Stability of a Jensen type equation in the space of generalized functions

We reformulate and solve the stability problem of a Jensen type functional equation

     

Steplengths in the extragradient type methods

The extragradient type methods are a class of efficient direct methods. For solving monotone variational inequalities, these methods only require function evaluation, and therefore are widely applied to black-box models. In this type of methods, the distance between the iterate and a fixed solution point decreases by iterations. Furthermore, in each iteration, the negative increment of such squared distance has a differentiable concave lower bound function without requiring any solution in its formula. In this paper, we investigate some properties for the lower bound. Our study reveals that the lower bound affords a steplength domain which guarantees the convergence of the entire algorithm. Based on these results, we present two new steplengths. One involves the projection onto the tangent cone without line search, while the other can be computed via searching the positive root of a one dimension concave lower bound function. Our preliminary numerical results confirm and illustrate the attractiveness of our contributions.     

一类(k,n-k)泛函微分方程共扼边值问题的正解

在不假定非线性项f单调的前提下研究一类混合型泛函微分方程边值问题.利用锥上的不动点定理获得了所考虑问题的正解的存在性和多解性结果.     

Tagungsberichte

Some analytical procedures for the determination of tritium, strontium-90 and iodine-129 in liquid radioactive wastes from nuclear power plants of the type WWER-440 are described. Liquid scintillation counters (³H), beta-counters applying an Al-absorber (⁹⁰Sr) and neutron activation analysis (¹²⁹I) applying a suitable separation process are used. The results are discussed with respect to the waste management manufactured in future and the deposition of radioactive wastes coming from the nuclear power station “Kozloduj”.     

MAGNETOHYDRODYNAMICS'S TYPE EQUATIONS OVER CLIFFORD ALGEBRAS

We study a system of equations modeling the stationary motion of incompressible electrical conducting fluid. Based on methods of Clifford analysis, we rewrite the system of magnetohydrodynamics fluid in the hypercomplex formulation and represent its solution in Clifford operator terms.     

Weak Solution to Pressureless Type System

ABSTRACT

In this paper, we study the Cauchy problem for a pressureless type system. The Riemann solutions only include two elementary waves, delta waves and contact discontinuity. The existence of an entropy solution is established by studying the interaction of the elementary waves and the generalized characteristics introduced in Dafermos (1977 Dafermos , C. M. (1977). Generalized characteristics and the structure of solutions of hyperbolic conservation laws. Indiana Univ. Math. J. 26(6):1097–1119. [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]).