a ring of upper triangular matrices of a c algebra n n matrices over a is a sum of an inner derivation and a derivation induced from a c derivation of a by an example we show that an extra assumption is needed for proving the above result of automorphisms of upper triangular matrices finally we consider automorphisms of subrings of n n matrices over a commutative ring c where entries over the diagonal are from c and below the diagonal are taken from a nil ideal we prove that all such automorphisms are inner

on the rate of convergence of iterated bregman projections and of the alternating algorithm abstract we study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth banach spaces for banach spaces which are convex and smooth of power type we exhibit a condition which implies linear convergence of this method we show these convergence results for iterates of bregman projections onto closed linear subspaces using an intimate connection between the metric projection onto a closed linear subspace and the bregman projection onto its annihilator we deduce the convergence rate results for the alternating algorithm from the corresponding results for the iterated bregman projection method

the automorphism group of a structural matrix algebra abstract we characterize the automorphism group of certain subalgebras of matrix algebras with entries from a field k known as structural matrix algebras these include the algebras of upper triangular matrices we also give necessary and sufficient conditions for every k automorphism of such a subalgebra to be inner

decomposition of jordan automorphisms of strictly triangular matrix algebra over local rings abstract let n n 1 r be the algebra of all strictly upper triangular n 1 by n 1 matrices over a 2 torsionfree commutative local ring r with identity in this paper we prove that any jordan automorphism of n n 1 r can be uniquely written as a product of a graph automorphism a diagonal automorphism an inner automorphism and a central automorphism for n 3 in the cases n 1 2 we also give a decomposition for any jordan automorphism of n n 1 r 1 n 2

multiplicative semigroup automorphisms of upper triangular matrices over rings abstract suppose r is a ring with 1 and c a central subring of r let tn r be the c algebra of upper triangular n n matrices over r recently several authors have shown that if r is sufficiently well behaved then every c automorphism of tn r is the composites of an inner automorphism and an automorphism induced from a c automorphism of r see 1 5 to generalize these results in this paper we prove that if n 2 and r is a semiprime ring or a ring in which all idempotents are central then f tn r tn r tn r is only regarded as a multiplicative semigroup is a multiplicative semigroup automorphism if and only if there exist a nonsingular matrix p in tn r and a ring automorphism of r such that f a p 1 a p a a ij n n n r where a aij n n

automorphisms of the standard borel subgroup of orthogonal group o 2m r over commutative rings abstract all automorphisms of the standard borel subgroup of orthogonal group o 2 m r are determined provided that r is a commutative ring with identity 2 3 are invertible in r and m 5

some linear preserver problems on block triangular matrix algebras in this article we classify rank one nonincreasing maps on n square block triangular matrix algebras with the assumption that in is of rank n as applications we obtain complete classifications of adjugate commuting maps and compound commuting maps on block triangular matrix algebras

finite size scaling for first order transitions potts model the finite size scaling algorithm based on bulk and surface renormalization of de oliveira is tesed onq state potts models in dimensionsd 2 and 3 our monte carlo data clearly distinguish between first and second order phase transitions continuous q analytic calculations performed for small lattices show a clear tendency of the magnetic exponenty d v to reach a plateau for increasing values ofq which is consistent with the first order transition valuey d monte carlo data confirm this trend

automorphisms of the lie algebra of strictly upper triangular matrices over a commutative ring let r be an arbitrary commutative ring with identity denote by n r the lie algebra over r consisting of all strictly upper triangular n 1 n 1 matrices over r with n 3 in addition for n 3 assume that the annihilator of 2 in r is zero the aim of this paper is to describe the automorphism group of n r we show that any automorphism of n r can be expressed as where and are graph extremal central and inner automorphisms respectively of n r

lie triple derivation of the lie algebra of strictly upper triangular matrix over a commutative ring abstract let n n r be the nilpotent lie algebra consisting of all strictly upper triangular n n matrices over a 2 torsionfree commutative ring r with identity 1 in this paper we prove that any lie triple derivation of n n r can be uniquely decomposited as a sum of an inner triple derivation diagonal triple derivation central triple derivation and extremal triple derivation for n 6 in the cases 1 n 5 the results are trivial

linear maps preserving commutativity abstract commutativity preserving maps on the real space of all real symmetric or complex self adjoint matrices are characterized related results are given for adjoint preserving maps defined on all n n matrices these results are extended to infinite dimensions in the case of invertible maps

a probabilistic automata network epidemic model with births and deaths exhibiting cyclic behaviour a probabilistic automata network model for the spread of an infectious disease in a population of moving individuals is studied the local rule consists of two subrules the first one applied synchronously models infection birth and death processes it is a probabilistic cellular automaton rule the second applied sequentially describes the motion of the individuals the model contains six parameters the probabilities p for a susceptible to become infected by contact with an infective the respective birth rates bs and bi of the susceptibles from either a susceptible or an infective parent the respective death rates ds and di of susceptibles and infectives and a parameter m characterizing the motion of the individuals the model has three fixed points the first is trivial it describes a stationary state with no living individuals the second corresponds to a disease free state with no infectives the third and last one characterizes an endemic state with non zero densities of susceptibles and infectives moreover the model may exhibit oscillatory behaviour of the susceptible and infective densities as functions of time through a hopf type bifurcation the influence of the different parameters on the stability of all these states is studied with a particular emphasis on the influence of motion which has been found to be a stabilizing factor of the cyclic behaviour

linear preservers on triangular matrices abstract let t n f denote the vector space of all n n upper triangular matrices over a field f we characterize those linear transformations t on t n f that satisfy one of the following properties 1 t preserves rank one matrices 2 t preserves both singular and nonsingular matrices 3 t is nonsingular and t adj a adj t a for all a t n f

nonexpansive iterations in hyperbolic spaces one of the most active research areas in nonlinear functional analysis is the asymptotics of nonexpansive mappings most of the results however have been obtained in normed linear spaces it is natural therefore to try to develop a theory of nonexpansive iterations in more general infinite dimensional manifolds this is the purpose of the present paper more specifically we propose the class of hyperbolic spaces as an appropriate background for the study of operator theory in general and of iterative processes for nonexpansive mappings in particular this class of metric spaces which is defined in section 2 includes all normed linear spaces and hadamard manifolds as well as the hilbert ball and the cartesian product of hilbert balls in section 3 we introduce co accretive operators and their resolvents and present some of their properties in the fourth section we discuss the concept of uniform convexity for hyperbolic spaces section 5 is devoted to two new geometric properties of infinite dimensional banach spaces theorem 5 6 provides a characterization of banach spaces having these properties in terms of nonlinear accretive operators in sections 6 7 and 8 we study explicit implict and continuous iterations repectively using the same approach in all three sections we illustrate this common approach with the following special case let c be a closed convex subset of a hyperbolic space x p let t c f c be a nonexpansive mapping and let x be a point in c in order to study the iteration t x n 0 1 2 we set z 1 l n x 0 l n t x k clco zj j i l and d inf p y ty y e c the first step is to show that p x k lim p x t x n d this leads to the convergence m of lz when x is uniformly convex and to the weak convergence of z when x is a banach space which is reflexive and strictly convex when t is an averaged mapping we are also able to establish the following triple equality for all k 2 1

approximation of zeros of inverse strongly monotone operators in banach spaces abstract in this paper we consider the projection algorithm studied by iiduka and takahashi 2008 10 for finding a solution of the variational inequality problem for an inverse strongly monotone operator in a banach space we first remark that under the assumptions imposed on the operator in their paper the iterative sequence converges weakly to a zero of the operator not just a solution of the variational inequality problem in our proof slightly modified from the original we do not assume the uniform smoothness of a space as was the case there finally using halpern s type method we modify this algorithm to obtain the strong convergence to a zero of an inverse strongly monotone operator which is nearest to the initial element of the algorithm in the sense of the bergman distance associated with the function 1 2 2

multiplicative semigroup automorphisms of the strictly upper triangular matrices over a commutative ring let r be an arbitrary commutative ring with identity and nn r b e the multiplicative semigroup consisting of all n n strictly upper triangular matrices over r t he aim of this paper is to give an explicit description of any automorphism of the semigroup nn r

maps on matrix spaces it is well known that every automorphism of the full matrix algebra is inner we give a short proof of this statement and discuss several extensions of this theorem including structural results for multiplicative maps on matrix algebras characterizations of monotone and orthogonality preserving maps on idempotent matrices some nonlinear preserver results and some recent theorems concerning geometry of matrices we show that all these topics are closely related and point out the connections with physics and geometry several open problems are posed

spectrum and commutativity preserving mappings on triangular matrices we give the description of continuous mappings on the algebra of all upper triangular complex matrices that preserve spectrum and commutativity

stable oscillations of a predator prey probabilistic cellular automaton a mean field approach we analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator prey system the individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the lotka volterra model two levels of mean field approximations are set up the simple approximation is equivalent to an extended patch model a simple metapopulation model with patches colonized by prey patches colonized by predators and empty patches this approximation is capable of describing the limited available space for species occupancy the pair approximation is moreover able to describe two types of coexistence of prey and predators one where population densities are constant in time and another displaying self sustained time oscillations of the population densities the oscillations are associated with limit cycles and arise through a hopf bifurcation they are stable against changes in the initial conditions and in this sense they differ from the lotka volterra cycles which depend on initial conditions in this respect the present model is biologically more realistic than the lotka volterra model

the group of automorphisms of certain subalgebras of matrix algebras the purpose of this note is to find and characterize the full group of automorphisms of certain prime algebras which are subalgebras of matrix algebras over commutative rings here we extend the methods which we used in 6 to characterize automorphisms of certain upper triangular matrix rings for a central simple k algebra a the group of k automorphisms of a is extensively treated in the literature 5 theorem 6 21 other cases where the automorphism group of a ring is known are the automorphism group of a polynomial ring in two indeterminates over a field and the free algebra in two variables over a field 4 chap 61 finally if a is a prime p z algebra with center c then every c automorphism of a is x inner 7 example 3 91

majority vote on directed erdős renyi random graphs abstract through monte carlo simulation the well known majority vote model has been studied with noise on directed random graphs in order to characterize completely the observed order disorder phase transition the critical noise parameter q c as well as the critical exponents and 1 have been calculated as a function of the connectivity z of the random graph

an iterative method for equilibrium problems and a finite family of relatively nonexpansive mappings in a banach space abstract in this paper we introduce a new iterative method for finding a common element of the set of fixed points of a finite family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in uniformly convex and uniformly smooth banach spaces then we prove a strong convergence theorem by using the generalized projection

automorphism groups of generalized triangular matrix rings abstract we call a ring strongly indecomposable if it cannot be represented as a non trivial i e m 0 generalized triangular matrix ring r m 0 s for some rings r and s and some r s bimodule r m s examples of such rings include rings with only the trivial idempotents 0 and 1 as well as endomorphism rings of vector spaces or more generally semiprime indecomposable rings we show that if r and s are strongly indecomposable rings then the triangulation of the non trivial generalized triangular matrix ring r m 0 s is unique up to isomorphism to be more precise if r m 0 s r m 0 s is an isomorphism then there are isomorphisms r r and s s such that m m m is an r s bimodule isomorphism relative to and in particular this result describes the automorphism groups of such upper triangular matrix rings r m 0 s

the derivation lie algebra of the higher rank virasoro like algebra and its automorphism groups abstract in this paper we study the derivation lie algebra of the higher rank virasoro like algebra we prove that it isomorphic to the skew derivation lie algebra we also characterize the automorphism groups of the higher rank virasoro like algebra and the skew derivation lie algebra this generalizes the result of some related references

three automorphism theorems for triangular matrix algebras abstract let t n a be the algebra of upper triangular n n matrices with entries from an associative k algebra a where k is a commutative ring recently several authors barker coelho jondrup kezlan have shown that if a is sufficiently well behaved then every k algebra automorphism of t n a decomposes into a product of an inner automorphism and an automorphism defined by an automorphism of a in this paper we find new sufficient conditions for a that guarantee such decompositions and we give comparisons with previous results as an intermediate step we show that a single automorphism admits such a decomposition if and only if it respects the subspace of strict upper triangular matrices we also consider the case of infinite matrices

abel averages and holomorphically pseudo contractive maps in banach spaces abstract a class of maps in a complex banach space is studied which includes both unbounded linear operators and nonlinear holomorphic maps the defining property which we call pseudo contractivity is introduced by means of the abel averages of such maps we show that the studied maps are dissipative in the spirit of the classical lumer phillips theorem for pseudo contractive holomorphic maps we establish the power convergence of the abel averages to holomorphic retractions

epimorphisms of infinite triangular and unitriangular matrices we discuss the form of all epimorphisms of t f the group of all infinite upper triangular matrices over a field into itself we show that every such epimorphism is a composition of some standard maps moreover we present an analogous result for ut f we use the obtained results to describe the groups of automorphisms of these groups

commutativity preserving operators on symmetric matrices abstract if is a nonsingular linear operator on n n symmetric matrices over a formally real field n 3 and if preserves commutativity then a cu 1 au f a i where u t u and c are scalar and is a linear functional this is an extension of a result of chan and lim

probabilistic cellular automaton describing a biological immune system we have analyzed a probabilistic cellular automaton to describe the t helper cells response under parasitic infections the evolution rules are of totalistic type and possess up down symmetry the automaton displays a dynamical phase transition from a disordered state to an ordered one which takes place through a spontaneous symmetry breaking in the ordered phase one type of t helper cells predominates over the others the phase transition was studied both by a pair approximation and by monte carlo simulations in addition we were able to obtain some exact results for the densities of t helper cells

lie triple derivations of nest algebras on banach spaces abstract let n be a non trivial nest on x alg n be the associated nest algebra and l alg n b x be a linear mapping in this paper it is proved that l is a lie triple derivation if and only if there exist a derivation d alg n b x and a linear mapping h alg n c i with h x y z 0 for any x y z alg n such that l d h on alg n

automorphism groups of algebras of triangular matrices abstract if a is an algebra of n x n matrices over an integral domain we can associate with a a graph whose edges are pairs i j such that the i j entry of every element of a is zero the graph in turn defines a group of permutations and automorphisms of a which are conjugations by permutations matrices for a suitably restricted class of algebras a we show that the automorphism group of a is the semidirect product of this group of permutation matrices with the subgroup of inner automorphisms

strong convergence theorems for finitely many nonexpansive mappings abstract under the assumption that e is a reflexive banach space whose norm is uniformly geteaux differentiable and which has a weakly continuous duality mapping j with gauge function ceng cubiotti yao strong convergence theorems for finitely many nonexpansive mappings and applications nonlinear analysis 67 2007 1464 1473 introduced a new iterative scheme for a finite commuting family of nonexpansive mappings and proved strong convergence theorems about this iteration in this paper only under the hypothesis that e is a reflexive banach space which has a weakly continuous duality mapping j with gauge function and several control conditions about the iterative coefficient are removed we present a short and simple proof of the above theorem

commutative post lie algebra structures on nilpotent lie algebras and poisson algebras abstract we give an explicit description of commutative post lie algebra structures on some classes of nilpotent lie algebras for non metabelian filiform nilpotent lie algebras and lie algebras of strictly upper triangular matrices we show that all cpa structures are associative and induce an associated poisson admissible algebra

an alternative order parameter for the 4 state potts model abstract we have investigated the dynamic critical behavior of the two dimensional 4 state potts model using an alternative order parameter first used by vanderzande j phys a 20 1987 l549 in the study of the z 5 model we have estimated the global persistence exponent g by following the time evolution of the probability p t that the considered order parameter does not change its sign up to time t we have also obtained the critical exponents z and using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature

mappings preserving spectrum and commutativity on hermitian matrices the general form of a continuous mapping acting on the real vector space of all n n complex hermitian or real symmetric matrices and preserving spectrum and commutativity is derived it turns out that is either linear or its image forms a commutative set

lie triple derivations of triangular algebras abstract let r be a commutative ring with identity a b be unital algebras over r and m be a unital a b bimodule which is faithful as a left a module and also as a right b module let t a m 0 b be the triangular algebra consisting of a b and m this work is motivated by some intensive works of bresar 4 cheung 9 and zhang et al 30 here we study lie triple derivations of t it is shown that under mild assumptions every lie triple derivation on t is of standard form that is l can be expressed through an additive derivation and a linear functional vanishing on all second commutators of t examples of lie triple derivations on some classical triangular algebras are supplied

on operators preserving commutativity abstract let l x be the algebra of all bounded operators on a non trivial complex banach space x and f l x l x a bijective linear operator such that f and f 1 both send commuting pairs of operators into commuting pairs then either f a uau 1 p a i or f a ua u 1 p a i where p is a linear functional on l x u is a bounded linear bijective operator between the appropriate two spaces is a complex constant and a is the adjoint of a the form of an operator f for which f and f 1 both send projections of rank one into projections of rank one is also determined

the asymptotics of nonexpansive iterations abstract let d be a closed subset of a banach space x and t d d a nonexpansive mapping conditions are given on the space x for t to satisfy the following property of ergodic type t n x n converges either weakly or strongly to a vector v rather unexpectedly d is not assumed to be convex nor is i t assumed to satisfy any range condition in addition it is shown that v is the unique point of least norm in the closure of r i t if and only if i t satisfies a certain range condition at infinity several interesting applications to accretive operator and nonlinear semigroup theory are also included

on generalized lie derivations of lie ideals of prime algebras abstract let a be a prime algebra of characteristic not 2 with extended centroid c let r be a noncentral lie ideal of a and let b be the subalgebra of a generated by r if f d r a are linear maps satisfying that f x y f x y f y x xd y yd x for all x y r then there exist a generalized derivation g b ac c and a linear map r c such that f x g x x for all x r and r r 0 provided that a does not satisfy the standard identity of degree 18

high dimensional simulation of the shape space model for the immune system abstract for the reactions among the antibodies of the immune system fighting against a foreign antigen the recent model of de boer segel and perelson introduced a cellular automata approximation for the interaction of different types of b cells bone marrow derived lymphocytes in contrast to most physics models here each lattice site interacts mainly with its mirror image with respect to the lattice center in the opposite part of the lattice we simplify their model and then generalize it to include more than one or two shape space parameters thus instead of simulating a chain or square lattice we simulate a d dimensional hypercubic lattice with dimension d up to 10 in particular we check for the concentration of b cells and the stability against localized perturbations damage spreading

cumulants of the three state potts model and of nonequilibrium models with c3v symmetry the critical behaviour of two dimensional stochastic lattice gas models with c3v symmetry is analysed we study the cumulants of the order parameter for the three state equilibrium potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group c3v by means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems in particular we find that the binder reduced fourth order cumulant takes a universal value u which is the same for the three state potts model and for the irreversible models the same universal behaviour is observed for the reduced third order cumulant

critical behavior of a probabilistic cellular automaton describing a biological system we study nonequilibrium phase transitions occurring in a probabilistic cellular automaton which describes one part of the immune system in this model each site can be occupied by three type of cells and the immune response under parasitic infections is described in terms of two parameters p and r the local rules governing the evolution of this automaton possess up down symmetry similar to ising models performing monte carlo simulations on square and cubic lattices we verify that the model displays continuous kinetic phase transitions with spontaneous symmetry breaking we present detailed simulations and analysis of the critical behavior our results indicate that the model belongs to the ising universality class supporting the up down conjecture c 1998 elsevier science b v all rights reserved

additive rank one preserving mappings on triangular matrix algebras abstract we classify surjective additive maps on the space of block upper triangular matrices that preserve matrices of rank one as well as linear maps preserving matrices of rank one on fairly general subspaces of matrices

commutativity preserving maps we briefly describe several techniques that have been developed to solve the problem of characterizing commutativity preserving maps we prove a new result describing the general form of injective continuous commutativity preserving maps on full matrix algebras

derivations of the lie algebra of strictly upper triangular matrices over a commutative ring abstract let r be an arbitrary commutative ring with identity gl n r the general linear lie algebra consisting of all n n matrices over r n n r the subalgebra of gl n r consisting of all strictly upper triangular ones in this paper we give an explicit description of any derivations of n n r

a note on algebra automorphisms of triangular matrices over commutative rings abstract it is shown that if r is a commutative ring with unity then every r algebra automorphism of the algebra of upper triangular n n matrices over r is inner

on the automorphisms of incidence algebras abstract given a locally finite partially ordered set x a ring with identity r and an automorphism of the incidence algebra of x over r it is determined when is the composite of an inner automorphism an automorphism of x and an induced automorphism of r

commutativity preserving maps on lie ideals of prime algebras abstract one of the most studied linear preserver problems is the problem of characterizing maps preserving commutativity in this paper we study maps preserving commutativity on a lie ideal l of a prime algebra a we show by an example that in general we cannot expect the same standard conclusion as in the case when l a therefore we confine ourselves to some special classes of algebras where the usual result can be proved

invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements the invariants of solvable lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively bases of the invariant sets of all such algebras are constructed by an original purely algebraic algorithm based on cartan s method of moving frames

commutativity preserving linear maps and lie automorphisms of strictly triangular matrix space abstract in this paper we classify linear maps preserving commutativity in both directions on the space n f of strictly upper triangular n 1 n 1 matrices over a field f we show that for n 3 a linear map on n f preserves commutativity in both directions if and only if f where is a product of standard maps on n f and f is a linear map of n f into its center

dynamic exponents of a probabilistic three state cellular automaton abstract in this work a three state cellular automaton proposed to describe part of a biological immune system is revisited we obtain the dynamic critical exponent z of the model by means of a recent technique that mixes different initial conditions moreover by using two distinct approaches we have also calculated the global persistence exponent g related to the probability that the order parameter of the model does not change its sign up to time t p t t g

characterization of jordan homomorphisms on mn using preserving properties abstract let o mn mn n 3 be a continuous mapping preserving spectrum and commutativity in both directions neither linearity nor multiplicativity of i is assumed then i is either an automorphism or an antiautomorphism the same result holds if i preserves spectrum commutativity and rank one matrices

automorphisms of certain lie algebras of upper triangular matrices over a commutative ring abstract letrbe an arbitrary commutative ring with identity denote bytthe lie algebra overrconsisting of all upper triangularnbynmatrices overrand letbbe the lie subalgebra oftconsisting of all matrices of trace 0 the aim of this paper is to give an explicit description of the automorphism group of the lie algebrat which extends a result given by dokovic in addition we explicitly describe the automorphism group of the lie algebrabwhennis a unit ofr

automorphisms of the lie algebra of upper triangular matrices over a connected commutative ring abstract let r be a non trivial commutative ring having no idempotents except 0 and 1 denote by t the lie algebra over r consisting of all upper triangular n by n matrices over r we give an explicit description of the automorphism group of this lie algebra

automorphisms of a linear lie algebra over a commutative ring abstract suppose that m 5 and that r is a commutative ring with identity in which 2 is invertible this paper determines all automorphisms of the standard borel subalgebra of the orthogonal lie algebra o 2 m r