Variational principles for nonlinear dynamical systems

A variational method for Hamiltonian systems is analyzed. Two different variationalcharacterization for the frequency of nonlinear oscillations is also suppliedfor non-Hamiltonian systems

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Some variational problems from image processing

"Vegeu el resum a l'inici del document del fitxer adjunt."

Empirical approaches to inequality of opportunity: principles, measures, and evidence

We put together the different conceptual issues involved in measuring inequality of opportunity, discuss how these concepts have been translated into computable measures, and point out the problems and choices researchers face when implementing these measures. Our analysis identifies and suggests several new possibilities to measure inequality of opportunity. The approaches are illustrated with a selective survey of the empirical literature on income inequality of opportunity.

Let's talk: public evaluation of large projects: variational inequialities, bilevel programming and complementarity. a survey

Large projects evaluation rises well known difficulties because -by definition- they modify the current price system; their public evaluation presents additional difficulties because they modify too existing shadow prices without the project. This paper analyzes -first- the basic methodologies applied until late 80s., based on the integration of projects in optimization models or, alternatively, based on iterative procedures with information exchange between two organizational levels. New methodologies applied afterwards are based on variational inequalities, bilevel programming and linear or nonlinear complementarity. Their foundations and different applications related with project evaluation are explored. As a matter of fact, these new tools are closely related among them and can treat more complex cases involving -for example- the reaction of agents to policies or the existence of multiple agents in an environment characterized by common functions representing demands or constraints on polluting emissions.

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of Cl O2 and C4 H4 O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

An analysis of the accounting principles applied by the European Farm Accountancy Data Network

In spite of its relative importance in the economy of many countriesand its growing interrelationships with other sectors, agriculture has traditionally been excluded from accounting standards. Nevertheless, to support its Common Agricultural Policy, for years the European Commission has been making an effort to obtain standardized information on the financial performance and condition of farms. Through the Farm Accountancy Data Network (FADN), every year data are gathered from a rotating sample of 60.000 professional farms across all member states. FADN data collection is not structured as an accounting cycle but as an extensive questionnaire. This questionnaire refers to assets, liabilities, revenues and expenses, and seems to try to obtain a "true and fair view" of the financial performance and condition of the farms it surveys. However, the definitions used in the questionnaire and the way data is aggregated often appear flawed from an accounting perspective. The objective of this paper is to contrast the accounting principles implicit in the FADN questionnaire with generally accepted accounting principles, particularly those found in the IVth Directive of the European Union, on the one hand, and those recently proposed by the International Accounting Standards Committee’s Steering Committeeon Agriculture in its Draft Statement of Principles, on the other hand. There are two reasons why this is useful. First, it allows to make suggestions how the information provided by FADN could be more in accordance with the accepted accounting framework, and become a more valuable tool for policy makers, farmers, and other stakeholders. Second, it helps assessing the suitability of FADN to become the starting point for a European accounting standard on agriculture.

Variational Wigner-Kirkwood approach to relativistic mean field theory

The recently developed variational Wigner-Kirkwood approach is extended to the relativistic mean field theory for finite nuclei. A numerical application to the calculation of the surface energy coefficient in semi-infinite nuclear matter is presented. The new method is contrasted with the standard density functional theory and the fully quantal approach.

Variational analysis of the Gross-Neveu model in an S^1 space

The Gross-Neveu model in an S^1 space is analyzed by means of a variational technique: the Gaussian effective potential. By making the proper connection with previous exact results at finite temperature, we show that this technique is able to describe the phase transition occurring in this model. We also make some remarks about the appropriate treatment of Grassmann variables in variational approaches.

Variational study of 3He-4He mixtures

The ground-state properties of the 3He-4He mixture are investigated by assuming the wave function to be a product of pair correlations. The antisymmetry of the 3He component is taken into account by Fermi-hypernetted-chain techniques and the results are compared with those obtained from the lowest-order Wu-Feenberg expansion and the boson-boson approximation. A little improvement is found in the 3He maximum solubility. A microscopic theory to calculate 3He static properties such as zero-concentration chemical potential and excess-volume parameter is derived and the results are compared with the experiments.

Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains

Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekulé states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin s=1 / 2 and s=1 chains are carried out in a test of this argument.

First-principles periodic calculation of four-body spin terms in high-Tc cuprate superconductors

A general mapping between the energy of pertinent magnetic solutions and the diagonal terms of the spin Hamiltonian in a local representation provides the first general framework to extract accurate values for the many body terms of extended spin Hamiltonians from periodic first-principle calculations. Estimates of these terms for La2CuO4, the paradigm of high-Tc superconductor parent compounds, and for the SrCu2O3 ladder compound are reported. For La2CuO4, present results support experimental evidence by Toader et al. [Phys. Rev. Lett. 94, 197202 (2005)]. For SrCu2O3 even larger four-body spin amplitudes are found together with Jl/Jr=1 and non-negligible ferromagnetic interladder exchange.