‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

We develop an randomized approximation algorithm for the size of set union problem |A1 ∪ A2 ∪ ... ∪ Am|, which given a list of sets A1, ..., Am with approximate set size mi for Ai with mi ∈ ((1− βL)|Ai|, (1 + βR)|Ai|), and biased random generators with Prob(x = RandomElement(Ai)) ∈ [ 1−αL |Ai| , 1+αR |Ai| ] for each input set Ai and element x ∈ Ai, where i = 1, 2, ..., m. The approximation rati...

With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter have likelihood functions elude analytical formulations. Even under such adversity, when one can simulate from sampling distribution, Bayesian analysis be conducted using approximate methods as Approximate Computation (ABC) or ...