Orbital formal normal forms for general Bogdanov-Takens singularity

We solve completely the problem of classification of germs of complex planar vector fields with nilpotent singularity with respect to formal orbital equivalence.     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

Effect of genesis on the properties and hydrogen reducibility of NiO-ZnO mixed oxides

The physico-chemical properties and reactivity tested by hydrogen reduction have been studied for two series of NiO-ZnO mixed oxides of various composition. The solid nickel oxide or zinc oxide in interaction with the solution of nitrate of the second component were used as the precursors in each series. The differences in some physico-chemical parameters of the samples in both series were correlated with their reduction behaviour, followed both in iso- and non-isothermal regime. Moreower, the influence of various factors modifying the reactivity of mixed oxides was also investigated and the results were compared with those obtained from earlier studied analogous systems of quite different origin.This revised version was published online in November 2005 with corrections to the Cover Date.     

Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.     

Lyapunov-type inequalities for nonlinear systems

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.     

A preconditioned domain decomposition algorithm for the solution of the elliptic Neumann problem

A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited to parallel computation.     

Asymptotic conditions for the electromagnetic form factors of hadrons represented by the VMD model

A system of linear homogeneous algebraic equations for the coupling constant ratios of vector mesons to hadrons is derived by imposing the assumed asymptotic behavior upon the VMD pole parameterization of an hadron electromagnetic form factor. A similar system of equations with a simpler structure of the coefficients, taken as even powers of the vector-meson masses, is derived by means of integral superconvergent sum rules for the imaginary part of the considered form factor using its appropriate -function approximation. Although both systems have been derived starting from different properties of the electromagnetic form factor and they each have their own appearances, it is shown explicitly that they are fully equivalent. Received: 20 March 2002 / Revised version: 3 December 2002 / Published online: 7 March 2003     

WZW–Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting “WZW–Poisson” manifold M is characterized by a bivector Π and by a closed three-form H such that 1/2[Π,Π]_Schouten=H,ΠΠΠ.