Inverse Problem for a Mathematical Model of Adsorption Dynamics

A mixed problem is considered for a system of partial differential equations modeling the process of adsorption dynamics. An existence and uniqueness theorem is proved for this problem, and the solution properties are investigated. The inverse problem is posed, involving the determination of the system coefficient given additional information about the solution. A uniqueness theorem is proved for the solution of the inverse problem.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 5 – 14, 2004.     

Studies on the chemical constituents of the South China Sea sponge Phacellia fusca

Three pyrrololactam alkaloids have been isolated from the marine sponge Phacellia fusca Schmidt collected from the South China Sea, and their structures were determined as 1–3 , on the grounds of spectral data. This is the first report of these compounds from this sponge. The structure of 1 was confirmed by X-ray analysis.     

Trapped electrons in substoichiometric MoO3 observed by X-ray electron spectroscopy

Substoichiometric amorphous thin films of MoO₃ in both the transparent and absorptive forms have been studied by X-ray electron spectroscopy. The transparent films can be colored blue (absorptive) electrically or by UV irradiation. The electron distribution curve of the blue film exhibits a small band near the Fermi edge which is absent in the transparent sample. This new band is attributed to electrons trapped in positively charged anion vacancies in the substoichiometric MoO₃ lattice. This model provides an interpretation of the electrical conductivity and color of the films.     

From terminal alkynes directly to branched amines

The one-pot synthesis of several branched secondary aliphatic amines is described. Hydroamination of terminal alkynes with aliphatic primary amines in the presence of Cp₂Ti(η²-Me₃SiCCSiMe₃) gives the corresponding aldimines as intermediates. Reaction of these in situ produced aldimines with organolithium reagents (n-BuLi, PhLi) provides the α-branched amines in an easy way in upto 78% overall yield.     

Benzylic cleavage and McLafferty rearrangement under electron ionization conditions in the fragmentation of 5,6-dialkyl-2, 4-diarylpyrimidines

Several 5,6-dialkyl-2,4-diarylpyrimidines were prepared and their electron ionization (EI) mass spectra reported. The benzylic cleavage takes place easily together with an important McLafferty rearrangement. The involvement of the nitrogen atom appears to be important in the fragmentation of 5-methyl-substituted pyrimidines. In contrast, the 6-methyl-substituted pyrimidines undergo benzylic cleavage without hydrogen transfer. Thus, the difference in the mass spectrometric behaviour allows the identification of these isomeric compounds which, in contrast, exhibit only small differences in their NMR spectra. Copyright 1999 John Wiley & Sons, Ltd.     

Determination of chloride ion in aqueous samples by isotope-dilution Fourier-transform flame infrared emission (ID-FIRE) spectrometry

An isotope dilution method for the determination of chloride ion in aqueous samples is described. The method makes use of the isotopic shift in the rotational lines of the 1–0 band of HCl emitted in the near infrared region of the spectrum by vibrationally excited HCl molecules present in a hydrogen/entrained air flame. Chloride ion in the sample is converted to chlorine gas by electrolysis and swept into a hydrogen/entrained air flame where it is converted into HCl. Because isotope dilution is an absolute method of analysis, matrix effects are minimized, and the chlorine generation step need not be quantitative. With the system described in this paper, samples must contain at least 9 mg of chloride ion per ml, and a 2-ml sample is required. Over the range from 10 to 30 mg Cl⁻ ml⁻¹, the average error was −0.96%, and the average relative standard deviation was 3.3% for seven samples using seven of the more intense lines in the P branch. Compared with standard silver nitrate titrations, the isotope dilution procedure was not affected by such common interferences as bromide ion and iodide ion. The technique was applied to several seawater samples from different regions.     

Isotropization in Bianchi type IX vacuum cosmology

We find the most general Bianchi type IX solution in Brans-Dicke theory (BDT) for the vacuum case, with the local rotational symmetry. For BDT coupling parameterw > 500 the universe becomes isotropic for any amount of initial anisotropy. In the extended inflation scenario, the Brans-Dicke scalar field can avoid the inflation in one direction.     

Biologically active compounds through catalysis: efficient synthesis of N-(heteroarylcarbonyl)-N'-(arylalkyl)piperazines

A practical route for the synthesis of new biologically active 5-HT(2 A) receptor antagonists has been developed. In only three catalytic steps, this class of central nervous system (CNS) active compounds can be synthesized efficiently with high diversity. As the initial step, an anti-Markovnikov addition of amines to styrenes provides an easy route to N-(arylalkyl)piperazines, which constitute the core structure of the active molecules. Here, base-catalyzed hydroamination reactions of styrenes with benzylated piperazine proceeded in high yield even at room temperature. After catalytic debenzylation, the free amines were successfully carbonylated with different aromatic and heteroaromatic halides and carbon monoxide to yield the desired compounds in good to excellent yields. The two key reactions, base-catalyzed hydroamination of styrenes and palladium-catalyzed aminocarbonylation of haloarenes/heterocycles, showed tolerance towards various functional groups, thereby demonstrating the potential to synthesize a wide variety of new derivatives of this promising class of pharmaceuticals.     

X-ray analysis of the influence of various nucleating agents on the crystallinity of poly-α-butene

The influence of various nucleating agents on the crystallinity of poly-α-butene form I has been studied. The nucleating agents were: adipic acid, salicylic acid, p-aminobenzoic acid, sodium benzoate and sorbic acid; their influences on the lattice parameters, degree of crystallinity, size of crystallites and texture have been examined. The analysis was carried out by wide-angle X-ray diffraction. The relative degrees of crystallinity in poly-α-butene samples containing nucleating agents were measured using the Hermans-Weidinger procedure; in order to obtain the size of crystallites, the Debye-Scherrer method was applied. The lattice parameters show no change but the relative degree of crystallinity, the size of crystallites and their texture depend on the nucleating agent used.     

Evaluation of Ptitsyn-Eizner λ parameter in dilute solutions of poly(N-vinylcarbazole) and its variation in conformational transitions of poly(methyl methacrylate)

The Ptitsyn-Eizner λ flexibility parameter for poly(N-vinylcarbozole) solutions under theta conditions has been found to be 6.31, demonstrating the rigidity imparted to the polymer chain by the carbazole group. A study has been made of the variation of this parameter with solvent and temperature. A study has been made of the variation of λ in a conformational transition of poly(methyl methacrylate).