We consider examples of discrete nonlinear Schrödinger equations in Z admitting ground states which are orbitally but not asymptotically stable in l(Z). The ground states contain internal modes which decouple from the continuous modes. The absence of leaking of energy from discrete to continues modes leads to an almost conservation and perpetual oscillation of the discrete modes. This is quite ...

The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...

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 establish the following result. Theorem. Let α : G → L(X) be a σ(X, X∗) integrable bounded group representation whose Arveson spectrum Sp(α) is scattered. Then the subspace generated by all eigenvectors of the dual representation α∗ is w∗ dense in X∗. Moreover, the σ(X, X∗) closed subalgebra Wα generated by the operators αt (t ∈ G) is semisimple. If, in addition, X does not contain any copy ...

In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

A common assumption of the shape from texture problem is that a perceived image primarily contains only one type of texture with the same surface orientations. Unfortunately, a natural image is often composed of textured planes with different surface orientations. In order to deal with the shape from texture problem in a practical manner, we need to segment these surface orientations. The ridge...

Contents 1. Introduction 597 2. Braid groups in positive genus 601 3. Relative completion of mapping class groups 603 4. Mixed Hodge structures on Torelli groups 608 5. Review of continuous cohomology 613 6. Remarks on the representations of sp g 616 7. Continuous cohomology of Torelli groups 618 8. The lower central series quotients of a surface group 621 9. The action of t 1 g on p g 623 10. ...

Let (U, R) be an approximation space with U being non-empty set and R equivalence relation on U, let $${\overline{G}}$$ $${\underline{G}}$$ the upper lower of subset G U. A topological rough group is a $$G=({\underline{G}}, {\overline{G}})$$ endowed topology, which induced from , such that product mapping $$f: G\times G\rightarrow {\overline{G}}$$ inverse are continuous. In class groups, relati...