## Recursos de colección

1. #### Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity

Balakrishnan, A. V.; Shubov, M. A.
The 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...

2. #### Extending the Root-Locus Method to Fractional-Order Systems

Merrikh-Bayat, Farshad; Afshar, Mahdi
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...

3. #### Exponential Attractor for a First-Order Dissipative Lattice Dynamical System

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

4. #### A Strong Limit Theorem for Functions of Continuous Random Variables and an Extension of the Shannon-McMillan Theorem

Li, Gaorong; Chen, Shuang; Feng, Sanying
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.

5. #### Asymptotic Behavior of a Competition-Diffusion System with Variable Coefficients and Time Delays

Zapata, Miguel Uh; Avila Vales, Eric; Estrella, Angel G.
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.

6. #### A Markov Chain Approach to Randomly Grown Graphs

Knudsen, Michael; Wiuf, Carsten
A 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 $0, 1,\ldots,$ in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data.

7. #### Periodic Oscillation of Fuzzy Cohen-Grossberg Neural Networks with Distributed Delay and Variable Coefficients

Xiang, Hongjun; Cao, Jinde
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.

8. #### On the Nonlinear Theory of Micropolar Bodies with Voids

Marin, Marin
This 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.

9. #### Finite Element Formulation of Forced Vibration Problem of a Prestretched Plate Resting on a Rigid Foundation

Eröz, M.; Yildiz, A.
The 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.

10. #### Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Tridiagonal Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions

Salem, Abdelmalek
The 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.

11. #### A Perron-Frobenius Theorem for Positive Quasipolynomial Matrices Associated with Homogeneous Difference Equations

Anh, Bui The; Thanh, D. D. X.
We 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.

12. #### Chip Thickness and Microhardness Prediction Models during Turning of Medium Carbon Steel

Alrabii, S. A.; Zumot, L. Y.
Cutting tests were conducted to medium carbon steel using HSS tools with cutting florder. The experimental design used was based on response surface methodology (RSM) using a central composite design. Chips were collected at different machining conditions and thickness and microhardness measurements taken and analyzed using “DESIGN EXPERT 7” experimental design software. Mathematical models of the responses (thickness and microhardness) as functions of the conditions (speed, feed, and depth of cut) were obtained and studied. The resultant second-order models show chip thickness increases when increasing feed and speed, while increasing depth of cut resulted in a little effect on chip thickness. Chip microhardness increases with increasing depth...

13. #### Recovery of Time-Dependent Parameters of a Black-Scholes-Type Equation: An Inverse Stieltjes Moment Approach

Rodrigo, Marianito R.; Mamon, Rogemar S.
We show that the problem of recovering the time-dependent parameters of an equation of Black-Scholes type can be formulated as an inverse Stieltjes moment problem. An application to the problem of implied volatility calculation in the case when the model parameters are time varying is provided and results of numerical simulations are presented.

14. #### Waves Trapped by Submerged Obstacles at High Frequencies

Marín, A. M.; Ortíz, R. D.; Zhevandrov, P.
As is well known, submerged horizontal cylinders can serve as wavegorderes for surface water waves. For large values of the wavenumber $k$ in the direction of the cylinders, there is only one trapped wave. We construct asymptotics of these trapped modes and their frequencies as $k \to \infty$ in the case of one or two submerged cylinders by means of reducing the initial problem to a system of integral equations on the boundaries and then solving them using a technique suggested by Zhevandrov and Merzon (2003).

15. #### Approximation Technics for an Unsteady Dynamic Koiter Shell

We propose a mixed formulation in dynamical elasticity of shells which allows a locking-free finite element approximation in particular cases of Koiter shells.

16. #### Visitor and Firm Taxes Versus Environmental Options in a Dynamical Context

Antoci, Angelo; Galeotti, Marcello; Geronazzo, Lucio
The main objective of the paper is to analyze the effects on economic agents' behavior deriving from the introduction of financial activities aimed to environmental protection. The environmental protection mechanism we study should permit exchange of financial activities among citizens, firms, and Public Administration. Such a particular “financial market” is regulated by the Public Administration, but mainly fuelled by the interest of two classes of involved agents: firms and dwelling citizens. We assume that the adoption process of financial decisions is described by a two-population evolutionary game and we study the basic features of the resulting dynamics.

17. #### Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

Sikorska-Nowak, Aneta
We prove existence theorems for the integrodifferential equation $x'(t)=f(t,x(t),{\int}_{0}^{t}k(t,s,x(s))ds)$ , $x(0)={x}_{0}$ , $t\in {I}_{a}=[0,a]$ , $a>0$ , where $f,k,x$ are functions with values in a Banach space $E$ and the integral is taken in the sense of HL. Additionally, the functions $f$ and $k$ satisfy certain boundary conditions expressed in terms of the measure of noncompactness.

18. #### Minimizing Banking Risk in a Lévy Process Setting

Gideon, F.; Mukuddem-Petersen, J.; Petersen, M. A.
The primary functions of a bank are to obtain funds through deposits from external sources and to use the said funds to issue loans. Moreover, risk management practices related to the withdrawal of these bank deposits have always been of considerable interest. In this spirit, we construct Lévy process-driven models of banking reserves in order to address the problem of hedging deposit withdrawals from such institutions by means of reserves. Here reserves are related to outstanding debt and acts as a proxy for the assets held by the bank. The aforementioned modeling enables us to formulate a stochastic optimal control...

19. #### Lie Group Analysis of a Flow with Contaminant-Modified Viscosity

Moitsheki, Raseelo J.
A class of coupled system of diffusion equations is considered. Lie group techniques resulted in a rich array of admitted point symmetries for special cases of the source term. We also employ potential symmetry methods for chosen cases of concentration and a zero source term. Some invariant solutions are constructed using both classical Lie point and potential symmetries.

20. #### Maximizing Banking Profit on a Random Time Interval

Mukuddem-Petersen, J.; Petersen, M. A.; Schoeman, I. M.; Tau, B. A.
We study the stochastic dynamics of banking items such as assets, capital, liabilities and profit. A consideration of these items leads to the formulation of a maximization problem that involves endogenous variables such as depository consumption, the value of the bank's investment in loans, and provisions for loan losses as control variates. A solution to the aforementioned problem enables us to maximize the expected utility of discounted depository consumption over a random time interval, $[t,\tau ]$ , and profit at terminal time $\tau$ . Here, the term depository consumption refers to the consumption of the bank's profits by the taking and holding of deposits. In particular, we determine...

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