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We will introduce the sublinear expander and cover some applications of sublinear expander. Given a graph H, a balanced subdivision of H is a graph obtained from H by subdividing every edge the same n...
When two balls in a metric space have small intersection? We give some natural conditions to guarantee an exponential decay on the volume of such intersections. Our proof is conceptually simple, makin...
We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators,that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of glo...
Abstract: In this work, we aim to prove algebra properties for generalized Sobolev spaces $W^{s,p} \cap L^\infty$ on a Riemannian manifold, where $W^{s,p}$ is of Bessel-type $W^{s,p}:=(1+L)^{-s/m}(L^p...
Abstract: Let $\Phi$ be a concave function on $(0,\infty)$ of strictly lower type $p_{\Phi}\in(0,1]$ and $\omega\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orl...
Abstract: An operator system $\cl S$ with unit $e$, can be viewed as an Archimedean order unit space $(\cl S,\cl S^+,e)$. Using this Archimedean order unit space, for a fixed $k\in \bb N$ we construct...
Given a symplectic manifold (M; !) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L.
In this survey we consider main transmutation theory topics with many applications, including author’s own results. The topics covered are: transmutations for Sturm–Liouville operators, Vekua–Erdelyi...
We prove an implicit function theorem for functions on infinite dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variatio...
In this paper we develop new applications of variational analysis and generalized differ- entiation to the following optimization problem and its specifications: given n closed subsets of a Banach sp...
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed.
We slightly extend the fluctuation theorem obtained in [24] for sums of generators, considering continuous–time Markov chains on a finite state space whose underlying graph has multiple edges and no l...
Conditions for the second-order linear differential equation X3 i=0 a3,ixi ! y′′ + X2 i=0 a2,ixi ! y′− X1 i=0 τ1,ixi! y = 0 to have polynomial solutions are given. Several application of these r...
Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient.
In this paper by making use of the generalized Bernardi-Libera-Livingston integral operator we introduce and study some new subclasses of univalent functions. Also we investigate the relations between...

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