The push-out space of immersed spheres

Let f: M ^m → ? ^m+1 be an immersion of an orientable m-dimensional connected smooth manifold M without boundary and assume that ξ is a unit normal field for f. For a real number t the map f _tξ: M ^m → ? ^m+1 is defined as f _tξ(p) = f(p) + tξ(p). It is known that if f _tξ is an immersion, then for each p ∈ M the number of the focal points on the line segment joining f(p) to f _tξ(p) is a constant integer. This constant integer is called the index of the parallel immersion f _tξ and clearly the index lies between 0 and m. In case f: $\mathbb{S}^m \to \mathbb{R}^{m + 1} $ is an immersion, we study the presence of a component of index μ in the push-out space Ω(f). If there exists a component with index μ = m in Ω(f) then f is known to be a strictly convex embedding of $\mathbb{S}^m $ . We reveal the structure of Ω(f) when $f(\mathbb{S}^m )$ is convex and nonconvex. We also show that the presence of a component of index μ in Ω(f) enables us to construct a continuous field of tangent planes of dimension μ on $\mathbb{S}^m $ and so we see that for certain values of μ there does not exist a component of index μ in Ω(f).     

Solvent effects in the preparation of molecularly imprinted polymers for melatonin using N-propionyl-5-methoxytryptamine as the pseudo template

To clarify the role of diluents in the preparation of molecularly imprinted polymers utilizing only hydrogen bonding, we investigated the effects of diluents by using different solvents. Melatonin (N-acetyl-5-methoxytryptamine), an amide bond and indole ring-containing hormone was chosen as the target molecule. N-Propionyl-5-methoxytryptamine was used as the pseudo template, methacrylic acid as the functional monomer, and solvents were used as diluents. Interactions between the template, the functional monomer, melatonin, and the solvents, were observed by ¹H NMR spectroscopy. The polymers were evaluated by high-performance liquid chromatography. The results suggest the hydrogen bonding-acceptor capacity of the solvent is the most important factor in the preparation of molecularly imprinted polymers for hydrogen bonding-donating molecules. Hydrogen bonding between the template, the functional monomer, and solvent can be estimated from the chemical shifts in ¹H NMR spectra of those molecules in the solvent.     

Flexible polyaniline

Flexible polyaniline having excellent mechanical properties (e.g., elongation at break = 41% and tensile strength = 1.8 kg cm^?2) was prepared by electrochemical reduction of ordinary polyaniline in organic solvents. The flexibility is directly related with the polymer morphology which was definitely affected by the nature of electrolyte anion. Perchlorate or tetrafluoroborate anion were found suitable to obtain flexible polyaniline. At the same time, it is essential that the polymer so prepared should be reduced (undoped) in some suitable organic solvents before making a flexible free standing film.     

Electronic absorption spectra of phenol(H2O)n and (phenol)n as studied by the MS MPI method

The initial stages of solvation and crystallization were studied in phenol(H₂O)_n and (phenol)_n by the use of the mass-selected MPI method in a supersonic free jet. The spectral position exhibits an irregular shift by the change of the cluster size, which is interpreted in terms of the role of phenol as a proton donor, a proton acceptor or both in the hydrogen bonding. The O⁰₀ band of the phenol—water cluster was found to converge to 276.0 nm. The phenol trimer was concluded to have a cyclic structure.     

Synthesis and characterization of bis(N,N-diethylnicotinamide) <Emphasis Type="Italic">m</Emphasis>-hydroxybenzoate complexes of Co(II), Ni(H), Cu(II), and Zn(II)

Four novel mixed-ligand complexes of Co(II), Ni(II), Cu(II), and Zn(II) with m-hydroxybenzoate (m-Hba) and N,N-diethylnicotinamide (Dena) were synthesized and characterized on the basis of elemental analysis, FT-IR spectroscopic study, and solid state UV-Vis spectrophotometric and magnetic-susceptibility data. The thermal behavior of the complexes was studied by combined TG-DTA methods in static air atmosphere, and the mass spectra were recorded. The Co(II), Ni(II), and Zn(II) complexes, except for the Cu(II) complex, contain two molecules of coordinated water, two m-Hba, and two Dena ligands per formula unit. In these complexes, the m-Hba and Dena behave as monodentate ligands via acidic oxygen and nitrogen of the pyridine ring. In the Cu(II) complex, the m-Hba is coordinated as monoanionic bidentate ligand through acidic oxygen and carbonyl oxygen. Dena is bonded with Cu²⁺ as monodentate ligand by the nitrogen atom of the pyridine ring. The decomposition pathways and the stability of the complexes are interpreted in terms of the proposed structural data. The final decomposition products were found to be the respective metal oxides. The article was submitted by the authors in English.     

A simple method for predicting the frequency of the infrared inactive carbonyl stretching mode in LM(CO)5 molecules with C4V symmetry

The paper presents a new method for predicting the frequency of the b₁ mode, which is infrared-inactive, in complexes of the type LM(CO)₅ belonging to C_4V point group. The method was based on the relation λ₃=λ₄+[(1−δ/δ)](λ₁−λ₂), where δ=(λ₁−λ₂)/(λ₁−λ₂+λ₃−λ₄), λ₁, λ₂, λ₃ and λ₄ are the λ parameters of the , , b₁ and e modes, respectively. For a large numbers of complexes of the type LM(CO)₅ the average value of δ was found to be 0.80, with a standard deviation of 0.02. With the use of average value of δ, the frequencies of b₁ mode were estimated. The result obtained indicated that there exists a rather good fit between observed and calculated frequencies, with a mean error of 2.7 cm⁻¹. In addition, it was shown that the δ parameter can be used as a criterion of the correct band assignment for the complexes understudy.     

Excitation energy dependence of the photoluminescence band at 2.7 and 4.3 eV in silica glass at low temperature

In this paper, we report the excitation energy dependence of the 2.7 and 4.3 eV photoluminescence (PL) bands in oxygen deficient silica glass at low temperature (20 K). The increase or decrease of the PL intensity at low temperatures is different for different exciting light wavelengths. The PL intensity tended to decrease with low temperatures when the excitation was near the upper and lower end of the excited level. The peak energy of the excitation spectrum increases with cooling. These results indicate that the change in excitation level with cooling is associated with the low-temperature dependence of light emission. Thermal motion is suppressed, when the sample temperature is lowered, and the energy-width of the excited level decreases, i.e., the light emission probability decreases (the emission intensity decreases), when near the upper and lower end of the excitation level. These phenomena were observed in the low-temperature dependence of the 4.3 eV emission intensity.     

Finite element error analysis for a projection-based variational multiscale method with nonlinear eddy viscosity

The paper presents a finite element error analysis for a projection-based variational multiscale (VMS) method for the incompressible Navier-Stokes equations. In the VMS method, the influence of the unresolved scales onto the resolved small scales is modeled by a Smagorinsky-type turbulent viscosity.     

Synthesis and characterization of a pyridine-containing Schiff base oligomer

The oligomer of 4-(4-pyridylmethylideneimino)phenol was formed during oxidative polycondensation in aqueous alkaline medium using oxygen as the oxidant. Optimum conditions of the oxidative polycondensation and the main parameters of the process were found. The maximum yield of the oligomer was 52.4%. The product was characterized by elemental analysis, FT-IR spectroscopy, UV-Vis spectroscopy, and ¹H NMR spectroscopy. The molecular weight distribution was determined by size exclusion chromatography. Thermogravimetric and differential thermal analyses were carried out for 4-(4-pyridylmethylideneimino)phenol and its oligomer. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1785–1788, October, 2006.