Sufficient conditions for oscillatority in the sense of Yakubovich for a class of time delay nonlinear systems are proposed. Under proposed conditions, upper and lower bounds for oscillation amplitude are given. Examples illustrating analytical results by computer simulation are presented.

We consider a reaction-diffusion system modeling the spread of an epidemic disease within a population divided into the susceptible and infective classes. We first consider the question of the uniform boundedness of the solutions for which we give a positive answer. Then we deal with the asymptotic behavior of the solutions where in particular we are interested in reasonable conditions leading to the extinction of the infection disease as the time goes to infinity.

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, $\left[t,\tau \right]$, 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 an analytic solution for the associated Hamilton-Jacobi-Bellman (HJB) equation in the case where the utility functions are either of power, logarithmic, or exponential type. Furthermore, we analyze certain aspects of the banking model and optimization against the regulatory backdrop offered by the latest banking regulation in the form of the Basel II capital accord. In keeping with the main theme of our contribution, we simulate the financial indices return on equity and return on assets that are two measures of bank profitability.

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.

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 problem related to the minimization of reserve, depository, and intrinsic risk that are associated with the reserve process, the net cash flows from depository activity, and cumulative costs of the bank's provisioning strategy, respectively. A discussion of the main risk management issues arising from the optimization problem mentioned earlier forms an integral part of our paper. This includes the presentation of a numerical example involving a simulation of the provisions made for deposit withdrawals via treasuries and reserves.

We prove existence theorems for the integrodifferential equation $x\text{'}(t)=f\left(t,x\left(t\right),{\int }_0^{t}k\left(t,s,x\left(s\right)\right)ds\right)$, $x\left(0\right)=x_0$, $t\in I_a=\left[0,a\right]$, $a>0$, 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.

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.

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

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).

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.

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 of cut. It also increases with increasing speed and feed up to a certain level beyond which further increases cause a drop in microhardness.

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.

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.

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.

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.