Manifestation of biquadratic coupling in the smectic C* phase soft mode dielectric response

The soft mode dielectric response of three ferroelectric chiral smectic C* substances is studied in the vicinity of the smectic C*-smectic A* phase transition. For some substances the soft mode dielectric strength exhibits a pronounced anomaly in the C* phase just below the phase transition. We show how this anomaly can be systematically correlated with a corresponding anomaly in the experimentally determined ratio of spontaneous polarization over tilt. By comparing the experimental results with the theoretical predictions of an extended Landau model, we demonstrate how the crossover behaviour of the system can be interpreted as being the consequence of the presence of a biquadratic coupling between tilt and polarization in the Landau free-energy of the system.     

Boundary behavior in Hilbert spaces of vector-valued analytic functions

In this paper we study the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc D. More specifically, we give operator-theoretic conditions on Mz, where Mz denotes the operator of multiplication by the identity function on D, that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by Aleman, Richter and Sundberg in [A. Aleman, S. Richter, C. Sundberg, Analytic contractions and non-tangential limits, Trans. Amer. Math. Soc. 359 (2007)] to the case of vector-valued functions.     

The free loop space and the algebraic k-theory of spaces

Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let . Here (X) denotes the free loop space of X and Q denotes the functor . For X = Y, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) A (point), B(X) B (point) are equivalent as infinite loop spaces.     

Total Synthesis of Cyclothialidine

A total synthesis of cyclothialidine ( 1 ), a new DNA gyrase inhibitor isolated from Streptomyces filipinensis, is described. The synthetic concept was tested by preparing the lactone 13 (Scheme 2) which contains the characteristic bicyclic core entity of 1 . Key features of the synthesis of 1 are: preparation of 3,5-dihydroxy-2,6-dimethylbenzoic acid ( 23 ) from 3,5-dihydroxybenzoic acid ( 19 ) by two consecutive Mannich aminomethylation/hydrogenation sequences; benzylic N-bromosuccinimide bromination of an ester derivative 25 thereof and its subsequent coupling with Boc-Ser-Cys-OMe ( 11 ); cyclization of the ω-hydroxy acid 29 29 to the 12-membered lactone 30 using preferably Mitsunobu conditions; completion of the peptidic side chains of 1 using Boc strategy (Scheme 4). Optically pure cis-N-(tert-butoxycarbonyl)-3-hydroxy-L -proline ((–)- 14 ) was obtained by resolution of the racemate via an efficient reaction sequence containing a lipase-catalyzed enantiospecific acetate hydrolysis (Scheme 3). The structure of natural 1 was confirmed by comparison with the synthetic material. The synthetic route described provides also easy access to analogues of 1 , e.g., via the intermediate 30 .     

1,6-dithia-spiro[4.4]nonadiene aus 2-thiazolin-5-thionen

4,4-Dimethyl-2-phenyl-2-thiazolin-5-thione ($\text{4}$) reacts with 2,3-diphenylcyclopropenone ($\text{2a}$) at 145°C and with benzonitrilio-2-propanide ($\text{6}$) at room temperature to yield the 1,6-dithia-spiro[4.4]nonadienes $\text{5}$ and $\text{7}$, respectively.     

Carbocyclic analogs of nucleosides. Part 2.. Synthesis of 2′,3′-dideoxy-5′-homonucleoside analogs

A set of derivatives of cyclopentaneacetic acid cis-substituted at position 3 by nucleoside bases (both purines and pyrimidines) were prepared and characterized (see 11, 14 , and 23a, b; Schemes 2–4). These molecules are carbocyclic analogs of 2′,3′-dideoxy-5′-homonucleosides. In this synthesis, the skeleton was constructed from norbornanone and a novel method based on Mitsunobu chemistry used for the introduction of nucleoside-base substituents. The scope of this method was further explored via the preparation of a cyclobutyl analog of dideoxyguanosine (see 17 , Scheme 3).