A 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.

A Markov chain approach to the study of randomly grown graphs isproposed and applied to some popular models that have found use in biologyand elsewhere. For most randomly grown graphs used in biology,it is not known whether the graph or properties of the graph converge (insome sense) as the number of vertices becomes large. Particularly, we studythe behaviour of the degree sequence, that is, the number of vertices withdegree $0,1,\dots ,$in large graphs, and apply our results to the partial duplicationmodel. We further illustrate the results by application to real data.

A 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.

By 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.

We construct an exponential attractor for a first-order dissipative lattice dynamical system arising from spatial discretization of reaction-diffusion equations in ${ℝ}^k$. And we obtain fractal dimension of the exponential attractor.

The 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.

The present paper is the first in a series of works devoted to the solvability of thePossio singular integral equation. This equation relates the pressure distribution over atypical section of a slender wing in subsonic compressible air flow to the normal velocityof 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 arigorous reduction of the initial boundary value problem involving a partial differentialequation for the velocity potential and highly nonstandard boundary conditions to asingular integral equation, the Possio equation. The question of its solvability will beaddressed in our forthcoming work.

We 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.

We use the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudosphericalsurfaces for the KdV-Burgers-Kuramoto and nonlinear Schr\"{o}dinger 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.

The study sought to investigate thermosolutal convection and stability of two dimensional disturbancesimposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of achemical species using a self-consistent asymptotic method. The chemical species reacts as it diffusesinto the nearby fluid causing density stratification and inducing a buoyancy force. The existence ofsignificant temperature gradients near the plate surface results in additional buoyancy and decrease inviscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure ofthe perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohlernumbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS)instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing thereaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers,negative buoyancy stabilizes the boundary layer flow.

This study sought to investigate thermal radiation and buoyancyeffects 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 orinjection, 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.

We carry out the effect of the induced magnetic field on peristaltic transport of anincompressible conducting micropolar fluid in a symmetric channel. The flow analysis has been developed for low Reynolds number and long wavelength approximation. Exactsolutions have been established for the axial velocity, microrotation component, streamfunction, magnetic-force function, axial-induced magnetic field, and current distributionacross the channel. Expressions for the shear stresses are also obtained. The effectsof pertinent parameters on the pressure rise per wavelength are investigated by means ofnumerical integrations, also we study the effect of these parameters on the axial pressuregradient, axial-induced magnetic field, as well as current distribution across the channeland the nonsymmetric shear stresses. The phenomena of trapping and magnetic-force linesare further discussed.

}The obesity epidemic is considered a health concern of paramount importancein modern society. In this work, a nonstandard finite differencescheme has been developed with the aim to solve numerically a mathematicalmodel for obesity population dynamics. This interacting populationmodel represented as a system of coupled nonlinear ordinary differentialequations is used to analyze, understand, and predict the dynamics of obesitypopulations. The construction of the proposed discrete scheme is developedsuch that it is dynamically consistent with the original differentialequations model. Since the total population in this mathematical modelis assumed constant, the proposed scheme has been constructed to satisfythe associated conservation law and positivity condition. Numericalcomparisons between the competitive nonstandard scheme developed hereand Euler's method show the effectiveness of the proposed nonstandardnumerical scheme. Numerical examples show that the nonstandard differencescheme methodology is a good option to solve numerically differentmathematical models where essential properties of the populations need tobe satisfied in order to simulate the real world.

The 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.

We obtain some conditions under which the positive solution forsemidiscretizations of the semilinear equation $u_t=u_{xx}-a(x,t)f(u),0<x<1,t\in (0,T)$, with boundary conditions $u_x\left(0,t\right)=0$, $u_x\left(1,t\right)=b\left(t\right)g\left(u\left(1,t\right)\right)$, blows up in a finite time and estimate its semidiscrete blow-up time. We also establishthe convergence of the semidiscrete blow-up time and obtain some results aboutnumerical blow-up rate and set. Finally, we get an analogous result takinga discrete form of the above problem and give some computational results toillustrate some points of our analysis.