The purpose of the present paper is to initiate a systematic study of the relation of the boundary values for hyperbolic-dissipative systems of partial differential equations. We introduce a general framework for explicitly deriving the boundary kernel for the Dirichlet-Neumann map. We first use the Laplace and Fourier transforms, and the stability consideration to derive the Master Relationshi...

This paper presents majorization results for PH-generators. Based on the majorization results, bounds on the moments and Laplace-Stieltjes transforms of phase-type distributions are found. Exponential distributions and Coxian distributions are identified to be extremal PH-distributions with respect to all the moments and Laplace-Stieltjes transforms for certain subsets of PH-distributions. UN C...

In this paper, we present a stock model with Markov switching in the uncertainty markets, where the parameters of drift and volatility change according to the states of a Markov process. To price the option, we firstly establish a risk-neutral probability based on the uncertain measure given by Liu. Then a closed form of the European option pricing formula is obtained by applying the Laplace tr...

A two dimensional generalized thermoelastic problem of a thick circular plate of finite thickness and infinite extent subjected to continuous axisymmetric heat supply and an internal heat generation is studied within the context of generalized thermoelasticity. Unified system of equations for classical coupled thermoelasticity, Lord-Shulman and Green-Lindsay theory is considered. An exact solut...

The disc multiplier may be seen as a vector valued operator when we consider its projections in terms of the spherical harmonics. In this form, it represents a vector valued Hankel transform. We know that, for radial functions, it is bounded on the spaces Lplq (r n−1 dr) when 2n n+1 < p, q < 2n n−1 . Here we prove that there exist weak-type estimates for this operator for the extremal exponents...

together with appropriate boundary conditions, where S is the price of the underlying security and t < T is the time, with T being the expiry time. The parameters in the above equation are the risk-free rate, r, the dividend yield, D0, and the volatility, σ; all of them are assumed constant. In addition, we assume that r > D0 > 0. If an option is European, it can only be exercised at the expira...

The main goal of this research is to present a new approach double transforms called the Laplace–ARA transform (DL-ARAT). This novel combination Laplace and ARA transforms. We basic properties including existence, linearity some results related partial derivatives convolution theorem. To obtain exact solutions, applied several differential equations such as Klein–Gordon equation, heat wave equa...