Compromise values in cooperative game theory

Summary The aim of this paper is to give a survey on several well-known compromise values in cooperative game theory and its applications. Special attention is paid to the τ-value for TU-games, the Raiffa-Kalai-Smorodinsky solution for bargaining problems, and the compromise value for NTU-games.     

Transition probabilities in146Eu

Transition probabilities in the odd-odd nucleus¹⁴⁶Eu are measured. A recent determination of the lifetime of the 115.6 keV level has indicated a strong retardation of the 115.6 keVM1 transition. In contrast, the present results areT _1/2(230.3)≦165 ps,T _1/2(115.6)≦160 ps. TheE2 cross-over transitions of 269.5 and 230.3 keV were not found in the Ge(Li) gamma spectrum. All results are in agreement with the single particle model.     

Effect of salt gradients on the separation of dilute mixtures of proteins by ion-exchange in simulated moving beds

Salt gradients can improve the efficiency during fractionation of proteins by ion-exchange in simulated moving beds (SMBs). The gradients are formed using feed and desorbent solutions of different salt concentrations. The thus introduced regions of high and low affinity may reduce eluent consumption and resin inventory compared to isocratic SMB systems. This paper describes a procedure for the selection of the flow-rate ratios that enables successful fractionation of a dilute binary mixture of proteins in a salt gradient. The procedure is based on the so-called "triangle theory" and can be used both for upward gradients (where salt is predominantly transported by the liquid) and downward gradients (where salt is predominantly transported by the sorbent). The procedure is verified by experiments.     

On the broadening of the annihilation line

The broadening of annihilation line was studied with a Ge detector. The annihilation line was deconvoluted taking into account the instrumental resolution of 1.08 keV. The P_f in several metals are found. The contribution of core electrons to annihilation is deduced.     

Ln12‐Containing 60‐Tungstogermanates: Synthesis,Structure, Luminescence,and Magnetic Studies

A new class of hexameric Ln₁₂‐containing 60‐tungstogermanates, [Na(H₂O)₆?Eu₁₂(OH)₁₂(H₂O)₁₈Ge₂(GeW₁₀O₃₈)₆]^39? ( Eu₁₂ ), [Na(H₂O)₆?Gd₁₂(OH)₆(H₂O)₂₄Ge(GeW₁₀O₃₈)₆]^37? ( Gd₁₂ ), and [(H₂O)₆?Dy₁₂(H₂O)₂₄(GeW₁₀O₃₈)₆]^36? ( Dy₁₂ ), comprising six di‐Ln‐embedded {β(4,11)‐GeW₁₀} subunits was prepared by reaction of [α‐GeW₉O₃₄]^10? with Ln^III ions in weakly acidic (pH 5) aqueous medium. Depending on the size of the Ln^III ion, the assemblies feature selective capture of two (for Eu₁₂ ), one (for Gd₁₂ ), or zero (for Dy₁₂ ) extra Ge^IV ions. The selective encapsulation of a cationic sodium hexaaqua complex [Na(H₂O)₆]⁺ was observed for Eu₁₂ and Gd₁₂ , whereas Dy₁₂ incorporates a neutral, distorted‐octahedral (H₂O)₆ cluster. The three compounds were characterized by single‐crystal XRD, ESI‐MS, photoluminescence, and magnetic studies. Dy₁₂ was shown to be a single‐molecule magnet.     

On some balanced, totally balanced and submodular delivery games

This paper studies a class of delivery problems associated with the Chinese postman problem and a corresponding class of delivery games. A delivery problem in this class is determined by a connected graph, a cost function defined on its edges and a special chosen vertex in that graph which will be referred to as the post office. It is assumed that the edges in the graph are owned by different individuals and the delivery game is concerned with the allocation of the traveling costs incurred by the server, who starts at the post office and is expected to traverse all edges in the graph before returning to the post office. A graph G is called Chinese postman-submodular, or, for short, CP-submodular (CP-totally balanced, CP-balanced, respectively) if for each delivery problem in which G is the underlying graph the associated delivery game is submodular (totally balanced, balanced, respectively). For undirected graphs we prove that CP-submodular graphs and CP-totally balanced graphs are weakly cyclic graphs and conversely. An undirected graph is shown to be CP-balanced if and only if it is a weakly Euler graph. For directed graphs, CP-submodular graphs can be characterized by directed weakly cyclic graphs. Further, it is proven that any strongly connected directed graph is CP-balanced. For mixed graphs it is shown that a graph is CP-submodular if and only if it is a mixed weakly cyclic graph. Finally, we note that undirected, directed and mixed weakly cyclic graphs can be recognized in linear time. Received May 20, 1997 / Revised version received August 18, 1998?Published online June 11, 1999     

A fluorescence approach to investigate repartitioning of coalescing agents in acrylic polymer emulsions

Repartitioning of co-solvents between particles of latex emulsions was investigated by means of a fluorescence method based on the detection of the amount of co-solvent via the solvatochromic shift of the emission maximum of a fluorescent probe, copolymerized at a low concentration. Complete repartitioning of co-solvents between particles of latex materials with a low T _g (ca. 25 °C) occurred within minutes. For a hydrophilic latex with a T _g of 68 °C, equilibration was achieved within an hour. Repartitioning was faster for more hydrophobic co-solvents. For a hydrophobic latex of similar T _g , co-solvent repartitioning took place on the same time scale, but complete equilibration was not reached. Possibly, there is an additional slow component in the repartitioning, or the prolonged presence of co-solvent causes a structural change in the latex particles that affects the outcome of the experiment.     

Asymptotic Behavior of Müntz Orthogonal Polynomials

We provide a representation for the Müntz orthogonal polynomials as a real integral. This allows us to establish a general result on their asymptotic behavior within the interval of orthogonality. This is the first time that such asymptotics have been obtained for general Müntz exponents {λ _n }. We consider some special cases, particularly when the exponents satisfy the asymptotic relation $\lim_{n\rightarrow\infty}\frac{n}{\lambda_n}=\rho $ for some constant ρ>0.