Rest points of generalized dynamical systems

In this paper we consider generalized dynamical systems whose integral vortex (that is, the set of all trajectories of the system starting at a given point) is an acyclic set in the corresponding space of curves. For such systems we apply the theory of fixed points for multi-valued maps in order to prove the existence of rest points. In this way we obtain new existence theorems for rest points of generalized dynamical systems. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 28–36, January, 1999.     

Norm-Based Approximation in Bicriteria Programming

An algorithm to approximate the nondominated set of continuous and discrete bicriteria programs is proposed. The algorithm employs block norms to find an approximation and evaluate its quality. By automatically adapting to the problem's structure and scaling, the approximation is constructed objectively without interaction with the decision maker. Mathematical and practical examples are included.     

Fluctuations of the total number of critical points of random spherical harmonics

We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implications on the sophistication degree of an appropriate percolation process for modelling nodal domains of eigenfunctions on generic compact surfaces or billiards.     

概率计算中易混淆问题的教法研究

首先从具体实例提出了物品检验概率计算中一类易混淆问题.然后从理论上证明了无放回逐次抽取中两种概率计算方法的合理性,其定理证明过程充分揭示了这类检验方法与其它相关抽取方式之间的关系并强调了最根本的分析问题思路.最后,研究了文中所得到的一般性结论的适用范围,从而使得这类易混淆问题的讲解变得清晰条理.     

Deterministic and random fixed points for maps on extension type spaces

We present a variety of deterministic and random fixed point results for very general spaces and classes of maps.     

Existence solutions for second order Hamiltonian systems

We study the existence of periodic solutions for a second order non-autonomous dynamical system containing variable kinetic energy terms. Subquadratic problems and superquadratic problems are both considered.     

A new class of nonhomogeneous differential operator and applications to anisotropic systems

We introduce a new class of operators that extend both generalized Laplace operators and generalized mean curvature operators. We start the discussion on general anisotropic systems with variable exponents that involve our operators, then we focus on a specific example of such system, we show that it admits a unique weak solution and we complete our work with some comments on other related systems. The newly introduced operators are appropriate for the study conducted in the anisotropic spaces with variable exponents, but at the end of the paper we also provide their versions corresponding to the studies conducted in the anisotropic Sobolev spaces with constant exponents, or in the isotropic variable exponent Sobolev spaces, since, to the best of our knowledge, they represent a novelty even for the classical Sobolev spaces.     

The Robin problem for singular p-Laplacian equation in a cone

We study the behaviour near the boundary angular or conical point of weak solutions to the Robin problem for elliptic quasi-linear second-order equation with the p-Laplacian.