let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

A new type of splicing is defined, namely the interchange of two fixed subwords, without moving the sequences situated after them. Idea of splicing grammar systems is introduced by Dassow and Mitrana, ([2]); in this paper only the derivation type is changed. The generative power is the same (are necessarily only two modules to generate all recursive enumerable languages). Two variants of deriva...

In the papers [1, 2, 4–6, 8] the similarities and differences between systems of sequents and systems of natural deduction for some fragments of intuitionistic logic were presented. The main goal of almost all of these papers was to study the connection between cut-free derivations and normal derivations. It is a well-known property that the natural deduction image of a cut-free derivation is a...

Bounded rewriting for linear term rewriting systems has been defined in (I. Durand, G. Sénizergues, M. Sylvestre. Termination of linear bounded term rewriting systems. Proceedings of the 21st International Conference on Rewriting Techniques and Applications) as a restriction of the usual notion of rewriting. We extend here this notion to the whole class of left-linear term rewriting systems, an...

Let R be a ring and S a nonempty subset of R. Suppose that θ and φ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ,φ)-derivation (resp., Jordan left (θ,φ)derivation) on S if δ(xy) = θ(x)δ(y)+φ(y)δ(x) (resp., δ(x2) = θ(x)δ(x)+φ(x)δ(x)) holds for all x,y ∈ S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is show...

In [17] Lee and Shiue showed that if R is a non-commutative prime ring, I a nonzero left ideal of R and d is a derivation of R such that [d(x)x, x]k = 0 for all x ∈ I, where k,m, n, r are fixed positive integers, then d = 0 unless R ∼= M2(GF (2)). Later in [1] Argaç and Demir proved the following result: Let R be a non-commutative prime ring, I a nonzero left ideal of R and k,m, n, r fixed posi...

This paper takes Chinese five-syllable compounds as examples to re-examine the derivation of Chinese synthetic compounds. With phonological evidences which show that Chinese synthetic compounds are left stressed, the paper proves that Chinese synthetic compounds are derived in the interface of lexicon and syntax, based on argument structures of the root verbs. The paper assumes that Chinese syn...

Let M be a 2-torsion free prime Γ-ring and X a nonzero faithful and prime ΓM -module. Then the existence of a nonzero Jordan left derivation d : M → X satisfying some appropriate conditions implies M is commutative. M is also commutative in the case that d : M → M is a derivation along with some suitable assumptions. AMS (MOS) Subject Classification Codes: 03E72, 54A40, 54B15