The price of fairness with the extended Perles–Maschler solution

In Nash bargaining problem, due to fairness concerns of players, instead of maximizing the sum of utilities of all players, an implementable solution should satisfy some axioms or characterizations. Such a solution can result in the so-called price of fairness, because of the reduction in the sum of utilities of all players. An important issue is to quantify the system efficiency loss under axiomatic solutions through the price of fairness. Based on Perles–Maschler solution of two-player Nash bargaining problem, this paper deals with the extended Perles–Maschler solution of multi-player Nash bargaining problem. We give lower bounds of three measures of the system efficiency for this solution, and show that the lower bounds are asymptotically tight.     

Three dimensional steady subsonic Euler flows in bounded nozzles

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic–sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div–curl system, and delicate estimate for the transport equations.     

GENERAL MINIMAX ESTIMATORS ON THE LOCATION MATRIX OF A MIXTURE OF NORMALS

This paper considers the estimate problem on the mean matrix of mixtureof normals. In order to evaluate estimators of the mean matrix, a fundamental frameof Ф-(general) decision problem is established. Under the frame, a class of Ф-minimax estimators are constructed.     

含R_2dtc配体Mo-Cu化合物的动态~(95)Mo NMR

本实验利用动态~(95)Mo NMR监测Mo-Cu系列化合物的形成过程,对反应CuCl+NaR_2dtc+MoO_nS,摩尔比3:3:1,溶剂为DMF;R=Et,n=0(Ⅰ);R=Me,n=0(Ⅱ);R=Et,n=2(Ⅲ)进行了研究,观察到具有不同簇骼的多种中间产物的存在及随反应进程相互转化等现象。     

Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

Syntheses，Structures and Spectroscopic Properties of Mo（W）－Cu－S－Cluster Compounds with Dialkyldithiocarbamate Ligands

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兼容多波长及多脉宽输出的频率转换系统设计

通过对多种频率转换方案的深入对比分析,设计了一套兼容多波长及多脉宽高效输出的频率转换系统。采用"Ⅱ+Ⅱ"类双晶体级联的方式,可以实现"偏振失配"三倍频和Ⅱ类双晶体正交级联二倍频两种模式间的快速切换。通过数值模拟程序优化了晶体构型,结果表明,当两块晶体厚度均为10mm时,可以兼顾低功率长脉冲和高功率短脉冲对效率和稳定性的需求。     

Measurements of NO2 mixing ratios with topographic target light scattering-differential optical absorption spectroscopy system and comparisons to point monitoring technique

A topographic target light scattering-differential optical absorption spectroscopy(ToTaL-DOAS) system is developed for measuring average concentrations along a known optical path and studying surface-near distributions of atmospheric trace gases.The telescope of the ToTaL-DOAS system points to targets which are located at known distances from the measurement device and illuminated by sunlight.Average concentrations with high spatial resolution can be retrieved by receiving sunlight reflected from the targets.A filed measurement of NO2 concentration is performed with the ToTaL-DOAS system in Shijiazhuang in the autumn of 2011.The measurement data are compared with concentrations measured by the point monitoring technique at the same site.The results show that the ToTaL-DOAS system is sensitive to the variation of NO2 concentrations along the optical path.