Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

This paper is devoted to studying a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under the suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.     

An efficient DC programming approach for portfolio decision with higher moments

Portfolio selection with higher moments is a NP-hard nonconvex polynomial optimization problem. In this paper, we propose an efficient local optimization approach based on DC (Difference of Convex functions) programming—called DCA (DC Algorithm)—that consists of solving the nonconvex program by a sequence of convex ones. DCA will construct, in each iteration, a suitable convex quadratic subproblem which can be easily solved by explicit method, due to the proposed special DC decomposition. Computational results show that DCA almost always converges to global optimal solutions while comparing with the global optimization methods (Gloptipoly, Branch-and-Bound) and it outperforms several standard local optimization algorithms.     

Intense terahertz emission from undoped GaAs/n-type GaAs and?InAs/AlSb structures grown on Si substrates in the transmission-geometry excitation

Intense terahertz radiation was generated from femtosecond laser-irradiated InAs and GaAs layers on Si substrates. Results show that InAs/Si and GaAs/Si films can be excited in reflection and transmission geometries. The InAs/Si film exhibited weaker emission for both excitation cases but it will be more feasible as a spectroscopic THz source due to the absence of complex spectral features in its emission spectrum. The GaAs/Si emission is characterized by Fabry?CPerot oscillations but it is 90% of that of p-InAs bulk crystal emission intensity in the reflection geometry. Excitation fluence measurements showed that the InAs/Si film saturates easily due to the laser??s shallow penetration depth in InAs.     

Antioxidative and α-glucosidase inhibitory constituents of Polyscias guilfoylei: experimental and computational assessments

Molecular Diversity - Searching for bioactive agents from medicinal plants, eleven constituents were isolated from Polyscias guilfoylei stem for the first time, including a nucleoside uracil (1),...     

Finiteness of Profinite Groups with a Rational Probabilistic Zeta Function

We prove that every profinite group in a certain class with a rational probabilistic zeta function has only finitely many maximal subgroups.     

Outer Γ-Convexity in Vector Spaces

A subset S of some vector space X is said to be outer Γ-convex w.r.t. some given balanced subset Γ ? X if for all x ₀, x ₁ ? S there exists a closed subset Λ ? [0,1] such that {x _λ | λ ? Λ} ? S and [x ₀, x ₁] ? {x _λ | λ ? Λ} + 0.5 Γ, where x _λ: = (1 ? λ)x ₀ + λ x ₁. A real-valued function f:D → ? defined on some convex D ? X is called outer Γ-convex if for all x ₀, x ₁ ? D there exists a closed subset Λ ? [0,1] such that [x ₀, x ₁] ? {x _λ | λ ? Λ} + 0.5 Γ and f(x _λ) ≤ (1 ? λ)f(x ₀) + λ f(x ₁) holds for all λ ? Λ. Outer Γ-convex functions possess some similar optimization properties as these of convex functions, e.g., lower level sets of outer Γ-convex functions are outer Γ-convex and Γ-local minimizers are global minimizers. Some properties of outer Γ-convex sets and functions are presented, among others a simplex property of outer Γ-convex sets, which is applied for establishing a separation theorem and for proving the existence of modified subgradients of outer Γ-convex functions.     

Strong Duality with Proper Efficiency in Multiobjective Optimization Involving Nonconvex Set-Valued Maps

In this paper, we consider some dual problems of a primal multiobjective problem involving nonconvex set-valued maps. For each dual problem, we give conditions under which strong duality between the primal and dual problems holds in the sense that, starting from a Benson properly efficient solution of the primal problem, we can construct a Benson properly efficient solution of the dual problem such that the corresponding objective values of both problems are equal. The notion of generalized convexity of set-valued maps we use in this paper is that of near-subconvexlikeness.     

Parallel methods for regularizing systems of equations involving accretive operators

In this paper, two parallel methods for solving systems of accretive operator equations in Banach spaces are studied. The convergence analysis of the methods in both free-noise and noisy data cases is provided.     

Parallel Hybrid Methods for a Finite Family of Relatively Nonexpansive Mappings

In this article, we propose two parallel hybrid methods for finding a common fixed point of a finite family of relatively nonexpansive mappings. The strong convergence of the methods is established and their effectiveness are examined by numerical experiments. Thanks to the parallel computation, we can reduce the overall computational effort under widely used assumptions on mappings and spaces.