In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

A quantisation of the KP equation on a cylinder is proposed that is equivalent to an infinite system of non-relativistic one-dimensional bosons carrying masses m = 1, 2, . . . The Hamiltonian is Galilei-invariant and includes the split Ψ m1 Ψ m2 Ψm1+m2 and merge Ψ m1+m2 Ψm1Ψm2 terms for all combinations of particles with masses m1, m2 and m1 + m2, with a special choice of coupling constants. Th...

the desire to achieve cosmetic rejuvenation and reduce effects of aging and photodamage urged scientists to develop effectual techniques which have minimal side effects and impressive long-term efficacy. traditional ablative resurfacing laser therapy has been used for several years;however, it has harmful side effects on the patient’s skin such as dyspigmentation, persistent erythema, infection...

We introduce and solve the non-commutative version of Hermite-Pad\'{e} type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to subclass solutions Hirota (discrete Kadomtsev--Petviashvili) system its linear also prove integrability constrained system, which simplest case is discrete-time Toda lattice equation known from theory Pad\'{e} approximants m...

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

In this paper we present a semantics for a little-studied and problematic class of adjectives, the so-called frequency adjectives (FAs), such as occasional and rare. FAs have been associated with three different readings, which we descriptively label the internal reading, the generic reading, and the adverbial reading, following the literature (Stump 1981, Larson 1998, Zimmermann 2003, Schäfer ...

the used activated carbon was derived from pine-cone and was used for the removal of acid black 1(ab1) and acid blue 113(ab113) dyes. a batch sorption study was carried out in order to obtain optimum isotherm model. the study showed the best fit of the adsorption isotherm data was obtained using the langmuir model for both dyes. the monolayer maximum saturation capacities of ab1 and ab113 dyes ...

In this article, we begin with Riesz potential. We then discuss some properties of the Finally a relation Potential fractional maximal function in sense that can be controlled by potential and maps space Lp to Lq whenever does.

Scanning tunneling microscopy study of O2 dissociation on Rh~110! at 170 K shows a low-energy dissociation coordinate for a precursor with the O-O axis aligned in the @001# azimuth, indicating a strong influence of the surface anisotropy on the potential-energy surface. This results in pairs of oxygen atoms oriented along @001#, which aggregate in chains along @11̄0# . The atomic distance in the...