Derivation of the Real-Rootedness of Coordinator Polynomials from the Hermite–Biehler Theorem

By using the Hermite–Biehler theorem, we give a new proof of the real-rootedness of the coordinator polynomials of type D, which was recently established by Wang and Zhao. As a consequence, we also obtain the compatibility between the coordinator polynomials of type D and those of type C.     

Crankshaft-bearing evolution indexes investigation and asperity contact identification based on neural network

The dynamic and lubrication characteristic analyses of the crankshaft–bearing system is quite a complex problem, and it is important to avoid asperity contact which may lead to bearing wear and increase of friction loss significantly in dynamic lubrication condition. In this paper, the dynamic characteristic that has an essential impact on lubrication was investigated over an inline six-cylinder engine. Multi-body dynamics method, tribology, finite element method (FEM), finite difference method (FDM) and component mode synthesis method (CMS) were combined to analyze the dynamic characteristic of crankshaft, oil leakage, oil film pressure, asperity contact pressure and friction loss. Then the orthogonal experiment that included 5 levels and 6 factors was conducted to obtain the training sample sets for neural network, and the probabilistic neural network (PNN) was employed to identify weather the asperity contact happened or not according to its nonlinear characteristic. The analyses which can provide the guidance for the design of main bearing, and avoid the asperity contact in the lubrication are significant to the design of the bearing at the development stage of the engine.     

Vanishing theorems on toric varieties in positive characteristic

We use the liftability of the relative Frobenius morphism of toric varieties and the strong liftability of toric varieties to prove the Bott vanishing theorem, the degeneration of the Hodge to de Rham spectral sequence and the Kawamata–Viehweg vanishing theorem for log pairs on toric varieties in positive characteristic. These results generalize those results of Danilov, Buch–Thomsen–Lauritzen–Mehta, Musta?ǎ and Fujino to the case where concerned Weil divisors are not necessarily torus invariant.     

The pasting constructions for effect algebras

The aim of this paper is to present several techniques of constructing a lattice-ordered effect algebra from a given family of lattice-ordered effect algebras, and to study the structure of finite lattice-ordered effect algebras. Firstly, we prove that any finite MV-effect algebra can be obtained by substituting the atoms of some Boolean algebra by linear MV-effect algebras. Then some conditions which can guarantee that the pasting of a family of effect algebras is an effect algebra are provided. At last, we prove that any finite lattice-ordered effect algebra E without atoms of type 2 can be obtained by substituting the atoms of some orthomodular lattice by linear MV-effect algebras. Furthermore, we give a way how to paste a lattice-ordered effect algebra from the family of MV-effect algebras.     

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.