the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process, A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has...

An analytic expression of transmittance based on the Airy wavefunctions approach has been derived for an electron through an anisotropic heterostructure with an applied voltage to the barrier of the heterostructure. The Si(110)|Si0.5Ge0.5|Si(110) heterostructure was used to examine the analytic expression. In order to evaluate the Airy wavefunctions approach, the transfer matrix method, which i...

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process, A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0 F 3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the ano...

We analyze axisymmetric deformations of a rotating disk with its thickness, mass density, thermal expansion coefficient and shear modulus varying in the radial direction. The disk is made of a rubberlike material that is modeled as isotropic, linear thermoelastic and incompressible. We note that the hydrostatic pressure in the constitutive relation of the material is to be determined as a part ...

abstract various mathematical water uptake models have been introduced for plants response to combined drought and salinity stress. the reduction functions are classified as additive, multiplicative and conceptual models. in this study six different macroscopic reduction functions, namely; van genuchten (additive and multiplicative), dirksen et al., van dam et al, skaggs et al and homaee were e...

the importance of constructing the appropriate green function to solve a wide range of problems inelectromagnetics and partial differential equations is well-recognized by those dealing with classical electrodynamics and related fields. although the subject of obtaining the green function for certain geometries has been extensively studied and addressed in numerous sources, in this paper a syst...