Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation

Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.

     

Thermodynamic investigation of zirconium diselenite

Summary On the basis of calorimetric research of selenium dioxide, zirconium dioxide and zirconium diselenite dissolution reactions in the hydrofluoric acid solution under 298 K a standard enthalpy of Zr(SeO₃)₂ formation reaction from ZrO₂ and SeO₂ and a standard enthalpy of zirconium diselenite formation have been obtained. The value of enthalpy has been equal to -58.1±3.43 kJ mol^-1 in ZrO_2(solid)+2SeO_2(solid) Zr(SeO₃)_2(solid) reaction. The standard enthalpy of zirconium diselenite formation is equal to H_f,298⁰Zr(SeO₃)_2(solid)= -1603.2±3.8 kJ mol^-1. The H_f,298⁰ Zr(SeO₃)_2(solid) value has been determined for the first time.     

Reactions of 4,7‐dihydro‐1,2,4‐triazolo[1,5‐a]pyrimidines with α,β‐unsaturated carbonyl compounds

The reaction of 5,7‐diphenyl‐4,7‐dihydro‐1,2,4‐triazolo[1,5‐a]pyrimidine ( 1 ) with α,β‐unsaturated carbonyl compounds 2a‐f led to the formation of the alkylated heterocycles 3a‐f (Figure 1). However, the reaction of 5‐methyl‐7‐phenyl‐4,7‐dihydro‐1,2,4‐triazolo[1,5‐a]pyrimidine ( 5 ) with 2a‐c yielded under the same conditions the triazolo[5,1‐b]quinazolines 6a‐c (Figure 3). In this case, the alkylation is followed by a cyclocondensation. The structure elucidation of the products is based on ir, ms, ¹H and ¹³C nmr measurements and on an X‐ray diffraction study.     

Synthesis, structure, and X-band (9.5 GHz) EPR characterization of the new series of pH-sensitive spin probes: N,N-disubstituted 4-amino-2,2,5,5-tetramethyl-3-imidazoline 1-oxyls

[reaction: see text] An approach to the synthesis of new imidazoline nitroxides bearing an N',N'-disubstituted amidine group is reported. The approach is based on the alkylation of diamagnetic 4-R-amino-1,2,2,5,5-pentamethyl-3-imidazolines with bromoacetic acid ethyl ester; the products of alkylation are further oxidized to the corresponding nitroxides. The approach allows a variety of functional groups to be introduced into the nitroxide molecule structure. Alkylation with bromoacetic acid ethyl ester was found to proceed with high regioselectivity and afford the products of exo-alkylation. The regiochemical assignment is made on the basis of 13C NMR spectra and confirmed by X-ray diffraction study. All of the nitroxides synthesized here were shown to have pH-dependent EPR spectra with pKa ranging from 3.5 to 6.2. For nitroxides 13 bearing the carboxylic group remote to the nitroxide moiety, the changes in isotropic magnetic parameters of EPR spectra due to reversible deprotonation of the carboxylic group were found to be small. For these nitroxides, we demonstrate an alternative approach for pKa determination that is based on measuring the peak-to-peak line width of the EPR spectrum in the presence of the paramagnetic broadening agent potassium ferricyanide. The partition coefficients of nitroxides in octanol/H2O and octanol/phosphate buffer solution mixtures were measured to reveal a range of their lipophilicities.     

Biophysical characterization of complexation of DNA with block copolymers of poly(2-dimethylaminoethyl) methacrylate, poly(ethylene oxide), and poly(propylene oxide)

The interactions of DNA (salmon testes) with two new cationic block copolymers made of poly(2-dimethylaminoethyl) methacrylate and poly(ethylene oxide), PEO-pDMAEMA, or poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), L92-pDMAEMA, were studied with the aim to understand their different in vitro transfection efficiencies when used as nonviral delivery vectors. PEO-pDMAEMA does not show surface activity while L92-pDMAEMA is as surface active as its parent Pluronic L92. Surface tension, titration microcalorimetry, ethidium bromide displacement, and zeta-potential measurements were carried out in phosphate buffers at pH 5 and 7. The association of L92-pDMAEMA with DNA was strongly exothermic at both pHs; the critical aggregation concentration (CAC) corresponded to a N/P ratio of 0.3, the maximum energy evolved was reached for N/P ratios of 0.82 and 1.27 at pH 5 and pH 7, respectively, and the saturation occurred for N/P ratios close to 2. The presence of L92 in the structure of this new block copolymer apparently did not modify the thermodynamic parameters of the interaction with DNA. In contrast, the interaction with PEO-pDMAEMA was significantly less exothermic, and CAC and saturation occurred for N/Ps equal to 0.43 and 1.37, respectively. The strong affinity of L92-pDMAEMA for DNA was reflected in its capacity to displace ethidium bromide and in the jump in the values of the zeta potential when N/P is near 1. Above the N/P ratio at which electroneutral polyplexes are formed, only at pH 5 an excess of L92-pDMAEMA is incorporated in the complexes, resulting in positively charged complexes. The profile of the zeta-potential values obtained for mixtures of L92-pDMAEMA with Pluronic P123 showed a shift to a lower N/P ratio, owing to an easier interaction of L92-pDMAEMA molecules with DNA in the presence of P123. Additionally, a visual inspection of the systems indicates that P123 contributes to stabilize/solubilize the DNA/cationic polymer aggregates, by avoiding the typical phase separation near the charge neutralization point. The information obtained can be particularly useful to optimize the conditions to form efficient polyplexes for gene delivery systems.     

NMR determination of enantiomeric composition of 1-substituted 3-amino-1,2-dicarba-closo-dodecaboranes using Eu(hfc)3

Experimental conditions for determination of enantiomeric composition of 1-substituted 3-aminocarboranes by ¹H and ¹³C NMR spectroscopy using chiral shift reagent Eu(hfc)₃ have been found.     

Methyl 2,3‐dideoxy‐2‐S‐methylmercurio‐2‐thio‐β‐d‐manno‐oct‐2‐ulo­pyranosonate‐(2,6)

The hexo­pyran­osyl ring of the title compound, [Hg(CH₃)(C₉H₁₅O₇S)], adopts the ⁴C₁ chair conformation, and the anomeric configuration of the thio­methyl­mercury linkage is β. The compound exists as two symmetry‐independent conformers, A and B, within the unit cell, and each shows an almost linear S—Hg—C arrangement. Most of the bond distances and angles in A and B are similar, although a marked difference exists in the side‐chain conformation. Weak secondary intramolecular (between Hg and ring O) and intermolecular (between A and B conformers) interactions are documented.     

A very large diversity space of synthetically accessible compounds for use with drug design programs

We have constructed a very large virtual diversity space containing more than 10¹³ chemical compounds. The diversity space is built from about 400 combinatorial libraries, which have been expanded by choosing sizeable collections of suitable R-groups that can be attached to each link point of their scaffolds. These R-group collections have been created by selecting reagents that have drug-like properties from catalogs of available chemicals. As members of known combinatorial libraries, the compounds in the diversity space are in general synthetically accessible and useful as potential drug leads. Hence, the diversity space can be used as a vast source of compounds by a de novo drug design program. For example, we have used such a program to generate inhibitors of HIV integrase enzyme that exhibited activity in the micromolar range.     

Identification of acylated xanthone glycosides by liquid chromatography-atmospheric pressure chemical ionization mass spectrometry in positive and negative modes from the lichen Umbilicaria proboscidea

The xanthoside composition of the crude extract of Umbilicaria proboscidea (L.) Schrader was characterized using LC-UV diode array detection and LC-atmospheric pressure chemical ionization (APCI) MS methods. The presence of acylated xanthone-O-glucosides was determined by both positive and negative ion LC-APCI-MS methods. Based on UV and MS spectral data and NMR spectroscopy, a total of 14 compounds (6-O-acylated umbilicaxanthosides A and B) were identified in U. proboscidea for the first time. In order to further develop the applicability of LC-MS techniques in phytochemical characterization, the effect of different ionization energy on fragmentation was studied using APCI. The optimal ionization conditions were achieved in positive ion APCI by using ammonium acetate buffer and in negative ion APCI by using formic acid (pH 4).