begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

In this Note, we consider traveling waves in a reaction-diffusion equation dimension one. Motivated by the motion of dislocations crystals, introduce an additive parameter σ reaction term, which may be interpreted as exterior force applied on crystal. Under certain natural assumptions and for every value σ∈[σ - ,σ + ], show existence ϕ velocity c. The range σ∈(σ ) corresponds to bistable cases ...

In this article, semi-ring and semi-algebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semi-ring of sets has already been formalized in [12], that is, strictly speaking, a definition of a quasi semi-ring of sets suggested in the last few decades [14]. We adopt a classical definition of a semi-ring of sets here to avoid such a confusion. Ring ...

We prove several dichotomy theorems which extend some known results on σ -bounded and σ -compactpointsets. In particular we show that, given a finite number of Δ1 equivalence relations F1 , . . . , Fn , any Σ1 set A of the Baire space either is covered by compact Δ1 sets and lightface Δ1 equivalence classes of the relations Fi , or A contains a superperfect subset which is pairwise Fi -inequiva...

The circumferential shear stress along the boundary of a traction-free circular hole in an infinite isotropic solid under antiplane shear is twice the circumferential shear stress along the corresponding circle in an infinite solid without a hole, under the same loading conditions. This result, originally derived by Lin et al. (Yielding, damage, and failure of anisotropic solids. EGF Publicatio...

We present a unifying empirical description of the structural and kinematic properties of all spheroids embedded in dark matter halos. We find that the stellar spheroidal components of galaxy clusters, which we call cluster spheroids (CSphs) and which are typically one hundred times the size of normal elliptical galaxies, lie on a “fundamental plane” as tight as that defined by ellipticals (rms...

categorial grammars are not intended as yet another grammatical formalism that would compete with other established formalisms. It should rather be seen as the kernel of a grammatical framework — in the spirit of (Ranta, 2002) — in which other existing grammatical models may be encoded. This paper illustrates this fact by showing how tree-adjoining grammars (Joshi and Schabes, 1997) may be embe...