New Achievements in the Field of Intramolecular Phenolic Coupling Reactions,Using Hypervalent (III) Iodine Reagent: Synthesis of Galanthamine

Our investigations on the oxidative possibilities of the hypervalent iodine(III) reagent established that phenyliodine(III)bis(trifluoroacclate) (PIFA) can provide one-pot contiguous coupling-cyclization reaction giving a product with narwedine skeleton, when used in a phenolic coupling reaction of p'-bromonorbelladine derivatives. A suitably selected precursor gave up to 60% yield of the coupled product.     

The relativistic Doppler broadening of the line absorption profile

The classical results of Doppler broadening of the line absorption profile are generalized to a relativistic gas in thermal equilibrium by taking into account the relativistic variance of the volume absorption coefficients of the gas, as derived by L.H. Thomas. This variance produces a small correction, even in the non-relativistic approximation.     

Reaktionen bei dem thermochemischen ZnSe-Cyclus zur Darstellung von Wasserstoff

Ohne Zusammenfassung     

KAM-tori near an analytic elliptic fixed point

We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector ω ₀ is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a Rüssmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that ω ₀ has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least d + 1 passing through 0 that is foliated by complex analytic KAM-tori with frequency ω ₀. This is an extension of previous results obtained in [1] to the case of an elliptic fixed point.     

Polypeptide‐based nanocomposite: Structure and properties of poly(L‐lysine)/Na+‐montmorillonite

The feasibility of constructing polymer/clay nanocomposites with polypeptides as the matrix material is shown. Cationic poly‐L‐lysine · HBr (PLL) was reinforced by sodium montmorillonite clay. The PLL/clay nanocomposites were made via the solution‐intercalation film‐casting technique. X‐ray diffraction and transmission electron microscopy data indicated that montmorillonite layers intercalated with PLL chains coexist with exfoliated layers over a wide range of relative PLL/clay compositions. Differential scanning calorimetry suggests that the presence of clay suppresses crystal formation in PLL relative to the neat polypeptide and slightly decreases the PLL melting temperature. Despite lower crystallinity, dynamic mechanical analysis revealed a significant increase in the storage modulus of PLL with an increase in clay loading producing storage modulus magnitudes on par with traditional engineering thermoplastics. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2579–2586, 2002     

The redistribution function for scattering by relativistic electrons

The frequency redistribution function r(ν_i, ν_f) for scattering by relativistic electrons is derived, when this scattering is isotropic in the electron rest frame and recoil effects are neglected. Unlike previous derivations, we obtain for r(ν_i, ν_f) an expression which reduces exactly to its classical value for a non-relativistic gas.     

A Kam Scheme for SL(2, {{\mathbb R}}) Cocycles with Liouvillean Frequencies

We develop a new KAM scheme that applies to SL(2, \mathbb R{{\mathbb R}}) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinaburg–Sinai’s theorem to arbitrary frequencies: under a closeness to constant assumption, the non-Abelian part of the classical reducibility problem can always be solved for a positive measure set of parameters.     

Strongly segregated cubic microdomain morphology consistent with the double gyroid phase in high molecular weight diblock copolymers of polystyrene and poly(dimethylsiloxane)

We report the observation of a cubic phase consistent with the double gyroid structure in strongly segregated diblock copolymers of PS‐b‐PDMS over a volume fraction (φ_PDMS) range of ～0.39 to 0.45. The samples have respective molecular weights of 127 kg/mol and 73 kg/mol and degree of segregation Nχ equal to 187 and 106, respectively, at annealing temperature of 130 °C. It is important to highlight that two out of the total four samples investigated, exhibited hexagonally close packed cylindrical domains of PDMS and alternating lamellae at φ_PDMS = 0.39 and 0.45, respectively, indicating the possible narrow range of the DG morphology for the specific diblock copolymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2419–2427, 2009     

Synthesis and Self-Assembly of 2nd Generation Dendritic Homopolymers and Copolymers of Polydienes with Different Isomeric Microstructures

Synthesis of 2^nd generation dendritic polymeric materials via anionic polymerization procedures in combination with chlorosilane chemistry, consisting either from one polydienic segment (homopolymers) or from two chemically different polydienic components (copolymers), is described. The polydienes used were poly(butadiene) (PB) with ∼90% 1,4-isomerism and poly(isoprene) (PI) with increased 3,4-isomerism (∼60%). Molecular characterization of intermediate products and the final dendritic materials was made with Gel Permeation Chromatography (GPC), Membrane and Vapour Pressure Osmometry (MO and VPO respectively), Gas Chromatography –Mass Spectroscopy (GC-MS) and ¹H-Nuclear Magnetic Resonance (¹H-NMR) Spectroscopy, leading to the conclusion that they can be considered model polymers. Morphological studies solely with Transmission Electron Microscopy (TEM) have been conducted on two of the four synthesized copolymer samples exhibiting microphase separation between the two polydiene segments.     

Determinants and the volumes of parallelotopes and zonotopes

The Minkowski sum of edges corresponding to the column vectors of a matrix A with real entries is the same as the image of a unit cube under the linear transformation defined by A with respect to the standard bases. The geometric object obtained in this way is a zonotope, Z(A). If the columns of the matrix are linearly independent, the object is a parallelotope, P(A). In the first section, we derive formulas for the volume of P(A) in various ways as , as the square root of the sum of the squares of the maximal minors of A, and as the product of the lengths of the edges of P(A) times the square root of the determinant of the matrix of cosines of angles between pairs of edges. In the second section, we use the volume formulas to derive real-case versions of several well-known determinantal inequalities—those of Hadamard, Fischer, Koteljanskii, Fan, and Szasz—involving principal minors of a positive-definite Hermitian matrix. In the last section, we consider zonotopes, obtain a new proof of the decomposition of a zonotope into its generating parallelotopes, and obtain a volume formula for Z(A).