in the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistatic approach (eqs) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.this...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

in the present paper an operator-differential equation of second order in complex domain isconsidered when the coefficients have singularity of pole type at the point z=0. a theorem of existence of thesolution of the equation is proved and the spectral property of the solution is separately investigated when thecoefficients are spectral operators.

in this paper, we obtain a suitable mathematical model for the seismic response of dams. by using the shear beam model (sb model), we give a mathematical formulation that it is a partial differential equation and transform it to the sturm-liouville equation.

We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.

In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

In relation with Monte-Carlo methods to solve some integro-differential equations, we study the approximation problem of IEg(XT ) by IEg(X̄n T ), where (Xt, 0 ≤ t ≤ T ) is the solution of a stochastic differential equation governed by a Lévy process (Zt), (X̄n t ) is defined by the Euler discretization scheme with step Tn . With appropriate assumptions on g(·), we show that the error IEg(XT ) − I...

Maximum drawdown is a risk measure that plays an important role in portfolio management. In this paper, we address the question of computing the expected value of the maximum drawdown using a partial differential equation (PDE) approach. First, we derive a two-dimensional convection-diffusion pricing equation for the maximum drawdown in the Black-Scholes framework. Due to the properties of the ...

A one dimensional stochastic differential equation of the form dX = AXdt+ 1 2 (−A) ∂ξ[((−A)X)]dt+ ∂ξdW (t), X(0) = x is considered, where A = 1 2∂ 2 ξ . The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar–Parisi–Zhang model. For α 6= 0, this equation conserves two important properties of the Kardar–Parisi–Zhang model: it contains a quadratic...