Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions of 2N‐point type

This paper is devoted to the study of a nonlinear wave equation with initial conditions and nonlocal boundary conditions of 2N‐point type, which connect the values of an unknown function u(x,t) at x = 1, x = 0, x = η_i(t) , and x = θ_i(t), where $0<{\eta }_1(t)<{\eta }_2(t)<\dots <{\eta }_{{}_{N?1}}(t)<1,$ $0<{\theta }_1(t)<{\theta }_2(t)<\dots <{\theta }_{{}_{N?1}}(t)<1,$ for all t ≥ 0. First, we prove local existence of a unique weak solution by using density arguments and applying the Banach's contraction principle. Next, under the suitable conditions, we show that the problem considered has a unique global solution u(t) with energy decaying exponentially as t → +∞ . Finally, we present numerical results.     

A new benzofuran derivative from the leaves of Ficus pumila L.

A new benzofuran derivative, pumiloside (1), together with seven known flavonoid glycosides, afzelin (2), astragalin (3), quercitrin (4), isoquercitrin (5), kaempferol 3-O-rutinoside (6), rutin (7) and kaempferol 3-O-sophoroside (8) were isolated from the leaves of Ficus pumila. Their structures were established by spectroscopic data and comparison with the literature values.     

Characterizing Finite Quasisimple Groups by Their Complex Group Algebras

A finite group L is said to be quasisimple if L is perfect and L/Z(L) is nonabelian simple, in which case we also say that L is a cover of L/Z(L). It has been proved recently (Nguyen, Israel J Math, 2013) that a quasisimple classical group L is uniquely determined up to isomorphism by the structure of ${{\mathbb C}} L$ , the complex group algebra of L, when L/Z(L) is not isomorphic to PSL₃(4) or PSU₄(3). In this paper, we establish the similar result for these two open cases and also for covers with nontrivial center of simple groups of exceptional Lie type and sporadic groups. Together with the main results of Tong-Viet (Monatsh Math 166(3–4):559–577, 2012, Algebr Represent Theor 15:379–389, 2012), we obtain that every quasisimple group except covers of the alternating groups is uniquely determined up to isomorphism by the structure of its complex group algebra.     

LAN property for a simple Lévy process

In this paper, we consider a simple Lévy process given by a Brownian motion and a compensated Poisson process, whose drift and diffusion parameters as well as its intensity are unknown. Supposing that the process is observed discretely at high frequency, we derive the local asymptotic normality (LAN) property. In order to obtain this result, Malliavin calculus and Girsanov's theorem are applied in order to write the log-likelihood ratio in terms of sums of conditional expectations, for which a central limit theorem for triangular arrays can be applied.     

Micro-mechanical modeling of anisotropic inelastic response of soft tissues under supra-physiological loading

Under supra-physiological loading, soft tissues exhibit many inelastic phenomena, such as stress softening, hysteresis and permanent set [1]. Knowledge of the mechanical response of soft tissues under such a large range of deformation is vital for optimizations of vascular medical devices or improvement of injury prevention techniques. In this work, a micro-mechanical model is proposed for soft collagenous tissues. Besides the anisotropy the model can also describe the aforementioned inelastic effects under extremal loadings. To this end, the dispersion of collagen fibers in the soft tissues is captured by a probability distribution of fiber orientations around preferred directions. The deformation induced damage inside the tissue is assumed to take place between collagen fibrils and is included within a statistical mechanical framework. Finally, the accuracy of the model is assessed by comparison with experimental data available in the literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions

We propose several additional kinds of semi-limits and corresponding notions of semicontinuity of a set-valued map. They can be used additionally to known basic concepts of semicontinuity to have a clearer insight of local behaviors of maps. Then, we investigate semicontinuity properties of solution maps to a general parametric quasivariational inclusion, which is shown to include most of optimization-related problems. Consequences are derived for several particular problems. Our results are new or generalize/improve recent existing ones in the literature.     

Existence,blow‐up,and exponential decay estimates for a system of nonlinear wave equations with nonlinear boundary conditions

This paper is devoted to the study of a system of nonlinear equations with nonlinear boundary conditions. First, on the basis of the Faedo–Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two local existence theorems of weak solutions. Next, we prove that any weak solutions with negative initial energy will blow up in finite time. Finally, the exponential decay property of the global solution via the construction of a suitable Lyapunov functional is presented. Copyright © 2013 John Wiley & Sons, Ltd.     

On the number of conjugacy classes of π-elements in finite groups

Let G be a finite group and π be a set of primes. Put ${d_{\pi}(G) = k_{\pi}(G)/|G|_{\pi}}$ , where ${k_{\pi}(G)}$ is the number of conjugacy classes of π-elements in G and |G| _π is the π-part of the order of G. In this paper we initiate the study of this invariant by showing that if ${d_{\pi}(G) > 5/8}$ then G possesses an abelian Hall π-subgroup, all Hall π-subgroups of G are conjugate, and every π-subgroup of G lies in some Hall π-subgroup of G. Furthermore, we have ${d_{\pi}(G) = 1}$ or ${d_{\pi}(G) = 2/3}$ . This extends and generalizes a result of W. H. Gustafson.