central simple superalgebras with anti automorphisms of order two of the first kind by a theorem of albert s a central simple associative algebra has an involution of the first kind if and only if it is of order 2 in the brauer group our main purpose is to develop the theory of existence of anti automorphisms of order 2 of the first kind on finite dimensional central simple associative superalgebras over k where k is a field of arbitrary characteristic first we need to generalize the skolem noether theorem to the superalgebra case then we show which kind of finite dimensional central simple superalgebras have an anti automorphism of order 2 of the first kind

functional identities in superalgebras abstract the aim of this paper is to establish the theory of functional identities in superalgebras as an application of this theory k supercommuting maps in superalgebras are investigated

the space of kahler metrics this paper the second of a series deals with the function space mathcal h of all smooth kahler metrics in any given n dimensional closed complex manifold v these metrics being restricted to a given fixed real cohomology class called a polarization of v this function space is equipped with a pre hilbert metric structure introduced by t mabuchi 10 who also showed that formally this metric has nonpositive curvature in the first paper of this series 4 the second author showed that the same space is a path length space he also proved that mathcal h is geodesically convex in the sense that for any two points of mathcal h there is a unique geodesic path joining them which is always length minimizing and of class c1 1 this partially verifies two conjectures of donaldson 8 on the subject in the present paper we show first of all that the space is as expected a path length space of nonpositive curvature in the sense of a d aleksandrov a second result is related to the theory of extremal kahler metrics namely that the gradient flow in mathcal h of the k energy of v has the property that it strictly decreases the length of all paths in mathcal h except those induced by one parameter families of holomorphic automorphisms of m

the existence of superinvolutions superinvolutions on graded associative algebras constitute a source of lie and jordan superalgebras graded versions of the classical albert and albert riehm theorems on the existence of superinvolutions are proven surprisingly the existence of superinvolutions of the first kind is a rare phenomenon as nontrivial central division superalgebras are never endowed with this kind of superinvolutions

remarks on the geodesic einstein metrics of a relative ample line bundle in this paper we introduce the associated geodesic einstein flow for a relative ample line bundle l over the total space mathcal x of a holomorphic fibration and obtain a few properties of that flow in particular we prove that the pair mathcal x l is nonlinear semistable if the associated donaldson type functional is bounded from below and the geodesic einstein flow has long time existence property we also define the associated s classes and c classes for mathcal x l and obtain two inequalities between them when l admits a geodesic einstein metric finally in the appendix of this paper we prove that a relative ample line bundle is geodesic einstein if and only if an associated infinite rank bundle is hermitian einstein

on the lie structure of the skew elements of a simple superalgebra with superinvolution abstract we investigate the lie structure of the lie superalgebra k of skew elements of a unital simple associative superalgebra a with superinvolution over a field of characteristic not 2 it is proved that if a is more than 16 dimensional over its center z then any lie ideal u of k satisfies either u z or u k k moreover any lie ideal u of k k satisfies either u z or u k k in particular k k z k k is a simple lie superalgebra

commuting traces of biadditive mappings commutativity preserving mappings and lie mappings biadditive mappings b r r r where r is a prime ring with certain additional properties satisfying b x x x xb x x for all x r are characterized as an application we determine the structures of commutativity preserving mappings lie isomorphisms and lie derivations of certain prime rings

on herstein s lie map conjectures i first published in transactions american mathematical society in vol 353 no 10 pp 4235 4260 published by the american mathematical society

lie superhomomorphisms in superalgebras with superinvolution abstract the main purpose of the present paper is to give a description of lie superhomomorphisms from the set of skew elements of a superalgebra with superinvolution into a unital superalgebra

near derivations in lie algebras abstract let l be a lie algebra we call a linear map f l l a near derivation if there exists a linear map g l l such that ad x f g ad x is a derivation for every x l the paper is devoted to describing the structure of near derivations in certain lie algebras arising from associative ones

on herstein s lie map conjectures iii abstract in the two papers on herstein s lie map conjectures i and ii solutions of all of herstein s problems concerning lie isomorphisms and derivations were given under the assumption that the algebras involved were of sufficiently high dimension in the present paper we remove this restriction thereby solving herstein s problems in full generality

a donaldson type functional on a holomorphic finsler vector bundle in this paper we solve a problem of kobayashi posed in complex finsler vector bundles american mathematical society providence 1996 by introducing a donaldson type functional on the space f e of strongly pseudo convex complex finsler metrics on e a holomorphic vector bundle over a closed kahler manifold m this donaldson type functional is a generalization in the complex finsler geometry setting of the original donaldson functional and has finsler einstein metrics on e as its only critical points at which this functional attains the absolute minimum

on lie admissible algebras whose commutator lie algebras are lie subalgebras of prime associative algebras abstract we describe third power associative multiplications on noncentral lie ideals of prime algebras and skew elements of prime algebras with involution provided that x y y x x y for all x y and the prime algebras in question do not satisfy polynomial identities of low degree we also obtain necessary and sufficient conditions for these multiplications to be fourth power associative or flexible

primitive superalgebras with superinvolution abstract our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras 5 6 10 and to classify primitive superrings with superinvolution having a minimal one sided superideal we were led to this problem by our work on finite dimensional central simple jordan superalgebras over fields of characteristic not 2 9 see also 7 of course just as symmetric elements give rise to jordan superalgebras skewsymmetric elements give rise to lie superalgebras 8 4 the results and methods are closely related to those of structure theory of associative rings and central simple associative algebras with involution 5 chap i 6 chaps ii iii 1 chap x 10 chap 2 some of the results have been announced in 13

initial and boundary conditions for the lattice boltzmann method an alternative approach of implementing initial and boundary conditions for the lattice boltzmann method is presented the basic idea is to calculate the lattice boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity the numerical performance of the lattice boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method the discretization error of the lattice boltzmann method decreases quadratically with finer resolution both in space and in time the roundoff error of the lattice boltzmann method creates problems unless double precision arithmetic is used

geodesic einstein metrics and nonlinear stabilities in this paper we introduce notions of nonlinear stabilities for a relative ample line bundle over a holomorphic fibration and define the notion of a geodesic einstein metric on this line bundle which generalize the classical stabilities and hermitian einstein metrics of holomorphic vector bundles we introduce a donaldson type functional and show that this functional attains its absolute minimum at geodesic einstein metrics and we also discuss the relations between the existence of geodesic einstein metrics and the nonlinear stabilities of the line bundle as an application we will prove that a holomorphic vector bundle admits a finsler einstein metric if and only if it admits a hermitian einstein metric which answers a problem posed by s kobayashi

a lattice boltzmann model for the shallow water equations a lattice boltzmann model for the shallow water equations labswe is developed it solves the equations with the source terms such as bed slope bed friction the model has been verified by solving both steady and unsteady flow problems excellent agreement is obtained between numerical predictions and analytical solutions the results show that the labswe is a very competitive method for computational hydraulics or hydrodynamics in terms of computational efficiency and accuracy

centralizing maps in prime rings with involution abstract let r be a prime ring with involution of characteristic 2 with center z skew elements k and extended centroid c theorem suppose k k 0 and k k is an additive map such that x x z for all x k then unless r is an order in a 16 dimensional central simple algebra there exists c and an additive map k c such that x x x for all x k

on maps preserving square zero matrices the problem of characterizing linear operators on matrix algebras that leave invariant certain functions subsets or relations has attracted the attention of many mathematicians see survey papers 20 22 27 for details for instance linear operators preserving zeroproduct of matrices are studied in 15 16 29 31 linear operators preserving idempotent matrices are studied in 1 11 13 14 linear operators preserving matrices annihilated by a fixed polynomial are studied in 12 13 18 linear operators preserving nilpotent matrices are studied in 9 and linear operators preserving square zero matrices are studied in 29 most linear preserver problems were investigated in the case of matrix algebras over fields in contrast not too much is known about matrix algebras over commutative rings to the best of our knowledge beside the papers by mcdonald 25 and waterhouse 30 only bresar and semrl 11 used elementary calculations to describe linear maps preserving idempotent matrices over commutative rings the reason why people seldom study matrix algebras over commutative rings is probably that one might encounter some difficulties that are not easy to overcome for example unlike matrix algebras over fields the automorphisms on matrix algebras over commutative rings can fail to be inner see 19 28

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

gpu accelerated lattice boltzmann model for shallow water flow and mass transport a lattice boltzmann method lbm for solving the shallow water equations swes and the advection dispersion equation is developed and implemented on graphics processing unit gpu based architectures a generalized lattice boltzmann equation glbe with a multiple relaxation time mrt collision method is used to simulate shallow water flow a two relaxation time trt method with two speed of sound techniques is used to solve the advection dispersion equation the proposed lbm is implemented to an nvidia computing processor in a single gpu workstation gpu computing is performed using the jacket gpu engine for matlab and cuda in the numerical examples the mrt lbm model and the trt lbm model are verified and show excellent agreement to exact solutions the mrt outperforms the single relaxation time srt collision operator in terms of stability and accuracy when the srt parameter is close to the stability limit of 0 5 mass transport with velocity dependent dispersion in shallow water flow is simulated by combining the mrt lbm model and the trt lbm model gpu performance with cuda code shows an order of magnitude higher than matlab jacket code moreover the gpu parallel performance increases as the grid size increases the results indicate the promise of the gpu accelerated lbm for modeling mass transport phenomena in shallow water flows copyright 2010 john wiley sons ltd

on functional identities in prime rings with involution abstract let a be a prime ring with involution let s be the symmetric elements let k be the skew elements let q ml be the maximal left ring of quotients x 1 x m noncommuting variables and e i f j g k h l a m 1 q ml i j k l 1 2 m we study functional identities of the form m i 1 e i i x i m j 1 x j f j j m k 1 g k k x k m l 1 x l h l l 0 for all x 1 x m a where e i i means e i x 1 x i x m etc in case s k is not algebraic of bounded degree 2 m definitive results are obtained as an application k commuting traces of symmetric n additive maps of either s or k into q ml are characterized

lie gradings on associative algebras abstract in this paper we apply the method of functional identities to the study of group gradings by an abelian group g on simple lie algebras under very mild restrictions on the grading group or the base field of coefficients