Variational Principles and Mean Value Estimates

Journal of Optimization Theory and Applications - In this paper, for a continuous function defined on a closed subset of a Banach space and differentiable on the interior of the domain, the infimum...     

Some properties of two-dimensional surjective <Emphasis Type="Italic">p</Emphasis>-homogeneous maps

The properties of real p-homogeneous polynomial maps in R² are examined. The relation between surjectivity and the existence of a nontrivial zero is investigated. Additionally, the relation between surjectivity and stable surjectivity is studied. Examples are discussed.     

On Nonlocality of Quantum Objects

We present an option of the experiment with a correlated pair of particles in the entangled state, which provides the effect of a change in the polarization for entangled photons, and demonstrate the reality of all different superposition states and the corresponding vector of the quantum system state; also we analyze possible consequences of this fact. We propose a quantum realism paradigm within the relational paradigm instead of the local realism concept disproved by the experiments on verifying the Bell inequalities. We analyze the results of experimental research of the Leggett inequality violation with respect to the verification of the adequacy of different kinds of nonlocal hidden variable theories and suggest a new way of their evaluation based on the study of the photon cross-correlation suppression after a beam splitter and preparation of quantum squeezed states. We show that the interpretation based on the nonlocal hidden variable theory is inconsistent.     

Kantorovich’s Fixed Point Theorem and Coincidence Point Theorems for Mappings in Vector Metric Spaces

Set-Valued and Variational Analysis - The fixed points and coincidence points of mappings of v-metric spaces, i.e., sets on which a vector metric is defined, are investigated. The values of such a...     

Highconducting oxide ceramics bimevox: Synthesis, structure, and properties

Materials on the basis of BIMEVOX compounds which are stable within wide concentration and temperature regions have been obtained. Refinement of crystal structure of different BIMEVOX modifications obtained at different temperatures and partial oxygen pressures has been carried out. The most promising solid solutions have been identified according to total conductivity value as well as to linearity of conductivity dependence on temperature and independence of that on partial oxygen pressure.     

Equilibrium price as a coincidence point of two mappings

The existence of an equilibrium price vector in a nonlinear market model is analyzed. In the model, the demand and supply functions are obtained by maximizing the producer utility and profit, respectively. Sufficient conditions for the existence of an equilibrium price vector and its stability with respect to small perturbations in the model are given. The results are consequences of theorems on the existence and stability of coincidence points in the theory of α-covering mappings.     

The Structure of the Set of Local Minima of Functions in Various Spaces

Siberian Mathematical Journal - We study the topological properties and cardinalities of the sets of strict local minima of functions on f-quasimetric and topological spaces.     

On covering of linear operators on polyhedral sets

We consider a problem of finding a covering constant for a restriction of a linear operator to a polyhedral set. The obtained result allows to reduce the initial problem to the problem of finding a covering constant for some linear bijective operators.     

Variational Principles in Nonlinear Analysis and Their Generalization

Mathematical Notes -