Fractional derivatives of the H-function of several variables

AbstractIn the present paper we derive a number of key formulas involving fractional derivatives for the H-function of several variables, which was introduced and studied in a series of papers by H. M. Srivastava and R. Panda [cf., e.g., J. Reine Angew. Math. 283/284 (1976), 265–274; J. Reine Angew. Math. 288 (1976), 129–145; Comment. Math. Univ. St. Paul. 24 (1975), fasc. 2, 119–137; ibid. 25 (1976), fasc. 2, 167–197; Nederl. Akad. Wetensch. Proc. Ser. A 81 = Indag. Math. 40 (1978), 118–131 and 132–144; Nederl. Akad. Wetensch. Proc. Ser. A 82 = Indag. Math. 41 (1979), 353–362; see also Bull. Inst. Math. Acad. Sinica 9 (1981), 261–277].We make use of the generalized Leibniz rule for fractional derivatives in order to obtain one of the aforementioned results, which involves a product of two multivariable H-functions. Each of these results is shown to apply to yield interesting new results for certain multivariable hypergeometric functions and, in addition, several known results due, for example, to J. L. Lavoie, T. J. Osler and R. Tremblay [SIAM Rev. 18 (1976), 240–268], H. L. Manocha and B. L. Sharma [J. Austral. Math. Soc. 6 (1966), 470–476; J. Indian Math. Soc. (N.S.) 38 (1974), 371–382] and R. K. Raina and C. L. Koul [Jñānābha 7 (1977), 97–105]

A theorem relating a certain generalized Weyl fractional integral with the Laplace transform and a class of Whittaker transforms

AbstractIn the present paper the authors prove a theorem which asserts an interesting relationship between the classical Laplace transform, a certain class of Whittaker transforms, and a Weyl fractional integral involving a general class of polynomials with essentially arbitrary coefficients. By specializing the various parameters involved, this general theorem would readily yield several (known or new) results involving simpler integral operators. It is also shown how the relationship asserted by the theorem can be applied to evaluate the generalized Weyl fractional integrals of various special functions

Extensions of sufficient conditions for starlikeness and convexity of order α for multivalent function

AbstractIn this paper, we obtain extensions of sufficient conditions for analytic functions f(z) in the open unit disk U to be starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for analytic functions discussed by Mocanu (1988) [4], Uyanik et al. (2011) [3] and others

Heavy quark production via leptoquarks at a neutrino factory

The proposed neutrino factory (NF) based on a muon storage ring (MSR) is an ideal place to look for heavy quark production via neutral current (NC) and charged current (CC) interactions. In this article, we address the issue of contribution coming from mediating leptoquarks (LQ) in $\nu_\mu (\bar\nu_e)-{\rm N}$ interactions leading to the production of $b(\bar b)$ at a MSR and investigate the region where LQ interactions are significant in the near-site experiments.Comment: 12 pages latex, 10 ps figures, uses axocolour.sty, Slightly revised version to appear in PR

Lattice QCD Simulations in External Background Fields

We discuss recent results and future prospects regarding the investigation, by lattice simulations, of the non-perturbative properties of QCD and of its phase diagram in presence of magnetic or chromomagnetic background fields. After a brief introduction to the formulation of lattice QCD in presence of external fields, we focus on studies regarding the effects of external fields on chiral symmetry breaking, on its restoration at finite temperature and on deconfinement. We conclude with a few comments regarding the effects of electromagnetic background fields on gluodynamics.Comment: 31 pages, 10 figures, minor changes and references added. To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

The Influence of an External Chromomagnetic Field on Color Superconductivity

We study the competition of quark-antiquark and diquark condensates under the influence of an external chromomagnetic field modelling the gluon condensate and in dependence on the chemical potential and temperature. As our results indicate, an external chromomagnetic field might produce remarkable qualitative changes in the picture of the color superconducting (CSC) phase formation. This concerns, in particular, the possibility of a transition to the CSC phase and diquark condensation at finite temperature.Comment: 27 pages, RevTex, 8 figures; the version accepted for the publication in PRD (few references added; new numerical results added; main conclusions are not changed

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Pion condensation of quark matter in the static Einstein universe

In the framework of an extended Nambu--Jona-Lasinio model we are studying pion condensation in quark matter with an asymmetric isospin composition in a gravitational field of the static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates and to point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is shortly discussed.Comment: RevTex4; 15 pages, 10 figure

Seller’s optimal credit period and replenishment time in a supply chain with up-stream and down-stream trade credits

[[abstract]]In practice, a supplier often offers its retailers a permissible delay period M to settle their unpaid accounts. Likewise, a retailer in turn offers another trade credit period N to its customers. The benefits of trade credit are not only to attract new buyers who consider it a type of price reduction, but also to provide a competitive strategy other than introduce permanent price reductions. On the other hand, the policy of granting credit terms adds an additional cost to the seller as well as an additional dimension of default risk. In this paper, we first incorporate the fact that trade credit has a positive impact on demand but negative impacts on costs and default risks to establish an economic order quantity model for the seller in a supply chain with up-stream and down-stream trade credits. Then we derive the necessary and sufficient conditions to obtain the optimal replenishment time and credit period for the seller. Finally, we use some numerical examples to illustrate the theoretical results.[[incitationindex]]SCI[[booktype]]電子