Trace Inequalities,Maximal Inequalities,and Weighted Fourier Transform Estimates

In the spirit of work of Kerman and Sawyer, a condition is given that is necessary and sufficient for the Fourier transform norm inequality $\Big(\int_{{\Bbb R}_d} \vert\hat{f}\vert^q d\mu\Big)^{1/q} \leq C\Big(\int_{{\Bbb R}_d} \vert f\vert^p v\Big)^{1/p}$ provided v is a radial weight for which v^?1/p is convexly decreasing and μ is a suitable measure. We also establish alternative conditions for such inequalities by proving corresponding trace type inequalities and maximal function inequalities that underlie the Fourier transform estimates. Our conditions are relatively simple to compute. Among applications we give extensions of a Sobolev restriction theorem.     

Synthesis of ansamycins: An approach to the naphthoquinone portion of the rifamycins and streptovaricins

Naphthoquinone $\text{1}$, a fully functionalized model for intermediates in ansamycin synthesis, was prepared by the intramolecular Claisen condensation of benzofuran $\text{9}$ followed by oxidation of the novel tricyclic compound $\text{10}$.     

A new tri-orthogonal strategy for peptide cyclization

A solid phase tri-orthogonal protection/cleavage strategy that uses acidic, basic, and neutral conditions is described. Strategically protected alpha-azido-gamma-9-fluorenylmethyl-L-glutamate (1) and alpha-azido-epsilon-N-Fmoc-L-lysine (2) were incorporated into growing peptides on Wang resin using a novel azide protection strategy. These residues, separated by 1-3 monomers, were deprotected at the side chains and cyclized via lactam formation. The N-terminus was further functionalized to extend the chain. This method represents a straightforward protocol for peptide cyclization on solid support.     

Optical electron transfer processes. The dependence of intervalence line shape and transition energy on chromophore concentration

Optical electron transfer in the mixed-valence cation of biferrocenylacetylene (BF⁺) has been examined in CD₂Cl₂ solvent. The intervalence absorption line shape is relatively narrow at both low and high chromophore concentrations, but broader at intermediate concentrations. The transition energy for metal-to-metal charge transfer increases from ≈4440 cm⁻¹ at infinite dilution to 5995 cm⁻¹ for 3.8 mM BF⁺. Related effects exist due to added electrolyte. Neither the electrolyte nor chromophore concentration effects are expected from a simple reading of electron transfer theories. Nevertheless, both phenomena can be understood and within the context of theory upon careful consideration of the effects of ion-pairing (and tripling) equilibria upon electron-transfer energetics.     

Total synthesis of (+)-aspidospermidine: a new strategy for the enantiospecific synthesis of aspidosperma alkaloids

A new strategy was developed for the enantiospecific synthesis of aspidosperma alkaloids. The key steps involve a novel ketene-lactonization reaction of a chiral vinyl sulfoxide to efficiently set up the quaternary carbon center, and a tandem Michael addition-alkylation reaction sequence to form the polycyclic core structure. This new strategy was employed in the total synthesis of natural product (+)-aspidospermidine.     

Reaction of sulphate radical anion (SO<Superscript>.</Superscript><Subscript>4</Subscript><Superscript>-</Superscript>) with hydroxy-and methyl-substituted pyrimidines: a pulse radiolysis study

Reactions of sulphate radical anion (SO·₄ ^-) with 4,6-dihydroxy-2-methyl pyrimidine (DHMP), 2,4-dimethyl-6-hydroxy pyrimidine (DMHP), 6-methyl uracil (MU) and 5,6-dimethyl uracil (DMU) have been studied by pulse radiolysis at pH 3 and at pH 10. The transient intermediate spectra were compared with those from the reaction of hydroxyl radical (·OH). It is proposed that SO·₄ ^- produces radical cations of these pyrimidines in the initial stage. These radical cations are short-lived except in the case of DMHP where a relatively longer lived radical cation is proposed to be formed. When there is a hydrogen atom attached to the N(1) or N(3) position, a deprotonation from these sites is highly favored. When there is no hydrogen attached to these sites, deprotonation from a substituted methyl group is favored. At acidic pH, deprotonation from nitrogen is observed for DHMP, MU and DMU. At basic pH, the radical cation reacts with OH^- leading to the formation of OH adducts.     

Functionalization of the 4(5)methyl group of imidazoles: A novel synthesis of substituted imidazoles

Acyl vinyl phosphonium salts react with amidines to form imidazolyl phosphonium salts. These imidazolyl salts can be readily converted to multifunctional imidazoles with quantitative recovery of triphenyl phosphine.     

An efficient synthesis of 6-formyl-1,2-dihydro-2-oxo-3-pyridinecarboxylic acid and some carbonyl derivatives of it and its 6-acetyl homologue

Starting with 1,1-dimethoxy-2-propanone ( 1 ), 6-formyl-1,2-dihydro-2-oxo-3-pyridinecarboxylic acid ( 5a ) has been prepared in large quantities by a highly efficient, 4-step synthesis. This compound, along with its one carbon homologue, 6-acetyl-1,2-dihydro-2-oxo-3-pyridinecarboxylic acid ( 5b ) has been reacted with several carbonyl derivative forming reagents to provide a series of side chains for β-lactams. Among these carbonyl derivatives are styrylamides which were prepared from Wittig and Horner-Emmons reagents. The preparation of the phosphonium salts and phosphonate esters is also described.