In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the parameters, and show that the numerical solution reproduces exactly the analytical solution. We also show that the generalization of the SIR model, including ...

This paper presents two new results on the enumeration of all extreme equilibria of the sequence form of a two person extensive game. The sequence form of an extensive game is expressed, for the first time to our knowledge, as a parametric linear 0− 1 program. Considering Ext(P ) as the set of all of the sequence form extreme Nash equilibria and Ext(Q) as the set of all the parametric linear 0 ...

Coexistence The special case when all the independent solutions of a linear, T -periodic ODE are T -periodic. Hill’s equation A second order ODE of the form ẍ + p(t)x = 0, with p(t) T -periodic. Instability pockets Finite domains, usually intersections of instability tongues, where the trivial solution of linear, T -periodic ODEs is unstable. Instability tongues Domains in parameter space where...

Privatization which refers to the transition of ownership and management of state-owned enterprises to the private sector, is one of the main drivers of economic prosperity. In this paper, the performance of the state, private, and privatized banks have been compared through examining the effects of privatization in the banking system on its performance. The data from 11 banks during the 13-yea...

Parametric regression models assume that the dependent variable is a linear relationship with independent variables and form of known. Nonparametric methods are applied in cases where type not known or assumptions cannot be provided. However, when there more than one variable, some may while nonlinear relationship. In order to model these variables, semiparametric models, which combination para...

When dealing with muqarnas, we are actually facing a design problem that consists of three main issues that has to be considered; first is the components, second is the assembly knowledge, and finally functional knowledge. In this context Design Procedures (DP) is presented as a methodology that enhances the design capability of a parametric model to perform design variations by using shapes as...

In this talk, we discuss the principle of Minimum Description Length (MDL) for problems of statistical modeling. By viewing models as a means of providing statistical descriptions of observed data, the comparison between competing models is based on the stochastic complexity (SC) of each description. The Normalized Maximum Likelihood (NML) form of the SC (Rissanen 1996) contains a component tha...

The fuzzy linear second order equations with fuzzy initial values are investigatedin this paper. The analytic general solution solutions of them usinga rst solution is founded. The parametric form of fuzzy numbers is appliedto solve the second order equations. General solutions for fuzzy linear secondorder equations with fuzzy initial values are investigated and formulatedin four cases. A examp...

The problem that we investigate in this note is the following: given p, find sufficient conditions that the parameters s and t should satisfy such as to ensure that Ps,t(p) contains the entire Zp. Let ε > 0 be any small number. Throughout this paper, we denote by c1, c2, . . . computable positive constants which are either absolute or depend on ε. From the way we formulated the above problem, w...

In this paper, a generalized Camassa–Holm equation is studied by using the integral bifurcation method. Many travelling waves such as peaked compacton, compacton, peaked solitary wave, solitary wave and kink-like wave are found. In some parameter conditions, exact parametric representations of these travelling waves in explicit form and implicit form are obtained. 2008 Elsevier Inc. All rights ...