A reverse isoperimetric inequality for J-holomorphic curves

We prove that the length of the boundary of a J-holomorphic curve with Lagrangian boundary conditions is dominated by a constant times its area. The constant depends on the symplectic form, the almost complex structure, the Lagrangian boundary conditions and the genus. A similar result holds for the length of the real part of a real J-holomorphic curve. The infimum over J of the constant properly normalized gives an invariant of Lagrangian submanifolds. We calculate this invariant to be \({2\pi}\) for the Lagrangian submanifold \({\mathbb{R} P^n \subset \mathbb{C} P^n.}\) We apply our result to prove compactness of moduli of J-holomorphic maps to non-compact target spaces that are asymptotically exact. In a different direction, our result implies the adic convergence of the superpotential.     

Gundelia tournefortii: Fractionation,Chemical Composition and GLUT4 Translocation Enhancement in Muscle Cell Line

Type 2 diabetes (T2D) is a chronic metabolic disease, which could affect the daily life of patients and increase their risk of developing other diseases. Synthetic anti-diabetic drugs usually show severe side effects. In the last few decades, plant-derived drugs have been intensively studied, particularly because of a rapid development of the instruments used in analytical chemistry. We tested the efficacy of Gundelia tournefortii L. (GT) in increasing the translocation of glucose transporter-4 (GLUT4) to the myocyte plasma membrane (PM), as a main strategy to manage T2D. In this study, GT methanol extract was sub-fractionated into 10 samples using flash chromatography. The toxicity of the fractions on L6 muscle cells, stably expressing GLUTmyc, was evaluated using the MTT assay. The efficacy with which GLUT4 was attached to the L6 PM was evaluated at non-toxic concentrations. Fraction 6 was the most effective, as it stimulated GLUT4 translocation in the absence and presence of insulin, 3.5 and 5.2 times (at 250 μg/mL), respectively. Fraction 1 and 3 showed no significant effects on GLUT4 translocation, while other fractions increased GLUT4 translocation up to 2.0 times. Gas chromatography–mass spectrometry of silylated fractions revealed 98 distinct compounds. Among those compounds, 25 were considered anti-diabetic and glucose disposal agents. These findings suggest that GT methanol sub-fractions exert an anti-diabetic effect by modulating GLUT4 translocation in L6 muscle cells, and indicate the potential of GT extracts as novel therapeutic agents for T2D.     

The effect of phase transfer catalysts on the Reimer-Tiemann reaction

Quaternary ammonium salts were found inactive as phase transfer catalysts in the Reimer-Tiemann reaction. Tertiary amines, on the other hand, proved to have significant effect on the process.     

Use of 13C isotope shifts for assignment of deuterium labelling sites in 1,3-diphenylpropan-1-one

¹³C NMR spectroscopy was used for the unequivocal analysis of the mixture of products of RuCl₂[P(C₆H₅)₃]₃-catalysed transfer deuteriation of benzylideneacetophenone by (a) DCOONa/H₂O, (b) HCOONa/D₂O and (c) DCOONa/D₂O. Signal assignments in the ¹³C spectra were obtained mainly from the deuterium-induced ¹³C isotope shifts. The geminal ¹³C? ²H shift of the β-carbon of deuteriated 1,3-diphenylpropan-1-one is almost twice that for the α-carbon.     

Phosphorus heterocycle synthesis by RPX2·AlX3 addition to [1,n]dienes VI : RPX2·AlX3 phosphorylations in the presence and absence of water

The electrophilic addition of RPX₂·AlX₃ (1) (R=Ph or Me; X=Cl or Br) to [1,n]dienes was found to be an efficient and useful reaction for the synthesis of a variety of new phospha-heterocycles such as substituted phospholanes, dihalophosphorinanes, phosphorinenes, 3-phosphabicyclo[3.1.0]hexanes, 2-phosphabicyclo[2.2.1] heptanes, 2-phosphabicyclo[3.2.1]octanes and substituted phosphetanes. An ionic multistep mechanism, governed by the stability of the intermediate carbonium ions, is suggested. The phosphorylation reaction was found to be most sensitive to water and in its presence (even 0.1 eq.) it takes a different course. The products, results from hydrogen and RP(O)X addition to the double bond. The phosphorylation is initiated by an unusual protonation process which employs the specific catalytic properties of the AlCl₃·H₂O complex (HX + RPX₂ in the presence or absence of AlCl₃ do not give any defined phosphorylation products but polymers). Some of the examined dienes give with water-doped RPX₂·AlX₃ phosphorylations and/or HX additions, involving in several cases participation of both double bonds to give intramolecular cyclisation products. These products may explain the substances obtained following phosphorylation of simple n-alkenes. Compound 16, one of the new addition compounds, was found to cyclise to the 2-oxaphospholane system (19).     

The 13C-NMR spectrum and stereochemistry of heteronemin

The ¹³C-NMR spectrum of heteronemin (1), a new sesterterpene from marine origin is reported. Assignment of most of the signals was accomplished by a combination of off-resonance decoupling, PRFT measurement, comparison with suitable known model compounds and LIS measurements. An all trand-anti-trans configuration is suggested from 1 according to the ¹³C-NMR data.     

Generalized ridge regression,least squares with stochastic prior information,and Bayesian estimators

The ridge estimator of the usual linear model is generalized by the introduction of an a priori vector r and an associated positive semidefinite matrix S. It is then shown that the generalized ridge estimator can be justified in two ways: (a) by the minimization of the residual sum of squares subject to a constraint on the length, in the metric S, of the vector of differences between r and the estimated linear model coefficients, (b) by incorporating prior knowledge, r playing the role of the vector of means and S proportional to the precision matrix. Both a Bayesian and an Aitken generalized least squares frameworks are used for the latter. The properties of the new estimator are derived and compared to the ordinary least squares estimator. The new method is illustrated with different assumptions on the form of the S matrix.     

Latrunculin,a new 2-thiazolidinone macrolide from the marine sponge latrunculia magnifica

Three new toxins were isolated from the Red Sea sponge $\text{Latrunculia magnifica}$ A full structure determination of these toxins, by spectroscopic methods, was aided by an X-ray diffraction analysis of a crystalline derivative ($\text{1}$b) of latrunculin-A. The Latrunculins exhibit a new class of 14 and 16 membered macrolides to which the rare 2-thiazolidinone moiety is attached. A biogenesis of these biologically active compounds is put forward.     

Disinfection and Mechanistic Insights of Escherichia coli in Water by Bismuth Oxyhalide Photocatalysis

This study demonstrates the potential of a new BiOCl_0.875Br_0.125 photocatalyst to disinfect Escherichia coli in water under simulated solar irradiation. Photocatalytic efficiency was examined for different photocatalyst loadings, solar wavelengths, exposure times, photocatalyst concentration × contact time (Ct) concept and with the use of scavengers. To elucidate the inactivation mechanism, we examined DNA damage, membrane damage, lipid peroxidation and protein release. Both photolysis and photocatalysis were negligible under visible irradiation, but enhanced photocatalytic activity was observed under solar UVA (λ > 320 nm) and UVB (λ > 280 nm), with 1.5 and 3.6 log inactivation, respectively, after 40 min of irradiation. The log inactivation vs Ct curve for E. coli by UVA/BiOCl_0.875Br_0.125 was fairly linear, with Ct = 10 g L^?1 × min, resulting in 2 log inactivation. Photocatalytic treatment led to membrane damage, but without lipid peroxidation. Accordingly, protein was released from the cells after UVA or UVA/BiOCl_0.875Br_0.125 treatment. Photocatalysis also increased endonuclease‐sensitive sites vs photolysis alone, by an unknown mechanism. Finally, E. coli inactivation was not influenced by the addition of tert‐butanol or l ‐histidine, implying that neither hydroxyl radicals nor singlet oxygen reactive species are involved in the inactivation process.     

Tulearins A, B, and C; structures and absolute configurations

The relative configuration of tulearin A (1) is determined by X-ray diffraction analysis of a cyclic carbonate derivative 2 and the absolute configuration (2R,3R,5S,8S,9S,15R,17S) from the 9-MTPA-esters 1R and 1S is determined using the modified Mosher’s method. A mechanism for the unexpected formation of carbonate 2 is suggested. Two N-phenyltriazolinedione derivatives 3 and 4 are also prepared. Two additional tulearins, B and C (5 and 6) are isolated in very small amounts and their structures are elucidated by spectroscopic means.