Mathematical and physical modelling of seismic faults (Poster Presentation)

Modelling of seismic faults by using spring block systems on a frictional surface, requires to solve coupled differential equation systems with a great number of equations, in order to avoid this problem, the spring-block model is mapped into a continuous, non-conservative cellular automaton. Every time the automaton is calculated a synthetic earthquake is obtained. We obtained catalogues of synthetic earthquake magnitude, which we can represent as a time series. Such series exhibit power law behavior so much for the magnitudes (Gutenberg-Richter law) as for the duration times. The analysis of these time series with methods of non-linear dynamics provides interesting results; for example, the time series show multifractality for large values of the conservation level. We present the correlation analysis of three kinds of time series: recurrence times, jumps or distance between consecutive earthquakes and magnitude for different thresholds. We obtained long correlations in recurrence times as it has been observed in real seismicity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A doubly optimal stopping of a risk process (Poster Presentation)

Problems which lead to an optimal stopping of a risk process are considered. Let an insurance company be endowed with an initial capital a > 0, receive insurance premiums and pay out successive claims. The losses occur according to renewal process. At any moment the company may broaden or narrow down the offer, what entails the change of the parameters. These changes concern the rate of income, the intensity of renewal process and the distribution of claims. The model of the risk process with two types of claims stream is considered. After the change the management wants to know the moment of the maximal value of the capital assets. Our goal is to find two optimal stopping times: the best moment of change the parameters and the moment of maximal value of the capital assets. A dynamic programming method to calculate the expected capital at that times is used. Based on the model which combine two types of risk the model of reinsurance with two firms is formulated. In this case the aim is to find for the firms the equilibrium strategy. The equilibrium is constructed in class of strategies driven by their risks. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Different problems associated with the stress trajectories element method (Poster Presentation)

This study deals with the determination of stresses in statically determined solids of arbitrary rheology. The stress trajectory concept is used as the basic element in numerical formulations. Different types of data can be employed, which necessitates consideration of different mathematical problems associated with the stress identification. Three classes of data are discussed and an example from geodynamic is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The ill-posed retrieval of aerosol extinction coefficient profiles (Poster Presentation)

We present an improvement for the determination of aerosol extinction coefficient profiles from Raman lidar data in using regularization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of the R-functions method to the solution of elliptic PDEs (Poster Presentation)

In the current work, the basics of the theory of R-functions have been presented. Applications of this theory were shown on two model problems – Poisson equation and biharmonic equation – in complex two-dimensional domains both with homogeneous Dirichlet boundary conditions. The solution is performed in conjunction with the Bubnov-Galerkin method. As the basis for approximation tensor products of monomials were taken. The convergence study includes the comparison of current results with the standard finite element solution and the dependence of the number of coordinate functions on the relative error in the maximum-norm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Iteration on notation and unary functions

In the first half of the 1990s, Clote and Takeuti characterized several function complexity classes by means of the concatenation recursion on notation operators. In this paper, we borrow from computability theory well‐known techniques based on pairing functions to show that , , and functions can be characterized by means of concatenation iteration on notation. Indeed, a function class satisfying simple constraints and defined by using concatenation recursion on notation is inductively characterized by means of concatenation iteration on notation. Furthermore, , , and unary functions are inductively characterized using addition, composition, and concatenation iteration on notation.     

Optimal design and optimal damping set for a hyperbolic problem (Poster Presentation)

In this work we analyze a 2D optimal design problem governed by a linear damped 1D wave equation. In this we would like to find simultaneously the spatio-temporal layout of two isotropic materials of constants α and β (0 < α < β) and the static position of a damping set in order to minimize certain functional ([5]). By means of the gradient Young measures, we compute a full relaxation of the problem which is justified by the presence of microstructures. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Bogolubov generating functional method in statistical physics and the Wigner transform (Poster Presentation)

We show that the N.N. Bogolubov generating functional method is a very effective tool for studying distribution functions of both equilibrium and non equilibrium states of classical many-particle dynamical systems. In some cases the Bogolubov generating functionals can be represented by means of infinite Ursell-Mayer diagram expansions, whose convergence holds under some additional constraints on statistical system. The classical Bogolubov idea [1] to use the Wigner density operator transformation for studying the non equilibrium distribution functions is developed and new analytic non-stationary solution to the classical N.N. Bogolubov evolution functional equation is constructed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A ranking for the nodes of directed graphs based on game theory (Poster Presentation)

We introduce a value that allows us to emphasize the importance of each player in a cooperative game when the cooperation possibilities are limited according to the links of an oriented network. The proposed concept of accessibility tries to conjugate the marginal contributions of each node as a game player with the cooperation geometry imposed by the directed graph that models the network. As a consequence, it is possible to offer a ranking for the nodes of directed graphs. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A combined chebyshev polynomials and sumudu transform for solving the neutron transport equation (Poster Presentation)

In the present paper we present a new approximation for the one dimensional transport equation, using Chebyshev polynomials [1] combined with the Sumudu transform. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ab-initio study of transition temperature of Mn-doped GaN diluted magnetic semiconductor (Poster Presentation)

We study the effect of clustering and random metal atoms distribution on the transition temperature of Mn-doped GaN Diluted Magnetic Semiconductors. To calculate the exchange coefficients between the Mn atoms, a Density functional theory-based Locally Self Consistent Multiple Scattering (LSMS) method has been used. Here we present the results of our calculations, which show that random metal distribution increases the calculated transition temperature of the material while the clustering decreases it. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiparametric frequency-domain criteria for stability of distributed systems with multiple equilibria (Poster Presentation)

For integral Volterra equations with periodic nonlinear functions and nonlinear functions satisfying the sector condition, new frequency domain criteria for gradient-like behavior are obtained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust analysis of discrete linear shift invariant systems represented by an interval matrix (Poster Presentation)

In this paper we describe a new bound in order to guaranteed the robust stability of a discrete linear shift invariant system which is represented by an interval matrix. This bound is based in the bound of Juang. The uncertainties are represented by an interval matrix. The system is represented in state variables with parametric uncertainty in the A matrix. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sufficient conditions of the existence forced periodic solutions in the automatic controlled systems with the hysteresis feedback (Poster Presentation)

This article is devoted to Control system with the Hysteresis Nonlinearities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ab-initio and modeling study of some amino acid-tRNA: NMR shielding and thermodynamic of solvent effect (Poster Presentation)

The tRNA molecule takes suitable amino acid to the ribosome for the formation of peptide bonds. In starting the peptide chain, the first amino acid which is taken to the ribosome is methionine. We have simulated methionine-amino acid bonding and amino acid-tRNA bonding, using a mixed study of quantum mechanics ab-initio and molecular mechanics. NMR shielding tensors and thermodynamic parameters and total energies are also calculated. It is important to understand the physical properties and the environmental conditions in which the dipeptides cause the tRNA to attach to a wrong amino acid. One of the properties studied is the dielectric environment of in which the bonding occurs. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modelling of the patent ductus arteriosus (PDA)

The heart is one of the most important and vital body organs, which is responsible for pumping blood to different body tissues. Abnormalities in each part of heart can lead to lack of proper blood circulation. The arterial duct is one of the most important parts of embryonic cycles which may provide the possibility of a relationship between the aorta and the pulmonary artery. The failure of this duct to close after birth causes the abnormality called patent ductus arteriosus (PDA). In this article, we propose a novel model for accurate simulation of PDA abnormality in the human heart. The model is obtained by exploiting the mathematical relation between hemodynamic parameters of heart, including pressure, blood, volume and flow. The proposed model is verified using clinical data.     

基于李群方法的贝塞尔函数数学实现

基于李群的表示理论,首先讨论了欧拉群的表示及其性质;然后,从该群的表示理论出发,分别导出了第一类贝塞尔函数的积分形式和幂级数形式.该研究表明了群方法可以求解对称边界问题的解析波函数,并为用群方法求解电磁场问题创造了条件.     

Smooth functions onC(K)

We show that every Fréchet differentiable real function onC(K), K scattered with locally uniformly continuous derivative has locally compact derivative. Using this and similar results, we investigate the existence ofC ²-Fréchet smooth surjections between various Banach spaces.