Embedding of a Banach algebra

Given a Banach space , we have shown in 1994 that a product can be defined on it in such a way that the resulting Banach algebra is isomorphic to a compact subalgebra of the algebra of all bounded linear operators on the topological dual of . Our purpose here is to prove that, more generally, any Banach algebra admitting a left approximate identity, is isomorphic to a subalgebra of , the isomorphism being isometric, provided the approximate identity is bounded by 1. As a consequence, we get a factorization through , of the elements in .

     

The high-valent iron-oxo species of polyoxometalate, if it can be made, will be a highly potent catalyst for C-H hydroxylation and double-bond epoxidation

This study uses density functional theory (DFT) calculations to explore the reactivity of the putative high-valent iron-oxo reagent of the iron-substituted polyoxometalate (POM-FeO4-), derived from the Keggin species, PW12O40(3-). It is shown that POM-FeO4- is in principle capable of C-H hydroxylation and C=C epoxidation and that it should be a powerful oxidant, even more so than the Compound I species of cytochrome P450. The calculations indicate that in a solvent, the barriers, and especially those for epoxidation, become sufficiently small that one may expect an extremely fast reaction. An experimental investigation (by R.N. and A.M.K.) shows, however, that the formation of POM-FeO4- using the oxygen donor, F5PhI-O, leads to a persistent adduct, POM-FeO-I-PhF5(4-), which does not decompose to POM-FeO4- + F5Ph-I at the working temperature and exhibits sluggish reactivity, in accord with previous experimental results (Hill, C. L.; Brown, R. B., Jr. J. Am. Chem. Soc. 1986, 108, 536 and Mansuy, D.; Bartoli, J.-F.; Battioni, P.; Lyon, D. K.; Finke, R. G. J. Am. Chem. Soc. 1991, 113, 7222). Subsequent calculations indeed reveal that the gas-phase binding energy of F5PhI to POM-FeO4- is high (ca. 20 kcal/mol) compared to the corresponding binding energy of propene (ca. 2-3 kcal/mol). As such, the POM-FeO-I-PhF5(4-) complex is expected to be persistent toward the displacement of F5PhI by a substrate like propene, leading thereby to sluggish oxidative reactivity. According to theory, overcoming this technical difficulty may turn out to be very rewarding. The question is, can POM-FeO4- be made?     

Direct-type catalytic three-component Mannich reaction in aqueous media

Bismuth triflate catalyzed direct-type Mannich reaction of cyclohexanone, aromatic aldehyde, and aromatic amine proceeded smoothly in water to afford the corresponding β-amino ketone with very good yield and moderate to good anti selectivity.     

Facile synthesis of alpha,alpha-diisobutylglycine and anchoring its derivatives onto PAL-PEG-PS resin

alpha,alpha-Diisobutylglycine has been synthesized using a Pd-mediated dialkylation of ethyl nitroacetate as a key first step. The free alphaalphaAA is N(alpha)-protected and has been applied to the assembly of conformationally constrained peptide analogues. Mixed anhydrides from BOP-Cl and Fmoc-alphaalphaAA-OH are used for anchoring alphaalphaAAs onto a trialkoxybenzyl linker on PEG-PS grafted support, upon which a beta-strand mimic with difficult sequence is assembled in a superior quality.     

Uranyl and strontium salt solvation in room-temperature ionic liquids. A molecular dynamics investigation

Using molecular dynamics simulations, we compare the solvation of uranyl and strontium nitrates and uranyl chlorides in two room-temperature ionic liquids (ILs): [BMI][PF(6)] based on 1-butyl-3-methylimidazolium(+),PF(6)(-) and [EMI][TCA] based on 1-ethyl-3-methylimidazolium(+),AlCl(4)(-). Both dissociated M(2+),2NO(3)(-) and associated M(NO(3))(2) states of the salts are considered for the two cations, as well as the UO(2)Cl(2) and UO(2)Cl(4)(2)(-) uranyl complexes. In a [BMI][PF(6)] solution, the "naked" UO(2)(2+) and Sr(2+) ions are surrounded by 5.8 and 10.1 F atoms, respectively. The first-shell PF(6)(-) anions rotate markedly during the dynamics and are coordinated, on the average, monodentate to UO(2)(2+) and bidentate to Sr(2+). In an [EMI][TCA] solution, UO(2)(2+) and Sr(2+) coordinate 5.0 and 7.4 Cl atoms of AlCl(4)(-), respectively, which display more restricted motions. Four Cl atoms sit on a least motion pathway of transfer to uranyl, to form the UO(2)Cl(4)(2)(-) complex. The free NO(3)(-) anions and the UO(2)Cl(4)(2)(-) complex are surrounded by imidazolium(+) cations ( approximately 4 and 6-9, respectively). The first shell of the M(NO(3))(2) and UO(2)Cl(2) neutral complexes is mostly completed by the anionic components of the IL, with different contributions depending on the solvent, the M(2+) cation, and its counterions. Insights into energy components of solvation are given for the different systems.     

Molecular cloning,gene structure and expression profile of two mouse peroxisomal 3-ketoacyl-CoA thiolase genes

Background  

In rats, two peroxisomal 3-ketoacyl-CoA thiolase genes (A and B) have been cloned, whereas only one thiolase gene is found in humans. The aim of this study was thus to clone the different mouse thiolase genes in order to study both their tissue expression and their associated enzymatic activity.     

Esters phosphoriques cycliques ou non cycliques de quelques O-isopropylidène-1,2-α-D-pentofurannoses. Communication préliminaire

Cyclic and acyclic phosphate esters of some 1,2-O-isopropylidene-α-D -pentofuranoses When treated with monophenyl phosphorodichloridate, 1,2-O-isopropylidene-α-D -xylofuranose gave the two possible, isolable isomers of the corresponding 3,5-cylic phenylphosphate. Upon phosphorylation of the same sugar derivative using bis (2,2,2-trichloroethyl) phosphorochloridate only one isomer was formed. The same situation obtained when preparing 1,2-O-isopropylidene-α-D -ribofuranose-3,5-cyclic phenylphosphate. The synthesis of a new kind of sugar phosphate with a branched-chain unsaturated sugar moiety namely the trans-3-deoxy-3-C-cyanomethylene-1,2-O-isopropylidene-D -erytho-pentofuranose 5-bis(2,2,2-trichloroethyl) phosphate is also described.     

Rang des courbes elliptiques et sommes d'exponentielles

Lety ²=x ³+a(t)x+b(t) be the equation of an elliptic curve over , wherea(t) andb(t) are polynomials over. We give an upper bound on average of the rank of such curves whent varies over under the assumption that theL-function attached to these curves satisfies classical assumptions. The proof is based on estimates of exponential sums, over varieties, which are treated by Deligne's theorem.