Dielectric relaxation analysis of starch oligomers and polymers with respect to their chain length

Starch belongs to the polyglucan group. This type of polysaccharide shows a broad β-relaxation process in dielectric spectra at low temperatures, which has its molecular origin in orientational motions of sugar rings via glucosidic linkages. This chain dynamic was investigated for α(1,4)-linked starch oligomers with well-defined chain lengths of 2, 3, 4, 6, and 7 anhydroglucose units (AGUs) and for α(1,4)-polyglucans with average degrees of polymerization of 5, 10, 56, 70, and so forth (up to 3000; calculated from the mean molecular weight). The activation energy (E_a) of the segmental chain motion was lowest for dimeric maltose (E_a = 49.4 ± 1.3 kJ/mol), and this was followed by passage through a maximum at a degree of polymerization of 6 (E_a = 60.8 ± 1.8 kJ/mol). Subsequently, E_a leveled off at a value of about 52 ± 1.5 kJ/mol for chains containing more than 100 repeating units. The results were compared with the values of cellulose-like oligomers and polymers bearing a β(1,4)-linkage. Interestingly, the shape of the E_a dependency on the chain length of the molecules was qualitatively the same for both systems, whereas quantitatively the starch-like substances generally showed higher E_a values. Additionally, and for comparison, three cyclodextrins were measured by dielectric relaxation spectroscopy. The ringlike molecules, with 6, 7, and 8 α(1,4)-linked AGUs, showed moderately different types of dielectric spectra. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 188–197, 2004     

The geometry of Hamilton spaces - An introduction

A short introduction of Hamilton, Cartan and Generalized Hamilton spaces is provided. The Hamilton--Jacobi equations are deduced by variational calculus.     

Measure functions for frames

This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful comparison of frames indexed by the same set. We define the ultrafilter measure function, an explicit frame measure function that we show is contained both algebraically and topologically inside all frame measure functions. We explore additional properties of frame measure functions, showing that they are additive on a large class of supersets—those that come from so called non-expansive frames. We apply our results to the Gabor setting, computing the frame measure function of Gabor frames and establishing a new result about supersets of Gabor frames.     

On the computation of scaling coefficients of Daubechies' wavelets

In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.     

The geometry of Ingarden spaces

The Randers spaces RFⁿ were introduced by R. S. Ingarden. They are considered as Finsler spaces Fⁿ = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fⁿ, as Finsler spaces I Fⁿ = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fⁿ and I Fⁿ are completely different. For I Fⁿ we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fⁿ is constructed.     

Hydrolysis-condensation of tetraethoxysilane in nonparental solvents studied by GC-MS

Gas-chromatography coupled with mass spectrometry was used to investigate the hydrolysis and condensation of tetra-ethoxysilane (TEOS) in nonparental solvents (MeOH and nPrOH). In the presence of nonparental solvents, the reaction that advanced at highest rate is alkoxy group scrambling, that changes the precursor at the molecular level. Subsequent stages of hydrolysis-polycondensation process are essentially determined by the reactivity of the new molecular species formed.     

Synthese de composes dihydro-2,3 furanniques par hydroboration d'alcools β-acetyleniques

Hydroboration of β-acetylenic alcohols followed by NaOH/H₂O₂ oxidation leads to hemiacetals of γ-aldols which are easily dehydrated to 2,3-dihydrofuran compounds. The reaction gives good yields with hindered alcohols and its stereochemistry may be controlled during the organometallic synthesis of the starting alcohol.     

Chalcogenide derivatives of imidotin cage complexes

Reaction of the secocubane [Sn3(mu2-NHtBu)2(mu2-NtBu)(mu3-NtBu)] (1) with dibutylmagnesium produces the heterobimetallic cubane [Sn3Mg(mu3-NtBu)4] (4) which forms the monochalcogenide complexes of general formula [ESn3Mg(mu3-NtBu)4] (5a, E = Se; 5b, E = Te) upon reaction with elemental chalcogens in THF. By contrast, the reaction of the anionic lithiated cubane [Sn3Li(mu3-NtBu)4]- with the appropriate quantity of selenium or tellurium leads to the sequential chalcogenation of each of the three Sn(II) centres. Pure samples of the mono- or dichalcogenides are, however, best obtained by stoichiometric redistribution reactions of [Sn3Li(mu3-NtBu)4]- and the trichalcogenides [E3Sn3Li(mu3-NtBu)4]- (E = Se, Te). These reactions are conveniently monitored by using 119Sn NMR spectroscopy. The anion [Sn3Li(mu3-NtBu)4]- also acts as an effective chalcogen-transfer reagent in reactions of selenium with the neutral cubane [{Snmu3-N(dipp)}4] (8) (dipp = 2,6-diisopropylphenyl) to give the dimer [(thf)Sn{mu-N(dipp)}2Sn(mu-Se)2Sn{mu-N(dipp)}2Sn(thf)] (9), a transformation that results in cleavage of the Sn4N4 cubane into four-membered Sn2N2 rings. The X-ray structures of 4, 5a, 5b, [Sn3Li(thf)(mu3-NtBu)4(mu3-Se)(mu2-Li)(thf)]2 (6a), [TeSn3Li(mu3-NtBu)4][Li(thf)4] (6b), [Te2Sn3Li(mu3-NtBu)4][Li([12]crown-4)2] (7b') and 9 are presented. The fluxional behaviour of cubic imidotin chalcogenides and the correlation between NMR coupling constants and tin-chalcogen bond lengths are also discussed.