Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

Development of Variational Thinking Skills in Programming Teaching

The paper presents an example of methodological approach to the development of variational thinking skills in teaching programming. Various ways in solving a given task are implemented for the purpose. One of the forms, through which the variational thinking is manifested, is related to trail practical actions. In the process of comprehension of the properties thus acquired, students are doing their own (correct or incorrect) conclusions for other, hidden properties and at the same time they discover possibilities for new ways of action and acquiring of new effects. The variability and the generalizing function of thinking are in a close interrelation, and their interaction to a great extend determines the dynamics of the cognitive activity of the student.

On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties

In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich, Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methods fail on the next step. For these methods all non-attractive sets are found. This is a subsequent improvement of previously developed techniques and known facts. The users of these methods can use the results presented here for software implementation in Distributed Applications and Simulation Environ- ments. Numerical examples with graphics are shown.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

Variational Principles for Monotone and Maximal Bifunctions

2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05

On the Convergence of (0,1,2) Interpolation

2000 Mathematics Subject Classification: 41A05.

The Graves Theorem Revisited II: Robust Convergence of the Newton Method

AMS subject classification: 65J15, 47H04, 90C30.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Weak Convergence to the Tangent Process of the Linear Multifractional Stable Motion

2000 Mathematics Subject Classification: 60G18, 60E07

An extension of Lorentz's almost convergence and applications in Banach spaces

2000 Mathematics Subject Classification: Primary 40C99, 46B99.

Fractional Korovkin Theory Based on Statistical Convergence

2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

Inflation convergence in Europe

Convergence has been a popular theme in applied economics since the seminal papers of Barro (1991) and Barro and Sala-i-Martin (1992). The very notion of convergence quickly becomes problematic from an academic viewpoint however when we try and formalise a framework to think about these issues. In the light of the abundance of available convergence concepts, it would be useful to have a more universal framework that encompassed existing concepts as special cases. Moreover, much of the convergence literature has treated the issue as a zero-one outcome. We argue that it is more sensible and useful for policy decision makers and academic researchers to consider also ongoing convergence over time. Assessing the progress of ongoing convergence is one interesting and important means of evaluating whether the Eastern European New Member Countries (NMC) of the European Union (EU) are getting closer to being deemed “ready” to join the European Monetary Union (EMU), that is, fulfilling the Maastricht convergence criteria.

Globalization of the Internet: Convergence or a multicultural community?

The purpose of this dissertation was to investigate cross-cultural differences in the use of the Internet. Hofstede's model of national culture was employed as the theoretical foundation for the analysis of cross-cultural differences. Davis's technology acceptance model was employed as the theoretical foundation for the analysis of Internet use. ^ Secondary data from an on-line survey of Internet users in 22 countries conducted in April 1997 by the Georgia Tech Research Corporation measured the dependent variables of Internet use and the independent variables of attitudes toward technology. Hofstede's stream of research measured the independent variables of the five dimensions of national culture. ^ Contrary to expectations, regression analyses at the country level of analysis did not detect cultural differences. As expected, regression analyses at the individual level of analysis did detect cultural differences. The results indicated that perceived usefulness was related to the frequency of Internet shopping in the Germanic and Anglo clusters, where masculinity was high. Perceived ease of use was related to the frequency of Internet shopping in the Latin cluster, where uncertainty avoidance was high. Neither perceived usefulness nor perceived ease of use was related to the frequency of Internet shopping in the Nordic cluster, where masculinity and uncertainty avoidance were low. ^ As expected, analysis of variance at the cluster level of analysis indicated that censorship was a greater concern in Germany and Anglo countries, where masculinity was high. Government regulation of the Internet was less preferred in Germany, where power distance was low. Contrary to expectations, concern for transaction security. was lower in the Latin cluster, where uncertainty avoidance was high. Concern for privacy issues was lower in the U.S., where individualism was high. ^ In conclusion, results suggested that Internet users represented a multicultural community, not a standardized virtual community. Based on the findings, specific guidance was provided on how international managers and marketers could develop culturally sensitive strategies for training and promoting Internet services. ^