Solving incomplete inorganic chemical systems through a fuzzy knowledge frame

A model for the completion and balancing of inconsistent inorganic reactions is presented. A series of fuzzy parameters is proposed. These parameters are considered within a knowledge frame representing inorganic reactions via a semantic/functional network and, through the calculation of possibility measures, allow the completion and solution of such reactions by considering new inorganic species to be added to the reaction. Species to be added are formulated on the basis of atoms present and/or absent in the reaction, along with valence, system features, and a series of flags that determines the cardinality of the possible solution set. Incorporation of the proposed model into an inorganic chemistry formulation system would contribute to the development of powerful computer-assisted learning systems, given the extent of information extracted from a reaction.     

Ferromagnetic Coupling through Spin Polarization in a Dinuclear Copper(II) Metallacyclophane

No Abstract     

Exchange coupling in carboxylato-bridged dinuclear copper(II) compounds: a density functional study

A computational study of the exchange coupling is presented for a selected sample of carboxylato-bridged dinuclear copper(II) compounds. Model calculations have been used to examine the influence of several factors on the coupling constants: a) the electron-withdrawing power of the bridging ligands; b) the nature of the axial ligands; c) the number of bridging carboxylato groups; d) some structural distortions frequently found in this family of compounds; and e) the coordination mode of the carboxylato bridge. Coupling constants calculated for some complete structures, as determined by X-ray diffraction, are in excellent agreement with experimental data, confirming the ability of the computational strategy used in this work to predict the coupling constant for compounds for which experimental data are not yet available.     

A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

A new characterisation of hereditary pi rings

In this paper we prove a new characterisation of hereditary PI rings, namely we show that a Noetherian, but not Artinian, PI ringR that is an order in an Artinian ring splits into a direct sum of an Artinian ring of finite representation type and hereditary semiprime rings if and only if all its proper Artinian factor rings are of finite representation type. We also show, through examples, that the above characterisation does not hold for some more general settings. Supported by the EC via TMR-Fellowship ERB4001GT63713.     

Domination by Positive Narrow Operators

We prove that each positive operator from a Köthe function-space E() to a Banach lattice F with a narrow majorant is itself narrow provided the norm on F is order continuous. We also prove that every l ²-strictly singular regular operator from L ^p[0,1], 1p < , to a Banach lattice F is narrow, provided F has an order continuous norm.     

Intersection Local Times of Independent Brownian Motions as Generalized White Noise Functionals

A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R ^d is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their L ^p -properties are discussed. An important tool for deriving the chaos expansion is a computation of the 'S-transform' of the corresponding regularized intersection local times and a control about their singular limit.     

A Nonlinear Problem Associated to the Motion of a Membrane

A nonlinear model associated to the motion of a membrane is considered as limit of a sequence of approximate models, for which a global existence and uniqueness theorem can be proved. The paper investigates the relationship between the solutions of the real and approximate models.     

Fixed Point Index in Hyperspaces: A Conley-Type Index for Discrete Semidynamical Systems

Let X be a locally compact metric absolute neighbourhood retractfor metric spaces, U X be an open subset and f: U X be a continuousmap. The aim of the paper is to study the fixed point indexof the map that f induces in the hyperspace of X. For any compactisolated invariant set, K U, this fixed point index produces,in a very natural way, a Conley-type (integer valued) indexfor K. This index is computed and it is shown that it only dependson what is called the attracting part of K. The index is usedto obtain a characterization of isolating neighbourhoods ofcompact invariant sets with non-empty attracting part. Thisindex also provides a characterization of compact isolated minimalsets that are attractors.