In this work, an innovative method for controlling the current distribution of radiating patch by adjusting input phase is investigated to achieve both pattern and polarization reconfigurable characteristics multifunction. A compact low-profile antenna with four fed ports designed implement proposed method, which can operate linear, right-hand circular (RHCP) left-hand (LHCP) different beam dir...

The subject of the present paper are stability properties solution set to set-valued inclusions. latter problems emerging in robust optimization and mathematical economics, which can not be cast traditional generalized equations. analysis here reported focuses on several quantitative forms semicontinuity for mappings, widely investigated variational analysis, include, among others, calmness. Su...

This paper addresses an important issue about the compact representation of the conditional probability distribution (CPD) applied in the well known Bayesian Networks in uncertain causality representation and probabilistic inference. That is, there is an essential difference between the single-valued cases and the multi-valued cases, while this difference does not exist when the CPD is represen...

The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

We show that, in complex interpolation, an operator function that is compact on one side of the interpolation scale will be compact for all proper interpolating spaces if the right hand side (Y , Y ) is reduced to a single space. A corresponding result, in restricted generality, is shown if the left hand side (X, X) is reduced to a single space. These results are derived from the fact that a ho...

Abstract We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) bounded variation. In our approach we define analogue the partial sums with help Dirichlet kernel using newly defined weighted metric integral. derive error bounds for these approximants. As a consequence, prove that sequence converges pointwisely in Hausdorff values approximated...

We consider whether the “inequality-splitting” property established in the Brøndsted– Rockafellar theorem for the subdifferential of a proper convex lower semicontinuous function on a Banach space has an analog for arbitrary maximal monotone multifunctions. We introduce the maximal monotone multifunctions of type (ED), for which an “inequality-splitting” property does hold. These multifunctions...

Let F be a continuous multifunction on IR with compact convex values. For any vector w, let F(x) ⊆ F (x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w : [0, T ] 7→ IR with the following property: all solutions to the Cauchy problem ẋ(t) ∈ F(x(t)), x(0) = 0, are also solutions to ẋ(t) ∈ extF (x(t)). We prove that W is residual in C(...