In common finance literature, Black-Scholes partial differential equation of option pricing is usually derived with no-arbitrage principle. Considering an asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his continuous-time consumption-portfolio problem, deriving general equilibrium relationships among the securities in the asset market. In special case where the interest ...

The purpose of this paper is to study a class of differential]difference equations with two delays. First, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. General stability criteria involving the delays and the parameters are obtained. Second, by choosing one of the delays as a bifurcation...

The energy conditions of Einstein gravity (classical general relativity) are designed to extract as much information as possible from classical general relativity without enforcing a particular equation of state for the stress-energy. This systematic avoidance of the need to specify a particular equation of state is particularly useful in a cosmological setting — since the equation of state for...

It is unnecessary, nowadays, to point out the importance of the Schrodinger equation to disciplines of science and technology. In principle, one can understand any natural phenomenon if one can solve the corresponding Schrodinger equations. Unfortunately, the Schrodinger equation can only be analytically solved in a few special cases. Therefore, it is very important to know the properties of th...

S. Prešić ([6]) determined the all reproductive general solutions of the equation r(x) = 1, where r was a unary relation of a given set T . In this paper we determine the all general solutions of this equation. S. Prešić ([6]) introduced the most general concept of equations. Namely, he considered the equation of the form r(x) = 1, where r was a unary relation of a non–empty set S. He gave the ...

We study normal forms of scalar integrable dispersive (not necessarily Hamiltonian) conservation laws, via the Dubrovin-Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrized by infinitely many arbitrary functions that can be identified with the coefficients of the quasi-linear part of the equation. Moreover, in general, we conjecture that two...

 ∂tu = − i ∂xj (ajk(x, t, u, ū,∇u,∇ū)∂xku) +~b1(x, t, u, ū,∇u,∇ū) · ∇u+~b2(x, t, u, ū,∇u,∇ū) · ∇ū + c1(x, t, u, ū)u+ c2(x, t, u, ū)ū+ f(x, t), where x ∈ R, t > 0, and A = (ajk(·))j,k=1,..,n is a real, symmetric matrix. Our aim is to study the existence, uniqueness and regularity of local solutions to the initial value problem (IVP) associated to the equation (1.1). In the case where A = (ajk(·...

In this paper we are concerned with the solutions of the differential equation f ′′′+ ff ′′+g(f ′) = 0 on [0,∞), satisfying the boundary conditions f(0) = α, f ′(0) = β ≥ 0, f ′(∞) = λ, and where g is some given continuous function. This general boundary value problem includes the Falkner-Skan case, and can be applied, for example, to free or mixed convection in porous medium, or flow adjacent ...

The general image quality equation (GIQE) [Leachtenauer et al., Appl. Opt. 36, 8322-8328 (1997)] is an empirical formula for predicting the quality of imagery from a given incoherent optical system in terms of the National Imagery Interpretability Rating Scale (NIIRS). In some scenarios, the two versions of the GIQE (versions 3.0 and 4.0) yield significantly different NIIRS predictions. We comp...