let h be an infinite--dimensional hilbert space and k(h) be the set of all compact operators on h. we will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher jordan derivation on k(h) associated with the following cauchy-jencen type functional equation 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).

We establish three completeness properties (descriptive, relative and observational completeness) for the program logic for aliasing and higher-order functions, first studied in [1]. We then extend the results to the logic with local state in [6].

Let $mathcal{A}$ be a $C^*$-algebra and $Z(mathcal{A})$ the‎ ‎center of $mathcal{A}$‎. ‎A sequence ${L_{n}}_{n=0}^{infty}$ of‎ ‎linear mappings on $mathcal{A}$ with $L_{0}=I$‎, ‎where $I$ is the‎ ‎identity mapping‎ ‎on $mathcal{A}$‎, ‎is called a Lie higher derivation if‎ ‎$L_{n}[x,y]=sum_{i+j=n} [L_{i}x,L_{j}y]$ for all $x,y in  ‎mathcal{A}$ and all $ngeqslant0$‎. ‎We show that‎ ‎${L_{n}}_{n...

The phase-based approach to grammatical derivation and one rooted in the Tree Adjoining Grammar (TAG) formalism share the idea that the derivation of a complex sentence is divided into separate derivations of local domains. These approaches differ, however, in their treatment of syntactic dependencies spanning across such local domains. Under the phase approach, operations in a higher domain ca...

Wrappers export the schema and data of existing heterogeneous databases and support queries on them. In the context of cooperative information systems, we present a exible approach to specify the derivation of object-oriented export databases from local relational databases. Our export database derivation consists of a set of extent derivation structures which de-nes the extent and deep extent ...

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.

A derivation of Young's equation based on the energy balance near the contact line is presented. Our proposal is rigorous and avoids the errors identified in the usual local derivation. It is valid under very general conditions (for any geometry, in a gravitational field and for compressive fluids). Deviations of the contact angle from Young's equation are discussed in several cases: surfaces o...