The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011     

A two-objective mathematical model without cutting patterns for one-dimensional assortment problems

This paper considers a one-dimensional cutting stock and assortment problem. One of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model. Since the total number of cutting patterns to be generated may be very huge, both the generation and the use of such a set lead to computational difficulties in solution process. The purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters. We propose a new, two-objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory, in order to fulfill a given set of cutting orders. The model does not require pre-specification of cutting patterns. We suggest a special heuristic algorithm for solving the presented model. The superiority of both the mathematical model and the solution approach is demonstrated on test problems.     

Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping

In this paper, based on some mesh-dependent estimates on the extreme eigenvalues of a general finite element system defined on a simplicial mesh, novel and sharp bounds on the permissible time step size are derived for the mass lumping finite element approximations of parabolic equations. The bounds are dependent not only on the mesh size but also on the mesh shape. These results provide guidance to the stability of numerical solutions of parabolic problems in relation to the unstructured geometric meshing. Numerical experiments on both uniform meshes and adaptive meshes are presented to validate the theoretical analysis.     

恰有两个子群共轭类长的有限群

设G是有限群,Ns(G)表示G的子群共轭类长构成的集合.本文研究Ns(G)中只有两个元素时有限群G的结构,在非幂零情形时给出了G的完全分类,在幂零情形时获得了G的一些性质.     

OPTIMAL HARVEST FEEDBACK RULE ACCOUNTING FOR THE FISHING‐UP EFFECT AND SIZE‐DEPENDENT PRICING

Abstract Fishing leads to truncation of a population's age and size structure. However, large‐sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size‐related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon–Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon–Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size‐dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies, potentially causing rent dissipation and suboptimal utilization of renewable resources.     

2×2列联表中二属性相关的Bayes检验

2×2列联表中二属性相关的假设检验是定性数据分析中的热点问题,针对此问题的研究频率学派已做过大量的工作,其理论方法已趋于成熟.利用Bayes检验研究2×2列联表中二属性的相关性迄今为止国内外的相关文献还为数不多.将依据Bayes理论对此问题提出新的检验方法,推出其Bayes因子计算公式,利用正态近似研究三项假设计算出有关的后验概率,不仅解决了频率学派难以处理的问题,并且为吸烟有害健康提供了理论支撑.     

水资源短缺风险因子的筛选模型

水资源短缺评价首先需要确定指标体系,投影寻踪模型与灰色关联度法相结合,可以有效地筛选出水资源短缺风险因子,为进一步进行风险评价奠定了基础,同时也为制定风险的防范措施和对策提供了理论依据.综合应用这两种模型,对北京市2001～2009年的水资源短缺风险进行研究,结果表明:降水量、日照时数、雨日数、单位GDP污水排放量、人均GDP、工业总产值占有率、污水处理率和水循环使用率这8个指标是北京市水资源短缺的主要风险因子.     

Relationship between selectivity and average resolution in comprehensive two-dimensional separations with spectroscopic detection

The average value of the multivariate selectivity (SEL) of randomly positioned peaks in a multi-component separation is shown to equal the average fraction of peaks that are singlets, as predicted by statistical-overlap theory (SOT). This equality is the basis for proposing a useful metric, specifically the average minimum resolution of nearest-neighbor peaks, for the performance of comprehensive two-dimensional (2D) separations. Furthermore this metric was computed both without ancillary spectroscopic information and with the assistance of such help, specifically multi-wavelength UV-vis spectra, acquired during the separation. Separations are simulated with randomly positioned peaks over wide ranges of total number of peaks, first- and second-dimension peak capacity, dimensionless first-dimension sampling time, and spectral diversity. The specific version of the general multivariate selectivity concept that is used here--identified as SEL--gives the relative precision of quantification when using the PARAFAC (parallel factor analysis) method, a popular curve resolution algorithm. The SEL values of all peaks were calculated, averaged, and compared to the predictions of SOT. In the absence of auxiliary spectral data, the SEL-based average minimum resolution required to separate two peaks in a 2D separation is 0.256, compared to resolution of 0.5 if no chemometric assistance is available. This was found to be valid over a wide range of conditions and is essentially independent of peak crowding. With the assistance of the spectral data, the requisite minimum resolution substantially improves, that is, it decreases, especially when peak crowding is severe. The requisite minimum resolution decreases even further, up to a limit, as the spectral diversity is increased. In contrast, the SEL-based average under-sampling correction factor is virtually independent of the presence of the additional spectral data, and additionally is about the same as calculated with SOT from the average number of maxima in closely analogous simulations. The use of selectivity greatly increases the fraction of peaks that are singlets, relative to the number of singlet maxima, especially when spectral assistance is added. The insensitivity of the under-sampling correction factor to either the use of selectivity or added spectral data simplifies optimization of the corrected peak capacity in on-line comprehensive 2D separations.     

One target, different effects: a comparison of distinct therapeutic antibodies against the same targets

To date, more than 30 antibodies have been approved worldwide for therapeutic use. While the monoclonal antibody market is rapidly growing, the clinical use of therapeutic antibodies is mostly limited to treatment of cancers and immunological disorders. Moreover, antibodies against only five targets (TNF-α, HER2, CD20, EGFR, and VEGF) account for more than 80 percent of the worldwide market of therapeutic antibodies. The shortage of novel, clinically proven targets has resulted in the development of many distinct therapeutic antibodies against a small number of proven targets, based on the premise that different antibody molecules against the same target antigen have distinct biological and clinical effects from one another. For example, four antibodies against TNF-α have been approved by the FDA -- infliximab, adalimumab, golimumab, and certolizumab pegol -- with many more in clinical and preclinical development. The situation is similar for HER2, CD20, EGFR, and VEGF, each having one or more approved antibodies and many more under development. This review discusses the different binding characteristics, mechanisms of action, and biological and clinical activities of multiple monoclonal antibodies against TNF-α, HER-2, CD20, and EGFR and provides insights into the development of therapeutic antibodies.