Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.     

FT IR ATR Study of Molecular Interactions in the Urea/Dimethyl Sulfoxide and Urea/Diethyl Sulfoxide Binary Systems

FT IR ATR spectra of urea/dimethyl sulfoxide and urea/diethyl sulfoxide mixtures in the S=O and N—H stretching vibration regions at different molar ratios have been measured. On the basis of the band deconvolution data, various types of intermolecular associated forms, including dimers and hydrogen-bonded urea–sulfoxide complexes, have been revealed. The latter has been confirmed also by ab initio calculations.     

Solution conformation of a nitrobenzoxadiazole derivative of the polyene antibiotic nystatin: a FRET study

Nystatin is a polyene antibiotic frequently applied in the treatment of topical fungal infections. In this work, a 7-nitrobenz-2-oxa-1,3-diazole (NBD) hexanoyl amide derivative of nystatin was synthesized and its detailed photophysical characterization is presented. The average conformation of the labelled antibiotic in tetrahydrofuran, ethanol and methanol was determined by intramolecular (tetraene to NBD) fluorescence resonance energy transfer measurements. At variance with the literature [Can. J. Chem. 63 (1985) 77-85], it was concluded that there is no need to invoke a solvent-dependent conformational equilibrium between extended and closed conformers of the antibiotic, because the mean tetraene-to-NBD separating distance was found to remain constant (approximately 18 A) in all the solvents studied. In addition, the large solvent dependence of the fluorescence anisotropy observed for the non-derivatized nystatin, was rationalized on the basis of the prolate ellipsoidal geometry of the molecule. It was concluded that the rod shaped and amphipathic antibiotic remains monomeric in different solvents within the concentration range studied (2-20 microM).     

Two-stage latexes of polystyrene acrylates

ABSTRACT

The modification of decomposition rate of the potassium persulfate initiator during the synthesis of “two-stage latexes” polystyrene-ethyl acrylate (EtA) of butyl acrylale (BuA) and of 2-ethylhexyl acrylate (EHA) is studied. This rate is minimum for BuA and maximum for EHA, in good agreement with the value of solubility parameters. The appearance of poryacrvlaf.es determines the existence of water bonded to the polar polymer. The amount of water bonded increases in the sequence PEtA?PBuA?PEHA, function of the modification of the diameters of the particles resulted from the latexes obtained.     

Microwave Synthesis of 5-Substituted 1H-Tetrazoles Catalyzed by Bismuth Chloride in Water

Bismuth chloride was used to catalyze the [2 + 3] cycloaddition between sodium azide with aryl nitriles, aliphatic nitriles, and vinyl nitriles. A number of 5-substituted 1H-tetrazoles were synthesized in water or isopropanol/water mixtures using microwave heating. Good yields were obtained for these reactions when heated for 1 h at 120–160 °C in a 3:1 isopropanol/water mixture. A few of the less reactive nitriles required longer reaction times for good yields.     

Cinnamic acid hydrogen bonds to isoniazid and N′‐(propan‐2‐ylidene)isonicotinohydrazide,an in situ reaction product of isoniazid and acetone

A new polymorph of the cinnamic acid–isoniazid cocrystal has been prepared by slow evaporation, namely cinnamic acid–pyridine‐4‐carbohydrazide (1/1), C₉H₈O₂·C₆H₇N₃O. The crystal structure is characterized by a hydrogen‐bonded tetrameric arrangement of two molecules of isoniazid and two of cinnamic acid. Possible modification of the hydrogen bonding was investigated by changing the hydrazide group of isoniazid via an in situ reaction with acetone and cocrystallization with cinnamic acid. In the structure of cinnamic acid–N′‐(propan‐2‐ylidene)isonicotinohydrazide (1/1), C₉H₈O₂·C₉H₁₁N₃O, carboxylic acid–pyridine O—H...N and hydrazide–hydrazide N—H...O hydrogen bonds are formed.     

Modeling of electrocatalysis at polyaniline-modified electrodes: autoacceleration of the process by the reaction product

We extend our previous model taking into account a possible autoacceleration mechanism of electrochemical processes. It is supposed that protons generated in an electrochemical oxidation of ascorbate are responsible for an increase of electric conductivity of polyaniline. Accordingly, the current–time profiles have been calculated taking into account a “threshold” value for proton concentration to increase the electric conductivity of polyaniline by one or more orders of magnitude. Different kinds of corresponding profiles, including ones with a sigmoid character and possessing sharp current flashes as well, were obtained and analyzed.     

Mullite crystallization using fully hydrolyzed silica sol: the gelation temperature influence

Mullite is an aluminosilicate widely used as a structural material for high temperature applications. This paper studies the effect of the gelation temperature on the synthesis of two mullite precursors: polymeric and colloidal silica, using both in fully-hydrolyzed silica sol, derived from sodium silicate. The gels were synthesized using aqueous silicic acid and aluminum nitrate. Ethylene glycol was added into polymeric gels. Two gelation temperatures were used: 80 and 100 °C. In the polymeric precursor, the increasing of the gelation temperature caused an increase in the silica incorporation inside the mullite crystalline lattice at 1,000 °C, and it also generated an increase in the reaction extent at all calcination temperatures. In the colloidal precursors, these effects were more intense than in the polymeric precursors in terms of yield. Colloidal samples calcined at 1,250 °C crystallized cristobalite and alpha alumina in addition to mullite when they were previously gelled at 80 °C. On the other hand, the same sample gelled at 100 °C led to only crystallized mullite. The reaction extent increased by more than 20 % for colloidal samples gelled at 100 °C compared to colloidal samples gelled at 80 °C (calcined at 1,250 °C). This increase was due to the almost total incorporation of alumina and silica in the crystalline lattice of mullite.     

Synthesis of (1′S*,2R*,3R*)- and (1′S*,2R*,3S*)-N-arylsulfonyl-2-(1′-halogenethyl)-3-methylindolines and their selective toxicity against SH-SY5Y cell line

N-tosyl-2- and N-tosyl-4-halogen-substituted derivatives of 2-(1-methylbut-2-en-1-yl)aniline were synthesized and their molecular iodine-mediated cyclization was investigated. The cyclization upon interaction of N-tosyl-6-methyl-2-(1-methylbut-2-en-1-yl)aniline with molecular iodine in methyl tert-butyl ether or acetonitrile was studied, as well as the interaction of this sulfonamide with N-bromosucinimide in dichloromethane. Synthesized (2R*,3R*)- and (2R*,3S*)-N-arylsulfonyl-2-(1-halogenoethyl)-3-methylindoline derivatives showed cytotoxic activity against HEK293 cells, SH-SY5Y, Jurkat, and HepG2 cell lines. The compounds (2R*,3S*)-N-arylsulfonyl-7-bromo-2-(1-halogenoethyl)-3-methylindoline cis- 4a , stereoisomeric (2R*,3R*)-trans- 4h and (2R*,3S*)-N-tosyl-7-chloro-2-(1-halogenoethyl)-3-methylindoline cis- 4h demonstrated selective toxicity against SH-SY5Y cell line (IC₅₀ ≈ 3 ÷ 5 μM), and did not affect HEK293, Jurkat, and HepG2 cells.     

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Bo? R.I., Wanka G., On gap functions for equilibrium problems via Fenchel duality, Pac. J. Optim., 2006, 2(3), 667–678] and [Altangerel L., Bo? R.I., Wanka G., On the construction of gap functions for variational inequalities via conjugate duality, Asia-Pac. J. Oper. Res., 2007, 24(3), 353–371]. By particularizing the perturbation function we rediscover several gap functions from the literature. We also characterize the solutions of various variational inequalities and equilibrium problems by means of the properties of the convex subdifferential. In case no regularity condition is fulfilled, we deliver also necessary and sufficient sequential characterizations for these solutions. Several examples are illustrating the theoretical aspects.