KIRCHHOFF FORMULA WITH LINE INTEGRAL FORM AND ITS APPLICATIONS

In this paper, Kirchhoff formula has been transformed from surface integral form into a line integral form. The new form of the formula can be applied to separate geometrical optical field from diffraction field, and reduce the time of numerical computation greatly. Based on the new form, an analytical formula of diffraction field in the far zone has been presented for the polygonal aperture illuminated by a uniform plane wave.

Analytic Expression of Meso-Criterion on Dynamic Fracture

This study presents a meso-criterion of dynamic fracture, on the basis of stress in integral form In such way the difficulty due to the singularity of stress distribution at the crack tip is overcome. A micro-parameter, the atom radius, is introduced into the criterion.Meanwhile a characteristic time concept is taken into account for describing the inertia effect of material. The criterion reveals The criterion reveals the effects of loading rate, defect and sample geometry,material constants including the micro-structure parameter.

New Majorized Results on Hilbert's Integral Inequality

In this paper, some new majorized results on Hilbert’s integral inequality are showed.

远程开放教育网络学习平台动力机制刍议

本文通过对目前网络学习平台的动力机制进行分析 ,阐述网络学习平台动力机制的创设和实施。议述了网络学习平台必须注重“自主学习、兴趣激励、评价与监控”的教育动力机制及“积分式网络教学管理机制的创设 。

A Note on HilbertsIntegral Inequalities

In this note,by introudcing a couple of parameters T,t and estimating the weight function effectively,Hilberts integral inequalities are well generalized. As applications,we give some new Hilbers type inequalities.

Operator Fredholm Integration Equation in Intermediate Coordinate-Momentum Representation and Its Analogue to Thermo Conduction Equation

Using the technique of integration within an ordered product （IWOP） of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation that is an operator generalization of the solution of thermo conduction equation. Then we seach for the solution of operator Fredholm integration equations, which provides us with a new approach for deriving some operator identities.

Covariant Prolongation Structure of Konno-Asai-Kakuhata Equation

Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtain the inverse scattering equations given by Konno et al. and the corresponding Riccati equation. The Baecklund transformations are also presented.

Exact Traveling Wave Solutions for a Kind of Generalized Ginzburg-Landau Equation

Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.

Debris Flow Formation Process and Critical Hydrodynamic Conditions in the Meizoseismal Area of the Wenchuan Earthquake

Abstract： The Wenchuan earthquake generated strong surface disturbances and triggered a large number of loose deposits, resulting in the disaster- prone environment with special watershed hydrological characteristics. This paper was to propose a debris flow formation process and explore the permeability characteristics and critical hydrodynamic conditions of the loose deposits triggered by the earthquake. The Guo Juanyan gully （31005＇27＂ N to 31005＇46＂ N, 103036＇58＂ E to 103037＇09＂ E） in Du Jiangyan City, located in the meizoseismal areas of the Wenchuan earthquake, was chosen as the study area and the disaster-prone environment was analyzed. The formation process of the debris flow was first proposed using a stability analysis, and then, the permeability characteristics of loose deposits were determined via in situ permeability experiments. Finally, the critical 1 h rainfall was simulated through a distributed hydrological model and verified by field observations. The formation process of debris flow could be divided into three stages based on the relationship between the hydrodynamic force and loose deposit resistance. The critical 1 h rainfall amounts under three antecedent moisture conditions （I-dry, Ⅱ-normal and Ⅲ-wet） were 52 mm/h, 43 mm/h and 34 mm/h, respectively. This study proposed a debris flow formation process in the meizoseismal areas of the Wenchuan earthquake based on the stability analysis and defined the rainfall threshold for debris flow early warning at the local level, which is significant for debris flow mitigation and risk management.

Application of Eigenkets of Bosonic Creation Operator in Deriving Some New Formulas of Associated Laguerre Polynomials

Using the resolution of unity composed of bosonic creation operator＇s eigenkets and annihilation operator＇s un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L^ρm （｜z｜^2） and its generalized generating function formula. A series of recursive relations regarding to L^ρm （｜z｜^2） are also deduced in the context of the Fock representation by algebraic method.

New Route to Deducing Integration Formulas by Virtue of the IWOP Techniqu~

We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.

Operator Methods in High Order Partial Differential Equation

For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.

3D Modeling and Born approximation inversion for the borehole surface electromagnetic method

We present a 3D approach to numerical modeling of the borehole-surface electromagnetic （BSEM） method. The 3D electromagnetic response created by a vertical line current source in a layered medium is modeled using the 3D integral equation method. The modeling results are consistent with analytical solutions. 3D Born approximation inversion of BSEM data is also conducted for reservoir delineation. The inversion method is verified by a synthetic reservoir model.

A NEW SINGULARITY EXTRACTION TECHNIQUE FOR TDEFIE

A new singularity extraction technique is presented to calculate accurately the singular integrals in Time Domain Electric Field Integral Equation (TDEFIE).In singularity extraction pro- cedure,through the aid of the first order Taylor series of time base function including time-retardation,the singularity of the integrand can be removed.The surface current density and backscattered far-field response of a conducting cube illuminated by a Gaussian plane wave is com- puted using the presented technique.Comparisons are made with the results obtained by the Inverse Discrete Fourier Transform (IDFT) of the frequency domain and the results obtained by using Ve- chinski's time averaging technique,which demonstrate that the presented method with this new time domain singularity extraction technique to solve TDEFIE is very accurate and stable.

On exponential stability for systems with state delays

This paper considers the issue of delay-dependent exponential stability for time-delay systems. Both nominal and uncertain systems are investigated. New sufficient conditions in terms of linear matrix inequalities(LMIs) are obtained. These criteria are simple owing to the use of an integral inequality. The model transformation approaches,bounding techniques for cross terms and slack matrices are all avoided in the derivation. Rigorous proof and numerical examples showed that the proposed criteria and those based on introducing slack matrices are equivalent.

European Option Pricing under a Class of Fractional Market

In order to price European contingent claim in a class of fractional Black-Scholes market, where the prices of assets follow a Wick-Ito stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions, the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of tile fractional Brownian motion. A result about fractional Clark derivative was also obtained.

VOICE ACTIVITY DETECTION UNDER RAYLEIGH DISTRIBUTION

This paper presents an improved Voice Activity Detection （VAD） algorithm which uses the Signal-to-Noise Ratio （SNR） measure. We assume that noise Power Spectral Density （PSD） in each spectral bin follows a Rayleigh distribution. Rayleigh distributions with its asymmetric tail characteristics give a better description of the noise PSD distribution than Gaussian distribution. Under this asstlmption, a new threshold updating expression is derived. Since the analytical integral of the false alarm probability, the threshold updating expression can be represented without the inverse complementary error function and low computational complexity is achieved in our system. Experimental results show that the proposed VAD outperforms or at least is comparable with the VAD scheme presented by Davis under several noise environments and has a lower computational complexity.

Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.

On Quantum Mechanical Hankel Transform and Its Applications

Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.

Integrating Automatic Patch Snatching System by the Concept of Generalized Mechanisms

An automatic patch snatching system is described which has three machine cells including dividing equipment, tackling equipment and patch removing equipment. The electromechanical integration design of in-piece tackling system based on the concept of generalized mechanisms is introduced. The design of the dividing equipment, the design of micro-feeding machine equipped with micro-level pressure sensor, and the realizing of computer path for patch snatching are investigated.