Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...

In this paper we use results on reducibility, localization and duality for the Almost Mathieu operator, (Hb,φx)n = xn+1 + xn−1 + b cos (2πnω + φ) xn on l2(Z) and its associated eigenvalue equation to deduce that for b 6= 0,±2 and ω Diophantine the spectrum of the operator is a Cantor subset of the real line. This solves the so-called “Ten Martini Problem” for these values of b and ω. Moreover, ...

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

In this paper‎, ‎we consider a general integral operator $G_n(z).$ The main object of the present paper is to study some properties of this integral operator on the classes $mathcal{S}^{*}(alpha),$ $mathcal{K}(alpha),$ $mathcal{M}(beta),$ $mathcal{N}(beta)$ and $mathcal{KD}(mu,beta).$‎

A bstract We investigate several aspects of BPS latitude Wilson loops in gauge theories three dimensions with $$ \mathcal{N} N ? 4 supersymmetry. derive a matrix model for the bosonic loop ABJM using supersymmetric localization, and show how to extend computation more general Chern-Simons-matter theories. the...

The localization of vibrations is a widely observed, but little understood physical phenomenon. Roughly speaking, the effect of localization is a confinement of some eigenfunctions of an elliptic operator to a small portion of the original domain in the presence of irregularities of the boundary or of the coefficients of the underlying operator. Until recently, there have been essentially no ma...

in this paper‎, ‎we consider a general integral operator $g_n(z).$ the main object of the present paper is to study some properties of this integral operator on the classes $mathcal{s}^{*}(alpha),$ $mathcal{k}(alpha),$ $mathcal{m}(beta),$ $mathcal{n}(beta)$ and $mathcal{kd}(mu,beta).$‎

A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation is derived in order for the localization of a particle to represent a space-time event. It is shown that there exists a conflict between this relation and t...