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101.
Approximation by translates of refinable functions 总被引:23,自引:0,他引:23
Summary.
The functions
are
refinable if they are
combinations of the rescaled and translated functions
.
This is very common in scientific computing on a regular mesh.
The space of approximating functions with meshwidth
is a
subspace of with meshwidth
.
These refinable spaces have refinable basis functions.
The accuracy of the computations
depends on , the
order of approximation, which is determined by the degree of
polynomials
that lie in .
Most refinable functions (such as scaling functions in the theory
of wavelets) have no simple formulas.
The functions
are known only through the coefficients
in the refinement equation – scalars in the traditional case,
matrices for multiwavelets.
The scalar "sum rules" that determine
are well known.
We find the conditions on the matrices
that
yield approximation of order
from .
These are equivalent to the Strang–Fix conditions on the Fourier
transforms
, but for refinable
functions they can be explicitly verified from
the .
Received
August 31, 1994 / Revised version received May 2, 1995 相似文献
102.
Magnetic and structural data for 28 compounds containing the tetrabromocuprate ion are presented. The parameters which affect the strength and sign of the magnetic superexchange interaction via non-bonding contacts between bromide ions are described and a system for describing the topology of the interaction between tetrahedra is proposed. Analysis of the data suggests that the primary factors affecting the magnetic exchange are the Br?Br distance, the Cu-Br?Br angle and the Cu-Br?Br-Cu dihedral angle. 相似文献
103.
Stambuli JP Incarvito CD Bühl M Hartwig JF 《Journal of the American Chemical Society》2004,126(4):1184-1194
A series of monomeric arylpalladium(II) complexes LPd(Ph)X (L = 1-AdPtBu2, PtBu3, or Ph5FcPtBu2 (Q-phos); X = Br, I, OTf) containing a single phosphine ligand have been prepared. Oxidative addition of aryl bromide or aryl iodide to bis-ligated palladium(0) complexes of bulky, trialkylphosphines or to Pd(dba)2 (dba = dibenzylidene acetone) in the presence of 1 equiv of phosphine produced the corresponding arylpalladium(II) complexes in good yields. In contrast, oxidative addition of phenyl chloride to the bis-ligated palladium(0) complexes did not produce arylpalladium(II) complexes. The oxidative addition of phenyl triflate to PdL2 (L = 1-AdPtBu2, PtBu3, or Q-phos) also did not form arylpalladium(II) complexes. The reaction of silver triflate with (1-AdPtBu2)Pd(Ph)Br furnished the corresponding arylpalladium(II) triflate in good yield. The oxidative addition of phenyl bromide and iodide to Pd(Q-phos)2 was faster than oxidative addition to Pd(1-AdPtBu2)2 or Pd(PtBu3)2. Several of the arylpalladium complexes were characterized by X-ray diffraction. All of the arylpalladium(II) complexes are T-shaped monomers. The phenyl ligand, which has the largest trans influence, is located trans to the open coordination site. The complexes appear to be stabilized by a weak agostic interaction of the metal with a ligand C-H bond positioned at the fourth-coordination site of the palladium center. The strength of the Pd.H bond, as assessed by tools of density functional theory, depended upon the donating properties of the ancillary ligands on palladium. 相似文献
104.
Solvolysis of asymmetric homoallylic triflates bearing a terminal stannyl substituent gives disubstituted cyclopropanes and bicyclopropanes bearing differentiated termini in high enantiopurity. 相似文献
105.
Abstract— Methionine (Met) photooxidation sensitized by rose bengal has been studied as a function of pH and other variables. At pH ≤ 6, the reaction is a simple one, 2 Met + O2→ 2 Methionine sulfoxide (MetO). At pH 6–10, another mechanism becomes important, leading to dehydromethionine; the structure of this compound was correctly assigned by Lavine (1945) as the heterocyclic N-S compound 2. One mole of H2O2 is also produced in this process. Dehydromethionine hydrolyzes slowly to MetO. Above pH9, a process leading directly to MetO + H2O2 becomes important. The stoichiometry of the latter two processes are Met + O2+ H2O → MetO + H2O2; competition among these three processes accounts for the puzzling variations in O2 uptake. N-Formylated derivatives of methionine undergo only the first and third processes. Substantial catalytic effects of buffers complicate the picture. All the reactions appear to involve singlet oxygen, since there is the predicted effect of D2O vs H2O on the rate of reaction, although the situation is complicated by apparent aggregation of Met above 5 mM. 相似文献
106.
Moody CJ 《Chemical communications (Cambridge, England)》2004,(12):1341-1351
Oxime ethers prepared from (R)- or (S)-O-(1-phenylbutyl)hydroxylamine (ROPHy or SOPHy) are versatile intermediates for the asymmetric synthesis of a range of nitrogen containing compounds including simple amines, 1,2-aminoalcohols, alpha- and beta-amino acids, heterocyclic building blocks of natural products, piperidine alkaloids, lactams, 5- to 8-membered ring nitrogen heterocycles, imino-sugars, and chiral ferrocene based receptors. 相似文献
107.
Many biologically active natural products are constrained by macrocyclization and modified with carbohydrates. These two types of modifications are essential for their biological activities. Here we report a chemoenzymatic approach to make carbohydrate-modified cyclic peptide antibiotics. Using a thioesterase domain from the decapeptide tyrocidine synthetase, 13 head-to-tail cyclized tyrocidine derivatives were obtained with one to three propargylglycines incorporated at positions 3-8. These cyclic peptides were then conjugated to 21 azido sugars via copper(I)-catalyzed cycloaddition. Antibacterial and hemolytic assays showed that the two best glycopeptides, Tyc4PG-14 and Tyc4PG-15, have a 6-fold better therapeutic index than the natural tyrocidine. We believe this method will also be useful for modifying other natural products to search for new therapeutics. 相似文献
108.
The S(1)<--S(0) transition of 1-phenylimidazole (1PI) has been studied in a supersonic jet expansion by resonant two-photon ionization. The origin band at 36 075 cm(-1) is accompanied by a low frequency progression associated with torsion about the bond connecting phenyl and imidazole groups. Torsional potentials have been determined for both states. In S(0), phi(min)=37.2+/-0.5 degrees and the planar barrier is 339+/-20 cm(-1), while in S(1), phi(min)=17.6+/-0.5 degrees and the planar barrier is 57+/-2 cm(-1). The transition moment alignment is observed to be consistent with an excited state of L(b) character, in spite of the "off-axis" conjugation provided by the imidazole ring. These results are compared with ab initio calculations on both states, performed using Hartree-Fock, M?ller-Plesset second-order perturbation, density functional theory with the Becke3-Lee-Yang-Parr functional, time-dependent density functional theory, configuration interaction singles, and complete active space self-consistent field methods. Solution-phase UV spectra of neutral and protonated 1PI are also reported. 相似文献
109.
Nonribosomal peptide synthetases (NRPS) are multimodular biocatalysts that bacteria and fungi use to assemble many complex peptides with broad biological activities. The same modular enzymatic assembly line principles are found in fatty acid synthases (FAS), polyketide synthases (PKS), and most recently in hybrid NRPS/PKS multienzymes. FAS as well as PKS are known to function as homodimeric enzyme complexes, raising the question of whether NRPS may also act as homodimers. To test this hypothesis, biophysical methods (size exclusion chromatography, analytical equilibrium ultracentrifugation, and chemical crosslinking) and biochemical methods (two-affinity-tag-system and complementation studies with enzymes being inactivated in different catalytic domains) were applied to NRPS subunits from the gramicidin S (GrsA-ATE), tyrocidine (TycB(1)-CAT and TycB(2-3)-AT.CATE), and enterobactin (EntF-CATTe) biosynthetic systems. These methods had revealed the dimeric structure of FAS and PKS previously, but all three NRPS systems investigated are functionally active as monomers. 相似文献
110.
Frederick MO Mulder JA Tracey MR Hsung RP Huang J Kurtz KC Shen L Douglas CJ 《Journal of the American Chemical Society》2003,125(9):2368-2369
A copper-catalyzed new C-N bond formation involving a sp-hybridized carbon is described here leading to a facile entry for syntheses of chiral ynamides. This direct N-alkynylation of amides should have a significant impact on the future development of synthetic methodologies employing ynamides. 相似文献