The formation of a liquid crystalline main chain polymer by means of photopolymerization

A nematic liquid crystal material containing a mercapto group and an olefinic group was synthesized. Photopolymerization of this compound in the liquid crystalline state resulted in a liquid crystalline main chain polymer which showed a relatively high birefringence. Due to scattering, the material had a low transmission at ambient temperatures.     

Enantioselective Alternating Olefin-Carbon Monoxide Copolymerization: A new concept for activity and stereoselectivity

Cationic Pd-complexes modified by dicyclohexyl{(R)-1-[(S)-2-(diphenylphosphino)ferrocenyl]ethyl}phosphine ( 1a ) give very active catalytic systems for the regioregular isotactic specific copolymerization of propene with CO. Other alk-1-enes also give stereoregular and regioregular copolymers, even if with lower productivity. The copolymers are isolated as poly(4-alkyl-tetrahydrofuran-2,2,5,5-tetrayl-2-oxy-2-methylenes) B in the solid state and give the isomeric poly(2-alkyl-1-oxopropane-1,3-diyls) A by dissolution in (CF₃)₂CHOH. Solid polymer A (R = Et) is formed back at least partially when the dissolved material is reprecipitated from MeOH. The use of the related (ferrocenyl)diphosphine ligands 1b ? e and 2 as the catalyst modifier shows that the presence of both elements of chirality and of large substituents on the P-atoms of the ligand is necessary to achieve good stereocontrol, and that the large difference in basicity between the two P-atoms is probably the reason for the good catalytic activity.     

Perfect MV-algebras and their Logic

In this paper, after recounting the basic properties of perfect MV-algebras, we explore the role of such algebras in localization issues. Further, we analyze some logics that are based on Łukasiewicz connectives and are complete with respect to linearly ordered perfect MV-algebras.      

Spironolactone and its Complexes with β-cyclodextrin: Modern NMR Characterization and Structural DFTB-SCC Calculations

In the present work, inclusion complexes of spironolactone (SP) with β-cyclodextrin (β-CD) in solid phase and aqueous solution were studied by solubility methods, NMR spectroscopy and thermal analysis. The results showed different kinds of complexations when freeze-drying and kneading methods were used. The freeze-drying product (1:1, SP:β-CD) showed lower degree of complexation and stability than the (1:2, SP:β-CD) compound obtained by kneading method. The spironolactone molecule was also studied by NMR spectroscopy at 400 MHz. The chemical shifts of all spironolactone atoms and their inclusion compounds were assigned. Extensive use of 1D and 2D NMR techniques, including ROESY experiment, allowed verifying the position of the spironolactone molecule inside the cyclodextrin cavity in both situations. In addition, DFTB-SCC quantum mechanical calculations of the inclusion compounds were performed. The predicted structural properties are in good agreement with ROESY NMR results.     

Numerical calculation of cutoff frequencies of optical fibers by a variational technique

A numerical method for calculating cutoff frequencies of modes of weakly guiding optical fibers is described. Starting from a properly constructed field representation, the method follows a variational approach to obtain an eigenvalue problem for the cutoff frequencies which can be easily solved by a standard numerical routine. The field representation uses an expansion in terms of the Laguerre–Gauss functions in the fiber core and limiting form for small arguments of modified Bessel functions in the fiber cladding. Fibers with power-law refractive index profiles and fibers with a profile showing a dip on the axis are analyzed. Results obtained for modes of arbitrary order (both azimuthal and radial) show that our method is very efficient and accurate.     

Poly(epichlorohydrin) modified with 3,4,5‐tris(dodecyloxy)benzoate: The structure and dynamics of the aliphatic side chains in the columnar mesophase

We investigated the dynamics and structure of the aliphatic side chains of a randomly grafted copolymer, obtained through the chemical modification of poly(epichlorohydrin) with potassium 3,4,5‐tris(dodecyloxy)benzoate, with solid‐state ¹³C NMR. Below 283 K, the aliphatic chains partially crystallized in an all‐anti conformation. The calorimetric data were compatible with an orthorhombic packing. Below 323 K, the polymer exhibited a columnar mesophase. Spin–lattice relaxation times were determined in this temperature range and at 333 K, that is, in the isotropic phase. In the liquid‐crystalline state, some carbons exhibited a double decay in the spin–lattice relaxation, and this was attributed to presence of the liquid‐crystalline phase. This hypothesis was supported by a conformational analysis performed by molecular modeling. The activation energies of the relaxation processes in the mesophase were also estimated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2099–2111, 2005     

0–1 equivalent model representations for air traffic management

We present two equivalent representations of a 0–1 model for the Air Traffic Flow Management Problem. We show that the LP relaxation of the second representation is tighter than the LP relaxation of the first one. As a direct implication, the Branch-and-Cut effort can be reduced. Computational results are reported on a set of large-scale instances. The preparation of this paper is partially supported by DGICYT through grant PB95-0407     

Degenerate Evolution Equations in Weighted Continuous Function Spaces, Markov Processes and the Black-Scholes Equation — Part I

The present paper is mainly devoted to the study of initial boundary problems associated with a wide class of degenerate second-order differential operators on real intervals, in the framework of weighted continuous function spaces. Such operators are of particular interest, since they often occur, for instance, while building up theoretical models in Mathematical Finance. In order to develop our approach, essentially based on semigroup theory, we provide here some general tools which, perhaps, cover an interest on their own, being concerned with the generation of positive strongly continuous semigroups and their deep connection with Markov processes, in the setting of weighted spaces of continuous functions on a locally compact space. Due to its length, the paper is split up into two parts; the second part will appear in this same journal.