Abstract:
Using the generalized Ginzburg-Landau-Devonshire theory, the characteristics of phase transformation of a ferroelectric thin film with surface layers are investigated. We study the effect of the surface layer on the properties (coercive field, critical thickness) of a ferroelectric thin film. Our theoretical results show that the surface layer is likely to answer for the emergence of phase transformation.

Abstract:
Electron transport properties in a triple-quantum-dot ring with three terminals are theoretically studied. By introducing local Rashba spin-orbit interaction on an individual quantum dot, we calculate the charge and spin currents in one lead. We find that a pure spin current appears in the absence of a magnetic field. The polarization direction of the spin current can be inverted by altering the bias voltage. In addition, by tuning the magnetic field strength, the charge and spin currents reach their respective peaks alternately.

Abstract:
Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.

Abstract:
Analogy to heat diffusion equation, an instant diffusion equation of price changing is obtained and explained by “time-space exchange” via Newton’s second law, in which the partial derivative of price respected to time is viewed as a “force”, and the derivative of transportation velocity of price between commodities is viewed as an “acceleration”. It is a partial differential equation of second order. The solution of this equation is found and the definitions of “order of commodities”, “distance between commodities” are given. An important relationship of “time-space exchange” in a stationary process of diffusion of price changing is found. This provides a base for describing the relation of “time-space exchange” quantitatively. Examples for calculating and checking the diffusion of price changing in pork, beef, and mutton based on the data taken on February 5th 2008 are given.

Abstract:
The purpose of this paper is application of the instant diffusion equation to the calculation of strategy on changing of owning shares or currencies. The strategy of selling share(s) with maximum changing rate of price-ratio and purchasing share(s) with minimum changing rate of price-ratio (SMaPMi) is calculated by instant diffusion equation with multiple sources of stock-price changing. The spacial coordinate is defined by stock-price changing ratio at a time before diffu-sion, which ensures that the changing of holding shares using SMaPMi has maximum profit at time next to diffusion ending, based on the comparability of changing rates of stock-price. Summary, SMaPMi would be worked if operation is proper. Calculating example of owning currencies using SMaPMi is given.

In this paper, three types of modeling of diffusion equations for price changing of commodity are studied. In which, the partial derivatives of price of commodity respected to time on the left hand side are integer-derivative, fractal derivative, and fractional derivative respectively; while just a second order derivative respected to space is considered on the right hand side. The solutions of these diffusion equations are obtained by method of departing variables and initial boundary conditions, by translation of variables, and by translation of operators. The definitions of order of commodity x and the distance between commodity x_{i }and x_{j} are defined as [1]. Examples of calculation of price of pork, beef and mutton mainly due to price raising of pork in 2007-07 to 2008-02 inChina are given with same market data as [1]. Conclusion is made.

This paper studies the practicable of hydrogen as a renewable energy source. The study proves a theorem on indirect energy conversion, suggests a monetary unit measured by unit energy, in which, comparing values of different industrial products and comparing different techniques used in production of the same product are better than that of money measured by gold, and proves an assertion, in which, the energy by decomposing a unit water is greater than that by composing a unit water, based on the law of conservation energy. According to the above, we get a conclusion: investment in hydrogen engine must be ended with failure.

Abstract:
We theoretically investigate the collective response of an ensemble of leaky integrate-and-fire neuron units to a noisy periodic signal by including local spatially correlated noise. By using the linear response theory, we obtained the analytic expression of signal-to-noise ratio (SNR). Numerical simulation results show that the rms amplitude of internal noise can be increased up to？an optimal value where the output SNR reaches a maximum value. Due to the existence of the local spatially correlated noise in the units of the ensemble, the SNR gain of the collective ensemble response can exceed unity and can be optimized when the nearest-neighborhood correlation is negative. This nonlinear collective phenomenon of SNR gain amplification in an ensemble of leaky integrate-and-fire neuron units can be related to the array stochastic resonance (SR) phenomenon. Furthermore, we also show that the SNR gain can also be optimized by tuning the number of neuron units, frequency and？amplitude of the weak periodic signal. The present study illustrates the potential to utilize the local spatially correlation noise and the number of ensemble units for optimizing the collective response of the neuron to inputs, as well as a guidance in the design of information processing devices to weak signal detection.

Liver cirrhosis portal hypertension patients to reduce the number of blood cells are common in clinical, and often affect the prognosis. This paper discusses cirrhotic portal hypertension patients complicated by the reason of the decrease in the number of peripheral blood cells and what is the clinical significance of these reasons so as to provide theoretical support for the choice of treatment. Splenomegaly and hypersplenism caused should be the main reason for reducing the number of blood cells, but not all, other reasons are alcohol and virus inhibition of bone marrow, liver function impairment, autoimmune damage and loss of blood, etc. If it is a function of the spleen hyperfunction caused by blood cells decreases, blood should rise to normal after splenectomy, or consider other reason or there are other reasons at the same time.