Approximate controllability of fractional neutral stochastic evolution equations in Hilbert spaces with fractional Brownian motion

In this paper, the approximate controllability for Sobolev-type fractional neutral stochastic evolution equations with fractional stochastic nonlocal conditions and fractional Brownian motion in a Hilbert space are studied. The results are obtained by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem, and methods adopted directly from deterministic control problems for the main results. Finally, an example is given to illustrate the application of our result.     

Additive preservers of Drazin invertible operators with bounded index

Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n ≥ 1, we show that an additive surjective map Φ on B(X)preserves Drazin invertible operators of index non-greater than n in both directions if and only if Φ is either of the form Φ(T) = αATA~(-1) or of the form Φ(T) = αBT~*B~(-1) where α is a non-zero scalar,A:X → X and B:X~*→ X are two bounded invertible linear or conjugate linear operators.     

Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients

One of the basic inverse problems in an anisotropic media is the determination of coefficients in a bounded domain with a single measurement. We consider the problem of finding the coefficient of the second derivatives in a second-order hyperbolic equation with variable coefficients.

Under a weak regularity assumption and a geometrical condition on the metric, we prove the uniqueness in a multidimensional hyperbolic inverse problem with a single measurement. Moreover we show that our uniqueness results yield the Lipschitz stability estimate in L ² space for solution to the inverse problem under consideration.     

About embedded eigenvalues for a spectral problem arising in the study of elastic surface waves in a topographical waveguide

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half‐space, of which the cross‐section is a local perturbation of a homogeneous half‐plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves propagating more rapidly than S‐waves. Thanks to the boundary of the deformed half‐plane and some reduced equations, these eventual eigenmodes must locally vanish. Adapting to our case a unique continuation principle for the elasticity system, we conclude that these eigenmodes vanish everywhere. Copyright © 2002 John Wiley & Sons, Ltd.     

Hermitean Matrix Ensembles and Orthogonal Polynomials

In this article, we investigate orthogonal polynomials associated with complex Hermitean matrix ensembles using the combination of the methods of Coulomb fluid (or potential theory), chain sequences, and Birkhoff–Trjitzinsky theory. We give a general formula for the largest eigenvalue of the N×N Jacobi matrices (which is equivalent to estimating the largest zero of a sequence of orthogonal polynomials) and the two-level correlation function for the α ensembles (α>0) introduced previously for α>1. In the case of 0<α<1, we give a natural representation for the weight function that is a special case of the general Nevanlinna parametrization. We also discuss Hermitean matrix ensembles associated with general indeterminate moment problems.     

Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms

The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three‐dimensional thin domain Ω^ε. Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter ε. These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation.     

The node-edge weighted 2-edge connected subgraph problem: Linear relaxation, facets and separation

Let G=(V,E) be a undirected k-edge connected graph with weights c_e on edges and w_v on nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G, of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable.     

Theory of vibronic interactions in D2 and H2: a comparison between multichannel-quantum-defect and coupled-equation approaches

New experimental energy levels for the 2pπC(1)Π(u)(-) state of D(2) are reported extending up to the dissociation limit and including rotational quantum numbers up to N = 10. These data are extracted from recent high resolution optical emission spectra, and they are used for a detailed comparison of two theoretical approaches, both of which are fully ab initio and are based on the same state-of-the-art clamped-nuclei potential energy curves. These are the coupled differential equations (CE) and the multichannel quantum defect theory (MQDT) approaches, each of which accounts for adiabatic corrections and non-adiabatic couplings. Both theoretical approaches reproduce the experimental levels to within a fraction of a wavenumber unit (cm(-1)) for the lower vibrational quantum numbers, with the MQDT surpassing the CE method. As the dissociation limit is approached, the residuals observed-calculated increase up to several cm(-1) and the MQDT method is up to a factor of two less accurate than the CE method. The same analysis is carried out with existing data for the H(2) isotopomer and yields similar results. An analogous comparison is also made for the 3pπD(1)Π(u)(-) and 4pπD('1)Π(u)(-) states for both isotopomers, where the MQDT is found to be superior to the CE approach.     

Study of various parameters influencing the fixation of metallic ions Cu2+, Zn2+, and Ni2+ at the catalytic Amberlyst-15 resin in the presence of alcohols

The ionic exchange behavior of Zn²⁺, Ni²⁺, and Cu²⁺ metallic ions on Amberlyst-15 commercial resin was studied as a function of resin solution contact time, initial concentration of metallic ions, nature of the solvent, and the amount of resin. The metallic ions were studied in ternary mixtures using both column and batch experiments. In addition, water, methanol, ethanol, and propan-2-ol were used as solvents for dissolving metallic ions. It was found that the resin behavior depends on the solvent nature and the metallic ion concentration. The analysis of solutions by atomic absorption spectrometry revealed that the affinity of the resin for the studied metallic ions followed the sequence Cu²⁺ > Ni²⁺ > Zn²⁺ in the case of an aqueous medium. Furthermore, uptake increased with increasing amount of resin. A better uptake was observed in the case of the 75:25 % water/methanol compositions when the column technique was used. For the batch technique, we noted a better uptake using 100 % water. The uptake rate decreased with an increase in the number of carbons for the 50 % water–50 % alcohol solvents. The acid–base properties of Amberlyst-15 commercial resin were studied by 2-propanol decomposition test. Propene and acetone are the main expected products and it is believed that they are formed through dehydration or dehydrogenation reaction on acid and base sites, respectively.