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Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Spectral Method 量子化学中线性常微分方程的谱解法数值解
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2012-03-21 DOI: 10.5772/34790
M. Saravi, S. Mirrajei
{"title":"Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Spectral Method","authors":"M. Saravi, S. Mirrajei","doi":"10.5772/34790","DOIUrl":"https://doi.org/10.5772/34790","url":null,"abstract":"The problem of the structure of hydrogen atom is the most important problem in the field of atomic and molecular structure. Bahr’s treatment of the hydrogen atom marked the beginning of the old quantum theory of atomic structure, and wave mechanics had its inception in Schrodinger ‘s first paper, in which he gave the solution of the wave equation for the hydrogen atom. Since the most differential equations concerning physical phenomenon could not be solved by analytical method hence, the solutions of the wave equation are based on polynomial (series) methods. Even if we use series method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., 砿嫗嫗 + 岫に兼継h貸態 − 糠態捲態岻砿 = ど,","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"248 1","pages":"57-60"},"PeriodicalIF":0.0,"publicationDate":"2012-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76989088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
The Influence Of The Inlet Conditions On The Airside Heat Transfer Performance Of Plain Finned Evaporator 进口条件对平板翅片蒸发器空侧换热性能的影响
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2011-11-23 DOI: 10.5281/ZENODO.1085568
Abdenour Bourabaa, M. Saighi, I. Belal
{"title":"The Influence Of The Inlet Conditions On The Airside Heat Transfer Performance Of Plain Finned Evaporator","authors":"Abdenour Bourabaa, M. Saighi, I. Belal","doi":"10.5281/ZENODO.1085568","DOIUrl":"https://doi.org/10.5281/ZENODO.1085568","url":null,"abstract":"A numerical study has been conducted to investigate the influence of fin pitch and relative humidity on the heat transfer performance of the fin-and-tube heat exchangers having plain fin geometry under dehumidifying conditions. The analysis is done using the ratio between the heat transfer coefficients in totally wet conditions and those in totally dry conditions using the appropriate correlations for both dry and wet conditions. For a constant relative humidity, it is found that the heat transfer coefficient increases with the increase of the air frontal velocity. By contrast, the fin efficiency decreases when the face velocity is increased. Apparently, this phenomenon is attributed to the path of condensate drainage. For the influence of relative humidity, the results showed an increase in heat transfer performance and a decrease in wet fin efficiency when relative humidity increases. This is due to the higher amount of mass transfer encountered at higher relative humidity. However, it is found that the effect of fin pitch on the heat transfer performance depends strongly on the face velocity. At lower frontal velocity the heat transfer increases with fin pitch. Conversely, an increase in fin pitch gives lower heat transfer coefficients when air velocity is increased.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":" 22","pages":"1667-1670"},"PeriodicalIF":0.0,"publicationDate":"2011-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91414603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Polarization Modulation by free-Standing Asymmetric Hole Arrays 独立非对称孔阵列的偏振调制
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2011-10-28 DOI: 10.5281/ZENODO.1057698
Hong-Wen Hsieh, S. Yen
{"title":"Polarization Modulation by free-Standing Asymmetric Hole Arrays","authors":"Hong-Wen Hsieh, S. Yen","doi":"10.5281/ZENODO.1057698","DOIUrl":"https://doi.org/10.5281/ZENODO.1057698","url":null,"abstract":"We theoretically demonstrate modulation of light\u0000polarization by a crossed rectangular hole array with asymmetric arm\u0000lengths. There are two waveguide modes that can modulate the x- and\u0000y- polarized incident waves independently. A specific structure is\u0000proposed to convert a left-hand incident wave to a right-hand outgoing\u0000wave by transmission.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"9 1","pages":"1556-1559"},"PeriodicalIF":0.0,"publicationDate":"2011-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76704634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Marangoni Instability in a Fluid Layer with Insoluble Surfactant 含不溶性表面活性剂的流体层中的马兰戈尼不稳定性
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2011-10-28 DOI: 10.1063/1.4932443
Ainon Syazana Ab Hamid, S. A. Kechil, A. Aziz
{"title":"Marangoni Instability in a Fluid Layer with Insoluble Surfactant","authors":"Ainon Syazana Ab Hamid, S. A. Kechil, A. Aziz","doi":"10.1063/1.4932443","DOIUrl":"https://doi.org/10.1063/1.4932443","url":null,"abstract":"The effect of linear proportional feedback thermal controller on the onset of steady Marangoni instability in a horizontal fluid layer with insoluble surfactants is studied theoretically by using linear stability analysis. The exact analytical solution for the stationary modes is obtained and the effects of elasticity number, thermal controller gain, surface deformation, Galileo number, Lewis number and Biot number on the onset of Marangoni convection are determined.The elasticity number, Biot number, Galileo number and small controller gain are found to have stabilizing effects on the fluid layer but the Lewis number and large controller gain are destabilizing factors. The heat transfer mechanism and the presence of insoluble surfactant at the free surface significantly stabilize the fluid system.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"34 1","pages":"1547-1551"},"PeriodicalIF":0.0,"publicationDate":"2011-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90524219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Model for the Characterization and Selection of Beeswaxes for use as base Substitute Tissue in Photon Teletherapy 用于光子远程治疗的蜂蜡基底替代组织的表征和选择模型
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2011-08-21 DOI: 10.4236/MSA.2012.34032
R. M. Silva, D. Souza
{"title":"A Model for the Characterization and Selection of Beeswaxes for use as base Substitute Tissue in Photon Teletherapy","authors":"R. M. Silva, D. Souza","doi":"10.4236/MSA.2012.34032","DOIUrl":"https://doi.org/10.4236/MSA.2012.34032","url":null,"abstract":"This paper presents a model for the characterization and selection of beeswaxes for use as base substitute tissue for the manufacture of objects suitable for external radiotherapy using megavoltage photon beams. The model of characterization was divided into three distinct stages: 1) verification of aspects related to the origin of the beeswax, the bee species, the flora in the vicinity of the beehives and procedures to detect adulterations; 2) evaluation of physical and chemical properties; and 3) evaluation of beam attenuation capacity. The chemical composition of the beeswax evaluated in this study was similar to other simulators commonly used in radiotherapy. The behavior of the mass attenuation coefficient in the radiotherapy energy range was comparable to other simulators. The proposed model is efficient and enables convenient assessment of the use of any particular beeswax as a base substitute tissue for radiotherapy.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"87 1","pages":"1132-1137"},"PeriodicalIF":0.0,"publicationDate":"2011-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88777688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Existence Of Solutions For A Nonlinear Fractional Differential Equation With Integral Boundary Condition 一类具有积分边界条件的非线性分数阶微分方程解的存在性
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2011-01-20 DOI: 10.5281/ZENODO.1085182
Meng Hu, Lili Wang
{"title":"Existence Of Solutions For A Nonlinear Fractional Differential Equation With Integral Boundary Condition","authors":"Meng Hu, Lili Wang","doi":"10.5281/ZENODO.1085182","DOIUrl":"https://doi.org/10.5281/ZENODO.1085182","url":null,"abstract":"This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"89 1","pages":"55-58"},"PeriodicalIF":0.0,"publicationDate":"2011-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83452427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
A Contractor for the Symmetric Solution Set 对称解集的承包者
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2010-11-22 DOI: 10.5281/ZENODO.1333366
M. Hladík
{"title":"A Contractor for the Symmetric Solution Set","authors":"M. Hladík","doi":"10.5281/ZENODO.1333366","DOIUrl":"https://doi.org/10.5281/ZENODO.1333366","url":null,"abstract":"The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"121 1","pages":"1422-1427"},"PeriodicalIF":0.0,"publicationDate":"2010-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89872383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Three-Dimensional Simulation of Free Electron Laser with Prebunching and Efficiency Enhancement 具有预聚束和增强效率的自由电子激光三维模拟
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2010-09-28 DOI: 10.13140/2.1.2363.8401
M. Chitsazi, B. Maraghechi, M. Rouhani
{"title":"Three-Dimensional Simulation of Free Electron Laser with Prebunching and Efficiency Enhancement","authors":"M. Chitsazi, B. Maraghechi, M. Rouhani","doi":"10.13140/2.1.2363.8401","DOIUrl":"https://doi.org/10.13140/2.1.2363.8401","url":null,"abstract":"Three-dimensional simulation of harmonic up generation in free electron laser amplifier operating simultaneously with a cold and relativistic electron beam is presented in steady-state regime where the slippage of the electromagnetic wave with respect to the electron beam is ignored. By using slowly varying envelope approximation and applying the source-dependent expansion to wave equations, electromagnetic fields are represented in terms of the Hermit Gaussian modes which are well suited for the planar wiggler configuration. The electron dynamics is described by the fully three- dimensional Lorentz force equation in presence of the realistic planar magnetostatic wiggler and electromagnetic fields. A set of coupled nonlinear first-order differential equations is derived and solved numerically. The fundamental and third harmonic radiation of the beam is considered. In addition to uniform beam, prebunched electron beam has also been studied. For this effect of sinusoidal distribution of entry times for the electron beam on the evolution of radiation is compared with uniform distribution. It is shown that prebunching reduces the saturation length substantially. For efficiency enhancement the wiggler is set to decrease linearly when the radiation of the third harmonic saturates. The optimum starting point of tapering and the slope of radiation in the amplitude of wiggler are found by successive run of the code.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"76 1","pages":"1272-1274"},"PeriodicalIF":0.0,"publicationDate":"2010-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86514126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Results on Parallel Alternating Methods 关于并行交替方法的一些结果
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2010-08-28 DOI: 10.0000/IJAMC.2011.3.1.131
Guangbin Wang, F. Tan
{"title":"Some Results on Parallel Alternating Methods","authors":"Guangbin Wang, F. Tan","doi":"10.0000/IJAMC.2011.3.1.131","DOIUrl":"https://doi.org/10.0000/IJAMC.2011.3.1.131","url":null,"abstract":"In this paper, we investigate two parallel alternating methods for solving the system of linear equations Ax = b and give convergence theorems for the parallel alternating methods when the coefficient matrix is a nonsingular H-matrix. Furthermore, we give one example to show our results. Keywords—nonsingular H-matrix, parallel alternating method, convergence.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"20 1","pages":"1070-1072"},"PeriodicalIF":0.0,"publicationDate":"2010-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81147575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Hopf Bifurcation for a New Chaotic System 一类新型混沌系统的Hopf分岔
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2010-08-25 DOI: 10.5281/ZENODO.1071572
Kejun Zhuang
{"title":"Hopf Bifurcation for a New Chaotic System","authors":"Kejun Zhuang","doi":"10.5281/ZENODO.1071572","DOIUrl":"https://doi.org/10.5281/ZENODO.1071572","url":null,"abstract":"In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"1 1","pages":"1094-1097"},"PeriodicalIF":0.0,"publicationDate":"2010-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89819399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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