The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers

Let k 5 be a fixed integer and let m = (k – 1)/2. It is shown that the independence number of a C _k-free graph is at least c ₁[ d(v)^{1/(m – 1)}]^{(m – 1)/m} and that, for odd k, the Ramsey number r(C _k, K _n) is at most c ₂(n ^{m + 1}/log n)^1/m , where c ₁ = c ₁(m) > 0 and c ₂ = c ₂(m) > 0.     

神秘数字“七”再发微

本文以数字"七"在中国民俗中的广泛应用为表象,依据我国古代先哲对宇宙天体运动节律(即"天道唯七")和人体生命节律(7—8年)的认识,以及现代医学对人的生物节律的进一步确认,指出数字"七"之所以具有宇宙数字的性质及巫术的、神话的意义,"获得模式数字的资格",根本原因在于它体现了以上两个节律。     

"新写实"的零度审视及其审美意蕴

本文旨在通过对表面客观冷静话语下蕴涵的深层情感判断的揭示、表面原生态生活下独具现代意味的生存生命真实的展现来说明新写实零度审视的当下优势与独特的审美意蕴.这样的零度写作一方面适应了社会发展,另一方面又保留了文学的价值意义与审美功能;一方面顺应了中国读者的接受心理,另一方面又实现了传统写实主义的现代转换,新写实对其完美把握以自身独特风貌实现了中国文学走向世界的目标.     

Distance graphs on R n with 1-norm

Suppose S is a subset of a metric space X with metric d. For each subset D⊆{d(x,y):x,y∈S,x≠y}, the distance graph G(S,D) is the graph with vertex set S and edge set E(S,D)={xy:x,y∈S,d(x,y)∈D}. The current paper studies distance graphs on the n-space R ₁ ⁿ with 1-norm. In particular, most attention is paid to the subset Z ₁ ⁿ of all lattice points of R ₁ ⁿ . The results obtained include the degrees of vertices, components, and chromatic numbers of these graphs. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. Supported in part by the National Science Council under grant NSC-94-2115-M-002-015. Taida Institue for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan. National Center for Theoretical Sciences, Taipei Office.     

An immune algorithm with stochastic aging and kullback entropy for the chromatic number problem

We present a new Immune Algorithm, IMMALG, that incorporates a Stochastic Aging operator and a simple local search procedure to improve the overall performances in tackling the chromatic number problem (CNP) instances. We characterize the algorithm and set its parameters in terms of Kullback Entropy. Experiments will show that the IA we propose is very competitive with the state-of-art evolutionary algorithms.     

Estimating population size with truncated sampling

Let X₁, X₂,…,X_n be independent, indentically distributed random variables with density f(x,θ) with respect to a σ-finite measure μ. Let R be a measurable set in the sample space X. The value of X is observable if X ? (X?R) and not otherwise. The number J of observable X’s is binomial, N, Q, Q = 1?P(X ? R). On the basis of J observations, it is desired to estimate N and θ. Estimators considered are conditional and unconditional maximum likelihood and modified maximum likelihood using a prior weight function to modify the likelihood before maximizing. Asymptotic expansions are developed for the [Ncirc]’s of the form [Ncirc] = N + α√N + β + o_p(1), where α and β are random variables. All estimators have the same α, which has mean 0, variance σ² (a function of θ) and is asymptotically normal. Hence all are asymptotically equivalent by the usual limit distributional theory. The β’s differ and Eβ can be considered an “asymptotic bias”. Formulas are developed to compare the asymptotic biases of the various estimators. For a scale parameter family of absolutely continuous distributions with X = (0,∞) and R = (T,∞), special formuli are developed and a best estimator is found.     

局部环上典型群的非双曲型

引入域上典型群的生成问题所得的成果；对局部环R上典型群生成问题研究，构造度量函数及一平延，为局部环R上典型群向域F上的典型群导入，给出典型群的非双曲型．     

Kullback-leibler information approach to the optimum measurement point for bayesian estimation

When an appropriate parametric model and a prior distribution of its parameters are given to describe clinical time courses of a dynamic biological process, Bayesian approaches allow us to estimate the entire profiles from a few or even a single observation per subject. The goodness of the estimation depends on the measurement points at which the observations were made. The number of measurement points per subject is generally limited to one or two. The limited measurement points have to be selected carefully. This paper proposes an approach to the selection of the optimum measurement point for Bayesian estimations of clinical time courses. The selection is made among given candidates, based on the goodness of estimation evaluated by the Kullback-Leibler information. This information measures the discrepancy of an estimated time course from the true one specified by a given appropriate model. The proposed approach is applied to a pharmacokinetic analysis, which is a typical clinical example where the selection is required. The results of the present study strongly suggest that the proposed approach is applicable to pharmacokinetic data and has a wide range of clinical applications.     

非定常控制系统的绝对稳定性

从研究中间变量σ情况和判断控制系统解的界及k类函数法来讨论控制系统零解的绝对稳定,并给出了判断非线性非定常系统零解绝对稳定的一种新方法.     

大数幂剩余的二进制冗余数Montgomery算法

介绍了大数幂剩余的Montgomery算法,提出了基于二进制冗余数的大数幂剩余Montgomery算法模型。理论分析表明,采用二进制冗余数可减少乘法的进位传播,同时使算法的迭代步数减少17.2%。进一步提高了大数幂剩余的运算速度。