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.     

Cooperative recognition of Cu<Superscript>2+</Superscript> based on amino acids tethered benzothiadiazoyl-bistriazoles

Fluoroionophoric properties of benzothiadiazoyl-bistriazoyl amino acids derivatives toward metal ions were investigated by UV-Vis and fluorescence spectroscopy. Our results show that the watersoluble lysine derivative 2 exhibited a significant selectivity toward Cu²⁺ in “on-off” type response in buffer solution at pH 7.4.     

ZnO nanorod arrays: Dependence of morphology upon ammonia

Well-aligned ZnO nanorod arrays were prepared on FTO substrate by hydrothermal method at low temperature for 5 h. The effect of ammonia on the length of ZnO nanorod was studied in detail. The resulting materials were extensively characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD) and UV-visible absorption spectra (scatter mode). With the increase of ammonia, the length of ZnO nanorod increases.