in this paper, we present recent results in integral inequality theory. our results are based on thefractional integration in the sense of riemann-liouville

Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann--Hilbert problems Dbar approach, long-time asymptotic behavior solutions to fifth-order modified Korteweg-de Vries equation line is studied in case initial conditions that belong some weighted Sobolev spaces. Using techniques Fourier analysis idea $I$-method, we give its global well-posedness lower regulari...

We consider both the bosonic and fermionic second quantization of spectral triples in presence a chemical potential. show that von Neumann entropy average energy Gibbs state defined by grand partition function can be expressed as actions. It turns out all action coefficients given terms modified Bessel functions. In case, we for entropy, limit when potential μ approaches 0, Riemann zeta functio...

Model of Riemann–Cartan gravity with varying signature metric is considered. The basic dynamical variables the formalism are vierbein, spin connection, and an internal in tangent space. corresponding action contains new terms, which depend on these fields. In general case determined dynamically. Minkowski preferred dynamically because configurations other signatures suppressed. We also discuss ...

This paper is devoted to the approximation of a certain class analytic functions by shifts Z(s+iτ), τ∈R, modified Mellin transform Z(s) square Riemann zeta-function ζ(1/2+it). More precisely, we prove existence closed non-empty set F such that there are infinitely many which approximate given function from with accuracy. In proof, weak convergence measures in space applied. Then, coincides supp...

The goal of this paper is to make mathematically precise, then illustrate, how to “email” a Riemann surface. We assume each of our Riemann surfaces are orientable and connected. We will follow the notation from [2] and will cite theorems from this source whenever possible. To email a Riemann surface we want a unique Riemann surface to correspond to a set L of finitely many matrices whose entrie...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating equation, as well as in the Lax-Sato form. A dressing scheme based on nonlinear vector Riemann problem is presented for this class. The hierarchies connected...

As a basic model, the fourth-order quasilinear thin film equation (the TFE– 4) with a concentration-dependent doubly degenerate mobility coefficient vanishing at two equilibrium levels u = ±1, ut = −(|1− u|uxxx)x , is studied. The basic Riemann problem for the TFE–4 with discontinuous initial data