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.      

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.     

Synthesis and characterization of model 3‐miktoarm star copolymers of poly(dimethylsiloxane) and poly(2‐vinylpyridine)

3‐Miktoarm star copolymers, 3μ‐D₂V, with two poly(dimethylsiloxane) (PDMS) and one poly(2‐vinylpyridine) (P2VP) arm, were synthesized by using anionic polymerization–high vacuum techniques and (chloromethylphenylethyl)methyl dichlorosilane, heterofunctional linking agent, with two SiCl groups and one CH₂Cl group. The synthetic strategy involves the selective reaction of the two ? SiCl groups with PDMSOLi living chains, followed by reaction of the remaining chloromethyl group with P2VPLi. Combined molecular characterization results (size exclusion chromatography, membrane osmometry, and ¹H NMR spectroscopy) revealed a high degree of structural and compositional homogeneity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 614–619, 2006     

Synthesis of A2B star block copolymers from a heterotrifunctional initiator

We described the obtention of A₂B star block copolymers through the use of a new heterotrifunctional initiator. That way, well‐defined (PCL)₂‐arm‐PtBuMA and (PCL)₂‐arm‐PS star block copolymers have been synthesized from a heterotrifunctional initiator bearing two hydroxyl groups able to initiate ROP of CL (with AlEt₃ or Sn(Oct)₂ as coinitiator) and a bromide function able to initiate ATRP of tBuMA or styrene. Firstly, we have proceeded using a sequential process (two‐steps), leading to an intermediate macroinitiator. Secondly, attempt to polymerize these two monomers in a simultaneous process (one‐step), that is directly from the mixture of monomers, initiator, coinitiators, and solvent, has been realized and has shown that some interferences between the two polymerizations occurred, leading to an inhibition of ATRP when Sn(Oct)₂ was used and an unexpected increase in control when AlEt₃ was used as catalyst for the ROP (obtention of well‐defined (PCL)₂‐arm‐PtBuMA with pdi of 1.18). © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1796–1806, 2006     

Numerical simulation of critical dependences for symmetric two-layered Josephson junctions

Partial critical dependences of the form current-magnetic field in a two-layered symmetric Josephson junction are modeled. A numerical experiment shows that, for the zero interaction coefficient between the layers of the junction, jumps of the critical currents corresponding to different distributions of the magnetic fluxes in the layers may appear on the critical curves. This fact allows a mathematical interpretation of the results of some recent experimental results for two-layered junctions as a consequence of discontinuities of partial critical curves.     

Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.