abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

stability of strong travelling waves for a non local time delayed reaction diffusion equation the paper is concerned with a non local time delayed reaction diffusion equation we prove the time asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength i e the so called strong wavefront by means of the technical weighted energy method when the initial perturbation around the wave is small the exponential convergent rate is also given selection of a suitable weight plays a key role in the proof

new generalized simple lie algebras of cartan type over a field with characteristic 0 abstract we construct four new series of generalized simple lie algebras of cartan type using the mixtures of grading operators and down grading operators our results in this paper are further generalizations of those in osborn s work j algebra 185 1996 820 835

operator monotone functions jacobi operators and orthogonal polynomials abstract we reveal a connection between operator monotone functions and orthogonal polynomials especially we express an operator monotone function with a jacobi operator and show that it is a limit of rational operator monotone functions further we prove that the principal inverse of an orthogonal polynomial is operator monotone and hence it has a holomorphic extension to the open upper half plane namely a pick function or nevanlinna function

novikov poisson algebras abstract we classify novikov poisson algebras whose novikov algebras are simple with an idempotent element moreover a class of simple novikov algebras without idempotent elements is constructed through novikov poisson algebras certain new simple lie superalgebras induced by novikov poisson algebras are introduced

classification of balinsky novikov superalgebras with dimension 2 2 the notion of balinsky novikov bn superalgebra was introduced to construct super virasoro type lie superalgebras we classify the 2 2 dimensional complex bn superalgebras whose odd parts products are not zero in addition to the known results on the classification of 2 2 dimensional novikov superalgebras we give an explicit comparison among them and their associated lie superalgebras as an application we construct some lie superalgebras whose even parts are the w 2 2 lie algebra finally we reformulate the classification results in terms of the even parts being the known classification results of two dimensional novikov algebras

on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus they are a class of left symmetric algebras with commutative right multiplication operators which can be viewed as bosonic fermionic novikov algebras are a class of left symmetric algebras with anti commutative right multiplication operators they correspond to a certain hamiltonian superoperator in a supervariable in this paper we commence a study on fermionic novikov algebras from the algebraic point of view we will show that any fermionic novikov algebra in dimension 3 must be bosonic moreover we give the classification of real fermionic novikov algebras on four dimensional nilpotent lie algebras and some examples in higher dimensions as a corollary we obtain kinds of four dimensional real fermionic novikov algebras which are not bosonic all of these examples will serve as a guide for further development including the application in physics

inverse functions of polynomials and orthogonal polynomials as operator monotone functions we study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient let p n n o be a sequence of orthonormal polynomials and p n the restriction of p n to a n where a n is the maximum zero of p n then p 1 n and the composite p n 1 o p 1 n are operator monotone on 0 furthermore for every polynomial p with a positive leading coefficient there is a real number a so that the inverse function of p t a p a defined on 0 oo is semi operator monotone that is for matrices a b 0 p a a p a 2 p b a p a 2 implies a 2 b 2

schrodinger uncertainty relation wigner yanase dyson skew information and metric adjusted correlation measure abstract in this paper we give schrodinger type uncertainty relation using the wigner yanase dyson skew information in addition we give schrodinger type uncertainty relation by use of a two parameter extended correlation measure we finally show a further generalization of schrodinger type uncertainty relation by use of the metric adjusted correlation measure these results generalize our previous result in phys rev a 82 2010 034101

on spinor vertex operator algebras and their modules abstract in this paper we first present a generator theorem and introduce an asymmetric tensor of two colored vertex operator superalgebras with the same grading and supermap then we give axioms which characterize a class of vertex operator superalgebras constructed from clifford algebras in particular we are able to give a shorter argument for the jacobi identity than the existing proofs by using elements analogous to coherent states and our generator theorem using the new tensor and the same techniques we classify twisted irreducible modules of these algebras in a constructive way

arithmetic geometric mean and related inequalities for operators abstract in recent years certain arithmetic geometric mean and related inequalities for operators and unitarily invariant norms have been obtained by many authors based on majorization technique and so on we first point out that they are direct consequences of integral expressions of relevant operators furthermore we obtain related new inequalities theorems 4 5 and 6 based on our current approach

classification of simple novikov algebras and their irreducible modules of characteristic 0 abstract in this paper we first present a classification theorem of simple infinite dimensional novikov algebras over an algebraically closed field of characteristic 0 then we classify all the irreducible modules of certain infinite dimensional simple novikov algebras with an idempotent element whose left action is locally finite

stability of non monotone critical traveling waves for reaction diffusion equations with time delay abstract this paper is concerned with the stability of critical traveling waves for a kind of non monotone time delayed reaction diffusion equations including nicholson s blowflies equation which models the population dynamics of a single species with maturation delay such delayed reaction diffusion equations possess monotone or oscillatory traveling waves the latter occurs when the birth rate function is non monotone and the time delay is big it has been shown that such traveling waves x c t exist for all c c and are exponentially stable for all wave speed c c 13 where c is called the critical wave speed in this paper we prove that the critical traveling waves x c t monotone or oscillatory are also time asymptotically stable when the initial perturbations are small in a certain weighted sobolev norm the adopted method is the technical weighted energy method with some new flavors to handle the critical oscillatory waves finally numerical simulations for various cases are carried out to support our theoretical results

submodular spectral functions of principal submatrices of a hermitian matrix extensions and applications we extend the multiplicative submodularity of the principal determinants of a nonnegative definite hermitian matrix to other spectral functions we show that if f is the primitive of a function that is operator monotone on an interval containing the spectrum of a hermitian matrix a then the function i mapsto rm tr f a i is supermodular meaning that rm tr f a i rm tr f a j leq rm tr f a i cup j rm tr f a i cap j where a i denotes the i times i principal submatrix of a we discuss extensions to self adjoint operators on infinite dimensional hilbert space and to m matrices we discuss an application to cur approximation of nonnegative hermitian matrices

poisson and hamiltonian superpairs over polarized associative algebras a poisson superpair is a pair of poisson superalgebra structures on a supercommutative associative algebra whose any linear combination is also a poisson superalgebra structure in this paper we first construct certain linear and quadratic poisson superpairs over a semi finitely filtered polarized 2 graded associative algebra then we give a construction of certain hamiltonian superpairs in the formal variational calculus over any finite dimensional 2 graded associative algebra with a supersymmetric nondegenerate associative bilinear form our constructions are based on the adler mapping in a general sense our results in this paper can be viewed as noncommutative generalizations of the adler gel fand dikii hamiltonian pair

on a correspondence between regular and non regular operator monotone functions abstract we prove the existence of a bijection between the regular and the non regular operator monotone functions satisfying a certain functional equation as an application we give a new proof of the operator monotonicity of certain functions related to the wigner yanase dyson skew information

nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species abstract this paper is concerned with nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species it is proved that all traveling wavefronts with speed c c are exponentially stable in l space by the weighted energy method and comparison principle moreover the time decay rates are obtained by weighted energy estimates

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

operator inequalities from a general theorem to concrete inequalities abstract the aim of this paper is to give a method to extract concrete inequalities from a general theorem which is established by making use of majorization relation between functions by this method we can get a lot of inequalities among others we extend furuta inequality as follows let f i g j be positive operator monotone functions on 0 and put k t t r 0 f 1 t r 1 f m t r m h t t p 0 g 1 t p 1 g n t p n where p 0 1 and r i 0 p j 0 then 0 a c b implies for 0 1 r 0 p r 0 with p p 0 p n k c 1 2 h a k c 1 2 k c 1 2 h c k c 1 2 k c 1 2 h b k c 1 2 moreover we show log c 1 2 e a c 1 2 log c 1 2 e c c 1 2 log c 1 2 e b c 1 2 provided c is invertible we also refer to operator geometric mean

quadratic conformal superalgebras abstract in this paper we shall classify quadratic conformal superalgebras by certain compatible pairs of a lie superalgebra and a novikov superalgebra four general constructions of such pairs are given moreover we shall classify such pairs related to simple novikov algebras

operator monotonicity of some functions abstract we investigate the operator monotonicity of the following functions f t t t 1 1 t 2 1 t n 1 t 1 1 t 2 1 t n 1 t 0 where r and i j 0 with i j i j 1 2 n this property for these functions has been considered by v e s szabo 14

on some operator inequalities a real valued continuous function f 2 defined on a finite or infinite interval of the real line is said to be operator monotone if for any pair of bounded selfadjoint operators a b on an infinite dimensional hilbert space a b implies f a f b here f a and f b are defined according to the usual functional calculus and refers to the order relation induced by the cone of positive semi definite operators operator monotony is quite a restrictive condition in fact for p 0 the function f 2 2 p is operator monotone on the half line 0 c if and only if 0 1 the function f 2 2 p possesses some property akin to operator monotony in this direction furuta i 3 recently observed that if r 0 p 0 q 1 satisfies 1 2r q p 2r then a b 0 implies a tp 2 q arbpa r l if p 2r and q 2 the requirement is automatically satisfied hence a p ap 2bpap 2 i 2 whenever a b 0 when a is invertible this means that

monotone metrics on matrix spaces abstract the study of monotone inner products under stochastic mappings on the space of matrices was initiated by morozova and chentsov motivated by information geometry they did not show a monotone metric but proposed several candidates the main result of the present paper is to provide an abundance of monotone metrics by means of operator monotone functions and to characterize them it turns out that there is a correspondence between monotone metrics and operator means in the sense of kubo and ando it follows that all proposals of morozova and chentsov are indeed monotone metrics

mean matrices and infinite divisibility abstract we consider matrices m with entries mij m i j where 1 n are positive numbers and m is a binary mean dominated by the geometric mean and matrices w with entries wij 1 m i j where m is a binary mean that dominates the geometric mean we show that these matrices are infinitely divisible for several much studied classes of means

operator monotone functions which are defined implicitly and operator inequalities the function t 0 1 is operator monotone on 0 t this is known as the lowner heinz inequality however not too many examples of concrete operator monotone functions are known so far we will systematically seek operator monotone functions which are defined implicitly this investigation is new and our method seems to be powerful we will actually find a family of operator monotone functions which includes t 0 1 moreover by constructing one parameter families of operator monotone functions we will get many operator inequalities especially we will extend the furuta inequality and the exponential inequality of ando

bilinear forms on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus fermionic novikov algebras correspond to a certain hamiltonian super operator in a super variable in this paper we show that there is a remarkable geometry on fermionic novikov algebras with non degenerate invariant symmetric bilinear forms which we call pseudo riemannian fermionic novikov algebras they are related to pseudo riemannian lie algebras furthermore we obtain a procedure to classify pseudo riemannian fermionic novikov algebras as an application we give the classification in dimension 4 motivated by the one in dimension 4 we construct some examples in high dimensions

hom gel fand dorfman bialgebras and hom lie conformal algebras the aim of this paper is to introduce the notions of hom gel fand dorfman bialgebra and hom lie conformal algebra in this paper we give four constructions of hom gel fand dorfman bialgebras also we provide a general construction of hom lie conformal algebras from hom lie algebras finally we prove that a hom gel fand dorfman bialgebra is equivalent to a hom lie conformal algebra of degree 2

pseudo riemannian novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus pseudo riemannian novikov algebras denote novikov algebras with nondegenerate invariant symmetric bilinear forms in this paper we find that there is a remarkable geometry on pseudo riemannian novikov algebras and give a special class of pseudo riemannian novikov algebras

novikov algebras with associative bilinear forms novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus the goal of this paper is to study novikov algebras with non degenerate associative symmetric bilinear forms which we call quadratic novikov algebras based on the classification of solvable quadratic lie algebras of dimension not greater than 4 and novikov algebras in dimension 3 we show that quadratic novikov algebras up to dimension 4 are commutative furthermore we obtain the classification of transitive quadratic novikov algebras in dimension 4 but we find that not every quadratic novikov algebra is commutative and give a non commutative quadratic novikov algebra in dimension 6

on simple novikov algebras and their irreducible modules abstract we give a complete classification of finite dimensional simple novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic moreover we introduce novikov poisson algebras and their tensor theory our tensor theory enables us to understand better certain finite dimensional simple novikov algebras and their irreducible modules

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

majorization and some operator monotone functions abstract let h t be a non decreasing function on i and k t an increasing function on j then h is said to be majorized by k if k a k b implies h a h b f t is operator monotone by definition if f t is majorized by t by making use of this majorization we will show that t a t b t r a r t 1 r b 1 r is operator monotone on 0 for 0 a b and for 0 r 1 the special case of a b 1 is the theorem due to petz hasegawa

a new majorization between functions polynomials and operator inequalities let p be the set of all non negative operator monotone functions defined on 0 and put p 1 h h 1 p then p p 1 p 1 and p 1 p 1 p 1 for a function h t and a strictly increasing function h we write

some results on strongly operator convex functions and operator monotone functions abstract this paper concerns three classes of real valued functions on intervals operator monotone functions operator convex functions and strongly operator convex functions strongly operator convex functions were previously treated in 3 and 4 where operator algebraic semicontinuity theory or operator theory were substantially used in this paper we provide an alternate treatment that uses only operator inequalities or even just matrix inequalities we show also that if t 0 is a point in the domain of a continuous function f then f is operator monotone if and only if f t f t 0 t t 0 is strongly operator convex using this and previously known results we provide some methods for constructing new functions in one of the three classes from old ones we also include some discussion of completely monotone functions in this context and some results on the operator convexity or strong operator convexity of f when f is operator convex or strongly operator convex

variational calculus of supervariables and related algebraic structures abstract we establish a formal variational calculus of supervariables which is a combination of the bosonic theory of gel fand dikii and the fermionic theory in our earlier work certain interesting new algebraic structures are found in connection with hamiltonian superoperators in terms of our theory in particular we find connections between hamiltonian superoperators and novikov poisson algebras that we introduced in our earlier work in order to establish a tensor theory of novikov algebras furthermore we prove that an odd linear hamiltonian superoperator in our variational calculus induces a lie superalgebra which is a natural generalization of the super virasoro algebra under certain conditions

a hom version of the affinizations of balinskii novikov and novikov superalgebras in this paper we introduce the notions of hom balinskii novikov and hom novikov superalgebras in which the defining identities are twisted by homomorphisms then we construct some infinite dimensional hom lie superalgebras by the affinizations of the above two hom superalgebras moreover we apply the bilinear forms with some invariance conditions on the hom balinskii novikov and hom novikov superalgebras to construct central extensions of the infinite dimensional hom lie superalgebras

hom novikov algebras we study a twisted generalization of novikov algebras called hom novikov algebras in which the two defining identities are twisted by a linear map it is shown that hom novikov algebras can be obtained from novikov algebras by twisting along any algebra endomorphism all algebra endomorphisms on complex novikov algebras of dimensions 2 or 3 are computed and their associated hom novikov algebras are described explicitly another class of hom novikov algebras is constructed from hom commutative algebras together with a derivation generalizing a construction due to dorfman and gel fand two other classes of hom novikov algebras are constructed from hom lie algebras together with a suitable linear endomorphism generalizing a construction due to bai and meng

traveling wavefronts in diffusive and cooperative lotka volterra system with delays existence of traveling wave front solutions is established for diffusive and cooperative lotka volterra system with delays the result is an extension of an existing result for delayed logistic scaler equation to systems and is somewhat parallel to the existing result for diffusive and competitive lotka volterra systems without delay the approach used in this paper is the upper lower solution technique and the monotone iteration recently developed by wu and zou j dynam differential equations 13 2001 651 687 for delayed reaction diffusion systems without the so called quasimonotonicity 2002 elsevier science usa all rights reserved

mixed matrix operator inequalities we will show that if 0 a b c and s s t t 1 then a s bs t ct implies that ar 2 s bss t cst ar 2 ar 2 s bts t ctt ar 2 s r t r fort 1 t s 0 r 0 and a1 r ar 2 s bts t ctt ar 2 1 r t r fort 1 r 0 these are the extensions of inequalities shown by t furuta proc amer math soc 101 1987 85 111 1991 511 moreover we will give an inequality say mixed inequality which includes the above inequalities and the inequality due to hansen pedersen math ann 258 1982 229

the hasegawa petz mean properties and inequalities abstract we study a family of means introduced by h hasegawa and d petz 1996 13 properties with respect to the parameter such as monotonicity and logarithmic concavity further monotonicity and concavity in the mean variables are shown besides the comparison between the hasegawa petz mean and the geometric mean is completely solved the connection to earlier results on operator monotonicity and some applications are also discussed

completely positive mappings and mean matrices abstract some functions f r r induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices moreover such a function f can define a linear mapping j d f 1 m n m n on matrices which is basic in the constructions of monotone metrics the present subject is to check the complete positivity of j d f 1 in the case of a few concrete functions f this problem has been motivated by applications in quantum information

asymptotic behaviour of travelling waves for the delayed fisher kpp equation abstract in this work we study the behaviour of travelling wave solutions for the diffusive hutchinson equation with time delay using a phase plane analysis we prove the existence of travelling wave solution for each wave speed c 2 we show that for each given and admissible wave speed such travelling wave solutions converge to a unique maximal wavetrain as a consequence the existence of a nontrivial maximal wavetrain is equivalent to the existence of travelling wave solution non converging to the stationary state u 1