Sergei Silvestrov

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing asymptotic expansionsfor power moments of hitting times and stationary andquasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are basedon special techniques of sequential phase space reduction, which can be applied to models with an arbitrary asymptoticcommunicative structure of phase spaces.

Fractional-Wavelet Analysis of Positive definite Distributions and Wavelets on D’(C)

In this chapter we describe a wavelet expansion theory for positive definite distributions over the real line and define a fractional derivative operator for complex functions in the distribution sense. In order to obtain a characterization of the complex fractional derivative through the distribution theory, the Ortigueira-Caputo fractional derivative operator (_{text {C}}text {D}^{alpha }) [13] is rewritten as a convolution product according to the fractional calculus of real distributions [8]. In particular, the fractional derivative of the Gabor–Morlet wavelet is computed together with its plots and main properties.

PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph

In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank as the system dynamically changes either by contracting or expanding such as when adding or subtracting nodes or links or groups of nodes or links. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others. We will look at PageRank as the solution of a linear system of equations and do our examination in both the ordinary normalized version of PageRank as well as the non-normalized version found by solving corresponding linear system. We will show that using two different methods we can find explicit formulas for the PageRank of some simple link structures.

PageRank, Connecting a Line of Nodes with a Complete Graph

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most releva ...

Generalisation of the Damping Factor in PageRank for Weighted Networks

In this article we will look at the PageRank algorithm used to rank nodes in a network. While the method was originally used by Brin and Page to rank home pages in order of “importance”, since then many similar methods have been used for other networks such as financial or P2P networks. We will work with a non-normalised version of the usual PageRank definition which we will then generalise to enable better options, such as adapting the method or allowing more types of data. We will show what kind of effects the new options creates using examples as well as giving some thoughts on what it can be used for. We will also take a brief look at how adding new connections between otherwise unconnected networks can change the ranking.

Application of the Multi-Peaked Analytically Extended Function to Representation of Some Measured Lightning Currents

A multi-peaked form of the analytically extended function (AEF) is used for approximation of lightning current waveforms in this paper. The AEF function’s parameters are estimated using the Marquardt least-squares method (MLSM), and the general procedure for fitting the p-peaked AEF function to a waveform with an arbitrary (finite) number of peaks is briefly described. This framework is used for obtaining parameters of 2-peaked waveforms typically present when measuring first negative stroke currents. Advantages, disadvantages and possible improvements of the approach are also discussed.

On Generalized Walsh Bases

This paper continues the study of orthonormal bases (ONB) of L2[0,1]

Nonlinearly Perturbed Semi-Markov Processes

L^{2}[0,1]

Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink

introduced in Dutkay et al. (J. Math. Anal. Appl. 409(2):1128–1139, 2014) by means of Cuntz algebra ON

Measured electrostatic discharge currents modeling and simulation

mathcal{O}_{N}