Aryl Boronic Acid Catalysed Dehydrative Substitution of Benzylic Alcohols for C−O Bond Formation

A combination of pentafluorophenylboronic acid and oxalic acid catalyses the dehydrative substitution of benzylic alcohols with a second alcohol to form new C−O bonds. This method has been applied to the intermolecular substitution of benzylic alcohols to form symmetrical ethers, intramolecular cyclisations of diols to form aryl-substituted tetrahydrofuran and tetrahydropyran derivatives, and intermolecular crossed-etherification reactions between two different alcohols. Mechanistic control experiments have identified a potential catalytic intermediate formed between the aryl boronic acid and oxalic acid.     

Defining Integrality at Prime Sets of High Density over Function Fields

 Let F be a function field of characteristic over a finite field . Then for any finite set of F-primes S and any , there exists a set of F-primes W of density greater than such that and has a Diophantine definition over . (Here and is defined analogously.)     

Thermoplastic poly(ester‐imide)s derived from anhydride‐terminated polyester prepolymer and diisocyanate

The phase‐separation behavior of thermoplastic poly(ester‐imide) [P(E‐I)] multiblock copolymers, (A‐B)_n, was investigated by a stepwise variation of the imide content. All the multiblock copolymers were synthesized by solution polycondensation with dimethylformamide as a solvent. P(E‐I)s were prepared with anhydride‐terminated polyester prepolymer and diisocyanates. Polyester prepolymers were prepared by the reaction of pyromellitic dianhydride and two different polyols [poly(tetramethylene oxide glycol) (PTMG) and polycaprolactone diol (PCL)]. Structural determination was done with Fourier transform infrared spectroscopy and Fourier transform NMR, and the molecular weight was determined by gel permeation chromatography. The effect of the imide content on the thermal properties of the synthesized P(E‐I)s was investigated by thermogravimetric analysis and differential scanning calorimetry. The polymers were also characterized for static and dynamic mechanical properties. Thermal analysis data indicated that the polymers based on PTMG were stable up to 330 °C in nitrogen atmosphere and exhibited phase‐separated morphology. Polymers based on PCL showed multistage decomposition, and the films derived from them were too fragile to be characterized for static and dynamic mechanical properties. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 341–350, 2004     

Continuous modified Newton’s-type method for nonlinear operator equations

A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x ₀ and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support     

Hawking Absorption and Planck Absolute Entropy of Kerr-Newman Black Hole

We find the existence of a quantum thermal effect, “Hawking absorption.” near the inner horizon of the Kerr–Newman black hole. Redefining the entropy, temperature, angular velocity, and electric potential of the black hole, we give a new formulation of the Bekenstein–Smarr formula. The redefined entropy vanishes for absolute zero temperature of the black hole and hence it is interpreted as the Planck absolute entropy of the KN black hole.     

Diophantine Undecidability of Function Fields of Characteristic Greater than 2, Finitely Generated over Fields Algebraic over a Finite Field

Let F be a function field of characteristic p > 2, finitely generated over a field C algebraic over a finite field C _p and such that it has an extension of degree p. Then Hilbert's Tenth Problem is not decidable over F.     

Hydrogen-bonded block mesogens derived from semiperfluorinated benzoic acids and the non-mesogenic 1,2-bis(4-pyridyl)ethylene

Thermal properties of benzoic acids carrying one or two semiperfluorinated alkoxy tails on the aromatic core have been investigated in binary mixtures with the non-liquid crystalline bidirectional trans-1,2-bis(4-pyridyl)ethylene. The hydrogen bonded complexes built from the complementary molecular species show a significantly enhanced mesophase stability compared with the fluorinated acids in their pure states. The mesophase morphologies of the complexes are governed mainly by the number of the partially fluorinated chains grafted to the acid component. Mixed systems comprising the one-chain acids exhibit a smectic C phase followed by a smectic A phase at more elevated temperatures. Incorporation of a second semiperfluorinated chain into the acid leads to the formation of columnar mesophases. These columnar phases of the H-bonded complexes should represent ribbon phases resulting from the collapse of the smectic layers.     

The observation of a large gauche preference when 2-fluoroethylamine and 2-fluoroethanol become protonated

The energies of the gauche and anti conformers of 2-fluoroethylamine, 2-fluoroethanol and their protonated analogues are calculated using density functional theory. Unlike the non protonated systems, the protonated systems show a strong gauche effect where the C-F and the C-(+)NH(3) or C-F and C-(+)OH(2) bonds are gauche rather than anti to each other. Single crystal X-ray diffraction studies of 2-fluoroethylammonium compounds identify the same conformational preference.