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1.
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
2.
Theresa J. Hermel-Davidock H. Sean Tang Daniel J. Murray Stephen F. Hahn 《Journal of polymer science. Part A, Polymer chemistry》2007,45(24):3338-3348
It has been found that by the addition of low concentrations of an amphiphilic block copolymer to an epoxy resin, novel disordered morphologies can be formed and preserved through curing. This article will focus on characterizing the influence of the block copolymer and casting solvent on the templated morphology achieved in the thermoset sample. The ultimate goal of this work is to determine the parameters that would control the microphase morphology produced. Epoxy resins blended with a series of amphiphilic block copolymers based on hydrogenated polyisoprene (polyethylene-alt-propylene or PEP) and polyethylene oxide (PEO), specifically, were investigated. In this article, the cure-induced order–order phase transition from the spherical to wormlike micelle morphology will also be discussed. It is proposed that the formation of the wormlike micelle structure from the spherical micelle structure is similar to the phase transition behavior that occurs in dilute block copolymer solutions as a function of the influence of the solvent on micelle morphology. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3338–3348, 2007 相似文献
3.
Sean D. Brooks M. F. Mahmood J. A. Donaldson 《Journal of Mathematical Modelling and Algorithms》2004,3(1):19-29
A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low
birefringent optical fiber is presented. The numerical algorithm is described in detail.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
4.
5.
Gavin D. Henry Author Vitae 《Tetrahedron》2004,60(29):6043-6061
6.
Jun Jiao Lifeng Dong Sean Foxley Catherine L Mosher David W Tuggle 《Microscopy and microanalysis》2003,9(6):516-521
In this article, we report a technique for growing carbon nanotubes in a more controllable fashion, which enables us to synthesize nanotubes directly in various forms of designed patterns. This nanofabrication process is based on a combination of focused ion beam (FIB) and chemical vapor deposition (CVD) techniques. In this process, arrays of conductive patterns were first deposited on silicon substrates by directing a gaseous compound (C(9)H(16)Pt) via the capillary needle-sized nozzles within a FIB system. The substrates were then coated with catalyst and further modified by the FIB to localize the position of the catalyst. Finally, the growth of carbon nanotubes on the designed substrates was carried out by CVD of hydrocarbon gases. This fabrication technique has the advantage of positioning carbon nanotubes in selected locations. This may open up opportunities for the direct synthesis of carbon nanotubes onto almost any substrate material, thus allowing fabrication of carbon nanotube-based devices. 相似文献
7.
Lakshmi N. Roy Rabindra N. Roy Cole E. Denton Sean R. LeNoue Chandra N. Roy Shahaf Ashkenazi Thomas B. Williams Daniel R. Church Michael S. Fuge Kartik N. Sreepada 《Journal of solution chemistry》2006,35(4):605-624
The values of the second dissociation constant, K
2, and related thermodynamic quantities of the ampholyte bis[(2-hydroxyethyl)amino]acetic acid (BICINE) have been determined at temperatures from 5 to 55 ∘C. The pH values of six equimolal buffer solutions, and four buffer solutions having ionic strengths (I = 0.16 mol⋅kg−1) similar to those in blood plasma, have been evaluated at 12 temperatures from 5 to 55 ∘C using the Bates–Guggenheim convention. The liquid junction potentials (E
j
) between the buffer solutions of BICINE and saturated KCl solution of the calomel electrode at 25 and 37 ∘C have been estimated by measurement with a flowing junction cell. These values of E
j
have been used to ascertain the operational pH values at 25 and 37 ∘C. The pK
2 values at 25 and 37 ∘C are 8.333 and 8.156, respectively. The thermodynamic quantities associated with the second acid dissociation have been calculated from the values of pK
2 as a function of temperature. The zwitterionic buffer BICINE was shown to be useful as a pH standard in the region close to that of blood serum. 相似文献
8.
We couple a morphological study of an immiscible binary AB mixture with a micromechanical simulation to determine how the spatial distribution of the A and B domains and the interfacial region (interphase) affects the mechanical behavior of the blend. The morphological studies are conducted through a three-dimensional Cahn-Hilliard (CH) simulation. Through the CH calculations, we obtain the size and structure of the domains for different blend compositions. The output of the CH model serves as the input to the Lattice Spring Model (LSM), which consists of a three-dimensional network of springs. In particular, the location of the different phases is mapped onto the LSM lattice and the appropriate force constants are assigned to the LSM sites. A stress is applied to the LSM lattice and we calculate the elastic response of the material. We find that the local stress and strain fields are highly dependent on the morphology of the system. By integrating the morphological and mechanical models, we can isolate how modifications in the composition of the mixture affect the macroscopic behavior. Thus, we can establish how choices made in the components affect the ultimate performance of the material. 相似文献
9.
Using flow microcalorimetry, the ion association reaction M2+(aq)+Fe(CN)
6
4–
(aq)=MFe(CN)
6
2–
(aq) (M=Ca, Mg) has been studied at 25°C over the ionic strength range 0.02 to 0.08 mol-dm–3. Analyses of the data to obtain Ho, the enthalpy change at infinite dilution, are described. The value obtained for Ho is sensitive to the kind of functions used to correct for non-ideal behavior. 相似文献
10.
Brandon D. ConleyBurl C. Yearwood Sean ParkinDavid A. Atwood 《Journal of fluorine chemistry》2002,115(2):155-160
The preparation and characterization of the ammonium hexafluorosilicate salts, 2[R]+ [SiF6]2− (where R=piperidinium (2), methylammonium (3), quinolinium (4), acridinium (5), 2,2,6,6-tetramethylpiperidinium (6), and propylammonium (7)) is described.The salts were prepared from the reaction of the corresponding alkylammonium fluoride with silica gel. The compounds were characterized by NMR, IR, mass spectrometry and in the case of 1 (piperidinium fluoride), 2-4 by X-ray crystallography. Compounds 1-3 crystallize in the orthorhombic crystal system (space groups Iba2, Fdd2, and Pnnm, respectively), with Z=8, 14, and 4, respectively. Compound 4 crystallizes in the triclinic space group P-1, with Z=2. Compounds 1-4 exhibit hydrogen bonding. 相似文献