We, herein, report synthesis of methyl ester of (E)-5-octadecen-7,9-diynoic acid, one of the novel acetylenic fatty acids of Paramacralabium caeruleum root bark with unique biological activity, by coupling synthesized C1 to C8 fragment with 1-decyne. 相似文献
Let q1 be an integer, denote the unit sphere embedded in the Euclidean space , and μq be its Lebesgue surface measure. We establish upper and lower bounds for
where is the unit ball of a suitable Besov space on the sphere. The upper bounds are obtained for choices of xk and wk that admit exact quadrature for spherical polynomials of a given degree, and satisfy a certain continuity condition; the lower bounds are obtained for the infimum of the above quantity over all choices of xk and wk. Since the upper and lower bounds agree with respect to order, the complexity of quadrature in Besov spaces on the sphere is thereby established. 相似文献
Wavelets in terms of sine and cosine functions are constructed for decomposing 2π-periodic square-integrable functions into different octaves and for yielding local information within each octave. Results on a simple mapping into the approximate sample space, order of approximation of this mapping, and pyramid algorithms for decomposition and reconstruction are also discussed. 相似文献
We obtain a characterization of local Besov spaces of periodic functions in terms
of trigonometric polynomial operators. We construct a sequence of operators whose values are
(global) trigonometric polynomials, and yet their behavior at different points reflects the behavior of the target function near each of these points. In addition to being localized, our operators preserve trigonometric polynomials of degree commensurate with the degree of polynomials given by the operators. Our constructions are “universal;” i.e., they do not require an a priori knowledge about the smoothness of the target functions. Several numerical examples are discussed, including applications to the problem of direction finding in phased array antennas and finding the location of jump discontinuities of derivatives of different order. 相似文献
Geodetic and meteorological data, collected via satellites for example, are genuinely scattered and not confined to any special set of points. Even so, known quadrature formulas used in numerically computing integrals involving such data have had restrictions either on the sites (points) used or, more significantly, on the number of sites required. Here, for the unit sphere embedded in , we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered sites. To be exact, these formulas require only a number of sites comparable to the dimension of the space. As a part of the proof, we derive -Marcinkiewicz-Zygmund inequalities for such sites.
We prove that an artificial neural network with multiple hidden layers and akth-order sigmoidal response function can be used to approximate any continuous function on any compact subset of a Euclidean space so as to achieve the Jackson rate of approximation. Moreover, if the function to be approximated has an analytic extension, then a nearly geometric rate of approximation can be achieved. We also discuss the problem of approximation of a compact subset of a Euclidean space with such networks with a classical sigmoidal response function.Dedicated to Dr. C.A. Micchelli on the occasion of his fiftieth birthday, December 1992Research supported in part by AFOSR Grant No. 226 113 and by the AvH Foundation. 相似文献
In this paper, we study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms have the same nth root behavior as the weighted norms for certain extremal polynomials. Our results include as special cases several of the previous results of Erd
s, Freud, Jentzsch, Szeg
and Blatt, Saff, and Simkani. Applications are given concerning the zeros of orthogonal polynomials over a smooth Jordan curve (in particular, on the unit circle) and the zeros of polynomials of best approximation on R to nonentire functions. 相似文献
Let , and for k=0,1,…, denote the orthonormalized Jacobi polynomial of degree k. We discuss the construction of a matrix H so that there exist positive constants c, c1, depending only on H, α, and β such that
Specializing to the case of Chebyshev polynomials, , we apply this theory to obtain a construction of an exponentially localized polynomial basis for the corresponding L2 space. 相似文献