The classical approach to linking lattice dynamics properties to continuum equations of motion, the “method of long waves,” is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the first part of the article, the derivation is made within the harmonic approximation for the perfect lattice response. Higher order terms are included in the...

Abstract We prove a product formula for the determinant of cohomology an étale sheaf with $\ell $ -adic coefficients over arbitrary proper scheme perfect field positive characteristic p distinct from . The local contributions are constructed by iterating vanishing cycle functors as well certain exact additive that can be considered linearised versions Artin conductors and $\varepsilon -factors....

In this note we show that the bilocal *-automorphisms of the C∗-algebra B(H) of all bounded linear operators acting on a complex infinite dimensional separable Hilbert space H are precisely the unital algebra *-endomorphisms of B(H). The study of local derivations of operator algebras has been initiated by Kadison [5] and Larson and Sourour [8]. A linear map ∆ on an algebra is called a local de...

The primary aim of this paper is to answer the question: what are the highest-order fiveor nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the oneand two-dimensional Poisson equation on uniform, quasi-uniform, and non-uniform face-to-face hyper-rectangular grids and directly prove the existence or non-...

let a be a unital algebra over a field of characteristic zero. we show that every derivation from( ) n m a into its dual ( ) n m a ∗ is the sum of an inner derivation and a derivation induced by a derivationfrom a into a∗

While the derived trees yielded by TAG derivations are uncontroversially taken to correspond to phrase structure, the status of TAG derivation structures as more than a record of TAG operations is less certain. An attractive possibility is to interpret the derivation structure as some representation of semantic meaning, such as a dependency analysis. However, the literature has identified cases...

A torsion theory is called differential (higher differential) if a derivation (higher derivation) can be extended from any module to the module of quotients corresponding to the torsion theory. We study conditions equivalent to higher differentiability of a torsion theory. It is known that the Lambek, Goldie and any perfect torsion theories are differential. We show that these classes of torsio...

The present paper is devoted to studying local derivations on the Lie algebra $W(2,2)$ which has some outer derivations. Using linear methods in \cite{CZZ} and a key construction for we prove that every derivation $W(2, 2)$ derivation. As an application, determine all deformed $\mathfrak{bms}_3$ algebra.