对吴震东公式中引入截面形状修正系数P的分析和讨论(上)

针对国内若干文献[2 ,3] 对吴震东公式引入“断面形状系数P”发表了不同看法和意见 ,认真研究并分析了湖南大学及新疆建筑科学研究所分别为验证吴震东公式与Б г Cкрамтаева公式计算精度所做的试验 ,从理论上严格论述了“断面形状系数P”是人为虚构的 ,用来对吴震东公式进行修正是错误的。同时指出 :“吴震东公式来源于广义蓄热微分方程严格完整的数学与析解 ,而分析解是不能修正的”

Error Analysis on Corrector Formula for Rectangular Rule

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.

Darboux Transformation for Tzitzeica Equation

We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem.The explicit solution of Tzitzeica equation is obtained,

Characterizations of Orthogonal Vector-valued Multivariate Wavelet Packets

In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.

Several Properties of p-w-hyponormal Operators

In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.

Some Remarks on an Integral Inequality

Given two positive constants α and β, we prove that the integral inequality ∫_0^1f^α＋β（x）dx≥∫_0^1∫^α（x）x^β dx holds for all non-negative valued continuous functions ∫ satisfying ∫_x^1f（t）dt≥∫_x^1tdt for x∈[0,1] if and only if α＋β≥1.This solves an open problem proposed recently by Ngo, Thang, Dat, and Tuan.

On the Acceleration Problem of q-Bernstein Polynomials

In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn（f, q; x） to B∞ （f, q; x） but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.

Some Results on Position Restriction Scheduling Problems

In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj = 1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.

Approximate Solutions of Perturbed Nonlinear Schroedinger Equations

By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.

P-kernel Normal Systems in Weakly P-inversive Semigroups

In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.

An Explicit Backlund Transformation of Burgers Equation with Applications

In this paper, an explicit Bgcklund transformation （BT） of the Burgers equation is obtained by using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669]. Based on the BT and some newly obtained seed solutions, infinite sequences of exact solutions for the Burgers equation are generated. Further more, this BT of the Burgers equation is applied to solve the variant Boussinesq equations and the approximate equations of long water wave.

Study Fields Optimalization within the Programme Applied Mathematics

The integration of the Czech Republic into the process of European space university education formation makes many demands on the higher education system--from creating new legislation and educational conception to changes in the study programme structure. With regard to the study programme structure, permeability and modular construction of the programme and the actual European Credit Transfer and Accumulation System （ECTS） implementation are some of requirements coming to the fore. The aim of this work is to present an analysis of bachelor study programme Applied Mathematics Structure at the University of Ostrava within the context of the above mentioned requirements.

Mathematical analysis of physicochemical phenomena in the catalyst during hydrogenating depolymerization of coal extract benzene insoluble fraction

Efficiency and selectivity of hydrogenating depolymerization of the coal extract benzene-insoluble part over the heterogeneous Co–Mo/Al2O3 catalyst were assessed using a mathematical model. The analytical equations of the mathematical model were generated based on material balance incorporating the physico-chemical phenomena(reaction and diffusion) both in the autoclave and the catalyst grain. The equations offer the possibility for predicting changes of the reactants in the autoclave during the process and for determining the distribution of reactant concentrations in the grain as a function of its radius. The analytical equations of the model serve as the basis of the algorithm for assessing the influence of restrictive diffusion on the effectiveness and selectivity of the catalyst, and also for defining the optimal radii of the catalyst's pores to enable free transport of reactants in the grain interior.

An Approach for Solving Short-Wave Models for Camassa-Holm Equation and Degasperis-Procesi Equation

In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.

Data Envelopment Analysis in Estimation of Technical Efficiency Change of Regional Agriculture Production EU, 1989-2007

Assessment of production efficiency in economic activity is a major issue focused on by economists since the middle of the 20th century. One of the methods suitable in this respect is data envelopment analysis （DEA） facilitating the estimation of technical efficiency based on results obtained by a specified set of producers. Dynamics of changes in efficiency in agricultural production may be assessed on the basis of time series of several years. In the study, one of the variants of DEA was applied to economic results recorded in the years 1989-2007 by average farms representing selected regions of the European Union. The resulting individual dynamics of technical efficiency changes were divided into four homogeneous groups to facilitate identification of differences in production technology. These differences were then explained by classical analysis of basic factors use in agricultural production.

Solvability Results on a Set-valued Input-output Equation

A class of set-valued Leontief input-output equation is introduced and two solvability theorems are obtained, which provide some corresponding existence, surjection as well as continuity results.

Analytical and numerical solutions for shear mechanical behaviors of structural plane

The original descriptive model of shear stress and shear displacement only reflects the stress deformation characteristics of plastic structural plane.The index model was revised and piecewise index model was built to describe the stress deformation characteristics of plastic structural plane and brittle structural plane.The relation of stress and strain to the failure mode of structural plane considering the effect of its shape was investigated,and a model which could reflect the relation between undulate angle and shear strength was built.The result indicates that structural plane presents nonlinear characteristics,specifically,the value of undulate angle,as well as corresponding shear strength,becomes larger as the normal stress decreases.

Automatic Analysis Reporting for Hydro-Chemical Data Using Updated DurovPwin Program

Graphical representation of groundwater major dissolved constituents greatly help researchers in understanding the hydro-chemical evolution, grouping and areal distribution. Durov diagram is one of the most widely used technique but it requires a lot of tedious calculations. The DurovPlot program, which is used to plot the expanded Durov diagram as a graphical representation of groundwater major dissolved constituents is working on Disk Operating System （DOS） environment. Therefore, the need of a new program working under windows is a must. The program termed as DurovPwinis developed using Microsoft visual studio 2010. The DurovPwin program not only calculates the Durov coordinates and plot it, but also plots the total dissolved solids （TDS） on logarithmic scale and the measure of the activity of hydrogen ion （pH） of the given samples. The updated DurovPwin adds many features such as interface with Microsoft Office package （Word and Excel） to read the input chemical elements and automatically write result interpretation report. The user facility to group wells based on data features is added and the selection of the electric balance tolerance （10% as default） value is given. Another feature of the modified DurovPwinis has the ability to do useful X-Y plot for different hydro-chemical parameters to assist in data interpretation. The sodium adsorption ratio （SAR） is also calculated and written in the final report. Also, in the present study, the usability of the new version of DurovPwin program has been tested on the chemical data from 59 groundwater samples collected from A1-Jawf area, Saudi Arabia. The collected water samples were mainly from the Secondary-Tertiary-Quaternary （STQ） aquifer and some from Tawil and Jaufaquifers. The grouping of the major ions in the three aquifers have been displayed and presented using the DurovPwin program. The TDS values of Tawil aquifer ranges from 257.9 to 822.3 （2.4115 to 2.915） and for Jawf aquifer from 494.4 to 1,070 （2.6941 to 3.0294） and for STQ aquifer ranges from 399.5 to 9,861.8 （2.6015 to 3.994）. The pH for the three aquifers ranges from 7 to 7.9, 7.6 to 7.8 and 7.2 to 8.3, respectively.

Exact Solutions for the Generalized KdV Equation： Modified Homogeneous Balance Method

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.