Bargaining over the division of a shrinking pie: An axiomatic approach

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).     

Extensions of Szegö's theory of orthogonal polynomials,III

Let {ø _n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø _n (dμ) when logμ′∈L ¹. In what follows we will discuss the asymptotic behavior of the ratioø _n (dμ ₂)/ø _n (dμ ₁) on the unit circle whendμ ₁ anddμ ₂ are close in a sense (e.g.,dμ ₂=gdμ ₁, where g≥0 is such thatQ(e ^it )g(t) andQ(e ^it )/g(t) are bounded for a suitable polynomialQ) and μ ₁ ^′ >0 almost everywhere or (a somewhat weaker requirement) lim _n→∞Φ _n (dμ ₁,0)=0 for the monic polynomial Φ _n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper.     

Graphs whose every transitive orientation contains almost every relation

Given a graphG onn vertices and a total ordering ≺ ofV(G), the transitive orientation ofG associated with ≺, denotedP(G; ≺), is the partial order onV(G) defined by settingx<y inP(G; ≺) if there is a pathx=x ₁ x ₂…x _r=y inG such thatx ₁ ≺x _j for 1≦i<j≦r. We investigate graphsG such that every transitive orientation ofG contains ₂ ⁿ −o(n ²) relations. We prove that almost everyG _n,p satisfies this requirement if , but almost noG _n,p satisfies the condition if (pn log log logn)/(logn log logn) is bounded. We also show that every graphG withn vertices and at mostcn logn edges has some transitive orientation with fewer than ₂ ⁿ −δ(c)n ² relations. Partially supported by MCS Grant 8104854.     

Über Anzahl und Verteilung der Scheitel ebener Bogen

Zusammenfassung Seit der Entdeckung des 4-Scheitel-Satzes durch S. Mukhopadhaya (1909) und A. Kneser (1912) hat sich eine umfangreiche Literatur über Scheitel- und verwandte Sätze entwickelt. Unter anderem wurden ebene Bogen auf Scheitel hin untersucht bzgl. Charakteristiken, welche von k 1 Parametern stetig abhängen. Wir legen für die wichtigsten Sätze aus diesem Teil der Theorie überarbeitete Definitionen und Beweise unter vereinfachten Voraussetzungen vor.

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大规模合成具有氧空位的多孔Bi2O3用于有效降解亚甲基蓝

光催化降解有机污染物由于其具有低能耗和绿色环保的特点,已经成为研究的热点. 氧化铋纳米晶体的带隙在2.0∽2.8 eV之间,利用它催化可见光降解有机污染物具有较高的活性,从而引起了越来越多的关注. 尽管近年来已经开发了几种制备Bi₂O₃基半导体材料的方法,但是仍然难以用简单的方法大规模地制备高活性的Bi₂O₃催化剂. 因此,开发简单可行的大规模制备Bi₂O₃纳米晶体的方法对于工业废水处理的潜在应用具有重要意义. 本文通过蚀刻商用BiSn粉末,然后进行热处理,成功地大规模制备了多孔Bi₂O₃. 获得的多孔Bi₂O₃在亚甲基蓝(MB)的光催化降解中表现出优异的活性和稳定性. 对该机理的进一步研究表明,多孔Bi₂O₃合适的能带结构允许生成活性氧物种,例如O₂^-·和·OH,可有效降解MB.     

Halogen bond between hypervalent halogens YF3/YF5 (Y=Cl,Br, I) and H2X (X= O,S, Se)

ABSTRACT

The complexes of H₂X (X?=?O, S, Se) with hypervalent halogens YF₃ and YF₅ (Y?=?Cl, Br, I) have been studied. The σ-hole on the Y atom participates in a halogen bond with the lone pair on the chalcogen atom. In addition, some secondary interactions coexist with the halogen bond in most complexes. The interaction energy correlates with the nature of both X and Y atoms. In most cases, the complex is more stable for the heavier Y atom and the lighter X atom. Of course, there are some exceptions in H₂X···YF₃. YF₃ forms a more stable complex with H₂X than does YF₅. These complexes are dominated by electrostatic interaction and the halogen bond involving H₂S and H₂Se exhibits some covalent character.

Halogen bond plays an important role in chemical reactions and multivalent halogens can regulate chemical reactions by participating in a halogen bond. Thus we compare the effect of the chalcogen electron donor on the strength and nature of halogen bonding involving multivalent halogens.     

Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field.Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.     

Systematic trends in the237neptunium Mössbauer isomer shift: Overlap of IV,V and VI neptunium oxidation states and correlation between isomer shift and crystal structure

The influence of the neptunium ion environment on the²³⁷Np Mössbauer isomer shifts has been studied in various metal coordination complexes: fluorides, oxides, oxide fluorides and polycarboxylates. A linear dependence between the isomer shift and the mean neptunium-ligand distance in a series of hexavalent Np compounds has been evidenced and the feasibility of overlapped isomer shift areas, namely Np(IV), Np(V) and Np(VI) has been established.     

Lase action on resonant molecular flows through capillaries

New experimental results are reported pointing to the possibility of a laser control of the resonant gases transit through capillaries in the Knudsen and intermediate regimes.