The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).     

Continuous Selectors of Fixed Point Sets of Multifunctions with Decomposable Values

Existence theorems of continuous selectors whose values are fixed points of multivalued contractions are proved. As an application, the existence of continuous selectors to generalized solution sets of partial differential inclusions, depending on a parameter, is obtained.     

Frequent oscillation in a nonlinear partial difference equation

This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures.      

Oxidative dehydrogenation of crotonaldehyde overK2HPMo12O40catalyst

Summary The oxidative dehydrogenation of crotonaldehyde to furan and maleic anhydride was carried out over K₂HPMo₁₂O₄₀catalyst. A positive effect of water vapor on furan formation is explained by ability of the catalyst to isomerize 2E- to 2Z-crotonaldehyde.</o:p>     

Catalytic Activity of Nickel Alloys in Anodic Oxidation of the Hypophosphite Ion as a Function of Their Composition

The rate of anodic oxidation of the hypophosphite ion on alloys Ni-P, Ni-B, and Ni-Mo-P is studied as a function of their composition and structure. The organic compounds that are customarily used to stabilize electrolytes of electroless nickel plating are shown to come useful when controlling composition of the Ni-P coatings at the expense of their different influence on the rates of partial processes of deposition of the alloy components. The formation of catalytic activity of such coatings is affected mostly by a structural factor. With alloys Ni-P, Ni-B, and Ni-Mo-P, whose composition was varied by altering the concentration of the source of the alloying component, dependence of catalytic activity of the surface on the composition is defined mainly by an electronic factor.__________Translated from Elektrokhimiya, Vol. 41, No. 8, 2005, pp. 972–980.Original Russian Text Copyright © 2005 by Sotskaya, Dolgikh, Ryabinina.     

Hilbert algebras as implicative partial semilattices

The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice (i.e., a relative subalgebra of an implicative semilattice),and conversely.The implication in an implicative partial semilattice is characterised in terms of ?lters of the underlying partial semilattice.     

The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs

In this article we consider partitioned Runge-Kutta (PRK) methods for Hamiltonian partial differential equations (PDEs) and present some sufficient conditions for multi-symplecticity of PRK methods of Hamiltonian PDEs.

     

A partial differential equation which describes an interatomic surface

In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

On the growth strain origin and stress evolution prediction during oxidation of metals

High temperature oxidation of metals leads to residual stresses in the metal and in the oxide. In this work, we try to predict the evolution of the residual stresses in the growing oxides layers, during isothermal oxidation. The origin of these stresses is based on the microstructural model of Clarke, however, another justification is proposed, assuming a proportional dependence of the growth strain with the oxide layer thickness. Using the mechanics of thin layers, as well as the analysis proposed to describe the growth strain, a system of equations are deduced that predict the stresses evolution with oxidation time. Numerical analysis is performed, leading to a set of theoretical curves.