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.

     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

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.     

Shaping Solid-State Supramolecular Cavities: Chemically Induced Accordionlike Movement of gamma-Zirconium Phosphate Containing Polyethylenoxide Pillars

The hydrophilic oxygen atoms of polyethylenoxide chains inserted as pillars in gamma-zirconium phosphate form hydrogen bonds with the acid groups of the host. As a result the pillars are almost perpendicular to the gamma layers. Upon changing the pH level of the supernatant solution the hydrogen bonds are broken and the pillars become almost perpendicular to the layers (shown schematically). Thus there is a reversible enlargement-shortening of the interlayer space.     

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.