Let M be a 2-torsion free prime Γ-ring satisfying the condition a α b β c=a β b α c,∀a,b,c∈M and α,β∈Γ, U be an admissible Lie ideal of M and F=(f i ) i∈N be a generalized higher (U,M)-derivation of M with an associated higher (U,M)-derivation D=(d i ) i∈N of M. Then for all n∈N we prove that [Formula: see text]. Mathematics Subject Classification (2010): 13N15; 16W10; 17C50.

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].

4. Nonlinear phenomena 4.1. Second-order nonlinear phenomena 4.2. Third-order nonlinear phenomena 4.3. Stimulated Raman scattering 4.4. Stimulated Brillouin scattering 4.5. Four-wave mixing (FWM) 4.6. Self-phase modulation (SPM) 4.7. Cross phase modulation (XPM) 4.8. Theoretical description of GVD phenomenon and self-phase modulation 4.8.1. Nonlinear Schrödinger equation 4.8.2. Inclusion of the...

Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...

We extend the construction of the authors’ paper of 2002 by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical...

The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg de Vries equation for purely uni-directional waves. In this paper we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, t...

In the present paper, a new design method for continuous-time powersymmetric active RC filters for Hybrid Filter Bank (HFB) is proposed. Some theoretical properties of continious-time power-symmetric filters bank in a more general perspective are studied. This includes the derivation of a new general analytical form, and a study of poles and zeros locations in s-plane. In the proposed design me...

This article is concerned with the analytic solution for a nonlinear flow problem of an incompressible viscous fluid. The fluid is taken in a channel having two weakly permeable moving porous walls. An incompressible fluid fills the porous space inside the channel. The fluid is magnetohydrodynamic in the presence of a time-dependent magnetic field. Lie group method is applied in the derivation ...