A simple method to construct soliton-like solution of the general KdV equation with external force

A simple and direct method is described to construct the soliton-like solution for the general KdV equation with external force. Crucial to the method is the assumption that the solution chosen is a special truncated expansion.     

n次单位根在代数问题中的应用

主要论述n次单位根在一些组合数求和、多项式的整除、因式分解中的应用,说明了n次单位根法可拓宽解题思路,是一种方便、快捷的数学解题方法.     

Exact Equilibrium Solutions for Linearly Elastic Plate-Like Bodies

A three-dimensional, explicit and exact, equilibrium solution is derived for transversely isotropic, linearly elastic bodies in the form of a right cylinder simply supported over its lateral boundary and loaded over its end faces. This solution, which generalizes an earlier proposal of Levinson in various respects, is to serve as a benchmark for the corresponding plate theories. This revised version was published online in August 2006 with corrections to the Cover Date.     

A successive quadratic programming algorithm with global and superlinear convergence properties

This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.This work was supported in part by a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan.     

An everywhere convergent series representation of the distribution of Hotelling's generalized T0

A new series representation of the exact distribution of Hotelling's generalized T₀² statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the non-central distributions. Earlier results by [1], 215–225), which are convergent on the interval [0, 1), are also derived quite simply from our formulae. The paper therefore provides a solution to the long standing problem of the exact distribution of the T₀² statistic in the general case.     

New Exact Solutions of the N-Coupled Nonlinear Schroedinger System

In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger （NLS） system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions.     

Second Order Efficient Estimating a Smooth Distribution Function and its Applications

Methodology and Computing in Applied Probability - Consider a problem of estimation of a cumulative distribution function of a random variable supported on a finite interval, with a circular random...     

广度kdv方程的精确解:改进的齐次平衡法

In this paper,we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method.Based on the modified homogeneous balance method,several kinds of exact(new)solutions of the generalized KdV equation are obtained.     

A note on the second problem of Stokes for Maxwell fluids

New exact solutions corresponding to the second problem of Stokes for Maxwell fluids have been established by means of Laplace transforms. For large times, these solutions reduce to the well-known steady-state solutions which are periodic in time and independent of the initial conditions. Furthermore, the transient solutions are in accordance with the previous solutions obtained using the Fourier sine transform. The required time to get the steady-state is determined by graphical illustrations. This time decreases if the frequency of the velocity increases. The effects of the material parameters on the decay of the transients in time are also investigated by graphs.     

Exact Recovery of Stochastic Block Model by Ising Model

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.