Generalized Fractional Integral of the Product of Two Aleph-Functions

This paper is devoted to the study and develops the generalized fractional integral operators for a new special function, which is called Aleph-function. The considered generalized fractional integration operators contain the Appell hypergeometric function F3 as a kernel. We establish two results of the product of two Aleph-functions involving Saigo-Maeda operators. On account of the general nature of the Saigo-Maeda operators and the Aleph-function, some results involving Saigo, Riemann-Liouville and Erdélyi-Kober integral operators are obtained as special cases of the main result

Integral involving Aleph-function and the generalized incomplete hypergeometric function

The aim of this paper is to establish a general definite integrals involving product of the Aleph function and generalized incomplete hypergeometric function with general arguments. Being unified and general in nature, this integral yield a number of known and new results as special cases. For the sake of illustration, several corollaries are also recorded here as special case of our main results.Publisher's Versio

Solutions of generalized fractional kinetic equations involving Aleph functions

In view of the usefulness and a great importance of the kinetic equation incertain astrophysical problems, the authors develop a new and further generalized form ofthe fractional kinetic equation in terms of Aleph-function by using Sumudu transform. Thisnew generalization can be used for the computation of the change of chemical compositionin stars like the sun. The manifold generality of the Aleph-function is discussed in termsof the solution of the above fractional kinetic equation. The main results, being of generalnature, are shown to be some unication and extension of many known results given, forexample, by Saxena et al. [23, 25, 31], Saxena and Kalla [22], Chaurasia and Kumar [6],Dutta et al. [8], and etc

FEYNMAN INTEGRALS PERTAINING TO ALEPH FUNCTION AND TWO GENERAL CLASS OF POLYNOMIALS

The object of the present paper is to derive certain integral properties of Aleph function and two general class of polynomials. During the course of finding, we obtain some particular cases, which are also new and of interest by themselves. The N-function is a generalization of the familiar H-function and the I-function. The results derived are of general character

Survey of present data on photon structure functions and resolved photon processes

Present data on the partonic content of the photon from LEP, TRISTAN and HERA accelerators are reviewed and the essential aspects of the underlying ideas and methods are pointed out. Results of the unpolarized photon structure function F_2 from DIS_{e gamma} experiments and on large p_T jet production processes in the resolved gamma-gamma collisions are presented for both real and virtual photons. The results of analysis of the hadronic final state accompanying the DIS_{e gamma} measurements, showing some discrepancies with the Monte Carlo models, are collected together and presented as a separate issue. Also results on the DIS_{e gamma} with leptonic final states are shown. The results from resolved real and virtual photon processes at HERA collider based on the single and double jet events, also charged particles and prompt photons, are presented. In the context of virtual photon processes the data for forward jet and forward particle production are included. In addition a short presentation of the recent data on the heavy quark content of the photon is given. Related topics - the polarized (spin dependent) structure functions for the real and virtual photon, the structure function of the electron and the photonic content of the proton are also shortly mentioned.Comment: latex, 220 pages, 195 ps figures; extended and updated version of hep-ph/9806291; to appear in Physics Report

On the two-dimensional Saigo-Maeda fractional calculus asociated with two-dimensional Aleph TRANSFORM

This paper deals with the study of two-dimensional Saigo-Maeda operators of Weyl type associated with Aleph function defined in this paper. Two theorems on these defined operators are established. Some interesting results associated with the H-functions and generalized Mittag-Leffler functions are deduced from the derived results. One dimensional analog of the derived results is also obtained

A New Avenue to Charged Higgs Discovery in Multi-Higgs Models

Current searches for the charged Higgs at the LHC focus only on the $\tau\nu$, $cs$, and $tb$ final states. Instead, we consider the process $pp\to \Phi\to W^\pm H^\mp \to W^+ W^- A$ where $\Phi$ is a heavy neutral Higgs boson, $H^\pm$ is a charged Higgs boson, and $A$ is a light Higgs boson, with mass either below or above the $b\bar{b}$ threshold. The cross-section for this process is typically large when kinematically open since $H^\pm \to W^\pm A$ can be the dominant decay mode of the charged Higgs. The final state we consider has two leptons and missing energy from the doubly leptonic decay of the $W^+ W^-$ and possibly additional jets; it is therefore constrained by existing SM Higgs searches in the $W^+ W^-$ channel. We extract these constraints on the cross-section for this process as a function of the masses of the particles involved. We also apply our results specifically to a type-II two Higgs doublet model with an extra Standard-Model-singlet and obtain new and powerful constraints on $m_{H^\pm}$ and $\tan\beta$. We point out that a slightly modified version of this search, with more dedicated cuts, could be used to possibly discover the charged Higgs, either with existing data or in the future.Comment: 38 pages, 14 figure