in this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

This paper contains graphs and tables of the function Aip,q(<*.x) = i-^Cin)-1 expiiyP/p-ayl/q + ixy} dy and its indefinite integral for p = 3, 5, 7, for q = 2, 4, 6, and for several values of a with a > 0. It is shown how these tables should influence the choice of an artificial viscosity for a difference scheme for a linear hyperbolic equation.

The theoretical study of the effect electron beam parameters, in particular, emittance and its asymmetry on radiation from relativistic electrons undulators is conducted both analytically numerically. reasons for odd even harmonic generation are explored. difference underlying physical spontaneous stimulated harmonics free lasers (FELs) elucidated. generalized forms special functions Bessel Air...

The quantum and classical aspects of a deformed c = 1 matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of the Toda lattice hierarchy. The Whittaker functions now play the role of generalized Airy functions in c < 1 strings. This matrix model has two distinct parameters. Identification of the string coupling constant is thereby not unique,...

Thermodynamic Bethe ansatz equations are coupled non-linear integral equations which appear frequently when solving integrable models. Those associated with models with N=2 supersymmetry can be related to differential equations, among them Painlevé III and the Toda hierarchy. In the simplest such case the massless limit of these non-linear integral equations can be solved in terms of the Airy f...

In this paper, a stochastic term is added to the classical generalized nonlinear Schrödinger Equation to describe the noise generated when light pulses propagate in a fiber. It has been shown that the generated supercontinuum light source fluctuates up to 50% of its output temporal intensity profile due to noises of different sources. The simulation method devised has been applied to the propag...

We demonstrate how the complex integral formula for the Airy functions arises from Penrose’s twistor contour integral formula. We then use the Lax formulation of the isomonodromy problem with one irregular singularity of order four to show that the Airy equation arises from the anti-self-duality equations for conformal structures of neutral signature invariant under the isometric action of the ...