Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions

The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.

Adsorption behaviors and mechanisms of gold recovery from thiosulfate solution by ion exchange resin

The adsorption behaviors and mechanisms of gold from thiosulfate solution on strong-base anion exchange resin were systematically investigated.The comparison experiment of adsorption ability and selectivity for gold showed that gel Amberlite IRA-400 resin with Type Ⅰ quaternary ammonium functional group had better adsorption performance.The increases of resin dosage,ammonia concentration and solution pH were favorable to gold adsorption,whereas the rises of cupric and thiosulfate concentrations were disadvantageous to gold loading.Microscopic characterization results indicated that gold was adsorbed in the form of [Au(S_(2)O_(3))_(2)]^(3–) complex anion by exchanging with the counter ion Cl^(–) in the functional group of the resin.Density functional theory calculation result manifested that gold adsorption was mainly depended on the hydrogen bond and van der Waals force generated between O atom in [Au(S_(2)O_(3))_(2)]^(3–) and H atom in the quaternary ammonium functional group of the resin.

Exact Travelling Wave Solutions of Two Nonlinear Schrödinger Equations by Using Two Methods

The special kind of (G’/G)-expansion method and the new mapping method are easy and significant mathematical methods. In this paper, exact travelling wave solutions of the higher order dispersive Cubic-quintic nonlinear Schrödinger equation and the generalized nonlinear Schrödinger equation are studied by using the two methods. Finally, the solitary wave solutions, singular soliton solutions, bright and dark soliton solutions and periodic solutions of the two nonlinear Schrödinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations.

New Complex Solutions of the Coupled KdV Equations

In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.

Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind

Integral equations theoretical parts and applications have been studied and investigated in previous works. In this work, results on investigations of the uniqueness of the Fredholm-Stiltjes linear integral equations solutions of the third kind were considered. Volterra integral equations of the first and third kind with smooth kernels were studied, and proof of the existence of a multiparameter family of solutions is described. Additionally, linear Fredholm integral equations of the first kind were investigated, for which Lavrent’ev regularizing operators were constructed.

Some Kinds of New Composite Solutions of a Kind of Coupled Schrodinger Equation

With the help of the method that combines the first kind of elliptic equation with the function transformation, some kinds of new composite solutions of a kind of coupled Schr?dinger equation are constructed. First, a kind of function transformation is presented, and then the problem of solving solutions of a kind of coupled Schr?dinger equation can be changed to the problem of solving solutions of the first kind of elliptic equation. Then, with the help of the conclusions of the B?cklund transformation and so on of the first kind of elliptic equation, the new infinite sequence composite solutions of a kind of coupled Schr?dinger equation are constructed. These solutions are consisting of two-soliton solutions and two-period solutions and so on.

Calculation of thermodynamic properties in liquid phase for ternary Al-Ni-Zn alloys

The results of the calculation of thermodynamic properties in liquid state for ternary Al-Ni-Zn alloys using the newest version of the general solution model for thermodynamic prediction are presented. Nine sections with different molar ratios of Ni to Zn, Zn to Al and Al to Ni were investigated in a temperature interval of 1800-2000 K. Partial and integral molar thermodynamic properties in liquid phase for the Al-Ni-Zn ternary system are determined and discussed.

Infinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation

To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.

Calculation of Phase Equilibria Based on the Levenberg-Marquardt Method

The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of nonlinear equations, is applied to calculate the stable phase equilibria. It can get the best combination between robustness and speed of the calculations. Its application to ternary AI-Si-Mg system is executed in detail. The calculated phase equilibria agree well with the experimental results. Furthermore, the Levenberg-Marquardt method is not sensitive to the initial values.

Constructing infinite sequence exact solutions of nonlinear evolution equations

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.

Hydrogen storage properties of magnesium hydride catalyzed by Ni-based solid solutions

The Ni−25%X(X=Fe,Co,Cu,molar fraction)solid solutions were prepared and then doped into MgH_(2) through high-energy ball milling.The initial dehydrogenation temperatures of MgH_(2)/Ni−25%X composites are all decreased by about 90℃relative to the as-milled pristine MgH_(2).The Ni−25%Co solid solution exhibits the most excellent catalytic effect,and the milled MgH_(2)/Ni−25%Co composite can release 5.19 wt.%hydrogen within 10 min at 300℃,while the as-milled pristine MgH_(2) can only release 1.78 wt.%hydrogen.More importantly,the dehydrogenated MgH_(2)/Ni−25%Co composite can absorb 5.39 wt.%hydrogen at 275℃within 3 min.The superior hydrogen sorption kinetics of MgH_(2)/Ni−25%Co can be ascribed to the actual catalytic effect of in-situ formed Mg_(2)Ni(Co)compounds.First-principles calculations show that the hydrogen absorption/desorption energy barriers of Mg/MgH_(2) systems decrease significantly after doping with transition metal atoms,which interprets well the improved hydrogen sorption properties of MgH_(2) catalyzed by Ni-based solid solutions.

Traveling Wave Solutions and Kind Wave Excitations for the (2 + 1)-Dimensional Dissipative Zabolotskaya-Khokhlov Equation

In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation (DZK) is derived. Based on the derived solitary wave solution, some novel kind wave excitations are investigated.

Thermodynamic Equilibrium of the Saturated Fluid with a Free Surface Area and the Internal Energy as a Function of the Phase-Specific Volumes and Vapor Pressure

This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.

Construction of Periodic Solutions of One Class Nonautonomous Systems of Differential Equations

In this article we proposed a method for constructing approximations to periodic solutions of one class nonautonomous system of ordinary differential equations. It is based on successive approximation scheme using parallel symbolic calculations to obtain solutions in analytical form. We showed the convergence of the scheme of successive approximations on the period, and also considered an example of a second order system where the described scheme of calculations can be applied.

Density Functional Theory and Electrochemistry Studies on LiFexMn1-xPO4 Solid Solutions

The thermodynamic stability and lithiated/delithiated potentials of LiFexMn1-xPO4 were studied with density functional theorical calculations. The results show that the formation free energy of the LiFexMn1-xPO4 solid solution is slightly higher than that of the phase-separated mixture of LiFePO4 and LiMnPO4, and the two forms may co-exist in the actual LiFexMn1-xPO4 materials. The calculation manifests that the lithiated/delithiated potentials of LiFexMn1-xPO4 solid solutions vary via the Mn/Fe ratio and the spatial arrangements of the transition metal ions, and the result is used to explain the shape of capacity-voltage curves. Experimentally, we have synthesized the LiFexMn1-xPO4 materials by solid-phase reaction method. The existence of the LiFexMn1-xPO4 solid solution is thought to be responsible for the appearance of additional capacity-voltage plateau observed in the experiment.

REGULARIZATION METHOD FOR IMPROVING OPTIMAL CONVERGENCE RATE OF THE REGULARIZED SOLUTION OF ILL-POSED PROBLEMS

This paper presents anew regularization method for solving operator equations of the first kind; the convergence rate of the regularized solution is improved, as compared with the ordinary Tikhonov regularization.

基于全概率公式的M-APSK误码率分析模型

为有效评估加性白高斯噪声信道中M-APSK的性能,提出了一种基于全概率公式的理论误码率分析模型。首先根据星座点分布及其编码特点对星座平面进行区域划分,然后由接收符号落在相应区域的概率推导出各比特的判决错误概率表达式,最后得到理论误码率的精确闭式解。以16APSK和32APSK为例,推导出了其各类星座图的理论误码率计算公式,与Monte Carlo仿真结果非常吻合。模型具有通用性,PSK、QAM、PAM、APSK等调制方式均可利用该模型得到理论误码率的精确闭式解。相较于依赖大量数值计算的复杂二维概率积分方法,所提模型能够更方便地给出M-APSK的误码率性能。

基于能流耦合机理的热电耦合综合能源系统潮流分析及对比

热电耦合综合能源系统对提高能源利用率、实现可持续发展具有重要意义,潮流计算作为研究稳态热电耦合综合能源系统的常用方法,能够计算出系统网络的能流分布,为后续的规划、运行、调度提供数据基础。该文基于热电耦合规律,考虑热力系统中回水热损失改进了传统热力系统模型,并结合电力系统模型组成了热电耦合综合能源系统潮流计算模型。在此基础上研究了统一求解法与分立求解法两种潮流计算方法。建立算例系统,分别采用分立求解法与统一求解法进行潮流计算,并对比分析二者的计算性能及结果。结果表明:在设定算例系统计算精度为10-2时,统一求解法与分立求解法均可满足热电耦合系统潮流计算要求。系统中电网节点功率满足基尔霍夫定律,热网由于需要工质来承载能量,在流动时产生损失时除单纯的能量损耗外还需考虑工质损失,因此回水总量少于供水总量。系统采用以热定电时,分立求解法总迭代次数为10次,耗时8.48s,统一求解法迭代次数为8次,耗时10.56 s,考虑热网和电网的相互影响时,分立求解法迭代次数和耗时大幅增加,统一求解法基本不变,因此采用以热定电时分立求解法更加简便,在考虑热网和电网的相互影响时,适合使用统一求解法。

拓展高原环境的航空炸弹弹道快速解算方法

为快速、精确地求解高原环境下的航空炸弹弹道,在经典弹道模型的基础上,面向高原环境提出一种基于改进Runge-Kutta的航空无控炸弹弹道解算(improved Runge-Kutta based uncontrolled bombs trajectory calculation,IRK-UBTC)方法。首先,针对炸弹下落过程中时刻变化的环境参数,提出了基于起飞点的空气比重函数估算方法。然后,引入战斗机所处环境的温度、湿度、纬度、科尔奥利力等信息对经典炸弹质心运动微分方程组进行重构。最后,在三阶Runge-Kutta算法的基础上,提出了带误差控制机制的微分方程组实时解算方法。实验结果表明,该方法在1.4 GHz主频的嵌入式计算机中的解算周期小于5 ms,且最大射程误差小于0.2%,能够被有效应用于高原地区航弹弹道的实时解算。

GaN/ZnO固溶体电子结构与光学性质的第一性原理研究

GaN/ZnO固溶体具有良好的光催化活性。为研究不同ZnO物质的量对GaN/ZnO固溶体能带结构和光吸收性能的影响,构建了一系列GaN/ZnO固溶体的随机原子结构模型。基于密度泛函理论计算不同ZnO物质的量对GaN/ZnO固溶体模型电子结构和光学性质的影响。研究结果表明:ZnO/GaN固溶体形成能与结合能均为负值,结构稳定。随着ZnO物质的量的增加,固溶体的带隙先呈现下降趋势,最后呈现小幅上升趋势。对于ZnO物质的量分数在13.89%至22.22%的GaN/ZnO固溶体,可以观察到光吸收峰强度在可见光区各个波长范围内均有较强吸收。通过研究不同ZnO物质的量对GaN/ZnO固溶体能带结构和光吸收性能的影响,为GaN/ZnO固溶体光催化材料的设计与制备提供了理论参考。