Approximation by translates of refinable functions

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     

Magnetic exchange interactions in tetrabromocuprate compounds

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.     

Synthesis, structure, theoretical studies, and Ligand exchange reactions of monomeric, T-shaped arylpalladium(II) halide complexes with an additional, weak agostic interaction

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.     

CHEMISTRY OF SINGLET OXYGEN—XXV. PHOTOOXYGENATION OF METHIONINE*

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.     

A chemoenzymatic approach to glycopeptide antibiotics

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.     

Novel alkyl-modified anionic siloxanes as pseudostationary phases for electrokinetic chromatography. III. Performance in organic-modified buffers

Anionic water-soluble siloxanes modified with different amounts of alkyl chains have been used as pseudostationary phases in electrokinetic chromatography. Ionic siloxane polymers with attached alkyl chains of C8 and C12 and having different alkyl chain densities have been employed previously to achieve selective and efficient separations with a range of electrophoretic mobilities and methylene selectivities. In this study, the performance of three alkyl-modified siloxanes is examined in different organic-modified buffers and at differing amounts of organic modifier. The organic modifiers used are acetonitrile and methanol. The siloxanes are stable in these organic solvents and show good mobility and good methylene selectivities even at high concentration of organic solvent. Siloxanes have also been used to separate a mixture of 14 polynuclear aromatic hydrocarbons in an acetonitrile-modified buffer.     

Reduction and methyl transfer kinetics of the alpha subunit from acetyl coenzyme a synthase

Stopped-flow was used to evaluate the methylation and reduction kinetics of the isolated alpha subunit of acetyl-Coenzyme A synthase from Moorella thermoacetica. This catalytically active subunit contains a novel Ni-X-Fe4S4 cluster and a putative unidentified n = 2 redox site called D. The D-site must be reduced for a methyl group to transfer from a corrinoid-iron-sulfur protein, a key step in the catalytic synthesis of acetyl-CoA. The Fe4S4 component of this cluster is also redox active, raising the possibility that it is the D-site or a portion thereof. Results presented demonstrate that the D-site reduces far faster than the Fe4S4 component, effectively eliminating this possibility. Rather, this component may alter catalytically important properties of the Ni center. The D-site is reduced through a pathway that probably does not involve the Fe4S4 component of this active-site cluster.     

Meso-tetraaryl cofacial bisporphyrins delivered by Suzuki cross-coupling

The Suzuki cross-coupling methodology provides a facile synthetic approach for the modular preparation of meso-tetraaryl cofacial bisporphyrins anchored by xanthene and dibenzofuran. This synthetic method furnishes cofacial bisporphyrin templates with enhanced steric and electronic protection from mu-oxo formation and oxidative degradation. The ability of these platforms to support multielectron oxidation chemistry mediated by proton-coupled electron transfer (PCET) is demonstrated by their reactivity for the catalytic disproportionation of hydrogen peroxide to oxygen and water.     

Intramolecular C-H activation by inferred terminal cobalt imido intermediates

Reaction of TpR,MeCo(I) dinitrogen complexes (R = iPr, tBu) with trimethylsilyl azide yields structurally characterized compounds that imply the formation of reactive intermediates of the type TpR,MeCo=NSiMe3. These cobalt imido species apparently abstract hydrogen from the 3-substituent of the Tp-ligand, leading to the formation of amido complexes accompanied by either Co-C bond formation (R = tBu) or C-C bond formation (R = iPr).