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We derive the distribution and three-term recurrence relation for the Koornwinder [2] polynomials with weight function shown above using the method developed in our paper [3]. We are able to obtain explicit expressions for the linear functional in terms of the coefficients of the three-term recurrence relation for the Jacobi polynomials and we obtain the distribution using a more direct approach. 相似文献
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In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844.... 相似文献
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Despite the tremendous utilities of metal‐mediated cross‐couplings in modern organic chemistry, coupling reactions involving nitrogenous heteroarenes remain a challenging undertaking – coordination of Lewis basic atoms into metal centers often necessitate elevated temperature, high catalyst loading, etc. Herein, we report a sulfur (IV) mediated cross‐coupling amendable for the efficient synthesis of heteroaromatic substrates. Addition of heteroaryl nucleophiles to a simple, readily‐accessible alkyl sulfinyl (IV) chloride allows formation of a trigonal bipyramidal sulfurane intermediate. Reductive elimination therefrom provides bis‐heteroaryl products in a practical and efficient fashion. 相似文献
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Ta‐Tsien Li Yue‐Jun Peng Yong‐Fu Yang Yi Zhou 《Mathematical Methods in the Applied Sciences》2008,31(2):193-227
One often believes that there is no shock formation for the Cauchy problem of quasilinear hyperbolic systems (of conservation laws) with linearly degenerate characteristic fields. It has been a conjecture for a long time (see Arch. Rational Mech. Anal. 2004; 172 :65–91; Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer: New York, 1984) and it is still an open problem in the general situation up to now. In this paper, a framework to justify this conjecture is proposed, and, by means of the concept such as the strict block hyperbolicity, the part richness and the successively block‐closed system, some general kinds of quasilinear hyperbolic systems, which verify the conjecture, are given. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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