Newton＇s polynomial interpolation may be the favourite linear interpolation in the sense that it is built up by means of the divided differences which can be calculated recursively and produce useful intermediate results. However Newton interpolation is in fact point based interpolation since a new interpolating polynomial with one more degree is obtained by adding a new support point into the current set of support points once at a time. In this paper we extend the point based interpolation to the block based interpolation. Inspired by the idea of the modern architectural design, we first divide the original set of support points into some subsets （blocks）, then construct each block by using whatever interpolation means, linear or rational and finally assemble these blocks by Newton＇s method to shape the whole interpolation scheme. Clearly our method offers many flexible interpolation schemes for choices which include the classical Newton＇s polynomial interpolation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of our method. 相似文献
Summary: A strategy for the synthesis of sol‐gel hybrid materials that contain perfluorocyclobutyl groups is reported. Sol‐gel films have been prepared from three types of siloxane monomers using a typical sol‐gel method in an acidic atmosphere, followed by UV irradiation and dimerization. The materials show high thermal stability that exceeds 400 °C. At a wavelength of 1 550 nm, the refractive index, the birefringence, and the optical loss of the sol‐gel materials are found to be in the ranges of 1.4568–1.4876, −0.0003–0.0029, and 0.34–0.45 dB · cm−1, respectively.
Zero mode birefringence (TE: solid, TM: dash dot) of sol‐gel materials (PFSI/TFVOSI/MSI = 6:1:3) (TE and TM represent polarization perpendicular and parallel to the plane of incidence, respectively). 相似文献
ABA block copolymers of polylactide and poly(ethylene glycol) as amphiphilic bioabsorbable polymers were synthesized by the ring-opening
polymerization of dl- lactide onto poly(ethylene glycol) (PEG 2000 or PEG 6000) and their structures were characterized on the basis of proton
NMR. Biodegradable nanocapsules of an aqueous insulin solution were prepared from the block copolymers and polylactide by
an improved interfacial coacervation technique. The results showed that the diameters of the nanocapsules were mainly dependent
on the ratio of the two chains in the block polymers. The size of the nanocapsules decreased with an increase in the amount
of surfactant used. More insulin solution resulted in an enlargement of the nanocapsules in diameter. In an optimum condition,
biodegradable nanocapsules could be achieved with a size around 250 nm with a narrow distribution. The encapsulation percentages
of insulin were larger in the nanocapsules from the PEG 2000 copolymers than in those from the PEG 6000 analogs and changed
with the ratios of the blocks in the block copolymers.
Received: 17 July 2000 Accepted: 24 November 2000 相似文献
