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61.
62.
For a ? R\alpha \in \mathbf{R}, the class of a-\alpha -order spherical harmonic functions in an open set W í\Omega \subseteq Sn-1\mathbf{S}^{n-1}, Ha(W)H^{\alpha }(\Omega ) is defined as the C2-C^{2}-solutions of Dau=0\Delta _{\alpha }u=0; where Da=Ds+a(n+a-2)\Delta _{\alpha }=\Delta _{s}+\alpha (n+\alpha -2) is the spherical Laplace--Beltrami operator of order a\alpha and Ds\Delta _{s} is the radially independent part of the Laplace operator. We obtain a Green's integral formula for the functions in Ha(W)H^{\alpha }(\Omega ) with kernel expressed as a Gegenbauer function. As generalizations, higher order spherical iterated Dirac operators are defined in a polynomial form. Integral representations of the null solutions to these operators and an intertwining formula relating these operators on the sphere and their analogues in Euclidean space are presented. 相似文献
63.
Fiber-optic reflex sensor for in-line production measurement 总被引:1,自引:0,他引:1
The paper describes experiments concerning distance measurement with fiber-optic sensor and improvement of the measurement principle. The sensor probe was well-designed with a small structure and multi-function. The novel optical fiber probe arrangement as well as the possibilities of use for complex measurement problems are explained using the measurement of an internal screw thread as an example. The experimental results show that the measurement uncertainty of the thread minor diameter can reach ±10 μm, and the stability of the measurement system is better than 0.07%. 相似文献
64.
65.
Let
d−1{(x1,…,xd)
d:x21+···+x2d=1} be the unit sphere of the d-dimensional Euclidean space
d. For r>0, we denote by Brp (1p∞) the class of functions f on
d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on
d−1,
and Pλk(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of Brp in Lq(
d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces XN of Lq(
d−1).The main result in this paper is that for r2(d−1)2,where ANBN means that there exists a positive constant C, independent of N, such that C−1ANBNCAN.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions. 相似文献
66.
Yun-Zhi Tang Shao-Song Qian Xi-Sen Wang Hong Zhao Xue-Feng Huang Yong-Hua Li Xing-Cai Jiao Ren-Gen Xiong Prof. Dr. 《无机化学与普通化学杂志》2004,630(11):1623-1626
The in situ hydrolysis of phthalyl-γ-glutaminyl-histidine with Cd(ClO4)2·6H2O in the presence of water and methanol affords a novel two-dimensional cadmium coordination polymer, a new phase, anhydrous cadmium(II) phthalate, ( 1 ). The structure was determined by single crystal X-ray diffraction. Crystal data: P21/c, a = 13.8168(14), b = 7.0351(7), c = 8.2054(8) Å, β = 105.540(2)°, V = 768.43(13) Å3, Z = 4, R1 = 0.0380, wR2 = 0.1111. 相似文献
67.
68.
一类积分不等式的推广 总被引:1,自引:0,他引:1
对一些基本的积分不等式进行了推广,给出了含有n个无关变元的更广泛的非线性积分不等式.利用所得的不等式讨论了某些非线性积分方程解的有界性. 相似文献
69.
Jong Chan Lee Jin Young Park So Young Yoon Yong Hun Bae Seung Jun Lee 《Tetrahedron letters》2004,45(1):191-193
A novel and direct method for the synthesis of α-halocarbonyl compounds using sequential treatment of carbonyl compounds with [hydroxy(tosyloxy)iodo]benzene followed by magnesium halides under solvent-free microwave irradiation conditions is described. 相似文献
70.
Various 2-substituted indoles were prepared by heteroannulation of o-iodoanilines and terminal alkynes in a one-pot reaction with a Pd(II)-NaY zeolite catalyst. The product formation largely depended on the solvent, base, and reaction temperature. The recycled catalyst showed good reusability in the heteroannulation reaction. 相似文献