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21.
In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep. 相似文献
22.
The coupling of visible nanosecond laser pulses to metallic targets irradiated in vacuum is studied. The expressions of the vapour and plasma ignition times are obtained. Two cases for vapour breakdown in the plasma ignition process are considered. The first case is that 40 generations of new electrons are born in vapour generation time before plasma formation as assumed in the literature. The second case is that 10 generations of new electrons are born in vapour generation time. Molybdenum (Mo), niobium (Nb) and aluminium (Al) targets are considered for illustrations of our results. The expression of the plasma ignition time for the Al target is substantially different from that reported in the literature. The vapour and plasma ignition threshold laser intensities are calculated and compared with those reported in the literature. Reasons for disagreement are discussed. The plasma ignition threshold estimated in the second case is noted to be in good agreement with the reported experimental result. 相似文献
23.
The present paper deals with the study of a Durrmeyer-type integral modification of certain modified Baskakov operators. Here
we study simultaneous approximation properties for these operators by using the iterative combinations. We obtain an asymptotic
formula and an error estimation in terms of higher order modulus of continuity for these operators.
相似文献
24.
In the present paper, we study the rate of convergence in simultaneous approximation for the Bézier variant of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation. 相似文献
25.
JPC – Journal of Planar Chromatography – Modern TLC - A high-performance thin-layer chromatographic (HPTLC) method has been established for simple and rapid quantification of two... 相似文献
26.
We present exact numerical results for a symmetric layered medium (prism/Ag film/nonlinear dielectric/Ag film/prism) where
the middle dielectric slab is assumed to have a saturation-type nonlinearity. We show bistable behaviour in the power dependence
of the reflectivity ofp-polarized light under the condition when coupled surface modes are excited in the structure. Moreover, we study the effect
of saturation on the bistable behaviour to show that multivalued character is inhibited by saturation effects. The field distributions
corresponding to the minimum reflectivity states of the nonlinear structure are also presented. 相似文献
27.
28.
Gamma ray bursts (GRBs) have been proposed as one possible class of sources of the ultrahigh energy cosmic ray (UHECR) events
observed up to energies ≳ 1020 eV. The synchrotron radiation of the highest energy protons accelerated within the GRB source should produce gamma rays up
to TeV energies. Here we briefly discuss the implications on the energetics of the GRB from the point of view of the detectability
of the prompt TeV γ-rays of proton-synchrotron origin in GRBs in the up-coming ICECUBE muon detector in the south pole. 相似文献
29.
30.
Vijay Kodiyalam 《Journal of Functional Analysis》2004,212(1):1-27
We show that certain numerical invariants associated naturally to a subfactor planar algebra constitute a complete family in the sense of determining the isomorphism class of the subfactor planar algebra.In the course of the proof, we show also that planar algebra isomorphisms of subfactor planar algebras can always be chosen to be ∗-preserving. This latter statement generalises the fact that ‘Hopf algebra isomorphisms of finite-dimensional Kac algebras can be chosen to be ∗-preserving’. 相似文献