The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...

Let F be the underlying base field of characteristic p > 3 and denote by W and S the even parts of the finite-dimensional generalized Witt Lie superalgebra W and the special Lie superalgebra S, respectively. We first give the generator sets of the Lie algebras W and S. Using certain properties of the canonical tori of W and S, we then determine the derivation algebra of W and the derivation spa...

Abstract Based on simple combinatorial arguments, we formulate a generalized cavity method where the Random Overlap Structure (ROSt) probability space of Aizenmann, Sims and Starr is obtained in constructive way, use it to give simplified derivation Parisi formula for free energy Sherrington–Kirkpatrick model.

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

This paper deals with Cramér-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces generalized versions of Fisher information. The contributions of this paper are (i) the derivation of new extended Cramér-Rao inequalities for the estimation of a parameter, involving general q-moment...

We prove the orthogonality (in the sense of Birkhoff) of the range and the kernel of an important class of elementary operators with respect to the Schatten p-class. 1. Introduction. Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of all bounded operators on H into itself. Given A, B ∈ B(H), we define the generalized derivation δ A,B : B(H) B(H) b...

The so-called generalized Kramers-Kirkwood expression for the average stress tensor of a system of interacting point particles, derived by Bird and Curtiss on using a phase-space-kinetic formalism has been reconsidered from different points of view. First a derivation based upon volume averaging is discussed, and after that a derivation based upon a virtual work principle. The latter approach o...

We prove that the automorphisms of the generalized Witt Lie algebras W(m , n) over arbitrary commutative rings of characteristic p > 3 all come from automorphisms of the algebras on which they are defined as derivations. By descent theory, this result then implies that if a Lie algebra over a field becomes isomorphic to W{m, n) over the algebraic closure, it is a derivation algebra of the type ...

A general formulation for the disorientation angle distribution function is derived. The derivation employs the hyperspherical harmonic expansion for orientation distributions, and an explicit solution is presented for materials with cubic crystal symmetry and arbitrary textures. The result provides a significant generalization to the well-known Mackenzie distribution function (Mackenzie JK. Bi...