Steric communication of chiral information observed in dendronized polyacetylenes

Structural and retrostructural analysis of helical dendronized polyacetylenes (i.e., self-organizable polyacetylenes containing first generation dendrons or minidendrons as side groups) synthesized by the polymerization of minidendritic acetylenes with [Rh(nbd)Cl]2 (nbd = 2,5-norbornadiene) reveals an approximately 10% change in the average column stratum thickness (l) of the cylindrical macromolecules with a chiral periphery, through which a strong preference for a single-handed screw-sense is communicated. The cylindrical macromolecules reversibly interconvert between a three-dimensional (3D) centered rectangular lattice (Phi r-c,k) exhibiting long-range intracolumnar helical order at lower temperatures and a two-dimensional (2D) hexagonal columnar lattice (Phi h) with short-range helical order at higher temperatures. A polymer containing chiral, nonracemic peripheral alkyl tails is found to have a larger l as compared to the achiral polymers. In methyl cyclohexane solution, the same polymer exhibits an intense signal in circular dichroism (CD) spectra, whose intensity decreases upon heating. The observed change in l indicates that the chiral tails alter the polymer conformation from that of the corresponding polymer with achiral side chains. This change in conformation results in a relatively large free energy difference (DeltaGh) favoring one helix-sense over the other (per monomer residue). The capacity to distort the polymer conformation and corresponding free energy is related to the population of branches in the chiral tails and their distance from the polymer backbone by comparison to recently reported first and second generation dendronized polyphenylacetylenes.     

Dependency of particle sizes and colloidal stability of polyelectrolyte complex dispersions on polyanion structure and preparation mode investigated by dynamic light scattering and atomic force microscopy

Polyelectrolyte complex (PEC) dispersions were prepared by controlled mixing of three random copolymers of sodium 2-acrylamido-2-methylpropanesulfonate (AMPS) with either t-butyl acrylamide (TBA) [P(AMPS54-co-TBA46) and P(AMPS37-co-TBA63)] or methyl methacrylate (MM) [P(AMPS52-co-MM48)] with an ionene-type polycation, containing 95 mol % N,N-dimethyl-2-hydroxypropyleneammonium chloride repeat units (PCA5), with their structural characteristics being deeply investigated by dynamic light scattering (DLS) and atomic force microscopy (AFM). Shape, size, and polydispersity of the PEC dispersions were directly observed by AFM as a function of polyanion structure, the ratio between charges, n-/n+, and the titrant addition rate (TAR). The particle sizes increased and the colloidal stability decreased with the increase of the nonionic comonomer content and with the decrease of TAR. It was demonstrated that the medium particle sizes of the complex nanoparticles adsorbed on silicon wafers measured by AFM, in the dry state, were close but always lower than those measured by DLS, both before and after the complex stoichiometry.     

Skeletal diversity through radical cyclization of tetrahydropyridine scaffolds

Suitably functionalized tetrahydropyridines (methyl pipecolates) have been used as conformationally biased templates for radical cyclizations to access benzoisoquinuclidines and linearly fused indenopiperidines. Variation of skeletal types is determined by location of a radical-initiating element.     

Thixotropic twin-dendritic organogelators

Twin-dendritic organogelators have been prepared through selective functionalization of N-(3-aminopropyl)-1,3-propanediamine (APPDA) with self-assembling dendrons by using 1,1'-carbonyldiimidazole (CDI). Subsequent modification of the APPDA linker provided an additional degree of structural diversity by which to tailor the gelator self-assembly in bulk or in the gel state. These compounds are able to gel cyclohexane, toluene, n-butyl acetate, ethyl acetate, dichloromethane, and tetrahydrofuran. 3,4-Disubstituted apical branching units provided the most efficient organogelators and show a propensity to form thixotropic gels, wherein the gel recovers its elasticity after being subjected to shear. Structural and retrostructural analysis of the twin-dendritic organogelators reveals the bulk structural characteristics to be indicative of the subsequent gel properties. Diverse self-organized arrays were identified in bulk and all are able to form gels, thus indicating the role of quasiequivalence in mediating self-assembly in the gel state. Furthermore, we have found that porous columnar mesophases provide a strategy by which to prepare thixotropic gels. We demonstrate the importance of weak lateral hydrogen bonding within a column stratum versus hydrogen bonding along the length of the column for forming porous columnar mesophases and, by extension, thixotropic gels.     

Rapid identification of common hexapyranose monosaccharide units by a simple TOCSY matching approach

Solution NMR spectroscopy is a well established technique for non-destructive characterization of the structures and conformations of complex oligo- and polysaccharides. One of the key experiments involves the use of 2D TOCSY to collect the 1H spins into groups that can be associated with the individual saccharide units that are present in the molecule under study. It is well known that the magnetization transfer rate through the 1H spin system during the TOCSY spin lock period is sensitive to the intervening 3J(H,H) scalar couplings, and therefore also to the saccharide stereochemistry. Here, we have investigated the potential to extract information on the stereochemistry of hexapyranose monosaccharide units directly from TOCSY spectra. Through a systematic experimental investigation of the magnetization transfer initiated from the anomeric 1H resonance in D-glucose, D-galactose and D-mannose it is shown that a 100 ms spin lock time provides optimal spectroscopic discrimination between these three commonly occurring building blocks. A simple matching scheme is proposed as a new tool for rapid attribution of the TOCSY traces originating from the anomeric 1H resonances towards the underlying monosaccharide type. The scheme appears robust with regard to structural variations and fairly tolerant to incidental overlap. Its application provides useful guidance during the subsequent NMR assignment process, as demonstrated with the PS7F polysaccharide from Streptococcus pneumonia. In addition, we show that our scheme affords a clear-cut distinction between the alpha- and beta-epimers of D-mannose-type units, which can be difficult to discriminate by NMR analysis. Application to the N-glycan 100.2 demonstrates the potential and wide applicability of this new discrimination approach.     

Asymptotic behaviour of families of real curves

We consider the family of fibres of a polynomial function f on a smooth noncompact algebraic real surface and we characterise the regular fibres of f which are atypical due to their asymptotic behaviour at infinity. We compare to the similar problem in the complex case. Received: 5 May 1998 / Revised version: 20 March 1999     

Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category

If H is a Hopf algebra with bijective antipode and α, β ∈ Aut _Hopf (H), we introduce a category , generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category having all the categories as components, which, if H is finite dimensional, coincides with the representations of a certain quasitriangular T-coalgebra DT(H) that we construct. We also prove that if (α, β) admits a so-called pair in involution, then is isomorphic to the category of usual Yetter-Drinfeld modules . Research partially supported by the programme CERES of the Romanian Ministry of Education and Research, contract no. 4-147/2004.     

Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction

Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of potential theory and rational approximation theory. The study of the asymptotic behavior of the roots of these polynomials reveals a surprisingly rich geometry, which reflects three characteristics: the relative position of an island in the archipelago, the analytic continuation picture of the Schwarz function of every individual boundary and the singular points of the exterior Green function. By way of explicit example, fine asymptotics are obtained for the lemniscate archipelago |z^m−1|<r^m, 0<r<1, which consists of m islands. The asymptotic analysis of the Christoffel functions associated to the same orthogonal polynomials leads to a very accurate reconstruction algorithm of the shape of the archipelago, knowing only finitely many of its power moments. This work naturally complements a 1969 study by H. Widom of Szegő orthogonal polynomials on an archipelago and the more recent asymptotic analysis of Bergman orthogonal polynomials unveiled by the last two authors and their collaborators.     

On the existence of solutions to a special variational problem

In this paper we establish an existence and regularity result for solutions to the problem

Fundamental solution for linear two-point boundary value problem

The quadratic functional minimization with differential restrictions represented by the command linear systems is considered. The optimal solution determination implies the solving of a linear problem with two points boundary values. The proposed method implies the construction of a fundamental solution S(t)—a n×n matrix—and of a vector h(t) defining an adjoint variable λ(t) depending of the state variable x(t). From the extremum necessary conditions it is obtained the Riccati matrix differential equation having the S(t) as unknown fundamental solution is obtained. The paper analyzes the existence of the Riccati equation solution S(t) and establishes as the optimal solution of the proposed optimum problem. Also a superior limit of the minimum for the considered quadratic functionals class are evaluated.