Solutions of elliptic equations involving critical Sobolev exponents with neumann boundary conditions

We consider the problem −Δu=|u| ^p−1u+λu in Ω with on δΩ, where Ω is a bounded domain inR ^N ,p=(N+2)/(N−2) is the critical Sobolev exponent,n the outward pointing normal and λ a constant. Our main result is that if Ω is a ball inR ^N , then for every λ∈R the problem admits infinitely many solutions. Next we prove that for every bounded domain Ω inR ³, symmetric with respect to a plane, there exists a constant μ>0 such that for every λ<μ this problem has at least one non-trivial solution. This work was supported by the Paris VI-Leiden exchange program Supported by the Netherlands organisation for scientific research NWO, under number 611-306-016.     

About counterintuitive orbital mixing and bond populations

It is shown that negative bond and orbital populations may be avoided by the introduction of a weight factor in a bond index definition, together with a suitable parameterization. The negative bond populations found for first-row metal complexes need not be ascribed to counterintuitive orbital mixing but rather, essentially, to the equipartition of the charge distribution. Different definitions of the bond population are compared for ferrocene and the effects of some parameterizations are discussed.     

Crystal Structure of 1,3-Alternate 25,26,27,28-Tetra(tert-butoxyethoxy)calix[4]arene: a Selective Ag+ Extractant

Alkylation of calix[4]arene by 2-tert-butoxyethyl bromide led to the tetraalkylatedcalix[4]arene in the 1,3-alternate, the conformation of which has been established byX-ray crystallography. This spatial structure included a cavity potentially useful forhost–guest complexes achieved with metal cations, especially with Ag⁺. The titlecompound crystallizes in the monoclinic space group Cc with cell constants a = 29.901(2),b = 8.139(1), c = 22.264(3) Å, = 90°, = 117.08(1)°and = 90°. This conformer represents an example for Ag⁺-tunnelingacross an aromatic cavity. This behaviour could lead to important implications with regardto the metal cation- interaction expected for metal transport through ion channels,metal inclusion in fullerenes, intercalation of metal cations into graphites, etc.     

Numerical simulation of the chromatographic process for direct ligand-macromolecule binding studies

A numerical simulation of the direct zonal liquid chromatographic method is described for studying the binding of a ligand to a macromolecule by quantification of the interacting species present in a sample at equilibrium. The algorithm accounts for both the kinetic exchanges in solution and the dispersion effects depicted by the Fick law. Dimensionless variables are used for the concentrations which are expressed as a function of the equilibrium constant, KD. The free ligand concentration was varied in the injected samples from 0.1 to 20 KD, while that of the macromolecule was kept constant. An apparent binding isotherm was obtained from the total ligand chromatogram generated by the simulation run, when the amount emerging at almost column dead volume is plotted against that eluting at the free ligand retention time. As a continuous dissociation of the complex may occur during its migration, the apparent binding curve and the theoretical binding isotherm coincide at extremely low dissociating rates. At larger dissociation rates (0.001 s(-1) < kd <0.1 s(-1), for a first peak eluting in 1 min) the simulations were used to test various chromatographic conditions. The flow rate (or column volume) is the major effect which influences the on-column dissociation process as an exponential decay was found when the apparently bound fraction is plotted against the analysis time. The apparent equilibrium coefficient is close to the theoretical one for a binding curve generated with an initial solution containing a relatively low total concentration of binding sites (< or = KD). The apparent stoichiometric term is largely underestimated as its value decreases exponentially at increasing dissociation rates. An extrapolation at extremely short analysis times could be used to determine the stoichiometric coefficient characterizing the binding interaction.     

Alkaline Hydrolytic Pathway of the Antitumor Drug,Cyclophosphamide

Abstract

In an attempt to clarify the alkaline hydrolytic pathway of the antitumor agent, cyclophosphamide (CP), the time course of its degradation was monitored by ³¹P NMR in 0.5 M KOH solution. After 16 hr at 25°C. 70% of CP is hydrolyzed (t_½ 9 hr) leading to a mixture of 8 phosphorated compounds. among them only 4 represented more than 5% of the initial CP. The chemical shifts and the intensities of these compounds were as follows: 1 1 .1 ppm. 30% of the initial CP (compound 1); 9.5 ppm, 12% (compound 2); 6.4 ppm, 9% (unknown) and 4.8 ppm, 9% (compound 3). The structures of compounds 1–3 were identified by NMR (13C and IH) and mass spectrometry after their isolation. The major degradation compound formed, the nine-membered ring compound I, was also observed during CP hydrolysis at neutral or moderately acid pHsill and was detected in urine of patients treated with CP[2] Compounds 2 and 3 were also formed during the hydrolysis of compound I in 0.5 M KOH solution. Based on the formation in time of the 31P NMR signals in KOH solutions of CP and compound I, the following scheme was established for the major degradation alkaline pathway of CP.     

Alkaline Hydrolysis of the Cytostatic Drug,Ifosfamide, and its N-Dechloroethylated Metabolites

Abstract

I fosfamide (IF) is an alkylating antitumor agent used in the treatment of solid tumors. Up to 50% of IF administered to patients undergoes an oxidative N-dealkylation reaction resulting in the loss or one, other or both chloroethyl side chain(s) to produce 2- or 3-dechloioethylIF (ZDCIF, 3DCIF) or 2,3-didechloroethyllF (DDCIF). The hydrolytic pathway of these four oxazaphosphorines has been studied earlier but only at acidic and neutral pHs^[l] In the present work, we monitored their time courses of hydrolysis at basic pHs using phosphorus-3 1 NMR. The structures of the compounds formed were determined by NMR (13C and 1H) and mass spectrometry. The results are reported in the following scheme.     

Characterization of Glycosyltransferase Activity of Wild-Type Leuconostoc mesenteroides Strains from Bulgarian Fermented Vegetables

Glycosyltransferase activity of 13 Leuconostoc mesenteroides strains isolated from Bulgarian fermented vegetables was investigated. All the strains displayed a mucoid phenotype on sucrose-containing agar media. Strains were characterized according to carbohydrate fermentation, species-specific multiple PCR using several primers, repetitive element-PCR fingerprinting using (GTG)₅ primers and glycosyltransferase activity. Level of activity and cellular localization (soluble or cell-associated) were variable among strains. Precipitation of exopolysaccharides produced from sucrose by the soluble fractions from these strains allowed recovery of only glucans and further characterization by ¹H and ¹³C NMR analysis and enzymatic digestion with dextranase revealed dextran production. However, levans could be detected in presence of raffinose as fructosyl donor. Both fructosyltransferase and glucosyltransferase encoding genes were detected by PCR and both active enzymes were detected after functional characterization by SDS-PAGE electrophoresis and in situ polymer production after incubation with sucrose. This work therefore showed that concomitant production of glucosyltransferase and fructosyltransferase is widespread in L. mesenteroides strains.