An Iterative Procedure for Evaluating Digraph Competitions

A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.     

Direct Sensitization Up-conversion Mechanism in Er3+∶Yb3+ Co-doped Fluoride Materials

Up-conversion luminescence have been studied on Yb3+-Er3+ co-doped fluoride samples. Two infrared lasers with wavelength of 930 nm and 858 nm are carefully chosen as excitation sources. The experimental results suggest direct cooperation sensitization up-conversion rather than two-step sensitization up-conversion is responsible for the increased population of 2H11/2 (Er3+) and thus the increased green emission in the region 514～574 nm in Yb3+-Er3+ co-doped system.     

Cooperative equilibria in discounted stochastic sequential games

This paper addresses the problem of computation of cooperative equilibria in discounted stochastic sequential games. The proposed approach contains as a special case the method of Green and Porter (developed originally for repeated oligopoly games), but it is more general than the latter in the sense that it generates nontrivial equilibrium solutions for a much larger class of dynamic games. This fact is demonstrated on two examples, one concerned with duopolistic economics and the other with fishery management.     

基于模糊博弈视角的企业联盟“双循环”合作对策研究

企业合作在“双循环”新发展格局下呈现出更多的模糊特征,能否形成稳定的模糊合作格局及持续合作的收益再分配策略成为合作联盟的关注点。将广义模糊超量博弈和模糊凸博弈及其广义解集应用到“双循环”新发展格局下企业联盟合作与收益再分配中,提出最大广义模糊超量博弈模型及其广义模糊谈判集,并基于最大广义模糊超量博弈均衡性的视角,对模糊凸博弈下广义模糊谈判集与核心的等价性质进行论证。研究结果不仅满足了“双循环”新发展格局下合作企业以部分资源参与合作的意愿,及企业联盟模糊凸合作博弈下再分配方案等价性证明需求,而且实现了保留部分收益用于联盟再发展的策略。     

Cooperative Bond Activation and Catalytic Reduction of Carbon Dioxide at a Group 13 Metal Center

A single‐component ambiphilic system capable of the cooperative activation of protic, hydridic and apolar H? X bonds across a Group 13 metal/activated β‐diketiminato (Nacnac) ligand framework is reported. The hydride complex derived from the activation of H₂ is shown to be a competent catalyst for the highly selective reduction of CO₂ to a methanol derivative. To our knowledge, this process represents the first example of a reduction process of this type catalyzed by a molecular gallium complex.     

Cooperative Crystallization of Heterometallic Indium–Chromium Metal–Organic Polyhedra and Their Fast Proton Conductivity

Metal–organic polyhedra (MOPs) or frameworks (MOFs) based on Cr³⁺ are notoriously difficult to synthesize, especially as crystals large enough to be suitable for characterization of the structure or properties. It is now shown that the co‐existence of In³⁺ and Cr³⁺ induces a rapid crystal growth of large single crystals of heterometallic In‐Cr‐MOPs with the [M₈L₁₂] (M=In/Cr, L=dinegative 4,5‐imidazole‐dicarboxylate) cubane‐like structure. With a high concentration of protons from 12 carboxyl groups decorating every edge of the cube and an extensive H‐bonded network between cubes and surrounding H₂O molecules, the newly synthesized In‐Cr‐MOPs exhibit an exceptionally high proton conductivity (up to 5.8×10^?2 S cm^?1 at 22.5 °C and 98 % relative humidity, single crystal).     

Regulating Molecular Recognition with C‐Shaped Strips Attained by Chirality‐Assisted Synthesis

Chirality‐assisted synthesis (CAS) is a general approach to control the shapes of large molecular strips. CAS is based on enantiomerically pure building blocks that are designed to strictly couple in a single geometric orientation. Fully shape‐persistent structures can thus be created, even in the form of linear chains. With CAS, selective recognition between large host and guest molecules can reliably be designed de novo. To demonstrate this concept, three C‐shaped strips that can embrace a pillar[5]arene macrocycle were synthesized. The pillar[5]arene bound to the strips was a better host for electron‐deficient guests than the free macrocycle. Experimental and computational evidence is provided for these unique cooperative interactions to illustrate how CAS could open the door towards the precise positioning of functional groups for regulated supramolecular recognition and catalysis.     

Simultaneous Aromatic–Beryllium Bonds and Aromatic–Anion Interactions: Naphthalene and Pyrene as Models of Fullerenes,Carbon Single‐Walled Nanotubes,and Graphene

The possibility of forming stable BeR₂:ArH:Y^? (R=H, F, Cl; ArH=naphthalene, pyrene; Y=Cl, Br) ternary complexes in which the beryllium compounds and anions are located on the opposite sides of an extended aromatic system is explored by means of MP2/aug‐cc‐pVDZ ab initio calculations. Comparison of the electron‐density distribution of these ternary complexes with the corresponding BeR₂:ArH and ArH:Y^? binary complexes reveals the existence of significant cooperativity between the two noncovalent interactions in the triads. The energetic effects of this cooperativity are quantified by evaluation of the three‐body interaction energy Δ³E in the framework of the many‐body interaction‐energy (MBIE) approach. Although an essential component of the interaction energies is electrostatic and is well reflected in the changes in the molecular electrostatic potential of the aromatic system on complexation, strong polarization effects, in particular for the BeR₂:ArH interactions, also play a significant role. The charge transfers associated with these polarization effects are responsible for significant distortion of both the BeR₂ and the aromatic moieties. The former are systematically bent in all the complexes, and the latter are curved to a degree that depends on the nature of the R substituents of the BeR₂ subunit.