Strong reality of finite simple groups

The classification of finite simple strongly real groups is complete. It is easy to see that strong reality for every nonabelian finite simple group is equivalent to the fact that each element can be written as a product of two involutions. We thus obtain a solution to Problem 14.82 of the Kourovka Notebook from the classification of finite simple strongly real groups.     

Strongly real elements in finite simple orthogonal groups

We prove the strong reality of an infinite series of groups and some elements of a special form in the simple real groups.     

A study of accelerated Newton methods for multiple polynomial roots

We analyze and compare several accelerated Newton methods with built in multiplicity estimates. We also introduce the concept of indicator functions and discuss the Crouse-Putt method. It is shown that many of the accelerated Newton methods not only derive from Schröder’s classic approach but are equivalent. The related computational experiments show that the built in multiplicity estimates can significantly decrease the number of Newton iterations, while the error of these estimates may significantly increase.     

Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1])

In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ω2-modulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].     

Support vector machines and neural networks used to evaluate paper manufactured using Eucalyptus globulus

Using advanced machine learning techniques as an alternative to conventional double-entry volume equations, a regression model of the inside-bark volume (dependent variable) for standing Eucalyptus globulus trunks (or main stems) has been built as a function of the following three independent variables: age, height and outside-bark diameter at breast height (DBH). The experimental observed data (age, height, outside-bark DBH and inside-bark volume) for 142 trees (E. globulus) were measured and a nonlinear model was built using a data-mining methodology based on support vector machines (SVM) and multilayer perceptron networks (MLP) for regression problems. Coefficients of determination and Furnival’s indices indicate the superiority of the SVM with a radial kernel over the allometric regression models and the MLP.     

On Nonlocal Cahn–Hilliard–Navier–Stokes Systems in Two Dimensions

We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier–Stokes equations coupled with a convective nonlocal Cahn–Hilliard equation. Several results were already proven by two of the present authors. However, in the two-dimensional case, the uniqueness of weak solutions was still open. Here we establish such a result even in the case of degenerate mobility and singular potential. Moreover, we show the weak–strong uniqueness in the case of viscosity depending on the order parameter, provided that either the mobility is constant and the potential is regular or the mobility is degenerate and the potential is singular. In the case of constant viscosity, on account of the uniqueness results, we can deduce the connectedness of the global attractor whose existence was obtained in a previous paper. The uniqueness technique can be adapted to show the validity of a smoothing property for the difference of two trajectories which is crucial to establish the existence of an exponential attractor. The latter is established even in the case of variable viscosity, constant mobility and regular potential.     

Approximation of Analytic Functions with an Arbitrary Order by Generalized Baskakov–Faber Operators in Compact Sets

By using a sequence \(\lambda _{n}>0\), \(n\in \mathbb {N}\) with the property that \(\lambda _{n}\rightarrow 0\) as fast we want, in this paper we obtain the approximation order \(O(\lambda _{n})\) for a generalized Baskakov–Faber operator attached to analytic functions of exponential growth in a continuum \(G\subset \mathbb {C}\). Several concrete examples of continuums G are given for which this operator can explicitly be constructed.     

Doubly nonlocal Cahn–Hilliard equations

We consider a doubly nonlocal nonlinear parabolic equation which describes phase-segregation of a two-component material in a bounded domain. This model is a more general version than the recent nonlocal Cahn–Hilliard equation proposed by Giacomin and Lebowitz [26], such that it reduces to the latter under certain conditions. We establish well-posedness results along with regularity and long-time results in the case when the interaction between the two levels of nonlocality is strong-to-weak.     

Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces

We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties.     

Stability analysis of plane wave solutions of the discrete ginzburg-landau equation

The discrete Ginzburg-Landau model for a family of oscillators linearly coupled with their first neighbors is studied. The full linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave number (k) of the basic states and the wave number (q) of the perturbations as free parameters. In particular, it is shown that nonlinear plane waves can be destabilized not only by long (q-->0) or short (q=pi) wave perturbations, but also by intermediate wave numbers (0相似文献