http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2010/263451.htmlThis paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.A. S. Deakin and Matt Davison© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/636271.htmlThis paper considers the problem of controlling the solution of an initial boundary-value problem for a wave equation with time-dependent sound speed. The control problem is to determine the optimal sound speed function which damps the vibration of the system by minimizing a given energy performance measure. The minimization of the energy performance measure over sound speed is subjected to the equation of motion of the system with imposed initial and boundary conditions. Using the modal space technique, the optimal control of distributed parameter systems is simplified into the optimal control of bilinear time-invariant lumped-parameter systems. A wavelet-based method for evaluating the modal optimal control and trajectory of the bilinear system is proposed. The method employs finite CAS wavelets to approximate modal control and state variables. Numerical examples are presented to demonstrate the effectiveness of the method in reducing the energy of the system.Taher Abualrub, Ibrahim Sadek, and Marwan Abukhaled© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/292183.htmlWe study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the (bounded) spatial domain consists of two subdomains: a collection of automatic cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.Robert Artebrant© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/890158.htmlWe discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variable t and x, respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.F. Huang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/740172.htmlThe problem of concentric pervious spheres carrying a fluid source at their centre and rotating slowly with different uniform angular velocities Ω1, Ω2 about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists, and the couple, rate of dissipated energy is found analytically in the present situation. The expression of couple on inner sphere rotating slowly with uniform angular velocity Ω1, while outer sphere also rotates slowly with uniform angular velocity Ω2, is evaluated. The special cases, like (i) inner sphere is fixed (i.e., Ω1=0), while outer sphere rotates with uniform angular velocity Ω2, (ii) outer sphere is fixed (i.e., Ω2=0), while inner sphere rotates with uniform angular velocity Ω1, and (iii) inner sphere rotates with uniform angular velocity Ω1, while outer sphere rotates at infinity with angular velocity Ω2, have been deduced.Deepak Kumar Srivastava© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/169790.htmlWe introduce the concept of generalized S(C,A,B)-pairs which is related to generalized S(A,B)-invariant subspaces and generalized S(C,A)-invariant subspaces for infinite-dimensional systems. As an application the parameter-insensitive disturbance-rejection problem with dynamic compensator is formulated and its solvability conditions are presented. Further, an illustrative example is also examined.Naohisa Otsuka and Haruo Hinata© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/291849.htmlWe deal with an application of the fixed point theorem for nonexpansive mappings to a class of control systems. We study closed-loop and open-loop controllable dynamical systems governed by ordinary differential equations (ODEs) and establish convexity of the set of trajectories. Solutions to the above ODEs are considered as fixed points of the associated system-operator. If convexity of the set of trajectories is established, this can be used to estimate and approximate the reachable set of dynamical systems under consideration. The estimations/approximations of the above type are important in various engineering applications as, for example, the verification of safety properties.Vadim Azhmyakov© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/818269.htmlA boundary value problem is posed for an integro-differential beam equation. An approximate solution is found using the Galerkin method and the Jacobi nonlinear iteration process. A theorem on the algorithm error is proved.Jemal Peradze© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/604695.htmlThis paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g(x,t)=I(t)(1−R)μe−μx while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.R. T. Al-Khairy and Z. M. AL-Ofey© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/524307.htmlWe consider the application of a new analytic method based on homotopy analysis to the solution of the steady flow of a viscous incompressible fluid past a fixed circular cylinder. The solutions obtained using this method produce some interesting results. For instance, an analytic verification of the critical Reynolds number Rd for which a standing vortex first appears behind the cylinder is given for the first time and found to be Rd≼2.4. Since these values of the critical Reynolds number are beyond the range of validity of Oseen theory, no analytic verification of this value had previously been given. As a check on the accuracy of the solutions, the calculated drag coefficients at 6th-order approximation are found to agree reasonably well with experimental measurements for Rd≃30 which is considerably larger than the Rd≃1 results currently available using other analytic techniques. This buttresses the usefulness of the homotopy analysis method (HAM) as an important tool in solving highly nonlinear problems.E. O. Ifidon© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/753518.htmlWe obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut=uxx−a(x,t)f(u),  0<x<1,  t∈(0,T), with boundary conditions ux(0,t)=0, ux(1,t)=b(t)g(u(1,t)), blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-up rate and set. Finally, we get an analogous result taking a discrete form of the above problem and give some computational results to illustrate some points of our analysis.Louis A. Assalé, Théodore K. Boni, and Diabate Nabongo© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2009/150420.htmlWe consider the uniform attractors for the two dimensional nonautonomous g-Navier-Stokes equations in bounded domain Ω. Assuming f=f(x,t)∈Lloc2, we establish the existence of the uniform attractor in L2(Ω) and D(A1/2). The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.Delin Wu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/586567.htmlThe velocity induced by a plane, uniform vortex is investigated through the use of an integral relation between Schwarz function of the vortex boundary and conjugate of the velocity. The analysis is restricted to a certain class of vortices, the boundaries of which are described through conformal maps onto the unit circle and the corresponding Schwarz functions possess two poles in the plane of the circle. The dependence of the velocity field on the vortex shape is investigated by comparing velocity and streamfunction with the ones of the equivalent Rankine vortex (which has the same vorticity, area, and center of vorticity). By changing the parameters of the Schwarz function (poles and corresponding residues), rather complicated vortex shapes can be easily analyzed, some of them mimicing an incipient filamentation of the vortex boundary.G. Riccardi and D. Durante© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/640154.htmlThe obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented as a system of coupled nonlinear ordinary differential equations is used to analyze, understand, and predict the dynamics of obesity populations. The construction of the proposed discrete scheme is developed such that it is dynamically consistent with the original differential equations model. Since the total population in this mathematical model is assumed constant, the proposed scheme has been constructed to satisfy the associated conservation law and positivity condition. Numerical comparisons between the competitive nonstandard scheme developed here and Euler's method show the effectiveness of the proposed nonstandard numerical scheme. Numerical examples show that the nonstandard difference scheme methodology is a good option to solve numerically different mathematical models where essential properties of the populations need to be satisfied in order to simulate the real world.Rafael J. Villanueva, Abraham J. Arenas, and Gilberto González-Parra© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/570825.htmlWe carry out the effect of the induced magnetic field on peristaltic transport of an incompressible conducting micropolar fluid in a symmetric channel. The flow analysis has been developed for low Reynolds number and long wavelength approximation. Exact solutions have been established for the axial velocity, microrotation component, stream function, magnetic-force function, axial-induced magnetic field, and current distribution across the channel. Expressions for the shear stresses are also obtained. The effects of pertinent parameters on the pressure rise per wavelength are investigated by means of numerical integrations, also we study the effect of these parameters on the axial pressure gradient, axial-induced magnetic field, as well as current distribution across the channel and the nonsymmetric shear stresses. The phenomena of trapping and magnetic-force lines are further discussed.Kh. S. Mekheimer© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/414830.htmlThis study sought to investigate thermal radiation and buoyancy effects on heat and mass transfer over a semi-infinite stretching surface with suction and blowing. Appropriate transformations were employed to transform the governing differential equations to nonsimilar form. The transformed equations were solved numerically by an efficient implicit, iterative finite-difference scheme. A parametric study illustrating the influence of wall suction or injection, radiation, Schmidt number and Grashof number on the fluid velocity, temperature and concentration is conducted. We conclude from the study that the flow is appreciably influenced by thermal radiation, Schmidt number, as well as fluid injection or suction.S. Shateyi© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/835380.htmlThe study sought to investigate thermosolutal convection and stability of two dimensional disturbances imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence of significant temperature gradients near the plate surface results in additional buoyancy and decrease in viscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure of the perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing the reaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers, negative buoyancy stabilizes the boundary layer flow.Stanford Shateyi, Precious Sibanda, and Sandile S. Motsa© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/576783.htmlWe use the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations with constant Gaussian curvature −1. Travelling wave solutions for the above equations are obtained by using a sech-tanh method and Wu's elimination method.S. M. Sayed, O. O. Elhamahmy, and G. M. Gharib© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/124269.htmlWe study the robustness of strong stability of the homogeneous difference equation via the concept of strong stability radii: complex, real and positive radii in this paper. We also show that in the case of positive systems, these radii coincide. Finally, a simple example is given.The Anh Bui and Dang Xuan Thanh Duong© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/846282.htmlThe present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing (downwash). In spite of the importance of the Possio equation, the question of the existence of its solution has not been settled yet. We provide a rigorous reduction of the initial boundary value problem involving a partial differential equation for the velocity potential and highly nonstandard boundary conditions to a singular integral equation, the Possio equation. The question of its solvability will be addressed in our forthcoming work.A. V. Balakrishnan and M. A. Shubov© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/528934.htmlThe well-known root-locus method is developed for special subset of linear time-invariant systems known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface because of their multivalued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis, and breakaway points are extended to fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm.Farshad Merrikh-Bayat and Mahdi Afshar© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/354652.htmlWe construct an exponential attractor for a first-order dissipative lattice dynamical system arising from spatial discretization of reaction-diffusion equations in ℝk. And we obtain fractal dimension of the exponential attractor.Xiaoming Fan© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/639145.htmlBy means of the notion of likelihood ratio, the limit properties of the sequences of arbitrary-dependent continuous random variables are studied, and a kind of strong limit theorems represented by inequalities with random bounds for functions of continuous random variables is established. The Shannon-McMillan theorem is extended to the case of arbitrary continuous information sources. In the proof, an analytic technique, the tools of Laplace transform, and moment generating functions to study the strong limit theorems are applied.Gaorong Li, Shuang Chen, and Sanying Feng© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/537284.htmlA class of time-delay reaction-diffusion systems with variable coefficients which arise from the model of two competing ecological species is discussed. An asymptotic global attractor is established in terms of the variable coefficients, independent of the time delays and the effect of diffusion by the upper-lower solutions and iteration method.Miguel Uh Zapata, Eric Avila Vales, and Angel G. Estrella© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/190836.htmlA Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree 0,1,…, in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data.Michael Knudsen and Carsten Wiuf© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2008/453627.htmlA class of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients is discussed. It is neither employing coincidence degree theory nor constructing Lyapunov functionals, instead, by applying matrix theory and inequality analysis, some sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and global exponential stability of the periodic solution for the fuzzy Cohen-Grossberg neural networks. The method is very concise and practical. Moreover, two examples are posed to illustrate the effectiveness of our results.Hongjun Xiang and Jinde Cao© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2007/015745.abs.htmlThis paper is concerned with the nonlinear theory of micropolar, porous, and elastic solids. By using the theory of Langenbach, within this context, we obtain some existence and uniqueness results.Marin Marin© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2007/012375.abs.htmlThe purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for reaction-diffusion systems (three equations) with a tridiagonal matrix of diffusion coefficients and with nonhomogeneous boundary conditions after the work of Kouachi (2004) on the system of reaction diffusion with a full 2-square matrix. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.Abdelmalek Salem© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2007/056360.abs.htmlThe three-dimensional linearized theory of elastodynamics mathematical formulation of the forced vibration of a prestretched plate resting on a rigid half-plane is given. The variational formulation of corresponding boundary-value problem is constructed. The first variational of the functional in the variational statement is equated to zero. In the framework of the virtual work principle, it is proved that appropriate equations and boundary conditions are derived. Using these conditions, finite element formulation of the prestretched plate is done. The numerical results obtained coincide with the ones given by Ufly and in 1963 for the static loading case.M. Eröz and A. Yildiz© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jam/2007/026075.abs.htmlWe extend the classical Perron-Frobenius theorem for positive quasipolynomial matrices associated with homogeneous difference equations. Finally, the result obtained is applied to derive necessary and sufficient conditions for the stability of positive system.Bui The Anh and D. D. X. Thanh© 2010, Hindawi Publishing Corporation. All rights reserved.