On efficient two-parameter methods for solving nonlinear equations

Derivative free methods for solving nonlinear equations of Steffensen’s type are presented. Using two self-correcting parameters, calculated by Newton’s interpolatory polynomials of second and third degree, the order of convergence is increased from 2 to 3.56. This method is used as a corrector for a family of biparametric two-step derivative free methods with and without memory with the accelerated convergence rate up to order 7. Significant acceleration of convergence is attained without any additional function calculations, which provides very high computational efficiency of the proposed methods. Another advantage is a convenient fact that the proposed methods do not use derivatives. Numerical examples are given to demonstrate excellent convergence behavior of the proposed methods and good coincidence with theoretical results.     

On the Recursive Sequence x_{n + 1} = {{ \mgreek{g} x_{n-1} + \mgreek{d} x_{n-2}} \over {Cx_{n-1} + Dx_{n-2}}}

We investigate the global character of solutions of the equation in the title with positive parameters and positive initial conditions. We obtain results about the global attractivity of the equilibrium, the existence and attractivity of the period-two solution and the semicycles.     

Simple groups and the number of countable models

Let T be a complete, superstable theory with fewer than ${2^{\aleph_{0}}}$ countable models. Assuming that generic types of infinite, simple groups definable in T ^eq are sufficiently non-isolated we prove that ω ^ω is the strict upper bound for the Lascar rank of T.     

Decomposition of Complex Fluorescence Spectra Containing Components with Close Emission Maxima Positions and Similar Quantum Yields. Application to Fluorescence Spectra of Proteins

Despite of widely application of multivariate analysis in chemometrics, problem of resolving closely positioned components in the fluorescence spectra remained unsolved, thus limiting the usage of fluorescence spectroscopy in analytical purpose. In this paper we have described a novel procedure, adapted especially for the analysis of complex fluorescence spectra with multiple, closely positioned components’ maxima. The method was first tested on the simulated spectra and then applied on the spectra of proteins whose fluorophores have similar properties of both the excitation and the emission spectra. In this paper, simple but efficient modification of the method was applied. Instead of analyzing full size emission matrix (12 spectra), 9 spectra wide windows were analyzed, and 4 factors (greatest possible number of factors with physical meaning both for actin and simulated spectra) were extracted in each pass. Obtained factor scores were grouped by using the K-means algorithm. Groups of factor scores obtained from K-means algorithm were passed through the one more factor analysis (FA) in order to find one factor that represents each group. Our approach provides resolution of extremely closed spectral components, which is a vital data for protein conformation analysis based on fluorescence spectroscopy.     

Electronic Bands of the BeOH and BeOD

The electronic bands appearing in the region 300–330 nm were produced in a low-pressure DC are with beryllium electrodes. The bands were obtained in the atmosphere of ordinary water vapour and heavy water vapour. From isotope shift studies, experimental conditions and the similarity with the bands of isoelectronic BeF, the emitting molecules were identified as BeOH and BeOD, respectively.     

Structure and stability of online chat networks built on emotion-carrying links

High-resolution data of online chats are studied as a physical system in the laboratory in order to quantify collective behavior of users. Our analysis reveals strong regularities characteristic of natural systems with additional features. In particular, we find self-organized dynamics with long-range correlations in user actions and persistent associations among users that have the properties of a social network. Furthermore, the evolution of the graph and its architecture with specific k$k$-core structure are shown to be related with the type and the emotion arousal of exchanged messages. Partitioning of the graph by deletion of the links which carry high arousal messages exhibits critical fluctuations at the percolation threshold.