Journal of Applied Mathematics最新文献

{"title":"Equivalent Finite Element Formulations for the Calculation of Eigenvalues Using Higher-Order Polynomials","authors":"C. Provatidis","doi":"10.5923/J.AM.20110101.02","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.02","url":null,"abstract":"This paper investigates higher-order approximations in order to extract Sturm-Liouville eigenvalues in one-dimensional vibration problems in continuum mechanics. Several alternative global approximations of polynomial form such as Lagrange, Bernstein, Legendre as well as Chebyshev of first and second kind are discussed. In an instructive way, closed form analytical formulas are derived for the stiffness and mass matrices up to the quartic degree. A rigorous proof for the transformation of the matrices, when the basis changes, is given. Also, a theoretical explanation is provided for the fact that all the aforementioned alternative pairs of matrices lead to identical eigenvalues. The theory is sustained by one numerical example under three types of boundary conditions.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250644","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}

{"title":"Exact Elliptic Solution for Non-Linear Klein-Gordon Equation Via Auxiliary Equation Method","authors":"G. Moatimid, M. Moussa, R. El-Shiekh, A. A. El-Satar","doi":"10.5923/J.AM.20120203.02","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.02","url":null,"abstract":"By using symbolic computation, we apply Auxiliary equation method to construct exact solutions of Non-Linear Klein-Gordon equation. We show that Auxiliary equation method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250887","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}

{"title":"Comparison of Linear and Nonlinear Programming Techniques for Animal Diet","authors":"Pratiksha Saxena","doi":"10.5923/J.AM.20110102.17","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.17","url":null,"abstract":"Linear programming techniques have been extensively used for animal diet formulation for more than last fifty years. To overcome the drawback of linear approximation of objective function for diet formulation, a mathematical model based on nonlinear programming technique is proposed to measure animal performance in terms of milk yield and weight gain. At the second step, it compares the result of proposed program with that of linear programming model. Result of proposed model gives better results using nonlinear programming. Thus the study is an attempt to develop a nonlinear programming model for optimal planning and best use of nutrient ingredients. Research on nutrition is under process for more than hundred years. Diet formulation is a process by which different ingredients are combined to provide necessary nutrition to animals at different stages of production. A diet should supply all essential nutrients and energy to maintain vital physiological functions of growth, reproduction and health of animals. Diet should be highly digestible and should have very less adverse environmental effect. A number of methods have been defined for the formulation of animal diet; square method, two by two matrix methods, simultaneous equation method, trial and error method and linear programming method to formulate least cost diet. Linear programming is widely used for this purpose. Diet formulated by linear programming is based on assumption of linearity between animal yield and nutrient ingredients included in the diet. To overcome the assumption of linearity and to include complexity of different nutrient ingredients, a nonlinear model is proposed in this paper to maximize milk yield. This concept of non-linear programming may be used to maximize the weight gain of the animal or animal yields approximately. A combination spreadsheet is represented for ration formulation using linear programming (VandeHaar M. J., Black J. R., 1991). Chance-constrained programming is used to formulate commercial feeds for animals (William B. Roush, Robert H. Stock, Terri L. Cravener and Thomas H. D'Alfonso, 1994). Genetic algorithms are applied for the cost","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251058","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}

{"title":"Squeeze Film Based on Ferrofluid in Curved Porous Circular Plates with Various Porous Structure","authors":"R. Shah, Dilip B. Patel","doi":"10.5923/J.AM.20120204.04","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.04","url":null,"abstract":"This paper theoretically studied the effects of various porous structure on the action of the squeeze film formed when a curved upper plate with porous facing approached an impermeable and flat lower plate using ferrofluid as lubricant. Two porous structures given by Kozeny - Carman( a globular sphere model ) and Irmay ( a capillary fissures model ) are considered for the study. Expressions are obtained for pressure and load capacity under an external magnetic field oblique the lower plate. It is found that the load capacity is increased in both the cases with the increase of magnetization. It is also found that the load capacity increased substantially in the case of concave plates and in the case of porous structure given by Kozeny - Carman. The load capacity is more for the porous structure given by Kozeny – Carman.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251629","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}

{"title":"Analysis of Mechanical Behavior of Red Cell Membrane in Sickle Cell Disease","authors":"D. Fisseha, V. K. Katiyar","doi":"10.5923/J.AM.20120202.08","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.08","url":null,"abstract":"Sickle cell disease (SCD) is a disease of abnormal rheology. The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In SCD, the intracellular polymerization of sickle he- moglobin upon deoxygnation leads to marked increase in intracellular viscosity and elastic stiffness and also having indirect effects on cell membrane .To examine mathematically, the abnormal cell rheology behavior due to polymerization process and that due membrane abnormalities , we mechanically modeled the whole cell deformability as viscoelastic solid and proposed a Voigt-model of nonlinear viscoelastic solid constitutive relation as \" mixture''of an elastic and viscous dissipative parts, with parameters of elastic and viscous moduli. The elastic part used to express stress-strain relations via strain energy function of the material and the viscous part derivation depends on strain - rate of deformation. The combination of both constitutive expressions is used to predict the viscoelastic properties of normal and sickle erythrocyte. Furthermore, sickle hemoglobin polymerization also leads to alter the osmotic behavior of the cell and to investigate such osmotic effect; we employ the van't Hoff law of osmotic pressure versus volume relation. The analysis of both formulations presented well the abnormal rheological /mechanical characterization of sickle erythrocyte membrane as we understood and concluded from our results.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250822","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}

{"title":"Unsteady Three Dimensional Free Convection Heat and Mass Transfer Flow Embedded in a Porous Medium with Periodic Permeability and Constant Heat and Mass Flux","authors":"N. Jain, D. Chaudhary, D. K. Vijay","doi":"10.5923/J.AM.20120203.05","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.05","url":null,"abstract":"We analyse an unsteady three dimensional free convection flow with combined heat and mass transfer over a vertical plate embedded in a porous medium with time dependent suction velocity and transverse sinusoidal permeability. The unsteadiness is due to the time dependent suction velocity. The governing equations with the boundary conditions are first converted into dimensionless form by non-similar transformations and then resulting system of coupled non-linear partial differential equations are solved by series expansion method. The effects of different parameters are shown on velocity (u), cross flow velocity (w), temperature (θ), Concentration (C), Skin friction (τx) and Nusselt number (Nu) graphically. We observe that skin friction is higher in air (Pr=0.71) than in water (Pr=7) but result differs for Nusselt number.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250936","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}

{"title":"The Numerical Solution of Heat Problem Using Cubic B-Splines","authors":"D. Demir, N. Bildik","doi":"10.5923/J.AM.20120204.06","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.06","url":null,"abstract":"This paper discusses solving one of the important equations in Physics; which is the one-dimensional heat equation. For that purpose, we use cubic B-spline fin ite elements within a Collocation method. The scheme of the method is presented and the stability analysis is investigated by considering Fourier stability method. On the other hand, a comparative study between the numerical and the analytic solution is illustrated by the figure and the tables. The results demonstrate the reliability and the efficiency of the method.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251219","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}

{"title":"On the Boundedness Properties of Solutions to Set Control Differential Equations","authors":"N. Phu, L. T. Quang, L. Dung","doi":"10.5923/J.AM.20120204.08","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.08","url":null,"abstract":"The set-valued differential equations (SDEs) are important parts of the set-valued analysis theory. It was investigeted by professor Lakshmikantham V., and many other authors (see(1)-(6),(8)-(10)). Beside that, we have to studied the problems of existence, co mparison and stability of set solutions to the set-valued control differential equations (SCDEs) (see(7),(11)-(16)). In this paper, we present the problems of boundedness for set solutions to the Set Control Differential Equations (SCDEs) by the Lyapunov-like functions and by admisib le control- feedback.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251240","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}

{"title":"Optimal Designs in a Simple Linear Regression with Skew-Normal Distribution for Error Term","authors":"Habib Jafari, R. Hashemi","doi":"10.5923/J.AM.20110102.11","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.11","url":null,"abstract":"The locally D-optimal design was derived for simple linear regression with the error term of Skew-Normal distribution. In this paper, to obtain a D-optimal design, the locally D-optimal criterion was considered, because of depending the information matrix on unknown parameters.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250363","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}

{"title":"A Recent Development of Numerical Methods for Solving Convection-Diffusion Problems","authors":"Anand Shukla, Akhilesh Kumar Singh, Pushpinder Singh","doi":"10.5923/J.AM.20110101.01","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.01","url":null,"abstract":"Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the cru x of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite element method, finite volu me method, finite volu me element method etc. in flu id mechanics. Here we discuss real life problems of fluid engineering solved by various numerical methods .which is very useful for finding solution of those type of governing equation, whose analytical solution are not easily found. Co mputational fluid dynamics is a branch of Engineering and science that,(1) with the help of d igital co mputers, produces quantitative prediction of fluid-flow phenomenon based on those conservation laws governing fluid mot ion. These predictions normally occur under those conditions defined in terms of flow geo metry. Convection- Diffusion Problems arises where fluid flow p lays a significant role .We must account for the effects of convection. Diffusion occurs always alongside convection in nature. The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flo w, in the modeling of semiconductors, and so forth(3). This paper describes several fin ite difference schemes for solving the convection-diffusion equation. Therefore; we examine computation methods to predict comb ined convection- diffusion equation. The convection-diffusion equation is a parabolic partial differential equation combin ing the diffusion equation and the advection equation, which describes physical phenomena where part icles or energy (or other physical quantities) are transferred inside a physical system due to two processes: diffusion and convection. In its simplest form (when the diffusion coefficient and the convection velocity are constant and there are no sources or sinks) the equation takes the form as following: 2 c D c v c t","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250595","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}