强正则自补图的一个注记

Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k 1, where 4k 1=x2 y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k 1 orders.     

A Generalization of Strongly Regular Graphs

Motivated from an example of ridge graphs relating to metric polytopes, a class of connected regular graphs such that the squares of their adjacency matrices are in certain symmetric Bose-Mesner algebras of dimension 3 is considered in this paper as a generalization of strongly regular graphs. In addition to analysis of this prototype example defined over (MetP₅)^*, some general properties of these graphs are studied from the combinatorial view point.AMS Subject Classification: 05E30.     

H-空间中上半连续集值映象一个新的不动点定理及其应用

本文在H-空间中建立了上半连续集值映象的一个新的不动点定理,作为应用,得到了两个新的拟变分不等式的解的存在性定理。     

基于次梯度选取的非光滑优化强次可行方向法

本文结合次梯度选取技术及割平面法和强次可行方向法的思想,提出了一个求解目标函数非光滑约束优化问题的强次可行方向算法.通过设计一个新的寻找搜索方向子问题和构造新型线搜索,算法不仅能接受不可行的初始点,而且能保持迭代点的强次可行性,同时避免在可行域外目标函数值的不适度增加.算法具备全局收敛性,且初步的数值试验表明算法是稳定有效的.     

On a theorem of Jaworowski on locally equivariant contractible spaces

Ancel's method of fiberwise trivial relations is applied to the problem of characterization of absolute equivariant extensors. We obtain a generalization of Jaworowski's theorem on characterization of equivariant extensors lying in to the case when the space is infinite-dimensional, has infinitely many orbit types and the acting compact group is not necessarily a Lie group.

     

A Liouville-Type Theorem for Strongly Subharmonic Functions on Complete Non-compact Riemannian Manifolds and Some Applications

We prove that if Mis a complete non-compact Riemannian manifold and ₁(M)=0, then any C ²solution of uk> 0 is unbounded. We apply this result to obtain an estimate for the size of the image set of some types of maps between Riemannian manifolds.     

关于m-值随机序列广义随机选择的一个强极限定理

§ 1.　Introduction　　ConsiderasequenceofBernoullitrials ,andsupposethatateachtrialthebettorhasthefreechoiceofwhetherornottobet.Asystemconsistsinfixedrulesselectingthosetrialsonwhichtheplayeristobet.ThetheoremongamblingsystemassertsthatunderanysystemthesuccessivebetsformasequenceofBernoullitrialwithunchangedprobabilityforsuccess.TheimportanceofthisstatementwasfirstrecognizedbyvonMises,whointroducedtheimpossibili tyofasuccessfulgamblingsystemasafundamentalaxiom(cf.[1 ],[2 ],[3],[4]) .Thecon …     

ɾʧ�ع�ģ����һ��LASSO�ͱ���ѡ��͹��Ʒ���

删失回归模型是一种很重要的模型,它在计量经济学中有着广泛的应用. 然而,它的变量选择问题在现今的参考文献中研究的比较少.本文提出了一个LASSO型变量选择和估计方法,称之为多样化惩罚$L_1$限制方法, 简称为DPLC. 另外,我们给出了非0回归系数估计的大样本渐近性质. 最后,大量的模拟研究表明了DPLC方法和一般的最优子集选择方法在变量选择和估计方面有着相同的能力.     

A Non-Uniform Estimate in the Central Limit Theorem for Sequences of Strongly Additive Functions

The value distribution of a normalised sequence of strongly additive arithmetic functions

非线性不等式约束最优化一个超线性与二次收敛的强次可行方法

本文讨论非线性不等式约束最优化问题，借助于序列线性方程组技术和强次可行方法思想，建立了问题的一个初始点任意的快速收敛新算法．在每次迭代中，算法只需解一个结构简单的线性方程组．算法的初始迭代点不仅可以是任意的，而且不使用罚函数和罚参数，在迭代过程中，迭代点列的可行性单调不减．在相对弱的假设下，算法具有较好的收敛性和收敛速度，即具有整体与强收敛性，超线性与二次收敛性．文中最后给出一些数值试验结果．     

正则m叉树T的S(n)={Ki:1≤i≤n}-因子数的递归公式

在正则m叉树T中,删除K₂及端点关联边,通过所得子正则m叉树中分枝点、叶数和m之间内在联系,本文导出正则m叉树T的S⁽ⁿ⁾={K_i:1≤i≤n}-因子数递归公式.特别当m=2时,正则2叉树递归公式为:A_t=A_t/2²+2A_t/4² A_t/2,t为正则2叉树T的叶数.     

Equilibria for set-valued maps on nonsmooth domains

A set-valued map defined on a compact lipschitzian retract of a normed space with nontrivial Euler characteristic and satisfying (i) a strong graph approximation property and (ii) a tangency condition expressed in terms of Clarke’s tangent cone, admits an equilibrium. This result extends in a simple way known solvability theorems to a large class of nonconvex set-valued maps defined on nonsmooth domains. Dedicated to Professor Felix Browder     

A Framework for Unbiased Model Selection Based on Boosting

Variable and model selection are of major concern in many statistical applications, especially in high-dimensional regression models. Boosting is a convenient statistical method that combines model fitting with intrinsic model selection. We investigate the impact of base-learner specification on the performance of boosting as a model selection procedure. We show that variable selection may be biased if the covariates are of different nature. Important examples are models combining continuous and categorical covariates, especially if the number of categories is large. In this case, least squares base-learners offer increased flexibility for the categorical covariate and lead to a preference even if the categorical covariate is noninformative. Similar difficulties arise when comparing linear and nonlinear base-learners for a continuous covariate. The additional flexibility in the nonlinear base-learner again yields a preference of the more complex modeling alternative. We investigate these problems from a theoretical perspective and suggest a framework for bias correction based on a general class of penalized least squares base-learners. Making all base-learners comparable in terms of their degrees of freedom strongly reduces the selection bias observed in naive boosting specifications. The importance of unbiased model selection is demonstrated in simulations. Supplemental materials including an application to forest health models, additional simulation results, additional theorems, and proofs for the theorems are available online.     

关联情境下物流服务外包商选择的混合型决策分析方法

现实中影响物流服务外包商选择的诸多因素通常具有主客观特性和关联性,针对此问题给出一种关联情境下物流服务外包商选择的混合型决策分析方法.首先,利用二元语义表示模型分别处理和集结专家给出的语言短语形式的因素关联信息和主观评价信息,并通过多因素关联分析确定因素的重要性和归类;然后,分别定义主客观测度因素的正负理想点,利用范数的概念构建规范化评价矩阵;进一步地,借鉴多准则优化妥协解(VIKOR)法的思想,计算每个备选外包商的群效用值和个体遗憾值以及折衷排序值,并根据折衷排序值选择出最理想的外包商.最后,通过一个实例分析说明给出方法的可行性和实用性.     

A Dynamic Supplier Selection and Inventory Management Model for a Serial Supply Chain with a Novel Supplier Price Break Scheme and Flexible Time Periods

A new supplier price break and discount scheme taking into account order frequency and lead time is introduced and incorporated into an integrated inventory planning model for a serial supply chain that minimizes the overall incurred cost including procurement, inventory holding, production, and transportation. A mixed-integer linear programming (MILP) formulation is presented addressing this multi-period, multi-supplier, and multi-stage problem with predetermined time-varying demand for the case of a single product. Then, the length of the time period is considered as a variable. A new MILP formulation is derived when each period of the model is split into multiple sub-periods, and under certain conditions, it is proved that the optimal solution and objective value of the original model form a feasible solution and an upper bound for the derived model. In a numerical example, three scenarios of the derived model are solved where the number of sub-period is set to 2, 3, and 4. The results further show the decrease of the optimal objective value as the length of the time period is shortened. Sufficient evidence demonstrates that the length of the time period has a significant influence on supplier selection, lot sizing allocation, and inventory planning decisions. This poses the necessity of the selection of appropriate length of a time period, considering the trade-off between model complexity and cost savings.     

A Lower Bound of <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> Norms in the CLT for Strongly Mixing Random Variables

We derive a lower bound of L _p norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X ₁,..., X _n with under the boundedness condition ℙ{|X _i | ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑ _r⩾1 r ²α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005.