Existence of Solution for a Class of Quasilinear Systems

This paper proves the existence of nontrivial solution for a class of quasilinear systems oil bounded domains in R(N), N >= 2, whose nonlinearity has a double criticality. The proof is based oil a linking theorem without the Palais-Smale condition.

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x) = g(1)x(-1) + g(2)x(-2), x is an element of R(+) = [0, infinity). For g(2) > 0 and g(1) < 0, the potential is known as the Kratzer potential V(K)(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein`s method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.

Tightened Lieb-Oxford Bound for Systems of Fixed Particle Number

The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a nonempirical tightening of that bound in both universal and electron number-dependent form. The test functional is PBE. Regarding both atomization energies (slightly worsened) and bond lengths (slightly improved), we find the PBE functional to be remarkably insensitive to the value of the Lieb-Oxford bound. This both rationalizes the use of the original Lieb-Oxford constant in PBE and suggests that enhancement factors more sensitive to sharpened constraints await discovery.

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, in particular, are important for the construction of improved density functionals. Here we investigate one such universal property-the Lieb-Oxford lower bound-for ionic and molecular systems. In recent work [J Chem Phys 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals. (C) 2008 Wiley Periodicals Inc.

Orbital-polarization terms: From a phenomenological to a first-principles description of orbital magnetism in density-functional theory

Phenomenological orbital-polarizition (OP) terms have been repeatedly introduced in the single-particle equations of spin-density-functional theory, in order to improve the description of orbital magnetic moments in systems containing transition metal ions. Here we show that these ad hoc corrections can be interpreted as approximations to the exchange-correlation vector potential A(xc) of current-density functional theory (CDFT). This connection provides additional information on both approaches: phenomenological OP terms are connected to first-principles theory, leading to a rationale for their empirical success and a reassessment of their limitations and the approximations made in their derivation. Conversely, the connection of OP terms with CDFT leads to a set of simple approximations to the CDFT potential A(xc), with a number of desirable features that are absent from electron-gas-based functionals. (C) 2008 Wiley Periodicals, Inc.

Solvatochromic and lonochromic Effects of Iron(II)bis-(1,10-phenanthroline)dicyano: a Theoretical Study

Solvatochromic and ionochromic effects of the iron(II)bis(1,10-phenanthroline)dicyano (Fe(phen)(2)(CN)(2)) complex were investigated by means of combined DFT/TDDFT calculations using the PBE and B3LYP functionals. Extended solvation models of Fe(phen)(2)(CN)(2) in acetonitrile and aqueous solution, as well as including interaction with Mg(2+), were constructed. The calculated vertical excitation energies reproduce well the observed solvatochromism in acetonitrile and aqueous solutions, the ionochromism in acetonitrile in the presence of Mg(2+), and the absence of ionochromic effect in aqueous solution. The vertical excitation energies and the nature of the transitions were reliably predicted after inclusion of geometry relaxation upon aqueous micro- and global solvation and solvent polarization effect in the TDDFT calculations. The two intense UV-vis absorption bands occurring for all systems studied are interpreted as transitions from a hybrid Fe(II)(d)/cyano N(p) orbital to a phenanthroline pi* orbital rather than a pure metal-to-ligand-charge transfer (MLCT). The solvatochromic and ionochromic blue band shifts of Fe(phen)(2)(CN)(2) were explained with preferential stabilization of the highest occupied Fe(II)(d)/cyano N(p) orbitals as a result of specific interactions with water solvent molecules or Mg(2+) ions in solution. Such interactions occur through the CN(-) groups in the complex, and they have a decisive role for the observed blue shifts of UV-vis absorption bands.

A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

New steps on Sobolev orthogonality in two variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quantum states, thermodynamic limits, and entropy in M theory

We discuss the matching of the BPS part of the spectrum for a (super) membrane, which gives the possibility of getting the membrane's results via string calculations. In the small coupling limit of M theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at a large coupling constant is computed by considering M theory on a manifold with a topology T-2 x R-9. We argue that the finite temperature partition functions (brane Laurent series for p not equal 1) associated with the BPS p-brane spectrum can be analytically continued to well-defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit p --> 0 (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.

Entropy and thermodynamic limits in M-theory

The matching of the BPS part of the (super) membrane's spectrum enables one to obtain membrane's results via string calculations. We compute the thermodynamic behavior at large coupling constant by considering M-theory on a manifold with topology T-2 X R-9. In the small coupling limit of M-theory the entropy coincides with the standard entropy of type IIB strings. We claim that the finite temperature partition functions associated with BPS p-brane spectrum can be analytically continued to well-defined functionals. This means that finite temperature can be introduced in brane theory. For the point particle limit (p --> 0) the entropy has the standard behavior of thermodynamic quantities.

Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The application of interpolating MLS approximations to the analysis of MHD flows

The element-free Galerkin method (EFGM) is a very attractive technique for solutions of partial differential equations, since it makes use of nodal point configurations which do not require a mesh. Therefore, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. However, the imposition of boundary conditions is not straightforward, since the EFGM is based on moving-least-squares (MLS) approximations which are not necessarily interpolants. This feature requires, for instance, the introduction of modified functionals with additional unknown parameters such as Lagrange multipliers, a serious drawback which leads to poor conditionings of the matrix equations. In this paper, an interpolatory formulation for MLS approximants is presented: it allows the direct introduction of boundary conditions, reducing the processing time and improving the condition numbers. The formulation is applied to the study of two-dimensional magnetohydrodynamic flow problems, and the computed results confirm the accuracy and correctness of the proposed formulation. (C) 2002 Elsevier B.V. All rights reserved.

Szego type polynomials and para-orthogonal polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.