A New Chemo‐Enzymatic Route to Side‐Chain Liquid‐Crystalline Polymers: The Synthesis and Polymerization of 6‐(4‐Methoxybiphenyl‐4′‐oxy)hexyl Vinyl Hexanedioate

A novel synthetic method combining chemo and enzymatic synthesis strategies was employed to prepare a vinyl acetate type monomer, 6‐(4‐methoxybiphenyl‐4′‐oxy)hexyl vinyl hexanedioate (VA‐LC). Homo‐ and copolymers of VA‐LC with maleic anhydride (MAn) were prepared by conventional free radical polymerization using 2,2′‐azobisisobutyronitrile (AIBN) and 1,1′‐azobis (cyclohexane carbonitrile) (AHCN) as an initiator at 95 and 60 °C, respectively. The thermal properties of the generated polymeric material were investigated by differential scanning calorimetry (DSC), and the optical texture was inspected by polarizing optical microscopy (POM). While the monomer VA‐LC does not exhibit liquid‐crystalline properties, poly(VA‐LC), and the alternating copolymer of VA‐LC with maleic anhydride both displayed such properties.

     

5-(N-Arylnortropan-3-yl)- and 5-(N-Arylpiperidin-4-yl)-2,4-diaminopyrimidines. Novel Inhibitors of Dihydrofolate Reductase

Based on a computer-assisted analysis of the three-dimensional structure of the binary complex of E.coli dihydrofolate reductase (DHFR) with methotrexate, 5-(N-arylnortropan-3-yl)- and 5-(N-arylpiperidin-4-yl)-2,4-diaminopyrimidines 2 and 4 were designed as inhibitors of DHFR. Syntheses of the designed compounds have been carried out. The most potent compound 2a inhibited E. coli DHFR with K_i = 0.49.10^?9M. The activities within the series of compounds synthesized could be rationalized by molecular-modelling experiments which served as the basis of this work. Several compounds within the presented series exhibit antimalarial activities in vitro and in vivo.     

GC–MS analysis of phenolic compounds in fuels after conversion to trifluoroacetate esters

The GC–MS characteristics of trifluoroacetate esters of phenolic compounds are discussed. Linear temperature programmed retention indices and total ion current MS response factors of over 120 phenolic esters are reported. The main GC advantages from analysis of trifluoroacetate esters as compared to plain phenols are enhanced volatility and improved resolution. For example, the elution temperature of a given phenol is typically 50 °C greater than that of the corresponding trifluoroacetate ester. Also, while retention of compounds with two trifluoroacetate groups is only moderately greater than mono esters, underivatized dihydroxy compounds are very difficult to elute from any GC column. Complete resolution of isomeric C₀-, C₁- and C₂-alkylphenol esters is readily achieved on conventional fused silica GC columns; resolution of the corresponding underivatized compounds requires specialized GC columns with low temperature limits. In general, mass spectra of trifluoroacetate esters are more characteristic of a given structure than those of the corresponding phenols and may be more rigorously interpreted towards structural elucidation. A table in the report summarizes some of the more important spectral features used in compound identification. Example applications in analysis of coal-, shale- and petroleum-derived materials are presented. Selected ion monitoring is used to determine individual phenolic components in whole distillates; reconstructed ion chromatograms are used to illustrate distributions of selected species as a function of fuel storage and thermal stress.     

Orthmodular lattices whose MacNeille completions are not orthomodular

The only known example of an orthomodular lattice (abbreviated: OML) whose MacNeille completion is not an OML has been noted independently by several authors, see Adams [1], and is based on a theorem of Ameniya and Araki [2]. This theorem states that for an inner product space V, if we consider the ortholattice ?(V,⊥) = {A \( \subseteq \) V: A = A ^⊥⊥} where A ^⊥ is the set of elements orthogonal to A, then ?(V,⊥) is an OML if and only if V is complete. Taking the orthomodular lattice L of finite or confinite dimensional subspaces of an incomplete inner product space V, the ortholattice ?(V,⊥) is a MacNeille completion of L which is not orthomodular. This does not answer the longstanding question Can every OML be embedded into a complete OML? as L can be embedded into the complete OML ?(V,⊥), where V is the completion of the inner product space V. Although the power of the Ameniya-Araki theorem makes the preceding example elegant to present, the ability to picture the situation is lost. In this paper, I present a simpler method to construct OMLs whose Macneille completions are not orthomodular. No use is made of the Ameniya-Araki theorem. Instead, this method is based on a construction introduced by Kalmbach [7] in which the Boolean algebras generated by the chains of a lattice are glued together to form an OML. A simple method to complete these OMLs is also given. The final section of this paper briefly covers some elementary properties of the Kalmbach construction. I have included this section because I feel that this construction may be quite useful for many purposes and virtually no literature has been written on it.     

Structure of 2,2′-bis(3-allyl-4-cyanatophenyl)isopropylidene

The structure of the title compound (I) was determined by direct methods using MoK diffractometer data, and refined by full-matrix least squares toR=0.066 for 1536 reflections (I3 (I)). The structure shows a central tetrahedral carbon atom surrounded by two methyl and two 3-allyl-4-cyanatophenyl groups. The geometry of the cyanato group in this molecule compares well with those in 2,2-bis(4-cyanatophenyl)isopropylideneII) and 4-chloro-3,5-dimethyl-phenylcyanate (III), the only other examples of organic compounds bearing the cyanato moiety in the Cambridge Crystallographic Database (V.3).     

Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space

We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceH _? ⁿ . We show that there exists a Γ-invariant real hypersurfaceF ?H _? ⁿ such that the Dirichlet fundamental polyhedron for Γ centered at z₀ has two sides (resp. infinitely many sides) if and only ifz ₀ ∈F (resp.z ₀ ?F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofH _? ⁿ is developed in terms of these horospherical coordinates.     

Orientation reversing involutions and the first betti number for finite coverings of 3-manifolds

LetMS ³,P ³ be a closed, orientable irreducible 3-manifold which admits an orientation reversing involution :MM. If dim(Fix )=0, suppose ₁ (M) has a subgroup of even index. We show thatM has finite coverMMM} with ₁(M<0). As an application we show that the hyperbolic dodecahedral space has a finite cover with positive 1st betti number.     

On a class of atmospheres occurring in stellar hydrodynamic theory

Summary A derivation is given of the basic equation governing the behaviour of small disturbances in a stratified compressible atmosphere (with a locally unstable region bounded by semi-infinite stable regions) in which the time of radiative relaxation is constant.By means of a new independent variable that is a function of the equilibrium entropy stratification, various properties of such media can be established in a straightforward manner. A general expression for the wave energy flux is derived, and integral properties arising from this quantity are used to obtain in particular, results pertaining to the eigenfunctions and eigenvalues for strongly radiating systems. In addition, a model of an atmosphere with a strongly-radiating region embedded in a convective zone, and bounded by semi-infinite radiation-free layers is discussed in some detail. The paper is an approach towards providing some preliminary but unified results in the theory of stellar hydrodynamics.

---

Résumé Nous donnons une dérivation de l'équation de base qui détermine la propagation des petites perturbations dans une atmosphère compressible stratifiée (présentant une zone d'instabilité locale entre des zones de stabilité semi-infinies) dont le temps de relaxation radiative est constant.Au moyen d'une nouvelle variable indépendante, fonction de la stratification de l'entropie en équilibre, diverses propriétés de tels milieux sont déterminées simplement. On donne une formulation du flux de l'énergie ondulative et on emploie les propriétés intégrales qui en résultent pour obtenir en particulier des résultats concernant les eigenfonctions et les eigenvalues pour des systèmes à forte radiation énergétique. En outre, on étudie en détail le modèle d'une amtosphère caractérisée par une zone à forte radiation insérée dans une zone convective entre des couches semi-infinies sans radiation.Ce travail présente quelques conclusions préliminaires mais cohérentes dans le domaine de la théorie de l'hydrodynamique stellaire.

     

Non-uniqueness of solutions of Percival's Euler-Lagrange equation

Percival [5,6] introduced a Langrangian and an Euler-Lagrange equation for finding quasi-periodic orbits. In [3], we studied area preserving twist homeomorphisms of the annulus, using Percival's formalism. We showed that Percival's Lagrangian has a maximum on a suitable function space, and that a point where it takes its maximum is a solution of Percival's Euler-Lagrange equation. Moreover, in the rigorous interpretation of Percival's formalism which we gave in [3], the solutions of Percival's Euler-Lagrange equation correspond bijectively to a certain class of minimal sets. (We will prove this in Sect. 2.) In [4], we showed that Percival's Lagrangian takes its maximum at only one point. In this paper, we show that there existC area preserving twist diffeomorphisms of the annulus, for which there exists at least one solution of Percival's Euler-Lagrange equation where Percival's Lagrangian does not take its maximum. In other words, solutions of Percival's Euler-Lagrange equation need not be unique.Supported by NSF Grant No. MCS 79-02017