Counting solutions to binomial complete intersections

We study the problem of counting the total number of affine solutions of a system of n binomials in n   variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is #P$\#P$-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.     

Lipase-Catalyzed Acylation and Deacylation Reactions of Pyridoxine,a Member of Vitamin-B6 Group

A series of acyloxy derivatives of pyridoxine ( 1 ) have been prepared by transesterification reactions of 1 and ethyl carboxylates, catalyzed by several lipases. Moreover, acetylated derivatives of 1 were selectively deacetylated by enzymatic catalysis in organic media.     

Catalyst-free alkanoylation of aromatic rings via arylstannanes. Scope and limitations

The reaction of alkanoyl chlorides with arylstannanes in 1,2-dichlorobenzene (180 °C) is a simple and direct route for the catalyst-free and regioselective synthesis of tertiary alkyl aryl ketones in good to excellent isolated yields (55-77%). Nevertheless, under similar conditions, reactions carried out with alkanoyl chlorides bearing α-hydrogens render only the product of protodestannylation.     

Effect of Perylene as Electron Acceptor and poly(tetrabromo-p-phenylene Diselenide) as “Buffer Layer” on Heterojunction Solar Cells Performances

Summary : Perylene derivatives, that behave as liquid crystal and might be used as electron acceptors, and poly(tetrabromo-p-phenylenediselenide) (PTBrPDSe) were synthesized with the purpose of using the polymer as buffer layer in solar cells. It was demonstrated that perylene compounds of N,N′-diheptyl-3,4,9,10-perylentetracarboxyldiimide (PTCDI-C7) and N,N′-diundecyl-3,4,9,10-perylentetracarboxyldiimide (PTCDI-C11) enabled obtaining photovoltaic effect when coupled with copper phthalocyanine (CuPc). The power conversion efficiency of the cells prepared from these perylenes is similar, whatever the x value. However this efficiency is smaller than the one achieved when the couple CuPc/C₆₀ (fullerene) is used. More precisely, the best efficiency was obtained when a PTBrPDSe/Au buffer layer is introduced between the ITO anode and the CuPc. It was established that the presence of the thin PTBrPDSe layer allows improving the shunt resistance and consequently the cells performance.     

The uncertainties about the relationships risk–return–volatility in the Spanish stock market

The relationships between the market risk premium, its conditional variance and the risk-free rate in the Spanish stock market are studied in this paper. Using daily data, the above mentioned relations are analyzed by quasi maximum likelihood for an EGARCH-M(1,1) model with normal innovations and by nonparametric maximum likelihood for a semiparametric EGARCH-M(1,1) model with arbitrarily distributed innovations. It is worth mentioning that the conclusions differ from one model to the other.     

The use of acridine orange base (AOB) as molecular probe to characterize nonaqueous AOT reverse micelles

The behavior of acridine orange base (AOB) in nonaqueous reverse micelles composed of n-heptane/AOT/polar solvent has been performed. Ethylene glycol (EG), propylene glycol (PG), glycerol (GY), formamide (FA), dimethylformamide (DMF), and dimethylacetamide (DMA) were employed as water substitutes. The studies were performed by static and time-resolved emission spectroscopy. Thus, the distribution of AOB between the two pseudophases of the aggregates was quantified by measuring the partition constants from emission spectra at different surfactant concentration. Similar values to those obtained by means of absorption spectroscopy were obtained. This match is indicating that AOB is not experiencing partition during the lifetime of the excited state. Partitioning to the micelles is strongly favored in micelles containing hydrogen-bond donor (HBD) solvents rather than non-HBD solvents. Variations of fluorescence lifetimes with AOT concentration confirm these results. By the solvatochromic behavior of AOB in the different systems it is shown that the microenvironment at the interface is distinct from that of the bulk polar solvent, indicating that the probe senses no "free" solvent. The steady state anisotropy (r) was measured for EG/AOT/n-heptane and DMF/AOT/n-heptane systems as representatives for HBD and non-HBD polar solvents, respectively. The value of r is higher in the micelles containing EG than that obtained with DMF, and increases with AOT concentration. This is explained as due to highly structured polar solvents in the inner core. EG is interacting with the polar heads of AOT through hydrogen-bond interaction, while DMF can only interact with the Na+ counterions. This is confirmed by the time-resolved emission spectra (TRES) of the probe in the micellar systems, in comparison with the bulk solvents.     

Selective cleavage of methoxy protecting groups in carbohydrates

The selective cleavage of methoxy protecting groups next to hydroxy groups is achieved using a radical hydrogen abstraction reaction as the key step. Under the reaction conditions, the hydroxy group generates an alkoxyl radical that reacts with the sterically accessible adjacent methoxy group, which is transformed into an acetal. In the second step, the acetals are hydrolyzed to give alcohols or diols. A one-pot hydrogen abstraction-hydrolysis procedure was also developed. Good yields were usually achieved, and the mild conditions of this methodology were compatible with different functional groups and sensitive substrates such as carbohydrates.     

Ancistrocladinium A and B, the first N,C-coupled naphthyldihydroisoquinoline alkaloids, from a Congolese ancistrocladus species

The isolation and structural elucidation of three novel-type naphthylisoquinoline alkaloids, ancistrocladinium A and B (the latter along with its atropisomer), from a Congolese Ancistrocladus species collected in the habitat Yeteto is reported. Their structures, including all stereochemical features, were elucidated by spectroscopic, chemical, and chiroptical methods. Ancistrocladinium A and B are the first N,C-coupled naphthyldihydroisoquinoline alkaloids found in nature, i.e., with an iminium-aryl axis. Although ancistrocladinium A, which is N,8'-coupled, is configurationally stable at this axis, ancistrocladinum B and its rotational isomer are based on a hitherto unprecedented N,6'-coupling type, with a slow rotation about the hetero biaryl axis at room temperature; they thus occur as a 46:54 mixture of two configurationally semistable atropo-diastereomers. For the isomerization of (P)-ancistrocladinium B to its (M)-diastereomer and for the opposite direction, the Gibbs free energies of activation were determined to be DeltaG double dagger1 = 105.8 kJ mol-1 and DeltaG double dagger2 = 105.7 kJ mol-1, respectively. In addition, the compounds were shown to have promising antileishmanial activities.     

The Use of Poly(Sodium N-Undecanoyl-l-Leucylvalinate), Poly(Sodium N-Undecanoyl-l-Leucinate) and Poly(Sodium N-Undecanoyl-l-Valinate) Surfactants as Chiral Selectors for Determination of Enantiomeric Composition of Samples by Multivariate Regression Modeling of Fluorescence Spectral Data

Steady-state fluorescence spectroscopy was employed to investigate the use of chiral polymeric surfactants as chiral selectors in chiral analysis by multivariate regression modeling of spectral data. Partial-least-squares regression modeling (PLS-1) was used to correlate changes in the fluorescence spectral data of 1,1'-bi-2-naphthol (BOH), 1,1'-binaphthyl-2,2'-diamine (BNA), or 2,2,2-trifluoroanthrylethanol (TFA) in the presence of poly(sodium N-undecanoyl-L-leucylvalinate), poly(sodium N-undecanoyl-L-leucinate) or poly(sodium N-undecanoyl-L-valinate) as the enantiomeric composition of the chiral analytes was varied. The regression models produced from the spectral data were validated by determining the enantiomeric composition of independently prepared test solutions. The ability of the model to correctly predict the enantiomeric composition of future samples was evaluated using the root-mean-square percent-relative error (RMS%RE) of prediction. In terms of RMS%RE, the ability of the model to accurately predict the enantiomeric composition of future samples was dependent on the chiral analyte, the polymeric surfactant used, and the surfactant medium, and ranged between 1.57 and 6.10%. Chiral analyte concentrations as low as 5 x 10(-6) M were found to give regression models with good predictability.     

Tuning the potentials of "extra" electrons in colloidal n-type ZnO nanocrystals via Mg2+ substitution

Colloidal reduced ZnO nanocrystals are potent reductants for one-electron or multielectron redox chemistry, with reduction potentials tunable via the quantum confinement effect. Other methods for tuning the redox potentials of these unusual reagents are desired. Here, we describe synthesis and characterization of a series of colloidal Zn(1-x)Mg(x)O and Zn(0.98-x)Mg(x)Mn(0.02)O nanocrystals in which Mg(2+) substitution is used to tune the nanocrystal reduction potential. The effect of Mg(2+) doping on the band-edge potentials of ZnO was investigated using electronic absorption, photoluminescence, and magnetic circular dichroism spectroscopies. Mg(2+) incorporation widens the ZnO gap by raising the conduction-band potential and lowering the valence-band potential at a ratio of 0.68:0.32. Mg(2+) substitution is far more effective than Zn(2+) removal in raising the conduction-band potential and allows better reductants to be prepared from Zn(1-x)Mg(x)O nanocrystals than can be achieved via quantum confinement of ZnO nanocrystals. The increased conduction-band potentials of Zn(1-x)Mg(x)O nanocrystals compared to ZnO nanocrystals are confirmed by demonstration of spontaneous electron transfer from n-type Zn(1-x)Mg(x)O nanocrystals to smaller (more strongly quantum confined) ZnO nanocrystals.