16,921 research outputs found
Picard-Fuchs Ordinary Differential Systems in N=2 Supersymmetric Yang-Mills Theories
In general, Picard-Fuchs systems in N=2 supersymmetric Yang-Mills theories
are realized as a set of simultaneous partial differential equations. However,
if the QCD scale parameter is used as unique independent variable instead of
moduli, the resulting Picard-Fuchs systems are represented by a single ordinary
differential equation (ODE) whose order coincides with the total number of
independent periods. This paper discusses some properties of these Picard-Fuchs
ODEs. In contrast with the usual Picard-Fuchs systems written in terms of
moduli derivatives, there exists a Wronskian for this ordinary differential
system and this Wronskian produces a new relation among periods, moduli and QCD
scale parameter, which in the case of SU(2) is reminiscent of scaling relation
of prepotential. On the other hand, in the case of the SU(3) theory, there are
two kinds of ordinary differential equations, one of which is the equation
directly constructed from periods and the other is derived from the SU(3)
Picard-Fuchs equations in moduli derivatives identified with Appell's
hypergeometric system, i.e., Burchnall's fifth order ordinary differential
equation published in 1942. It is shown that four of the five independent
solutions to the latter equation actually correspond to the four periods in the
SU(3) gauge theory and the closed form of the remaining one is established by
the SU(3) Picard-Fuchs ODE. The formula for this fifth solution is a new one.Comment: \documentstyle[12pt,preprint,aps,prb]{revtex}, to be published in J.
Math. Phy
Third order differential subordination and superordination results for analytic functions involving the Srivastava-Attiya operator
In this article, by making use of the linear operator introduced and studied
by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible
functions are investigated and the dual properties of the third-order
differential subordinations are presented. As a consequence, various
sandwich-type theorems are established for a class of univalent analytic
functions involving the celebrated Srivastava-Attiya transform. Relevant
connections of the new results are pointed out.Comment: 16. arXiv admin note: substantial text overlap with arXiv:1809.0651
Interpolation function of the genocchi type polynomials
The main purpose of this paper is to construct not only generating functions
of the new approach Genocchi type numbers and polynomials but also
interpolation function of these numbers and polynomials which are related to a,
b, c arbitrary positive real parameters. We prove multiplication theorem of
these polynomials. Furthermore, we give some identities and applications
associated with these numbers, polynomials and their interpolation functions.Comment: 14 page
Some new applications for heat and fluid flows via fractional derivatives without singular kernel
This paper addresses the mathematical models for the heat-conduction
equations and the Navier-Stokes equations via fractional derivatives without
singular kernel.Comment: This is a preprint of a paper whose final and definite form will be
published in Thermal Science. Paper Submitted 28/ Dec /2016; Revised
20/Jan/2016; Accepted for publication 21/Jan/201
Some New Symmetric Identities for the q-Zeta Type Functions
The main object of this paper is to obtain several symmetric properties of
the q-Zeta type functions. As applications of these properties, we give some
new interesting identities for the modified q-Genocchi polynomials. Finally,
our applications are shown to lead to a number of interesting results which we
state in the present paper.Comment: 8 pages; submitte
A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow
In this article we propose a new fractional derivative without singular
kernel. We consider the potential application for modeling the steady
heat-conduction problem. The analytical solution of the fractional-order heat
flow is also obtained by means of the Laplace transform.Comment: 1 figur
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