6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 5.1. INTRODUCTION 131 5.1.2 MPI's Support for Libraries The corresponding concepts that MPI provides, specifically to support robust libraries, are as follows: ffl

Abstract | This review provides an introduction to Sup-

Abstract. Any sufficiently smooth one-dimensional Calderón-Zygmund convolution op-erator is the average of Haar shift operators. The latter are dyadic operators which can be efficiently expressed in terms of the Haar basis. This extends the result of S. Petermichl [11] on restoring Hilbert

Abstract: In this paper we introduce the distributional function families Sα(x) and RBα (u) named Bessel Elliptic kernel and Bessel Ultrahyperbolic kernel de-fined by (1.1)and(2.4)respectively,where α is a complex number. In particular when α = 2k, S2k(x) and RB2k(u), k = 1, 2,... appear in([1

displacement method and the sieve analysis for palm kernel shell are 2.59 and it has an S-shape curve; while 4.70 and 0.265 obtained for the coefficient of uniformity (Cu) and coefficient of curvature (Cc) respectively indicate that the aggregate is uniformly graded and can be used for the production of light

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In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed.

In this paper we dene the pullback cat1-group and show that this Pullback has a right adjoint which is the induced cat1-group. Later we show that this right adjoint is a pushout of category of cat1-groups. We calculate the Peier subgroups to nd a nite group of the source of induced cat1-groups. The generating set of Peier subgroups are also given in this paper. All results are corrected by a GAP[13] program package in [4]. This paper also contains the some computational examples which are the calculation-induced cat1-group and comparative times between the induced crossed modules and induced cat1-groups.

(including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which eectively estimates the oscillatory eect due to the magnetic phase

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