Elliptic equations with BMO coefficients in Lipschitz domains

In this paper, we study inhomogeneous Dirichlet problems for elliptic equations in divergence form. Optimal regularity requirements on the coefficients and domains for the estimates are obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO semi-norms. The domain is supposed to have Lipschitz boundary with small Lipschitz constant. These conditions for the theory do not just weaken the requirements on the coefficients; they also lead to a more general geometric condition on the domain.

     

Poincaré embedding of the diagonal

There is a Poincaré embedding structure on the diagonal under the conditions: i) is formed by gluing two compact smooth manifolds along their boundaries using a homotopy equivalence and ii) a square-root closed condition is satisfied by the fundamental groupoid of the boundary.

     

Gold compound auranofin inhibits IkappaB kinase (IKK) by modifying Cys-179 of IKKbeta subunit

Antirheumatic gold compounds have been shown to inhibit NF-kappaB activation by blocking IkappaB kinase (IKK) activity. To examine the possible inhibitory mechanism of gold compounds, we expressed wild type and mutant forms of IKKalpha and beta subunits in COS-7 cells and determined the effect of gold on the activity of these enzymes both in vivo and in vitro. Substitution of Cys-179 of IKKbeta with alanine (C179A) rendered the enzyme to become resistant to inhibition by a gold compound auranofin, however, similar protective effect was not observed with an equivalent level of IKKalpha (C178A) mutant expressed in the cells. Auranofin inhibited constitutively active IKKalpha and beta and variants; IKKalpha (S176E, S180E) or IKKbeta (S177E, S181E), suggesting that gold directly cause inhibition of activated enzyme. The different inhibitory effect of auranofin on IKKalpha (C178A) and IKKbeta (C179A) mutants indicates that gold could inhibit the two subunits of IKK in a different mode, and the inhibition of NF-kappaB and IKK activation induced by inflammatory signals in gold-treated cells appears through its interaction with Cys-179 of IKKbeta.     

Stereoselective preparation of ceramide and its skeleton backbone modified analogues via cyclic thionocarbonate intermediates derived by catalytic asymmetric dihydroxylation of alpha,beta-unsaturated ester precursors

A novel and efficient synthetic route to ceramide 1a and skeleton backbone modified ceramide analogues 1b,c is reported. The syntheses utilize osmium-catalyzed asymmetric dihydroxylation of (E)-alpha, beta-unsaturated ester 5a-c as the chiral induction step, with the desired configurations in the products 1a-c, 2a, and 13 being generated by regioselective azide substitution at the alpha position of alpha,beta-dihydroxyesters 6a-c via a cyclic thionocarbonate intermediate. Azido esters 10a-c are converted to the corresponding ceramides 1a-c by a sequence of azide reduction, N-acylation, ester reduction (NaBH(4)/LiBr), and Birch reduction of the triple bond (Li, EtNH(2)). These seven- to eight-step syntheses afford the target compounds 1a-c with excellent stereocontrol and in 30-42% overall yields. Furthermore, propargylic alpha-azido-beta-hydroxyester 10a is converted to D-erythro-sphingosine 2a via simultaneous reduction of the triple bond, azido, and ester functional groups with LiAlH(4), providing a highly concise and practical four-step synthesis of this key naturally occurring sphingolipid. The L-erythro stereoisomers are also available in high enantiomeric purity by the method described herein.     

Determination of volatile N-nitrosamines in irradiated fermented sausage by gas chromatography coupled to a thermal energy analyzer

Volatile N-nitrosodimethylamine (NDMA) and N-nitrosopyrrolidine (NPYR) in irradiated pepperoni and salami sausages were determined using a gas chromatography coupled to a thermal energy analyzer (GC-TEA). These fermented sausages with aerobic or vacuum packaging were irradiated at 0, 5, 10, and 20 kGy, and then stored for 4 weeks at 4 degrees C. Both NDMA and NPYR in the fermented sausage were significantly reduced by irradiation. The vacuum packaging showed significantly lower (P < 0.05) N-nitrosamine levels than that of the aerobic ones. After storage, the contents of NDMA and NPYR in the irradiated sausage were lower than those of the non-irradiated control. Results indicated that a high dose of irradiation (>10 kGy) was needed to reduce the carcinogenic N-nitrosamines in the fermented sausage during storage and the GC-TEA analysis was effective in determining the N-nitrosamines in irradiated meats even at low trace levels.     

Synthesis and growth inhibitory activity of chiral 5-hydroxy-2-N-acyl-(3E)-sphingenines: ceramides with an unusual sphingoid backbone

The unusual sphingoid base 5-hydroxy-3-sphingenine was identified in the hydrolysate of brain sphingolipids more than 40 years ago. We present here the first synthesis of the 5R and 5S diastereoisomers of the N-acyl derivatives of 5-hydroxy-3-sphingenine, 2 and 3, respectively, which represent regioisomers of (2S,3R)-ceramide (1). The key steps include the synthesis of alpha,beta-unsaturated ketone intermediates 4 and 5 from N-Cbz- and N-Boc-l-serine and diastereoselective reduction of the enones. The configuration at the new carbinol center was deduced by proton NMR analysis of (R)- and (S)-Mosher [methoxy(trifluoromethyl)phenylacetate] ester derivatives. Ceramide analogues 2 and 3 showed a markedly higher antiproliferative activity than 1 on MCF-7 cells.     

A stereocontrolled, efficient synthetic route to bioactive sphingolipids: synthesis of phytosphingosine and phytoceramides from unsaturated ester precursors via cyclic sulfate intermediates

An efficient and highly enantioselective method for the preparation of D-ribo- and L-lyxo-phytosphingosines (1a,b, respectively) and phytoceramides (2a,b) has been developed. The key steps in the syntheses are as follows: (i) osmium-catalyzed asymmetric dihydroxylation of 4-O-protected (E)-alpha,beta-unsaturated ester 5 (generated by dihydroxylation of 1-hexadecene, followed by oxidation to the aldehyde and Horner-Wadsworth-Emmons olefination), (ii) conversion to cyclic sulfate intermediate 7, and (iii) regioselective alpha-azidation of 7. Reduction of 4-O-protected 2-azido ester 8 via alpha-azidolactone 9 afforded phytosphingosine 1a. Staudinger reduction of the azido group of 8, followed by in situ N-acylation in aqueous media and reduction of the ester functionality with NaBH(4)/LiBr, provided phytoceramide 2a. By using a similar approach, phytosphingosine 1b was synthesized. D-erythro-4, 5-Dihydrosphingosine 1c and D-erythro-4,5-dihydroceramide 2c were synthesized in high yield from 1-hexadecanol via cyclic sulfate intermediate 15. The desired configurations at C-2, C-3, and C-4 of the sphingoid chain can be accessed readily by the route described here.     

Convergent C-glycolipid synthesis via the Ramberg-Bäcklund reaction: active antiproliferative glycolipids

[formula: see text] A novel methodology has been developed, employing the Ramberg-B?cklund rearrangement and ionic hydrogenation to synthesize C-glycosides with high stereoselectivity at the anomeric center. The C-glycolipid 14b exhibits antiproliferative properties similar to those of O-glycoside analogue 14a.     

Tangent Fibration of a Poincare Complex

The unstable tangent fibration of a Poincaré complexis defined so that it is consistent with the manifold case.It exists uniquely for each Poincaré complex X up tofibrewise homotopy equivalence and, furthermore, if a Poincaréembedding structure exists on the diagonal XXxX, its normalfibration is the tangent fibration.     

Small-ring heterocycles as components of multidentate ligands: some structural studies relating to ring opening

Structural studies of seven complexes of ligands derived from various azetidine- and oxetane-containing ligands characterise the difference in reactivity of both free and bound forms of these two four-membered heterocycles. The relatively unreactive azetidine ring is preserved in a variety of transformations, whereas facile opening of the oxetane ring provides a convenient pathway to complexes with pendent functionality.