The Newton Polygon and Elliptic Problems with Parameter

In the study of the resolvent of a scalar elliptic operator, say, on a manifold without boundary there is a well-known Agmon-Agranovich-Vishik condition of ellipticity with parameter which guarantees the existence of a ray of minimal growth of the resolvent. The paper is devoted to the investigation of the same problem in the case of systems which are elliptic in the sense of Douglis-Nirenberg. We look for algebraic conditions on the symbol providing the existence of the resolvent set containing a ray on the complex plane. We approach the problem using the Newton polyhedron method. The idea of the method is to study simultaneously all the quasihomogeneous parts of the system obtained by assigning to the spectral parameter various weights, defined by the corresponding Newton polygon. On this way several equivalent necessary and sufficient conditions on the symbol of the system guaranteeing the existence and sharp estimates for the resolvent are found. One of the equivalent conditions can be formulated in the following form: all the upper left minors of the symbol satisfy ellipticity conditions. This subclass of systems elliptic in the sense of Douglis-Nirenberg was introduced by A. KOZHEVNIKOV [K2].     

浅调制下双二波混频：I.内部空间电场

互不相干的两对相干光束同进作用于一块光折变晶体，在小调制的情况下（即晶体对光强的反应是线性的）依然会了明显的空间频率为两个基频的组合的内部宽间电场分量，本文从基本的Ｋｕｋｈｔａｒｅｖ方程组出发，把电场和电子数密度直接分解为组合频率的傅里叶分量，以解析解的形式给出了空间频率分别为Ｋ１－Ｋ２，Ｋ１＋Ｋ２，２Ｋ１和２Ｋ２的电场分量，数值解表明在一定条件下这些高频和组合分量很大且不可忽视。     

企业科技行为系统的评价体系研究

现代企业科技行为属于高阶非线性系统行为，对其运行的评价应采用系统评价的思想和方法进行。本文确定了现代企业科技行为系统评价的基本准则，构建了评价的指标体系；提出了各指标值的归一化处理方法以及各指标权重的确定方法     

地球磁场的物理问题

地磁学的发展经历了两千多年的历史，文章回顾了这一漫长历史的四个主要阶段，对每一阶段研究的基本物理问题和主要进展做了简要概述．地磁场的空间分布、地磁场起源、地磁场长期变化和西向漂移、磁极移动和极性倒转、地磁场与人类生存环境等，是地磁学的基本物理问题．文章还从物理概念、研究现状和地磁学以及相关学科当前存在的问题等几个方面对地磁学未来的发展趋势做了简要的说明．     

无穷限积分的控制收敛理论

本文根据有限区间上Ｒｉｅｍａｎｎ积分的Ａｒｚｅｌａ控制收敛定理［１］，给出无穷限积分的控制收敛定理，并做了相应的推广。     

Correspondence Between Bell Bases and Oriented Links in Knot Theory

From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage 41 in knot theory.     

Remarks on Two Approaches to the Horizontal Cohomology: Compatibility Complex and the Koszul–Tate Resolution

The Koszul–Tate resolution is described in the context of the geometry of jet spaces and differential equations. The application due to Barnich, Brandt, and Henneaux of this resolution to computing the horizontal cohomology is analyzed. Relations with the Vinogradov spectral sequence are discussed.     

Equivalence of conditions for convergence of iterative methods for singular equations

Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operators.     

Uncertain input data problems and the worst scenario method

An introduction to the worst scenario method is given. We start with an example and a general abstract scheme. An analysis of the method both on the continuous and approximate levels is discussed. We show a possible incorporation of the method into the fuzzy set theory. Finally, we present a survey of applications published during the last decade. This work was supported by grant 201/04/1503 from the Czech Science Foundation and by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503