The Robin Problem for Singular Perturbed Integral Differential Equations of Volterra Type

In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.

A new method for integration of a Birkhoffian system

The idea of the gradient method for integrating the dynamical equations of a nonconservative system presented by Vujanovic is transplanted to a Birkhoffian system, which is a new method for the integration of Birkhoff＇s equations. First, the differential equations of motion of the Birkhoffian system are written out. Secondly, 2n Birkhoff＇s variables are divided into two parts, and assume that a part of the variables is the functions of the remaining part of the variables and time. Thereby, the basic quasi-linear partial differential equations are established. If a complete solution of the basic partial differential equations is sought out, the solution of the problem is given by a set of algebraic equations. Since one can choose n arbitrary Birkhoff＇s variables as the functions of n remains of variables and time in a specific problem, the method has flexibility. The major difficulty of this method lies in finding a complete solution of the basic partial differential equation. Once one finds the complete solution, the motion of the systems can be obtained without doing further integration. Finally, two examples are given to illustrate the application of the results.

Mathematical model for precursor gas residence time in isothermal CVD process of C/C composites

In the chemical vapor deposition（CVD） process of C/C composites,the dynamics and mechanism of precursor gas flowing behavior were analyzed mathematically,in which the precursor gas was infiltrated by the pressure difference of the gas flowing through felt.Differential equations were educed which characterized the relations among the pressure inside the felt,the pressure outside the felt of the precursor gas and the porosity of the felt as a function of CVD duration.The gas residence time during the infiltration process through the felt was obtained from the differential equations.The numerical verification is in good agreement with the practical process,indicating the good reliability of the current mathematical model.

f算子的某些性质

本文研究下列算子:f′((φ)(x))=f(x,(φ)(x))的一些性质。

The Integrable Conditions of Riccati Differential Equation

In this paper,the new integrable conditions of Riccati equation is presented by invarant of Riccati equation.

Structural dynamic responses analysis applying differential quadrature method

Unconditionally stable higher-order accurate time step integration algorithms based on the differential quadrature method (DQM) for second-order initial value problems were applied and the quadrature rules of DQM, computing of the weighting coefficients and choices of sampling grid points were discussed. Some numerical examples dealing with the heat transfer problem, the second-order differential equation of imposed vibration of linear single-degree-of-freedom systems and double-degree-of-freedom systems, the nonlinear move differential equation and a beam forced by a changing load were computed, respectively. The results indicated that the algorithm can produce highly accurate solutions with minimal time consumption, and that the system total energy can remain conservative in the numerical computation.

Computation of one—dimensional consolidation of double layered ground using differential quadrature method

The authors give the solution to the problem of one-dimensional conso l idation of double-layered ground with the use of the differential quadrature me t hod. Case studies showed that the computational results for pore-water pressure in soil layer agreed with those of analytical solution; and that in the computat ional results for the interface of soil layer also agreed with those of the anal ytical solution except for the small discrepancies during shortly after the star t of computation. The advantages of the solution presented in this paper are tha t compared with the analytical solution, it avoids the cumbersome work in solvin g the transcendental equation for eigenvalues, and in the case of the Laplace transform s olution, it can resolve the precision problem in the numerical solution of long time inverse Laplace transform. Because of the matrix form of the solution in th is paper, it is convenient for formulating computational program for engineering practice. The formulas for calculating double-layered ground consolidation may be easily extended to the case of multi-layered soils.

The Most Probable Mechanism Function and Kinetic Parameters of Gibbsite Dissolution in NaOH

Determination of probable mechanism function and kinetic parameters is important to hydrometallurgical kinetics.In this work,the most probable mechanism function and kinetic parameters of gibbsite dissolution in NaOH solution are studied.The sample,the mixture of synthetic gibbsite and sodium hydroxide solution,was scanned in high-pressure differential scanning calorimetry(DSC) equipment with the heating rate of 10 K·min-1. Integral equation and differential equation of non-isothermal kinetics were solved to fit the data related to DSC curve.According to the calculation results,the most probable mechanism function for pure synthetic gibbsite dissolution in sodium hydroxide solution is presented based on the optimum procedure in the database of the mechanism function.The apparent activation energy obtained is(75±1) kJ·mol-1,the frequency factor is 10 8±1mol·s-1,and the reaction is a second order reaction.

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.

The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

Parametric analysis of mixed lubrication characteristics in work zone of strip rolling

A theoretical model for mixed lubrication with more accurate contact length has been developed based on the average volume flow model and asperity flattening model,and the lubricant volume flow rate and outlet speed ratio are determined by integrating differential equations based on rolling parameters.The lubrication characteristics at the roll-strip interface with different surface roughness,rolling speed,reduction and lubricant viscosity are analyzed respectively.Additionally,the average volume flow rates of lubricant under different rolling conditions are calculated and used to explain the change rule of lubrication characteristics.The developed scheme is able to determine the total pressure,lubricant pressure,film thickness and real contact area at any point within the work zone.The prediction and analysis of mixed lubrication characteristics at the interface is meaningful to better control the surface quality and optimize the rolling process.

Existence of Positive Solution to a Singular System of Nonlinear Fractional Differential Equation

In this paper,we discuss a singular system of nonlinear fractional differential equation,in which the inhomogeneous term depends on the fractional derivative of lower order.By using the Krasnoselskii＇s fixed point theorem and the Leray-Schauder nonlinear alternative method,some suffcient conditions for the existence of positive solution of the singular system are obtained.

Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.

Oscillation Criteria Related to Integral Averaging Technique for Quasilinear Elliptic Equations

Sufficient conditions are obtained for oscillation of certain quasilinear elliptic equations div(｜Du｜m-2A（x）Du)+p（x）｜u｜m-2u=0, x∈ΩRn, where Ω is an exterior domain, m>1, and p（x） is an alternating function. The integral averaging technique is employed to establish our results.

Stability of Linear Integrodifferential Systems with Time-varied Confficients with Large Scale

In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated method. A group of sufficient conditions are given to guarantee asymptotic stability of zero solutions of systems.

Application of Fractional Calculus to a Linear Third Order (Nonhomogeneous and Homogeneous) Ordinary Differential Equation

In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.

A Finite Volume Backward Euler Difference Method for Nonlinear Parabolic Integral-differential Equation

The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.

CAUCHY PROBLEM FOR A NONLINEAR SINGULAR INTEGRAL－DIFFERENTIAL EVOLUTION SYSTEM

We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.

Vector Product and an Integrable Dynamical System

We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.

A COMPUTER-AIDED UNIFIED APPROACH TO MODELING PWM AND RESONANT CONVERTERS

This letter puts forward a method of modeling for the steady-state and small signal dynamic analysis on PWM, quasi-resonant and series/(parallel) resonant switching converters based on pulse-waveform integral approach. As an example, PWM and quasi-resonant converters are used to discuss the principle of the approach. The results are compared with those in the relative literatures. Computer aided analysis are made to confirm the correctness.