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。     

An interactive three-stage model for mutual funds portfolio selection

The aim of this work is to be a useful instrument for helping finance practitioners on the selection of suitable mutual fund portfolios. The portfolio selection problem is characterized by imprecision and/or vagueness inherent in the required data and more generally, in the context where investors have to make decisions. In order to mitigate these problems, a three stage model has been proposed based on a multi-index model and considering several market scenarios described in an imprecise way by an expert. The proposed fuzzy model allows the Decision Maker to select, by means of an outranking method, a suitable portfolio taking into account the uncertainty related to the market scenarios and the imprecision and/or vagueness associated with the model data.     

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．     

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。     

聚并苯和氯代聚并苯同系分子的总能量与同系序数的相关性研究

聚并苯和氯代聚并苯同系分子的总能量与同系序数之间满足下列相关方程ET=aN b,N =2n 1 ,R≈ 1 ,N为同系序数 ,n是苯环的结构单元数 .本文的计算值与文献值吻合 .     

农副产品营养质量模糊识别与评价

本文利用模糊集理论与决策科学，结合营养学知识，建立了农副产品营养质量识别与评价体系，并对1358种农副产品进行评判，效果较好。