An algorithm of analysis tools on points distribution in high dimension space: The distance of a point and an infinite sub-space

This paper discusses the algorithm on the distance from a point and an infinite sub-space in high dimensional space With the development of Information Geometry([1]), the analysis tools of points distribution in high dimension space, as a measure of calculability, draw more attention of experts of pattern recognition. By the assistance of these tools, Geometrical properties of sets of samples in high-dimensional structures are studied, under guidance of the established properties and theorems in high-dimensional geometry.

A Numerical Method for Calculating Transmission Coefficients Across Arbitrary Potential Barriers with High Accuracy

We report a new method for calculating transmission coefficients across arbitrary potential barriers based on the Runge-Kutta method. A numerical solution of the Schrodinger equation is calculated using the Runge-Kutta method,and a new model is established to analyze the numerical results to find the transmission coefficient. This technique is applied to various cases, such as parabolic potential barrier and double-barrier structures. Transmission probability with high precision is obtained and discussed. The tunnelling current density through a MOS structure is also explored and the result coincides with the Fowler-Nordheim model,which indicates the applicability of our method.

Four-dimensional Newton's constant in brane world with a sloping extra dimension

We show the four-dimensional Newton's constant obtained naturally from five-dimensional brane world with a tinily sloping extra dimension, which is independent of the bulk Weyl tensor. The corresponding universe is stiff fluid dominated when the slope of extra dimension is very small. Otherwise, the universe may be undergoing a self-acceleration at present epoch and have a decelerated phase in very recent past.

Study of alpha-, beta- and gamma-cyclodextrin/C-60 supramolecular complexes: Influence of the cavity dimension toward the host-guest complexes

Herein we report the spectroscopic, electrochemical, TEM and DLS characterizations Of C-60 supramolecular inclusion complexes with alpha-, beta- and gamma-cyclodextrins prepared using anionic C-60. The results indicate that the cyclodextrin itself has little effect on the encapsulated C-60 or on the properties of the inclusion complex. Instead, the cyclodextrin has a significant influence on the aggregation behavior of individual complex in aqueous solution, which in turn affects the property of the supramolecular complex of cyclodextrin and C-60 greatly, As the cavity dimension of cyclodextrin becomes smaller as it changes from gamma-CD to beta-CD, and finally to alpha-CD, it is observed that more aggregation occurs for the corresponding inclusion complex in aqueous solution.

A new flow field and its two-dimension model for polymer electrolyte membrane fuel cells (PEMFCs)

A new flow field was designed to search flow fields fitting polymer electrolyte membrane fuel cells (PEMFCs) better due its extensible. There are many independent inlets and outlets in the new flow field. The new flow field we named NINO can extend to be more general when pressures at the inlet and outlet vary and some usual flow fields will be obtained. A new mathematical model whose view angle is obverse is used to describe the flow field.

THE APPLICATION OF AN ULTRAMICROELECTRODE IN HOMOGENEOUS CATALYTIC REACTION .1. GENERAL CHARACTERISTIC OF A HOMOGENEOUS CATALYTIC REACTION AT AN ULTRAMICROELECTRODE WITH ARBITRARY GEOMETRY UNDER STEADY-STATE

A general characteristic of the electrochemical process coupling with a homogeneous catalytic reaction at an ultramicroelectrode under steady state is described. It was found that the electrochemical process coupling with homogeneous catalytic reaction has a similar steady state voltammetric wave at an ultramicroelectrode with arbitrary geometry. A method of determination for the kinetic constant of homogeneous catalytic reaction at an ultramicroelectrode with arbitrary geometry is proposed.

Dielectric responses of anisotropic graded granular composites having arbitrary inclusion shapes

The transformation field method (TFM) originated from Eshelby's transformation field theory is developed to estimate the effective permittivity of an anisotropic graded granular composite having inclusions of arbitrary shape and arbitrary anisotropic grading profile. The complicated boundary-value problem of the anisotropic graded composite is solved by introducing an appropriate transformation field within the whole composite region. As an example, the effective dielectric response for an anisotropic graded composite with inclusions having arbitrary geometrical shape and arbitrary grading profile is formulated. The validity of TFM is tested by comparing our results with the exact solution of an isotropic graded composite having inclusions with a power-law dielectric grading profile and good agreement is achieved in the dilute limit. Furthermore, it is found that the inclusion shape and the parameters of the grading profile can have profound effect on the effective permittivity at high concentrations of the inclusions. It is pointed out that TFM used in this paper can be further extended to investigate the effective elastic, thermal, and electroelastic properties of anisotropic graded granular composite materials.

Transformation field method for calculating the effective properties of isotropic graded composites having arbitrary shapes

A method of transformation field is developed to estimate the effective properties of graded composites whose inclusions have arbitrary shapes and gradient profiles by means of a periodic cell model. The boundary-value problem of graded composites having arbitrary inclusion shapes is solved by introducing the transformation field into the inclusion region. As an example, the effective dielectric response of isotropic graded composites having arbitrary shapes and gradient profiles is handled by the transformation field method (TFM). Moreover, TFM results are validated by the exact solutions of isotropic graded spherical inclusions having a power-law profile and good agreement is obtained in the dilute limit. Furthermore, it is found that the inclusion shapes and the parameters of the gradient profiles can have profound effect on the effective properties of composite systems at high concentration of inclusions.