Attractors of 3D Systems in Basic Models of Mechanics*

International Applied Mechanics - The theorems (statements) on the existence of attractor are proved. A generalized Shilnikov theorem is formulated. In the expression for the saddle of a homoclinic...     

Invertibility of Multidimensional Integral Operators with Bihomogeneous Kernels

Mathematical Notes -     

Heuristic Solution to the Diffraction Problem on a Superconducting Half-Plane

Journal of Communications Technology and Electronics - Abstract—The article presents a rigorous numerical solution, using the Wiener–Hopf method, to the problem of plane wave...     

Performance Investigations and PAPR Reduction Analysis Using Very Efficient and Optimized Amended SLM Algorithm for Wireless Communication OFDM System

Wireless Personal Communications - The orthogonal frequency division multiplexing (OFDM) is the most encouraging multi-carrier modulation system chosen for the high data rates but the objective is...     

Related Oscillations of Plasmons in Two Similar Nanocylinders from Silver

Journal of Communications Technology and Electronics - Abstract—The two-dimensional diffraction problem of a plane polarized TM-wave on two identical solid silver nanocylinders is considered....     

Anomaly-Based Intrusion Detection System in RPL by Applying Stochastic and Evolutionary Game Models over IoT Environment

Wireless Personal Communications - The rapid development of Information and Communication Technology and the growing number of devices connected to the Internet make the Internet of Things (IoT) as...     

A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.