jordan all derivable points in the algebra of all upper triangular matrices abstract let tm n be the algebra of all n n upper triangular matrices we say that l tm n is a jordan derivable mapping at g if st ts s t s t t s t s for any s t tm n with st g an element g tm n is called a jordan all derivable point of tm n if every jordan derivable linear mapping at g is a derivation in this paper we show that every element in tm n is a jordan all derivable point

all derivable points in nest algebras abstract suppose that a is an operator algebra on a hilbert space h an element v in a is called an all derivable point of a for the strong operator topology if every strong operator topology continuous derivable mapping at v is a derivation let n be a complete nest on a complex and separable hilbert space h suppose that m belongs to n with 0 m h and write m for m or m our main result is for any alg n with p m p m if m is invertible in alg n m then is an all derivable point in alg n for the strong operator topology

nonlinear mappings on upper triangular matrices derivable at zero point abstract let t n f be the set of all n n upper triangular matrices over a field f recently by using a technique from graph theory l wang in 8 proved that a bijective mapping on t n f with f a finite field preserves zero product i e x y 0 whenever x y 0 if and only if can be decomposed into the product of an inner automorphism an automorphism of t n f induced by an automorphism of f and a regular automorphism of the zero divisor graph of t n f algebraic group theory shows that derivations of an algebra often go parallel with automorphisms of the algebra this viewpoint encourages us to determine nonlinear mappings on t n f which are derivable at zero point i e x y x y 0 whenever x y 0 it is proved that a mapping on t n f is derivable at zero point if and only if is the sum of an inner derivation an additive derivation of t n f induced by an additive derivation of f and a regular mapping on t n f

additive maps derivable or jordan derivable at zero point on nest algebras abstract let alg n be a nest algebra associated with the nest n on a real or complex banach space x assume that every n n is complemented whenever n n let alg n alg n be an additive map it is shown that the following three conditions are equivalent 1 is derivable at zero point i e ab a b a b whenever ab 0 2 is jordan derivable at zero point i e ab ba a b a b b a b a whenever ab ba 0 3 has the form a a ca for some additive derivation and some scalar c it is also shown that is generalized derivable at zero point i e ab a b a b a i b whenever ab 0 if and only if is an additive generalized derivation finer characterizations of above maps are given for the case dim x

local derivations on operator algebras abstract when attempting to find sufficient conditions for a linear mapping to be a derivation an obvious candidate is the concept of a local derivation local derivations on operator algebras have been investigated in recent papers of kadison j algebra130 1990 494 509 and larson and sourour proc symp pure math 51 1990 187 194 a local derivation is a norm continuous linear map from an operator algebra a into an a bimodule m which agrees with some derivation at each point in the algebra we show that if a is the direct limit of finite dimensional csl algebras via extendable embeddings e g a triangular af algebra then a local derivation on a must be a derivation further we show that for many finite dimensional operator algebras any inner local derivation must be an inner derivation

the sine gordon equations complete and partial integrability the sine gordon equation in one space one time dimension is known to possess the painleve property and to be completely integrable it is shown how the method of singular manifold analysis obtains the backlund transform and the lax pair for this equation a connection with the sequence of higher order kdv equations is found the modified sine gordon equations are defined in terms of the singular manifold these equations are shown to be identically painleve also certain rational solutions are constructed iteratively the double sine gordon equation is shown not to possess the painleve property however if the singular manifold defines an affine minimal surface then the equation has integrable solutions this restriction is termed partial integrability the sine gordon equation in n 1 variables n space 1 time where n is greater than one is shown not to possess the painleve property the condition of partial integrability requires the singular manifold to be an einstein space with null scalar curvature the known integrable solutions satisfy this constraint in a trivial manner finally the coupled kdv or hirota satsuma equations possess the painleve property the associated modified equations are derived and from these the lax pair is found

preliminary group classification of equations vtt f x vx vxx g x vx a classification is given of equations vtt f v vx vxx g x vx admitting an extension by one of the principal lie algebra of the equation under consideration the paper is one of few applications of a new algebraic approach to the problem of group classification the method of preliminary group classification the result of the work is a wide class of equations summarized in table ii

hyperreflexivity of the derivation space of some group algebras let t be a continuous linear operator on a banach algebra a we address the question of whether the constant rm sup at b c a b c in a ab bc 0 a b c 1 being small implies that the distance from t to the space der a of all continuous derivations on a is small we show that this is the case for amenable group algebras as a consequence we deduce that der l 1 g is hyperreflexive for each amenable group in sin

annihilator preserving maps multipliers and derivations abstract for a commutative subspace lattice l in a von neumann algebra n and a bounded linear map f n alg l b h we show that if af b c 0 for all a b c n alg l satisfying ab bc 0 then f is a generalized derivation for a unital c algebra a a unital banach a bimodule m and a bounded linear map f a m we prove that if f a b 0 for all a b a with ab 0 then f is a left multiplier as a consequence every bounded local derivation from a c algebra to a banach a bimodule is a derivation we also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier

derivable mappings at unit operator on nest algebras abstract let a be an operator subalgebra with the unit operator i in b h we say that a linear mapping from a into itself is a derivable mapping at i if st s t s t for any s t a with st i in this paper we show the following main result every strongly operator topology continuous derivable mapping at i on a nest algebra alg n is an inner derivation

generalized derivable mappings at zero point on some reflexive operator algebras abstract let a be a subalgebra with the unit operator i in b h we say that a linear mapping from a into b h is a generalized derivable mapping at zero point if st s t s t s i t for any s t a with st 0 in this paper we show the following main result every norm continuous generalized derivable mapping at zero point on finite csl algebras is a generalized derivation

characterizations of derivations and jordan derivations on banach algebras abstract let a be an algebra and m be an a bimodule let x be in a and a m be a linear map which satisfies ab a b a b for all a b a with ab x it is shown that is a jordan derivation if is continuous and x is left or right invertible also it is shown that is a derivation if x is idempotent such that for m m the condition x a i x m 0 implies i x m 0 and the condition mx a i x 0 implies mx 0

group classification of nonlinear wave equations we perform complete group classification of the general class of quasilinear wave equations in two variables this class may be seen as a generalization of the nonlinear d alembert liouville sin sinh gordon and tzitzeica equations we derive a number of new genuinely nonlinear invariant models with high symmetry properties in particular we obtain four classes of nonlinear wave equations that admit five dimensional invariance groups

provably near optimal balancing policies for multi echelon stochastic inventory control models we develop the first algorithmic approach to compute provably good ordering policies for a multi echelon stochastic inventory system facing correlated nonstationary and evolving demands over a finite horizon specifically we study the serial system our approach is computationally efficient and provides worst case guarantees that is the expected cost of the algorithms is guaranteed to be within a constant factor of the optimal expected cost depending on the assumption the constant varies between two and three our algorithmic approach is based on an innovative scheme to account for costs in a multi echelon multi period environment as well as repeatedly balancing between opposing cost the cost accounting scheme called a cause effect cost accounting scheme is significantly different from traditional cost accounting schemes in that it reallocates costs with the goal of assigning every unit of cost to the decision that caused the cost to be incurred we believe it will have additional applications

characterizations of derivations of banach space nest algebras all derivable points abstract let n be a nest on a complex banach space x with n n complemented in x whenever n n and let alg n be the associated nest algebra we say that an operator z alg n is an all derivable point of alg n if every linear map from alg n into itself derivable at z i e a b a b z for any a b a with ab z is a derivation in this paper it is shown that if z alg n is an injective operator or an operator with dense range or an idempotent operator with ran z n then z is an all derivable point of alg n particularly if n is a nest on a complex hilbert space then every idempotent operator with range in n every injective operator as well as every operator with dense range in alg n is an all derivable point of the nest algebra alg n

all derivable points in continuous nest algebras let a be an operator algebra on a hilbert space we say that an element g a is an all derivable point of a for the strong operator topology if every strong operator topology continuous derivable linear mapping at g i e st s t s t for any s t algn with st g is a derivation let n be a continuous nest on a complex and separable hilbert space h we show in this paper that every orthogonal projection operator p m 0 m n is an all derivable point of algn for the strong operator topology

jordan higher all derivable points on nontrivial nest algebras abstract let a be a banach algebra with unity i and m be a unital banach a bimodule a family of continuous additive mappings d i i n from a into m is called a higher derivable mapping at x if n ab i j n i a j b for any a b a with ab x in this paper we show that d is a jordan higher derivation if d is a higher derivable mapping at an invertible element x as an application we also get that every invertible operator in a nontrivial nest algebra is a higher all derivable point

linear maps on c algebras which are derivations or triple derivations at a point abstract we prove new results about generalized derivations on c algebras by considering the triple product a b c 2 1 a b c c b a we introduce the study of linear maps which are triple derivations or triple homomorphisms at a point we prove that a continuous linear map t on a unital c algebra is a generalized derivation whenever it is a triple derivation at the unit element if we additionally assume t 1 0 then t is a derivation and a triple derivation furthermore a continuous linear map on a unital c algebra which is a triple derivation at the unit element is a triple derivation similar conclusions are obtained for continuous linear maps which are derivations or triple derivations at zero we also give an automatic continuity result that is we show that generalized derivations on a von neumann algebra and linear maps on a von neumann algebra which are derivations or triple derivations at zero are all continuous even if not assumed a priori to be so

group classification of heat conductivity equations with a nonlinear source we suggest a systematic procedure for classifying partial differential equations pdes invariant with respect to low dimensional lie algebras this procedure is a proper synthesis of the infinitesimal lie method the technique of equivalence transformations and the theory of classification of abstract low dimensional lie algebras as an application we consider the problem of classifying heat conductivity equations in one variable with nonlinear convection and source terms we have derived a complete classification of nonlinear equations of this type admitting nontrivial symmetry it is shown that there are 3 7 28 and 12 inequivalent classes of pdes of the type considered that are invariant under the one two three and four dimensional lie algebras correspondingly furthermore we prove that any pde belonging to the class under study and admitting the symmetry group of a dimension higher than four is locally equivalent to a linear equation this classification is compared with existing group classifications of nonlinear heat conductivity equations and one of the conclusions is that all of them can be obtained within the framework of our approach furthermore a number of new invariant equations are constructed which have rich symmetry properties and therefore may be used for mathematical modelling of say nonlinear heat transfer processes

additive maps derivable at some points on j subspace lattice algebras abstract let l be a j subspace lattice on a real or complex banach space dim x with x 2 and alg l be the associated j subspace lattice algebra let alg l alg l be an additive map it is shown that if is derivable at zero point i e ab a b a b whenever ab 0 then a a a a where is an additive derivation and is a scalar if is generalized derivable at zero point i e ab a b a b a i b whenever ab 0 then is a generalized derivation it is also shown that if x is complex then every linear map derivable at unit operator on alg l is a derivation

all derivable points of operator algebras abstract let a be an operator subalgebra in b h where h is a hilbert space we say that an element z a is an all derivable point of a for the norm topology strongly operator topology etc if every norm topology strongly operator topology etc continuous derivable linear mapping at z i e st s t s t for any s t a with st z is a derivation in this paper we show that every invertible operator in the nest algebra alg n is an all derivable point of the nest algebra for the strongly operator topology we also prove that every nonzero element of the algebra of all 2 2 upper triangular matrixes is an all derivable point of the algebra