Let R be a prime ring with center Z, I nonzero ideal of and D: × → symmetric bi–(α, α)-derivation d the trace D. In present paper, we have considered following conditions: i) [d(x), x]α,α = 0, ii)[d(x), ⊆ Cα,α, iii)(d(x), x)α,α iv)D1(d2(x), x) v)d1(d2(x)) f(x), for all x, y ∈ I, where D1 D2 are two bi-(α, α)-derivations, d1, d2 traces D1, respectively, B: is bi-additive mapping, f B.

In today‟s world of internet, secure communication among group of members has become vital, where multicasting plays an important role. In secure multicasting, security and scalability are the two important checks. Sometimes there is tradeoff between security and scalability. In order to transmit the data in a secure and scalable way, a suitable key management protocol should be implemented whi...

using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

The basic Schema Theorem for genetic algorithms is modiied for a grammatically-based learning system. A context-free grammar is used to deene a language in which each sentence is mapped to a tness value. The derivation trees associated with these sentences are used to deene the structure of schemata. The eeect of crossover and mutation on schemata is described. A schema theorem is developed whi...

Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M . In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following (i) d(U) ⊂ Z, (ii) d(U) ⊂ U and d(U) = 0, (iii) d(U) ⊂ U , d(U) ⊂ Z.

sequent of d) forms an inference tp(d) in cutfree ω-arithmetic with repetition rule Rep. Obviously, if d is a derivation of falsum ⊥, i.e. if End(d) = ⊥, then tp(d) can only be an instance of Rep, so that d[0] is again a derivation of ⊥. In a second step, to each d an ordinal o(d) < ε0 is assigned such that o(d[n]) < o(d) for all n ∈ |tp(d)|. Then the consistency of Z follows by (quantifierfree...

In [2] Singer and Wermer showed that a bounded derivation in a commutative Banach algebra 21 necessarily maps 21 into the radical 91. They conjectured at this time that the assumption of boundedness could be dropped. It is a corollary of results proved below that if 21 is in addition regular and semi-simple, this is indeed the case. What is actually proved here is that under the above hypothese...

In this paper we show that the image of any locally finite k-derivation of the polynomial algebra k[x, y] in two variables over a field k of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image ImD of every k-derivation D of k[x, y] such that 1 ∈ ImD and divD = 0 is a Mathieu subspace of k[x, y].

In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. So, we use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom shear stress, and also the decay rate for shallow (and not deep) water. In order to justify our derivation, we check it by deriving the viscous Korteweg-...