Bit-size estimates for triangular sets in positive dimension

We give bit-size estimates for the coefficients appearing in triangular sets describing positive-dimensional algebraic sets defined over Q. These estimates are worst case upper bounds; they depend only on the degree and height of the underlying algebraic sets. We illustrate the use of these results in the context of a modular algorithm.This extends the results by the first and the last author, which were confined to the case of dimension 0. Our strategy is to get back to dimension 0 by evaluation and interpolation techniques. Even though the main tool (height theory) remains the same, new difficulties arise to control the growth of the coefficients during the interpolation process.     

Preclusion of nano scale self-assembly in block-selective non-aqueous solvents for rod–coil and coil–rod–coil macromolecular surfactants based on perylene tetracarboxylic diimide

Self-assembly of amphiphilic molecules ranging from simple surfactants to block copolymers in a solvent depends on one part of the molecule (one block in block copolymers) being soluble, and the other not. The aggregation of the insoluble segment in the block-selective solvent leads to the self assembly. In this paper, we describe a system of amphiphilic rod–coil and coil–rod–coil molecules, which do not show self assembly in block-selective non-aqueous solvents. We prepared rod–coil molecules based on hydrophilic propylene oxide/ethylene oxide copolymer (PO–EO copolymer) (Jeffamine®) as the flexible segment and photo-conducting large aromatic perylenediimide (PTCDI) as the rod. PO–EO copolymer was attached either to one side of PTCDI (MJ–PTCDI) or both sides (DJ–PTCDI). The former can be considered an inverse macromolecular surfactant, since the tail is hydrophilic and the head is hydrophobic. The DJ–PTCDI is a pseudo Gemini surfactant. Because of the presence of the chromophore, UV–Vis and fluorescent spectra could be used to study the self assembly of these amphiphilic rod coil polymers in solution. PTCDI forms π-interaction mediated aggregates in aqueous solution and these are H-stacked in MJ–PTCDI and J-stacked in DJ–PTCDI. Variable temperature UV and NMR spectra show that the assembly is stable over a large temperature range in water. The aggregates are also stable up to a pH of 12. However, when a non-aqueous solvent is used, no aggregation occurs. This is attributed to the “solvation” of the π-system of the PTCDI. With the addition of water, such solvation seems to be interrupted and aggregation occurs when water becomes a major component. We find that the mole percentage of the aggregates in acetone/water mixtures increases almost linearly with the concentration of water, providing a route to control the extent of aggregation of the chromophores. Due to the long, waxy PO–EO copolymer, MJ–PTCDI and DJ–PTCDI do not show liquid crystalline behavior or nanorod morphology, which were seen with short side chains. The optical microscopy of the bulk material shows aggregated crystals of PTCDI in the waxy matrix, showing that even in the presence of PO–EO copolymer, the molecular assembly of PTCDI takes place in the bulk. Secondary assembly was seen, in that upon ageing of the aqueous solutions, the drop cast films show that the spherical aggregates one-dimensionally coalesced into long fibers. Although UV–Vis spectra indicated no aggregation in non-aqueous solvents, drop-cast films of these solutions show needle-like aggregates and Lego-like assemblies.     

Spatial properties of Wohlhart symmetric mechanism

The aim of this paper is to present a new analytical resolution to find closure equations of Wohlhart symmetric mechanism and to give some interesting spatial properties of this mechanism. These properties are used to put in evidence possible industrial applications for this type of mechanism. First, it concerns the analytic resolution of the twelve equations system obtained from the closure equation, system particularized for the case of Wohlhart symmetric mechanism. The matrix form of closure equations is written for a single loop overconstrained mechanism composed by six revolute joints, mechanisms called 6R. A kinematical analysis is made, putting in evidence some interesting kinematical and geometrical properties. These properties allow us to consider a new spatial disposition for this mechanism, by imposing three non-successive joints to remain in a determined plan. Thus, we obtain a translator, a possible future industrial application for this type of overconstrained mechanism.     

Synthesis and properties of π-conjugated donor–acceptor macrocycles derived from phenanthrylene building blocks

Phenanthrylene-ethynylidene macrocycles combining electron donor and electron acceptor subunits in their shape-persistent fully conjugated core were synthesized. The donor subunits consisted of two 9,10-dialkoxyphenanthrenes linked either with 1,2-ethynylidene or 2,5-thienylene bridge. The acceptors were 9,10-phenanthroquinone and dibenzoquinoxaline and dibenzophenazines derived from it. Solvatochromic photoluminescence from intramolecular-charge-transfer (ICT) excited state was observed mainly in non-polar solvents. In more polar solvents, the excited states favor non-radiative relaxation. DFT calculated HOMO/LUMO energies of the macrocycles correlate well with spectroscopic and electrochemical data. In the series of substituted dibenzophenazine acceptors a good correlation with Hammett substituent constants σ_p^– was found.