不可约圈并的补图的色唯一性

本文证明了:如果对于每个i∈{1,2,…,k},都有n_i≥5,且n_i是2的幂或素数,则是色唯一图。     

Approximations to the birthday problem with unequal occurrence probabilities and their application to the surname problem in Japan

Let X ₁, X ₂,..., X _n be iid random variables with a discrete distribution {p _i } _i =1 ^m . We will discuss the coincidence probability R _n , i.e., the probability that there are members of {X _i } having the same value. If m=365 and p _i 1/365, this is the famous birthday problem. Also we will give two kinds of approximation to this probability. Finally we will give two applications. The first is the estimation of the coincidence probability of surnames in Japan. For this purpose, we will fit a generalized zeta distribution to a frequency data of surnames in Japan. The second is the true birthday problem, that is, we will evaluate the birthday probability in Japan using the actual (non-uniform) distribution of birthdays in Japan.This research is supported in part by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture under the contact number 01540141 and 02640057.     

Power-series approximations for the optimal feedback control of noisy nonlinear systems

Power-series methods are developed for designing approximately optimal state regulators for a nonlinear system subject to white Gaussian random disturbances. The performance index of the control is an ensemble average of a quadratic form. A perfect observation of the system state is assumed. When the system nonlinearity is small and it is characterized by a polynomial function of the state, a definite method is presented to construct a suboptimal feedback control of a power-series form in a small nonlinearity parameter. If the variance of noise is small, an alternative method is also applicable which yields a suboptimal control in a power series with respect to a variance parameter. A simple one-dimensional problem is examined to make comparison between controls of the two different forms.     

一类树并的补图的色唯一性

彻底解决了一类不可约树并的补图是色唯一的 ,并得到了一些图的伴随多项式的最小根的重要规律 .     

关于直线拟合的注记

讨论了使残差的最大绝对值为最小准则和使残差的绝对值之和为最小的准则的直线拟合问题 ,采用线性规划可解决此问题 .最后讨论了多项式拟合的情况 .     

利用Newton多项式求解结构动力响应的新方法

提出了一种求解线性、确定性系统动力响应的新方法, 和现在常用的逐步积分法相比,本文方法不但具有较高的计算精度,避免了收敛性和稳定性的问题,而且大大减少了计算工作量.     

A Matrix-Vector Operation-Based Numerical Solution Method for Linear $m$-th Order Ordinary Differential Equations: Application to Engineering Problems

Many problems in engineering sciences can be described by linear, inhomogeneous, $m$-th order ordinary differential equations (ODEs) with variable coefficients. For this wide class of problems, we here present a new, simple, flexible, and robust solution method, based on piecewise exact integration of local approximation polynomials as well as on averaging local integrals. The method is designed for modern mathematical software providing efficient environments for numerical matrix-vector operation-based calculus. Based on cubic approximation polynomials, the presented method can be expected to perform (i) similar to the Runge-Kutta method, when applied to stiff initial value problems, and (ii) significantly better than the finite difference method, when applied to boundary value problems. Therefore, we use the presented method for the analysis of engineering problems including the oscillation of a modulated torsional spring pendulum, steady-state heat transfer through a cooling web, and the structural analysis of a slender tower based on second-order beam theory. Related convergence studies provide insight into the satisfying characteristics of the proposed solution scheme.     

关于完全三角和估计的华罗庚方法

完全有理三角和就是如下形式的和式 Ｓ（ψ，ｑ）＝Σ＾ｑｘ＝１ｅｑ（ψ（ｘ））， 其中ψ（ｘ）是整系数的多项式。许多作者得到了关于Ｓ（ψ，ｑ）的估计的结果。本文发展了华罗庚方法并研究了如下形式的完全有理三角和 Ｓ（Ｒ，ｑ）＝Σ＾ｑｘ＝１ｅｑ（Ｒ（ｘ）），     

The minimal polynomial of a matrix

Let Rbe a finite dimensional central simple algebra over a field FA be any n× n matrix over R. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomial q_A(λ) of A over F. By using q_A(λ), this paper discusses the structure of right (left) eigenvalues set of A, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix.     

On rings asymptotically close to associative rings

The subject of this work is an extension of A. R. Kemer’s results to a rather broad class of rings close to associative rings, over a field of characteristic 0 (in particular, this class includes the varieties generated by finite-dimensional alternative and Jordan rings). We prove the finite-basedness of systems of identities (the Specht property), the representability of finitely-generated relatively free algebras, and the rationality of their Hilbert series. For this purpose, we extend the Razymslov-Zubrilin theory to Kemer polynomials. For a rather broad class of varieties, we prove Shirshov’s theorem on height.