Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

Cooperative games of choosing partners and forming coalitions in the marketplace

Two games of interacting between a coalition of players in a marketplace and the residual players acting there are discussed, along with two approaches to fair imputation of gains of coalitions in cooperative games that are based on the concepts of the Shapley vector and core of a cooperative game. In the first game, which is an antagonistic one, the residual players try to minimize the coalition's gain, whereas in the second game, which is a noncooperative one, they try to maximize their own gain as a coalition. A meaningful interpretation of possible relations between gains and Nash equilibrium strategies in both games considered as those played between a coalition of firms and its surrounding in a particular marketplace in the framework of two classes of n-person games is presented. A particular class of games of choosing partners and forming coalitions in which models of firms operating in the marketplace are those with linear constraints and utility functions being sums of linear and bilinear functions of two corresponding vector arguments is analyzed, and a set of maximin problems on polyhedral sets of connected strategies which the problem of choosing a coalition for a particular firm is reducible to are formulated based on the firm models of the considered kind.     

Almost strongly regular matrices and a core theorem for double sequences

The idea of almost convergence for double sequences was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283-294] and they also characterized the four dimensional strong regular matrices. In this paper we define and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem.     

最小费用k度限制树对策

本在Glover—Klingman算法及最小费用支撑树对策的基础上，讨论了最小费用k度限制树对策问题．利用威胁、旁支付理论制订了两种规则，并利用优超、策略等价理论分别给出了在这两种规则下最小费用k度限制树对策核心中的解，从而证明了在这两种规则下其核心非空．     

k-边覆盖对策及其核心

本文针对从图的k-边覆盖问题引出的合作对策模型，利用线性规划对偶理论得到了其核心非空的一个充分条件和构造核心分配的多项式时间算法，并将这一结果推广到了一般的k-集合覆盖对策模型中．     

Studies on the Physicochemical Properties, Structure and Antitumor Activity of an Oligosaccharide Homologue SnS-2 from the Root of Scrophularia ningpoensis Hemsh

An oligosaccharide homologue named SnS-2 was isolated from the root of Scrophularia ningpoensis Hemsl.SnS-2 was purified by means of gel-permeation chromatography and ion-exchange chromatography. Its physicochemical properties, including carbohydrate content and molecular weight were determined. The structure of SnS-2 was elucidated by chemical methods along with ^1H and ^13C NMR spectroscopy, including two-dimensional DQCOSY and H-detected ^1H, ^13C HMQC experiments. These results show that SnS-2 possesses a backbone consisting of terminal α-Galp-(1→, α-Galp-(1→6), α-Glcp-(1→6) and nonreducing end β-Fruf-(2→. The bioactive assay showed that it could inhibit the growth of Lewis pulmonary carcinoma implanted in mice.     

A β-glucosidase from Sclerotinia sclerotiorum

The filamentous fungus Sclerotinia sclerotiorum, grown on a xylose medium, was found to excrete one β-glucosidase (β-glu x). The enzyme was purified to apparent homogeneity by ammonium sulfate precipitation, gel filtration, anion-exchange chromatography, and high-performance liquid chromatography (HPLC) gel filtration chromatography. Its molecular mass was estimated to be 130 kDa by HPLC gel filtration and 60 kDa by sodium dodecyl sulfate polyacrylamide gel electrophoresis, suggesting that β-glu x may be a homodimer. For p-nitrophenyl β-d-glucopyranoside hydrolysis, apparent K _m and V _max values were found to be 0.09 mM and 193 U/mg, respectively, while optimum temperature and pH were 55–60°C and pH 5.0, respectively. β-Glu x was strongly inhibited by Fe²⁺ and activated about 35% by Ca²⁺. β-Glu x possesses strong transglucosylation activity in comparison with commercially available β-glucosidases. The production rate of total glucooligosaccharides (GOSs) from 30% cellobiose at 50°C and pH 5.0 for 6 h with 0.6 U/mL of enzyme preparation was 80 g/L. It reached 105 g/L under the same conditions when using cellobiose at 350 g/L (1.023 M). Finally, GOS structure was determined by mass spectrometry and ¹³C nuclear magnetic resonance spectroscopy.     

反应性复合乳液的合成、表征及其交联反应

利用种子半连续乳液聚合方法合成了核层或壳层带有环氧基以及壳层带有羧基的3种不同核/壳结构的乳胶粒子,通过物理共混带环氧基和羧基的乳胶粒子,得到了两种反应性复合乳液.利用透射电镜和激光动态光散射对乳胶粒子进行了表征,其粒径分布较窄,粒径分布的多分散系数为0.062,平均粒径约76 nm,乳胶粒子具有明显的核/壳结构.通过胶膜的凝胶率和膨胀率的测定和红外光谱分析对反应性复合乳液中乳胶粒子的扩散及交联反应进行了研究,并探讨了不同核壳结构复合乳液对涂膜机械性能的影响.研究表明,当反应性复合乳液中的环氧基和羧基分别分布在乳胶粒子的核层和壳层时,有利于聚合物分子链的充分扩散和化学交联反应的进行,从而提高涂膜的物理化学性能,当甲基丙烯酸缩水甘油酯(GMA)含量为10 wt%时,涂膜的拉伸强度达20.3 MPa.     

A new approach to agglomeration problems

In this paper, we study a location problem with positive externalities. We define a new transferable utility game, considering there is no restriction on the transfer of benefits between firms. We prove that the core of this game is non-empty, provide an expression for it, and an axiomatic characterization. We also study several core allocations, selected by means of a certain bankruptcy problem.     

Synthesis of poly(styrene-co-3-trimethoxysilyl propyl methacrylate) microspheres coated with polysiloxane layer

A procedure has been developed to coat micron-sized poly(styrene-co-3-trimethoxysilyl propyl methacrylate) microspheres with a smooth layer of polysiloxane by the hydrolysis and condensation of methyl trimethoxylsilane (MTMS). Firstly, polystyrene microspheres containing silanol groups were prepared by conventional dispersion polymerization using 3-(trimethoxysilyl) propyl methacrylate (MPS) as a functional comonomer in an ethanol/water medium. Secondly, the synthesis of the polysiloxane shell was carried out using a sol–gel process of MTMS. The thickness of the shells can be easily varied with different copolymer seeds and MTMS feed ratio. When we used copolymer particles with 2.00 μm diameter as seeds, the thickness of the polysiloxane shells can be varied from 0.10 to 0.18 μm. The core/shell structure of the composite microspheres was characterized by transmission electron microscope (TEM).