in this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,t)$, subject to nulldirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. the optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

Let N be a prime Γ-near ring with multiplicative center Z. Let σ and τ be automorphisms of N and δ be a Γ− (σ, τ)-derivation of N such that N is 2-torsion free. In this paper the following results are proved: (1) If σγδ = δγσ and τγδ = δγτ and δ(N) ⊆ Z, or [δ(x), δ(y)]γ = 0, for all x, y ∈ N and γ ∈ Γ, then N is a commutative ring. (2) If δ1 is a Γ-derivation, δ2 is a Γ − (σ, τ) derivation of N...

motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎it is shown‎ ‎that every lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎the definition of lie $n$-higher‎ ‎derivations on operator algebras and related pote...

We introduce a new class of simple Lie algebras W (n, m) (see Definition 1) that generalize the Witt algebra by using " exponential " functions, and also a subalgebra W * (n, m) thereof; and we show each derivation of W * (1, 0) can be written as a sum of an inner derivation and a scalar derivation (Theorem. 2) [10]. The Lie algebra W (n, m) is Z-graded and is infinite growth [4].

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 gl(n, R) be the Lie algebra consisting of all n × n matrices over a commutative ring R with identity 1. In this paper, we prove that every generalized Lie triple derivation of gl(n, R)(n ≥ 2) is the sum of a Lie triple derivation and a homothety.

Lexical chains between two concepts are sequences of semantically related words interconnected via semantic relations. This paper presents a new approach for the automatic construction of lexical chains on knowledge bases. Experiments were performed building lexical chains on WordNet, Extended WordNet, and Extended WordNet Knowledge Base. The research addresses the problems of lexical chains ra...