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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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