On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum

In a previous paper (J. of Differential Equations, Vol. 249 (2010), 3081-3098) we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.

A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.

ZETA DETERMINANT AND OPERATOR DETERMINANTS

We apply techniques of zeta functions and regularized products theory to study the zeta determinant of a class of abstract operators with compact resolvent, and in particular the relation with other spectral functions.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Sampling associated with resolvent-type kernels and lagrange-type interpolation series

In this paper a new class of Kramer kernels is introduced, motivated by the resolvent of a symmetric operator with compact resolvent. The article gives a necessary and sufficient condition to ensure that the associ- ated sampling formula can be expressed as a Lagrange-type interpolation series. Finally, an illustrative example, taken from the Hamburger moment problem theory, is included.

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

Study of the influence of indium segregation on the optical properties of InGaAs/GaAs quantum wells via split-operator method

In the case of quantum wells, the indium segregation leads to complex potential profiles that are hardly considered in the majority of the theoretical models. The authors demonstrated that the split-operator method is useful tool for obtaining the electronic properties in these cases. Particularly, they studied the influence of the indium surface segregation in optical properties of InGaAs/GaAs quantum wells. Photoluminescence measurements were carried out for a set of InGaAs/GaAs quantum wells and compared to the results obtained theoretically via split-operator method, showing a good agreement.

Estimating losses in teleportation schemes using the phenomenological operator approach to dissipation in cavity quantum electrodynamics

In this paper, we estimate the losses during teleportation processes requiring either two high-Q cavities or a single bimodal cavity. The estimates were carried out using the phenomenological operator approach introduced by de Almeida et al. [Phys. Rev. A 62, 033815 (2000)].

Non-linear boundary element formulation applied to contact analysis using tangent operator

This work presents a non-linear boundary element formulation applied to analysis of contact problems. The boundary element method (BEM) is known as a robust and accurate numerical technique to handle this type of problem, because the contact among the solids occurs along their boundaries. The proposed non-linear formulation is based on the use of singular or hyper-singular integral equations by BEM, for multi-region contact. When the contact occurs between crack surfaces, the formulation adopted is the dual version of BEM, in which singular and hyper-singular integral equations are defined along the opposite sides of the contact boundaries. The structural non-linear behaviour on the contact is considered using Coulomb`s friction law. The non-linear formulation is based on the tangent operator in which one uses the derivate of the set of algebraic equations to construct the corrections for the non-linear process. This implicit formulation has shown accurate as the classical approach, however, it is faster to compute the solution. Examples of simple and multi-region contact problems are shown to illustrate the applicability of the proposed scheme. (C) 2011 Elsevier Ltd. All rights reserved.

Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials

This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the nonlinear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations. (C) 2009 Elsevier Ltd. All rights reserved.

Discrete approximation to the global spectrum of the tangent operator for flow past a circular cylinder

This paper deals with the calculation of the discrete approximation to the full spectrum for the tangent operator for the stability problem of the symmetric flow past a circular cylinder. It is also concerned with the localization of the Hopf bifurcation in laminar flow past a cylinder, when the stationary solution loses stability and often becomes periodic in time. The main problem is to determine the critical Reynolds number for which a pair of eigenvalues crosses the imaginary axis. We thus present a divergence-free method, based on a decoupling of the vector of velocities in the saddle-point system from the vector of pressures, allowing the computation of eigenvalues, from which we can deduce the fundamental frequency of the time-periodic solution. The calculation showed that stability is lost through a symmetry-breaking Hopf bifurcation and that the critical Reynolds number is in agreement with the value presented in reported computations. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.