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MATHEMATICS (642 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 6)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)
Foundations and Trends® in Networking     Full-text available via subscription   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Applied Mathematics
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  This is an Open Access Journal Open Access journal
   ISSN (Print) 2163-1409 - ISSN (Online) 2163-1425
   Published by SAP Homepage  [105 journals]
  • Equivalent Function to the Implicit Function X Y = Y X

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  José María MínguezThis short paper deals with the implicit function , X,Y> 0, and shows surprinsingly how accurately it is equivalent to another very much simpler and explicit function.
      PubDate: 10/17/2012 17:12:01
  • Crime Scene Investigation with Bayesian Probabilistic Expert Systems

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Marina Andrade,Manuel Alberto M. FerreiraCriminal identification problems are examples of situations in which forensic approach the DNA profiles study is a common procedure. In order to deal with these problems it is needed an introduction to present and explain the various concepts involved, since distinct areas must be considered. Some problems are presented and the use of the object-oriented Bayesian networks, example of probabilistic expert systems, is shown.
      PubDate: 10/17/2012 17:12:01
  • Umbral Methods, Combinatorial Identities and Harmonic Numbers

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  K. V. Zhukovsky,G. DattoliWe analyse and demonstrate how umbral methods can be applied for the study of the problems, involving combinatorial calculus and harmonic numbers. We demonstrate their efficiency and we find the general procedure to frame new and existent identities within a unified framework, amenable of further generalizations.
      PubDate: 10/17/2012 17:12:01
  • A Recent Development of Numerical Methods for Solving Convection-Diffusion

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  A. Shukla,A. K. Singh,P. SinghConvection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the crux 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 volume method, finite volume element method etc. in fluid 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.
      PubDate: 10/17/2012 17:12:01
  • Equivalent Finite Element Formulations for the Calculation of Eigenvalues
           Using Higher-Order Polynomials

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  C. G. ProvatidisThis 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.
      PubDate: 10/17/2012 17:12:01
  • Solution of Blasius Equation by Variational Iteration

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Yucheng Liu,Sree N. KurraTheBlasius equation is a well known third-order nonlinear ordinary differential equation, which arises in certain boundary layer problems in the fluid dynamics. This paper presents a way of applying He’s variational iteration method to solve the Blasius equation. Approximate analytical solution is derived and compared to the results obtained from Adomian decomposition method. Comparisons show that the present method is accurate and the using of He’s method does accelerate the convergence of the power series. A robust and efficient algorithm is also programmed using Matlab based on the present approach, which can be easily employed to solve Blasius equation problems
      PubDate: 10/17/2012 17:12:01
  • Characterizing Hysteresis Nonlinearity Behavior of SMA Actuators by
           Krasnosel’skii-Pokrovskii Model

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  M. R. Zakerzadeh,H. Sayyaadi,M. A. Vaziri ZanjaniKrasnosel’skii-Pokrovskii (KP) model is one of the great operator-based phenomenological models which is used in modeling hysteretic nonlinear behavior in smart actuators. The time continuity and the parametric continuity of this operator are important and valuable factors for physical considerations as well as designing well-posed identification methodologies. In most of the researches conducted about the modeling of smart actuators by KP model, especially SMA actuators, only the ability of the KP model in characterizing the hysteretic behavior of the actuators is demonstrated with respect to some specified experimental data and the accuracy of the developed model with respect to other data is not validated. Therefore, it is not clear whether the developed model is capable of predicting hysteresis minor loops of those actuators or not and how accurate it is in this prediction task. In this paper the accuracy of the KP model in predicting SMA hysteresis minor loops as well as first order ascending curves attached to the major hysteresis loop are experimentally validated, while the parameters of the KP model has been identified only with some first order descending reversal curves attached to the major loop. The results show that, in the worst case, the maximum of prediction error is less than 18.2% of the maximum output and this demonstrates the powerful capability of the KP model in characterizing the hysteresis nonlinearity of SMA actuators.
      PubDate: 10/17/2012 17:12:01
  • Hydromagnetic Unsteady Mixed Convection Flow Past an Infinite Vertical
           Porous Plate

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  B. K. Sharma,T. Chand,R. C. ChaudharyAn approximate analysis of unsteady mixed convection flow of an electrically conducting fluid past an infinite vertical porous plate embedded in porous medium under constant transversely applied magnetic field is presented here. The periodic transverse suction velocity is applied to the surface due to which the flow becomes unsteady. The surface is kept at oscillating wall temperature. Analytical expressions for the transient velocity, temperature, amplitude and phase of the skin-friction and the rate of heat transfer are obtained and discussed in detail with the help of graphs, under different parameter values.
      PubDate: 10/17/2012 17:12:01
  • Modelling Coagulation Systems: A Stochastic Approach

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Vasiliy RyazanovA general stochastic approach to the description of coagulating aerosol system is developed. As the object of description one can consider arbitrary mesoscopic values (number of aerosol clusters, their size etc). The birth-and-death formalism for a number of clusters can be regarded as a partial case of the generalized storage model. An application of the storage model to the number of monomers in a cluster is discussed.
      PubDate: 10/17/2012 17:12:01
  • Weak Insertion of a γ − Continuous Function1

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Majid MirmiranA sufficient condition in terms of lower cut sets are given for the weak insertion of a γ−continuous function between two comparable real-valued functions.
      PubDate: 10/17/2012 17:12:01
  • Averaging of Set Integrodifferential Equations

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Andrej V. Plotnikov,Tatyana A. KomlevaIn this article we prove the substantiation of the method of averaging for the set integrodifferential equations with small parameter. Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging
      PubDate: 10/17/2012 17:12:01
  • On the Slow Viscous Flow through a Swarm of Solid Spherical Particles
           Covered by Porous Shells

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Pramod Kumar YadavThis paper concerns the slow viscous flow through a swarm of concentric clusters of porous spherical particles. An aggregate of clusters of porous spherical particles is considered as a hydro-dynamically equivalent to a porous spherical shell enclosing a solid spherical core. The Brinkman equation inside and the Stokes equation outside the porous spherical shell in their stream function formulations are used. As boundary conditions, continuity of velocity, continuity of normal stress and stress-jump condition at the porous and fluid interface, the continuity of velocity components on the solid spherical core are employed. On the hypothetical surface, uniform velocity and Happel boundary conditions are used. The drag force experienced by each porous spherical shell in a cell is evaluated. As a particular case, the drag force experienced by a porous sphere in a cell with jump is also investigated. The earlier results reported for the drag force by Davis and Stone[5] for the drag force experienced by a porous sphere in a cell without jump, Happel[2] for a solid sphere in a cell and Qin and Kaloni[4] for a porous sphere in an unbounded medium have been then deduced. Representative results are presented in graphical form and discussed.
      PubDate: 10/17/2012 17:12:01
  • Soliton Solution for the BBM and MRLW Equations by Cosine-function Method

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Rajan Arora,Anoop KumarIn this paper, we obtained a traveling wave solution by using cosine-function algorithm for nonlinear partial differential equations. Here, the method is used to obtain the exact solutions for two different types of nonlinear partial differential equations such as, Benjamin-Bona-Mahony (BBM) equation and Modified Regularized Long Wave (MRLW) equation which are the important soliton equations
      PubDate: 10/17/2012 17:12:01
  • Steady State Solution of a Catastrophic-cum-Restorative M/G/1 Queuing
           System Using Supplementary Variable Technique

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Rakesh KumarNon- Markovian queuing models have their place in modeling the real life phenomena. In fact, their utility get enhanced when one is not able to get a particular probability distribution for either the inter-arrival times or for the service times. The service times are assumed to have general service time distribution in case of computer communication modeling. Recently, the emphasis is put on the catastrophe modeling and its applications in real situations. Keeping this in view, an M/G/1 queuing model has been developed with catastrophic and restorative effects. The steady-state solution of the model has been obtained using supplementary variable technique. Some queuing models have been obtained as particular cases of this model
      PubDate: 10/17/2012 17:12:01
  • Optimal Designs in a Simple Linear Regression with Skew-Normal
           Distribution for Error Term

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Habib Jafari,Reza HashemiThe 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
      PubDate: 10/17/2012 17:12:01
  • Complex Stability Analysis of Therapeutic Actions in a Fractional Reaction
           Diffusion Model of Tumor

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Oyesanya M. O.,Atabong T. A.Separate administration of either chemotherapy or immunotherapy has been studied and applied to clinical experiments but however, this administration has shown some side effects such as increased acidity which gives a selective advantage to tumor cell growth. We introduce a model for the combined action of chemotherapy and immunotherapy using fractional derivatives. This model with non-integer derivative was analysed analytically and numerically for stability of the disease free equilibrium. The analytic result shows that the disease free equilibrium exist and if the prescriptions of food and drugs are followed strictly (taken at the right time and right dose) and in addition if the basic tumor growth factor , then the only realistic steady state is the disease free steady state. We also show analytically that this steady state is stable for some parameter values. Our analytical results were confirmed with a numerical simulation of the full non linear fractional diffusion system
      PubDate: 10/17/2012 17:12:01
  • The Classical Solution of Burger’s Equation Arises Into The Fingering
           Phenomena in Fluid Flow Through Homogeneous Porous Media

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Twinkle Singh,Mathematics SectionThe basic burger’s equation arising into the fingering phenomena has been converted into perturb burger’s equation by introducing a term such that as and finally it is proved that given solution is not solution of perturb burger’s equation but it is solution of burger’s equation by using appropriate boundary condition under certain standard assumption.
      PubDate: 10/17/2012 17:12:01
  • Mathematical Modeling of Filtration from Canals and Sprinklers of
           Irrigation Systems

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  E. N. Bereslavskii,N. V. LikhachevaWe consider several schemes of seepage flows from canals and sprinklers of irrigation systems through the soil layer, underlain good underlying permeable confined aquifer or water-resistant base. For their study and formulated using the method of P.Y. Polubarinova-Kochina solved multivariable mixed boundary value problems of the theory of analytic functions. On the basis of these models are developed algorithms for calculating the size of the saturated zone in situations when the filter has to evaluate the combined effect of the painting movement of such important factors as seepage back pressure from the underlying confined aquifer or an impermeable base, cross-sectional shape and channel the power supply level of water in it , capillarity of the soil and evaporation from the free surface of groundwater. The results of calculations for all the schemes are compared with the same filtration filter parameters depending on the shape of the channel as a power source (canal or irrigation), and the type of foundation soil layer (silnopronitsaemy confined aquifer or aquitard).
      PubDate: 10/17/2012 17:12:01
  • The Domain of the Fourier Integral

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  V. N. TibabishevWe consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space of square integrable functions and the Hilbert space of almost periodic functions. Scalar product for different Hilbert spaces defined at the intersection of these spaces, which contains only one zero element. Therefore, the Fourier integral is not defined in the Hilbert space of square integrable functions with nonzero norm
      PubDate: 10/17/2012 17:12:01
  • Conjugate Transient Free Convective Heat Transfer from a Vertical Slender
           Hollow Cylinder with Heat Generation Effect

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  H. P. Rani,G Janardhana ReddyNumerical analysis is performed to study the conjugate heat transfer and heat generation effects on the transient free convective boundary layer flow over a vertical slender hollow circular cylinder with the inner surface at a constant temperature. A set of non-dimensional governing equations namely, the continuity, momentum and energy equations is derived and these equations are unsteady non-linear and coupled. As there is no analytical or direct numerical method available to solve these equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The discretized equations are solved using the tridiagonal algorithm. Numerical results for the transient velocity and temperature profiles, average skin-friction coefficient and average Nusselt number are shown graphically. In all these profiles it is observed that the time required to reach the steady-state increases as the conjugate-conduction parameter or heat generation parameter increases
      PubDate: 10/17/2012 17:12:01
  • Comparison of Linear and Nonlinear Programming Techniques for Animal Diet

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Pratiksha SaxenaLinear 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.
      PubDate: 10/17/2012 17:12:01
  • A Note on Fixed Points for Asymptotic Nonlinear Contractions

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Jennifer Love,Behzad Djafari RouhaniLet (M,d) be a complete metric space and T be a self-mapping of M. W.A. Kirk proved a fixed point theorem for a continuous asymptotic contraction T in[4] .Y.Z. Chen extended Kirk’s theorem in[2] by assuming weaker assumptions on T. Also Chen introduced some other conditions to replace the assumption on the boundedness of the orbit. We introduce the weaker condition liminfn → ∞ (d(x,Tnx)) = 0 for some x in M, and prove that this condition implies the existence of a fixed point and the convergence of the Picard iterates to this fixed point.
      PubDate: 10/17/2012 17:12:01
  • Self-Similar Cylindrical Ionizing Shock Waves in a Non-Ideal Gas with
           Radiation Heat-Flux

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  J. P. Vishwakarma,Mahendra SinghSelf-similar flows behind a gas-ionizing cylindrical shock wave, with radiation heat flux, in a non-ideal gas are studied. The ionizing shock is assumed to be propagating in a medium at rest with constant density permeated by an azimuthal magnetic field. The electrical conductivity of the gas is infinite behind shock and zero ahead of it. Effects of the non-idealness of the gas, the radiation flux and the rate of energy input from the inner contact surface (or piston) on the flow-field behind the shock and on the shock propagation are investigated.
      PubDate: 10/17/2012 17:12:01
  • On the Minimum ABC Index of Chemical Trees

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Tzvetalin S. Vassilev,Laura J. HuntingtonThe Atom Bond Connectivity index, also known as ABC index was defined by Estrada[4] with relation to the energy of formation of alkanes. It was quickly recognized that this index reflects important structural properties of graphs in general. The ABC index was extensively studied in the last three years, from the point of view of chemical graph theory[5,6], and in general graphs[1]. It was also compared to other structural indices of graphs[2]. Das derives multiple results with implications to the minimum/maximum ABC index on graphs. With relation to trees, it is known that among all the trees of the same number of vertices, the maximum ABC index is attained for the star graph. However, it is not known which tree(s) minimize(s) the ABC index. The problem seems to be hard. It is partially addressed in many sources[5,1,6], but remains open. In this paper we further investigate the trees that minimize the ABC index. Our investigations are limited to chemical trees, i.e. trees in which the maximum vertex degree is 4. The chemical trees were introduced to reflect the structure of the carbon chains and the molecules based on them. Our approach is algorithmic. We identify certain types of edges (chemical bonds) that are important and occur frequently in chemical trees. Further, we study how the removal of a certain edge, the introduction of certain edge or the contraction of certain edge affects the ABC-index of the tree. We pay particular attention to the examples of minimal ABC index chemical trees provided by Dimitrov[3].
      PubDate: 10/17/2012 17:12:01
  • Iterated Block-Pulse Method for Solving Volterra Integral Equations

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  K. Maleknejad,K. Mahdiani In this paper, an iterated method is presented to determine the numerical solution of linear Volterra integral equations of the second kind (VIEs2). This method initially uses the solution of the direct method to obtain the more accurate solution. The convergence and error analysis of this method are given. Finally, numerical examples illustrate efficiency and accuracy of the proposed method. Also, the numerical results of this method are compared with the results of direct method, collocation method and iterated collocation method.
      PubDate: 10/17/2012 17:12:01
  • Nonclassical Pseudospectral Method for a Class of Singular Boundary Value
           Problems Arising in Physiology

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  A. AlipanahIn this paper, nonclassical pseudospectral method is presented for solution of a classof nonlinear singular boundary value problems arising in physiology. Properties of non-classical pseudospectral method are presented. These properties are utilizeto reduce the computation of singular boundary value problems to system of equations. Numerical method is tested for its efficiency by considering two examples from physiology
      PubDate: 10/17/2012 17:12:01
  • A Numerical Patching Technique for Singularly Perturbed Nonlinear
           Differential-Difference Equations with a Negative Shift

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  R. Nageshwar Rao,P. Pramod ChakravarthyIn this paper, we present a numerical patching technique for solving singularly perturbed nonlinear differential-difference equation with a small negative shift. The nonlinear problem is converted into a sequence of linear problems by quasilinearization process. After linearization, it is divided into two problems, namely inner region problem and outer region problem. The boundary condition at the cutting point is obtained from the theory of singular perturbations. Using stretching transformation, a modified inner region problem is constructed and is solved by using the upwind finite difference scheme. The outer region problem is solved by a Taylor polynomial approach. We combine the solutions of both problems to obtain an approximate solution of the original problem. The proposed method is iterative on the cutting point. The process is repeated for various choices of the cutting point, until the solution profiles stabilize. Some numerical examples have been solved to demonstrate the applicability of the method. The method is analyzed for stability and convergence.
      PubDate: 10/17/2012 17:12:01
  • SOR- Steffensen-Newton Method to Solve Systems of Nonlinear Equations

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  M. T. Darvishi,Norollah DarvishiIn this paper, we present SOR-Steffensen-Newton (SOR-SN) algorithm to solve systems of nonlinear equations. We study the convergence of the method. The computational aspects of the method is also studied using some numerical experiment. In comparison of new method with SOR-Newton, SOR-Steffensen and SOR-Secant methods, our method are better in CPU time and number of iterations.
      PubDate: 10/17/2012 17:12:01
  • Self-Similar Flow under the Action of Monochromatic Radiation Behind a
           Cylindrical MHD Shock in a Non-Ideal Gas

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  J. P. Vishwakarma,Vijay Kumar Pandey Similarity solutions are obtained for one-dimensional flow under the action of monochromatic radiation behind a cylindrical magnetogasdynamic shock wave propagating in a non-ideal gas in presence of an axial magnetic field. The initial density of the medium and initial magnetic field are assumed to be constant. It is investigated that the presence of the magnetic field or the non-idealness of the gas decays the shock wave, and when the initial magnetic field is strong the non-idealness of the gas affects the velocity and pressure profiles significantly. Also, it is observed that the flow-variables behind the shock are affected significantly, by an increase in the parameter of radiation, when the initial magnetic field is strong. It is, therefore, inferred that the effect of the non-idealness of the gas and of the monochromatic radiation on the shock propagation become more significant when the strength of the initial magnetic field is increased.
      PubDate: 10/17/2012 17:12:01
  • Inverse Derivative and Solutions of Some Ordinary Differential Equations

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  K. V. ZhukovskyWe present a general method of operational nature to obtain solutions for several types of differential equations. Methodology of inverse differential operators for the solution of differential equations is developed. We apply operational approach to construct inverse differential operators and develop operational identities, involving inverse derivatives and generalized families of orthogonal polynomials. We employ them together with the exponential operator to investigate various differential equations. Advantages of operational technique for finding solutions of a wide spectrum of differential equations are demonstrated, in particular with regard to fractional differential equations.
      PubDate: 10/17/2012 17:12:01
  • Analysis of Mechanical Behavior of Red Cell Membrane in Sickle Cell

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Demeke Fisseha,V. K. KatiyarSickle 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 hemoglobin 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.
      PubDate: 10/17/2012 17:12:01
  • Two Integral Methods Applied to the (2+1) Dimensional Davey-Stewartson

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Nabil T. M. El-Dabe,M. H. M. Moussa,Rehab M. El –Shiekh,H. A. HamdyIn this paper, we use two integral methods, the first integral method and the direct integral method to study (2+1)- dimensional Davey-Stewartson equation . The first integral method was used to construct travelling wave solutions, those solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. By using the direct integration method shock wave solution and Jacobi elliptic function solutions are obtained. By comparison between the two methods, the direct integration is more impressive than the first integral method. The results obtained confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear systems of partial differential equations.
      PubDate: 10/17/2012 17:12:01
  • Exact Elliptic Solution for Non-Linear Klein-Gordon Equation Via Auxiliary
           Equation Method

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  G. M. Moatimid,M. H. M. Moussa,Rehab M. El-Shiekh,A. A. El-Satar 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.
      PubDate: 10/17/2012 17:12:01
  • Solution of Magnetohydrodynamic Flow in a Rectangular Duct by Chebyshev
           Polynomial Method

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  İbrahim Çelik In this study, Chebyshev polynomial method is applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. In present method, approximate solution is taken as truncated Chebyshev series. The MHD equations are decoupled first and then present method is used to solve for positive and negative Hartmann numbers. Numerical solutions of velocity and induced magnetic field are obtained for steady-state, fully developed, incompressible flow for a conducting fluid inside the duct. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann numbers .
      PubDate: 10/17/2012 17:12:01
  • Application of The (-Expansion Method For Solving The Generalized Forms
           B(n,1) andB(-n,1) of Burgers’ Equation

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Rajan Arora,Sanjay YadavIn this paper, the exact traveling wave solutions of thegeneralized forms B(n, 1) and B(-n, 1) of Burgers’ equation are obtained by using (G`/G)-expansion method. It has been shown that the (G`/G)-expansion method, with the help of computation, provides a very effective and powerful tool for solving non-linear partial differential equations
      PubDate: 10/17/2012 17:12:01
  • Unsteady Three Dimensional Free Convection Heat and Mass Transfer Flow
           Embedded in a Porous Medium with Periodic Permeability and Constant Heat
           and Mass Flux

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  N. C. Jain,D. Chaudhary, Dinesh K. VijayWe 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.
      PubDate: 10/17/2012 17:12:01
  • Mathematical Modelling of HIV/AIDS Dynamics with Treatment and Vertical

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Abdallah S. Waziri,Estomih S. Massawe,Oluwole Daniel MakindeThis paper examines the dynamics of HIV/AIDS with treatment and vertical transmission. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. Local stability of the disease free equilibrium of the model was established by the next generation method. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However, it is shown that using treatment measures (ARVs) and control of the rate of vertical transmission have the effect of reducing the transmission of the disease significantly. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.
      PubDate: 10/17/2012 17:12:01
  • Rational Approximation on Closed Curves

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  J.I. Mamedkhanov,I.B. DadashovaIn this paper, we study a problem of approximation for the classes of functions determined only on the boundary of domain in weighted integral spaces by means of the rational functions of the form (1) where is a point lying strictly inside the considered curve. Notice that the approximation estimations, generally speaking, coincide with the estimations of polynomial approximation for classes (Smirnov's class).
      PubDate: 10/17/2012 17:12:01
  • Working out The Principles of Adaptive Management to Educational Processes
           in The E-Learning

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  R.N. Usmonov,V.S. KhamidovSuggesting the technology of intellectualization the process of adaptive management, based on situational analysis of educational process in the networking of single supporting system of decision making in E-learning.
      PubDate: 10/17/2012 17:12:01
  • Interval – Valued Differential Equations with Generalized Derivative

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Natalia SkripnikIn this paper the concept of generalized differentiability (proposed in[17]) for interval-valued mappings is used. The interval-valued differential equations with generalized derivative are considered and the existence theorem is proved.
      PubDate: 10/17/2012 17:12:01
  • Mathematical Modeling of Oxygen Transport in theEye

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Deepti SethA simple mathematical model for the steady state oxygen distribution in the eye has been developed. The model introduces the krogh retinal cylinder surrounded by retinal capillary.The analytical solution to the governing equations are obtained in normalized forms by employing perturbation techniques for the arterial end ,the central region and the venous end of the retinal cylinder. Solutions are obtained for each of these regions. The computational results are presented through the graphs. The effect of important parameters on the retinal capillary concentration , are examined and discussed. The results of the model may contribute when axial diffusion is important and when it can be neglected.
      PubDate: 10/17/2012 17:12:01
  • Complete Classification of BKM Lie Superalgebras Possessing Strictly
           Imaginary Property

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  N. Sthanumoorthy,K. PriyadharsiniIn this paper, complete classifications of all BKM Lie superalgebras (withfinite order and infinite order Cartan matrices) possessing Strictly Imaginary Property are given. These classifications also include, in particular, the Monster BKM Lie superalgebra.
      PubDate: 10/17/2012 17:12:01
  • Squeeze Film Based on Ferrofluid in Curved Porous Circular Plates with
           Various Porous Structure

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Rajesh C. Shah,Dilip B. PatelThis 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.
      PubDate: 10/17/2012 17:12:01
  • Simultaneous Effects of Control Measures on the Transmission Dynamics of
           Chikungunya Disease

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  O. P. Misra,Dinesh Kumar MishraChikungunya is a vector borne communicable disease which is transmitted in human population through the bite of an infected Aedes-Aegeypti mosquito. In order to study the spread of Chikungunya disease a model has been proposed and analyzed in this paper. In the proposed model the human population and the mosquito population have been divided into three and two classes respectively. For controlling the disease, vector control measures such as, reduction in the breeding of vector population, killing of mosquitoes and isolation of infected humans have been also taken in to account in the model. Linear and non-linear stability analysis of the model has been carried out. From the analysis we have derived a threshold condition involving control reproductive number, and we have found that the disease free equilibrium point is locally asymptotically stable whenand unstable when.We have also proved that a unique endemic equilibrium point exists and is locally asymptotically stable when. Thus, we have concluded from the analysis of the model that the disease will either die out or will remain endemic depending on the value of control reproductive number. This study will assist the health department in controlling the spread of Chikungunya disease by introducing the control measures such as increasing the awareness in the society, killing of mosquitoes and isolating the infected individuals.
      PubDate: 10/17/2012 17:12:01
  • The Numerical Solution of Heat Problem Using Cubic B-Splines

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Duygu Dönmez Demir,Necdet BildikThis 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 finite 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.
      PubDate: 10/17/2012 17:12:01
  • Effect of Fiber Self Phase Modulation on the Splitting Error using the
           Strang Formulas

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Tsouria Zendagui,Mourad MahboubThe generalized nonlinear Schrödinger equation describes the different physical phenomena encountered when ultrashort pulses propagate through dispersive and nonlinear fibers. If the pulse duration is of picoseconds order, the nonlinear Schrödinger equation can be simplified. However the analytical solution remains inaccessible except for some special cases like soliton. The symmetric split-step Fourier method (S-SSFM) which is derived from the Strang formulas, subdivides the global propagation distance into small steps of length hto calculate the numerical solution of this equation. By using only the fact that the dispersive and nonlinear operators do not commute the Baker-Campbell-Hausdorff formula shows that the global relative error of this method is O(h2). Our numerical simulation results show that this error depends also on the self phase modulation nonlinear term. For this purpose, we employ in this work an explicit representation of the nonlinear operator and we present four implementations: the S-SSFM1, S-SSFM2, T-SM1 and T-SM2 obtained respectively from some weighting coefficients (c0, c1) = (0, 1), (c0, c1) = (1, 0), (c0,c1,c2) = (-1,1,1) and (c0,c1,c2) = (1,-1,1). Thus, we have computed for an input Gaussian pulse, the numerical solutions and the global relative errors for each implementation. As results, the estimated slopes of the linear variations of the global relative errors allow showing that the S-SSFM1 and T-SM1 errors are O(h), S-SSFM2 and T-SM2 errors are O(h2); furthermore, the S-SSFM is more accurate than the T-SM. In order to obtain an indicator of accuracies, we present the variations of the global relative errors for some values of the propagation length of the fiber.
      PubDate: 10/17/2012 17:12:01
  • On the Boundedness Properties of Solutions to Set Control Differential

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Nguyen Dinh Phu,Le Thanh Quang,Lam Quoc DungThe 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, comparison 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 admisible control- feedback.
      PubDate: 10/17/2012 17:12:01
  • Partial New Mock Theta Functions

    • Abstract: Publication year:  2011Source:Applied Mathematics,  Volume  1,  Number  1  Bhaskar SrivastavaBy using a simple identity of mine, I have proved sixty identities connecting the mock theta functions of Ramanujan with mock theta functions recently generated by Andrews and Bringmann et al, by taking their partial sums.
      PubDate: 10/17/2012 17:12:01
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