Algebraic Fractional-Step Schemes for Time-Dependent Incompressible Navier–Stokes Equations

The numerical investigation of a recent family of algebraic fractional-step methods (the so called Yosida methods) for the solution of the incompressible time-dependent Navier–Stokes equations is presented. A comparison with the Karniadakis–Israeli–Orszag method Karniadakis et al. (1991, J. Comput. Phys. 97, 414–443) is carried out. The high accuracy in time of these schemes well combines with the high accuracy in space of spectral methods.     

Translation of Algebraic Programs into Executable Codes

An approach to the problem of translation of algebraic programs into executable codes is presented. In particular, an algorithm for translation of algebraic programs represented in the language Aplan into C codes is proposed. An algorithm of reconstruction of types in Aplan is considered that also checks the absence of features used for dynamic specification of procedures in a code. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 168–176, September–October 2005.     

Solution of systems of linear algebraic equations with preliminary flattening

A method of improving computing properties of matrices of systems of linear algebraic equations is considered. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 144–149, September–October, 1999.     

Asymmetric Code-Theoretical Schemes Constructed with the Use of Algebraic Geometric Codes

Asymmetric coding schemes are developed that are constructed with the use of algebraic geometric codes. Basic analytical expressions are obtained that connect the parameters of algebraic geometric codes with the parameters of asymmetric coding schemes based on these codes. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 47–57, May–June 2005.     

Systems of Random Equations over Finite Algebraic Structures

The results on systems of random equations over finite algebraic structures are reviewed. Basic definitions, concepts, and problems in this field are presented.__________Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 82–116, January–February 2005.     

Direct methods of solving systems of linear algebraic ef ions with complex a-matrices

Algorithms of computer algebra are proposed for solving systems of linear algebraic equations with complex á- matrices. An analysis of roundoff errors for the computational schemes considered is given. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 144–156, March–April, 2000.     

RIJNDAEL算法S盒的等价生成

由于对RIJNDAEL算法的代数攻击将S盒具有严格的代数结构作为了攻击的突破口，该文对S盒的性质做了深入研究，发现了在30个形如Z2[x]／(f(x))的GF(2#)域中，采用不同的仿射变换矩阵，RIJNDAEL的S盒(按共轭等价划分)可以有240种生成方法．该文给出了必要的理论证明以及一种易于实现的仿射变换矩阵求取方法，并在附录中列出了这些能生成RIJNDAEL S盒的仿射变换矩阵．这些能产生等价S盒的矩阵的发现，很可能有助于代数攻击法的实施。     

A new algebraic modelling approach to distributed problem-solving in MAS

This paper is devtoed to a new algebraic modelling approach to distributed problem-solving in multi-agent systems(MAS),which is featured by a unified framework for describing and treating social behaviors,social dynamics and social intelligence.A coneptual architecture of algebraic modelling is presented.The algebraic modelling of typical social be-haviors,social situation and social dynamics is discussed in the context of distributed problem-solving in MAS .The comparison and simulation on distributed task allocations and resource assignments in MAS show more advantages of the algebraic approach than other conventional methods.     

A numerical solution of the stochastic discrete algebraic Riccati equation

This article proposes two algorithms for solving a stochastic discrete algebraic Riccati equation which arises in a stochastic optimal control problem for a discrete-time system. Our algorithms are generalized versions of Hewer’s algorithm. Algorithm I has quadratic convergence, but needs to solve a sequence of extended Lyapunov equations. On the other hand, Algorithm II only needs solutions of standard Lyapunov equations which can be solved easily, but it has a linear convergence. By a numerical example, we shall show that Algorithm I is superior to Algorithm II in cases of large dimensions. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Generalized linearly homogeneous production functions

The production functions are considered as functions of values of concave programming problems. Some properties of the functions, in particular, the property of homogeneity and linear homogeneity, are investigated. Examples of the construction of such functions are presented. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 124–132, September–October, 1999.     

Deductive tools of an algebraic programming system

A mathematical environment is a system of tools supporting interactive manipulation of knowledge represented in the form of (formalized) mathematical texts. A theoretical substantiation of a project proposed is the theory of interaction of agents and environments. At the present time, this theory is realized on the basis of a simulator of an action language developed in an algebraic programming system called APS. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 17–34, January–February, 2000.     

Invariance theorems for a class of systems of random nonlinear equations over an arbitrary finite ring with left unity

A class of homogenous systems of random nonlinear equations over an arbitrary finite ring with left unity is considered. The author analyzes the invariance boundaries for limit factorial moments of nonzero solutions, the limit distribution of the number of nonzero solutions, and the geometrical structure of the set of nonzero solutions of the system as the number of unknowns tends to infinity. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 106–115, November–December 2008.     

最大代数免疫度的偶变元对称函数的性质

代数免疫度达到最大的偶变元对称布尔函数的特征仍然是个公开问题。结合组合数学和数论的相关结论研究这类函数的性质,得到了此类函数值向量的几个特征。最后,对于变元个数为两类特殊偶数的情况,得到了代数免疫度达到最大的对称函数的一个特征。     

小汉明重量的布尔函数代数厚度上界研究

根据布尔函数代数厚度的定义,总结变量不交布尔函数的组合函数代数厚度与各布尔函数代数厚度的联系,指出代数厚度上界证明的局限性,得到布尔函数与其补布尔函数代数厚度的限制关系式。利用该关系式得到汉明重量为2和3的布尔函数及其补布尔函数的代数厚度上界,计算满足一定代数厚度的布尔函数的概率值。     

有理曲面的区间隐式化

利用一个低阶多项式区间隐式曲面来包围所给的参数式有理曲面,并构造了一些关于区间隐式曲面厚度和微分张量的目标函数.在最小化这些目标函数的条件下,该区间隐式曲面的中心曲面可以近似地逼近有理曲面,其逼近的误差可以利用区间隐式曲面的区间宽度进行估计.最后提供了具体的算法和一些实例.     

Algebraically rectifiable parametric curves

Sufficient and necessary conditions for the arc length of a polynomial parametric curve to be an algebraic function of the parameter are formulated. It is shown that if the arc length is algebraic, it is no more complicated than the square root of a polynomial. Polynomial curves that have this property encompass the Pythagorean-hodograph curves—for which the arc length is just a polynomial in the parameter—as a proper subset. The algebraically rectifiable cubics, other than Pythagorean-hodograph curves, constitute a single-parameter family of cuspidal curves. The implications of the general algebraic rectifiability criterion are also completely enumerated in the case of quartics, in terms of their cusps and intrinsic shape freedoms. Finally, the characterization and construction of algebraically rectifiable quintics is briefly sketched. These forms offer a rich repertoire of curvilinear profiles, whose lengths are readily determined without numerical quadrature, for practical design problems.     

On the construction of multi-output Boolean functions with optimal algebraic immunity

In this paper,we show a construction of multi-output Boolean functions with optimal algebraic immunity.And,the relationship between the algebraic immunity of a multi-output Boolean function and those of its component functions is studied.We show that all the component functions,together with their nonzero linear combination,of the multi-output Boolean functions achieved by this construction have optimal algebraic immunity simultaneously.     

Solution of two classes of diophantine equations with 2-Quasiperiodic functions

A set of solutions for the equationsf(x)±f(y) =k is described, where fis a 2-quasiperiodic and strictly monotonous function in N_o. The results are applied for investigation of a diametrically-threshold function for graphs and of a maximal type of complete bipartite graph. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 170–174, March–April, 2000     

一类特殊布尔函数的代数免疫度研究

构造具有好的代数免疫度的布尔函数是布尔函数研究的重要问题之一。基于布尔函数的级联构造方法,给出了一类具有好的代数免疫度的布尔函数;分析了所构造函数的性质,证明了构造布尔函数hn+1与其子函数代数免疫度之间的关系,并确定了已构造一阶级联函数的代数次数、平衡性以及非线性度。研究结果表明,在级联构造方法下,i次级联构造函数比一阶构造H0的代数免疫度有显著提高。     

寻找平面代数剖分样本点的改进算法

基于非线性多项式方程的零点配对算法以及临界点算法，给出了一种求平面代数剖分样本点的改进算法。该算法剔除了大量冗余样本点，并在计算过程中以区间表示代数数，有效避免了浮点数等近似计算。通过与已有的经典算法进行比较，实验结果表明该算法具有显著的效果。