Poincaré-Hopf inequalities

In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.

     

Mössbauer study of spin-glass Fe x Zn1−x F2 system

⁵⁷Fe Mössbauer effect measurements in the diluted Ising antiferromagnet Fe _x Zn_1?x F₂ withx=0.25 andx=0.57 at temperatures between 4.2 and 55 K, are reported. DC suceptibility measurements show a spin-glass (SG) phase at low temperatures forx≤0.31. Our Mössbauer spectra show a phase transition to a SG state with antiferromagnetic order (AFSG) forx=0.25 and only antiferromagnetic order forx=0.57.     

Preparation,characterization and a kinetic study oftrans-[Ru(NH3)4L(H2O)](PF6)2 [L=PPh3, AsPh3, or SbPh3]

Summary The complexestrans-[Ru(NH₃)₄(H₂O)PPh₃](PF₆)₂ and [Ru(NH₃)₅L](PF₆)₂, (L=AsPh₃ or SbPh₃) have been isolated and characterized by microanalysis, cyclic voltammetry and ultraviolet-visible spectroscopy. The specific rate constants for the aquation of [Ru(NH₃)₅L]²⁺ totrans-[Ru(NH₃)₄L(H₂O)]²⁺ are (2.5±0.1)×10^–5s^–1 and (1.8±0.1)×10^–5s^–1 for L=AsPh₃ and SbPh₃, respectively, at 25.0±0.1°C; =0.10 mol dm^–3, NaO₂CCF₃. Under the same conditions, the second-order rate constants for the substitution of water intrans-[Ru(NH₃)₄(H₂O)L]²⁺ by isonicotinamide (isn) are 1.2±0.1, (6.3±0.3)×10^–2 and (3.8±0.2)×10^–2 m ^–1s^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of decreasingtrans-effect is: PPh₃AsPh₃>SbPh₃. The formation constants for thetrans-[Ru(NH₃)₄L(isn)]²⁺ complexes are 75±3, (1.40±0.01)×10³ and (1.80±0.02)×10³M^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of increasingtrans-influence is: SbPh₃3PPh₃.     

Behavior of Humic Acid as a Micellar Phase in Micellar Electrokinetic Chromatography (MEKC)

The possibility of humic acids acting as micellar phase in micellar electrokinetic chromatography was evaluated. We investigated the separation of naphthalene in capillary electrophoresis using various samples of humic acids as micellar phase under different pH conditions, concentrations of humic acid, and temperature. The humic acid samples studied were from different origins including peat, vermicompost and a commercial sample acquired from Aldrich. Methanol was used as a marker for the electroosmotic flow. The results indicate that the formation of micelle depends on the number and nature of the hydrophobic association sites in an aqueous humic acid solution and on the origin and concentration of the humic acid at a defined pH. At lower pH values, the possibility of the humic acid molecule forming pseudomicelles increases due to a combination of neutralized and dissociated charged sites.     

Characterization of humic substances by capillary electrophoresis

Capillary electrophoresis was used for the separation of humic acid (HA) from peat, soil, and vermicompost. The electropherograms show the presence of at least three peaks eluted between 6 and 11 min for all HA. The best analysis resolution was obtained with the use of borate buffers at pH 8.9. The HA analyzed have structural and charge similarity, which increases the difficulty of separation. Therefore, the shape of the peaks is broad and the CE profiles of all HA are similar. It is reasonable to assume that the broad band in the three regions is due to the acidic groups that have a similar structure. By comparing the results obtained for HA extracted from soil, peat, vermicompost, and the commercial sample, HA from peat had the major carbon content.     

Antioxidant activity of aryltetralone lignans and derivatives from Virola sebifera (Aubl.)

Aryltetralone lignans bearing methylenedioxy groups (1a-b; 2a-b) were isolated from seeds of Virola sebifera. Their antioxidant activities were evaluated by inhibition of lipid peroxidation as indicated by TBARS and chemiluminescence emission (CL) assays. The lignan 1c, 'having a 2'-hydroxy-4',5'-methylenedioxyphenyl group, was the most active compound with TBARS/CL Q 1/2 values of 0.89 and 0.10 microg/mL, respectively. The catechol derivatives 3 and 4, obtained by demethylenation of lignans 1a and 2a, were of similar activity to 1c, and all were much more effective as antioxidants than alpha-tocopherol.     

Enzymatic synthesis of medium chain monoglycerides in a solvent-free system

The synthesis of monocaprin, monolaurin, and monomyristin in a solvent-free system was conducted by mixing a commercial immobilized lipase with the organic reactants (glycerol and fatty acids) in a 20-mL batch reactor with constant stirring. The effects of temperature, fatty acid/glycerol molar ratio, and enzyme concentration on the reaction conversion were determined. The addition of molecular sieves in the assays of monomyristin synthesis was also evaluated. The reactions were carried out for 5 to 6 h and the nonpolar phase was analyzed by gas chromatography. The best results in terms of selectivity and conversion (defined as the percentage of fatty acid consumed) were achieved when the stoichiometric amount of reagents (molar ratio=1) and 9% (w/w) commercial enzyme were used and the reaction was performed at 60°C. The addition of molecular sieves did not improve the synthesis of monomyristin. Conversions as high as 80%, with monoglycerides being the major products, were attained. After 5 h of reaction, the concentration of monoglyceride was about twice that of diglyceride, and only trace amounts of triglyceride were found. The results illustrate the technical possibility of producing medium chain monoglycerides in a solvent-free medium using a simple batch reactor.     

An NMR study of merocyanine-type dyes derived from barbituric acid

The 13C NMR of two solvatochromic dyes derived from a barbituric acid acceptor and dimethylaminophenyl donor fragments, compound 1 and the related merocyanine 2, were recorded in various solvents. The observed chemical-shift variations were used to interpret their structural differences and solvatochromic behavior in solution.     

Biosynthesis and antioxidant activity of 4NRC β-glycoside

This Letter describes glycosylation of 4-Nerolidylcatechol (4-NRC) the major secondary metabolite from Pothomorphe peltata and Pothomorphe umbellata showing remarkable antioxidant, antimalarial, anti-inflammatory, and anti-HIV activities. One step biosynthesis was catalyzed by Cunninghamella echinulata ATCC 9245 and the reaction was undertaken in PDSM medium at 27 °C, 200 rpm for 96 h. After purification by silica gel flash column chromatography the 4-NRC β-glycoside was identified by ultrahigh resolution mass spectrometry and ¹H NMR. The antioxidant activity was evaluated by differential pulse voltammetry.