Monodomain and polydomain helicoids in chiral liquid-crystalline phases and their biological analogues

Many natural composites exhibit an architecture known as twisted plywood which imparts to them a superior set of physical properties. The origin of this structure is complex and not yet understood. However, it is thought to involve a lyotropic chiral nematic liquid-crystalline mesophase. Indeed, striking structural similarities have been observed and reported between biological fibrous composites and ordered fluids. In this work, a mathematical model based on the Landau-de Gennes theory has been developed to investigate the role played by constraining surfaces in the structural development of a composite material that experiences a liquid-crystalline state during the early steps of its morphogenesis. The goal of this study is to verify the need for an initial constraining surface in the formation of monodomain twisted plywoods as hypothesized by Neville (Tissue & Cell 20, 133 (1988); Biology of Fibrous Composites (Cambridge University Press, 1993)). The numerical simulations qualitatively confirm this theory and highlight the important role that modelling of liquid-crystalline self-assembly plays in the study of tissue morphogenesis.Received: 15 September 2003, Published online: 11 November 2003PACS: 61.30.-v Liquid crystals - 61.30.Dk Continuum models and theories of liquid crystal structure - 61.30.Mp Blue phases and other defect-phases - 61.30.St Lyotropic phases     

On the diophantine equation

In this note, we find all positive integer solutions of the diophantine equation from the title with a prime power.

     

The K-SAT Problem in a Simple Limit

In this work we compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computation can be strongly simplified and the thermodynamic properties can be obtained with a high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, >_c.     

Another Note on the Greatest Prime Factors of Fermat Numbers

For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if F_m = 2^2m + 1 is the mth Fermat number, then P(F_m) 2^m+2(4m + 9) + 1 for all m 4. We also give a lower bound of a similar type for P(F_a,m), where F_a,m = a^2m + 1 whenever a is even and m a¹⁸.AMS Subject Classification (1991) 11A51 11J86     

Enantioselective Organocatalytic Diels–Alder Trapping of Photochemically Generated Hydroxy‐o‐Quinodimethanes

The photoenolization/Diels–Alder strategy offers straightforward access to synthetically valuable benzannulated carbocyclic products. This historical light‐triggered process has never before succumbed to efforts to develop an enantioselective catalytic approach. Herein, we demonstrate how asymmetric organocatalysis provides simple yet effective catalytic tools to intercept photochemically generated hydroxy‐o‐quinodimethanes with high stereoselectivity. We used a chiral organic catalyst, derived from natural cinchona alkaloids, to activate maleimides toward highly stereoselective Diels–Alder reactions. An unconventional mechanism of stereocontrol is operative, wherein the organocatalyst is actively involved in both the photochemical pathway, by leveraging the formation of the reactive photoenol, and the stereoselectivity‐defining event.     

Organocatalytic,Asymmetric Eliminative [4+2] Cycloaddition of Allylidene Malononitriles with Enals: Rapid Entry to Cyclohexadiene‐Embedding Linear and Angular Polycycles

A direct aminocatalytic synthesis has been developed for the chemo‐, regio‐, diastereo‐, and enantioselective construction of densely substituted polycyclic carbaldehydes containing fused cyclohexadiene rings. The chemistry utilizes, for the first time, remotely enolizable π‐extended allylidenemalononitriles as electron‐rich 1,3‐diene precursors in a direct eliminative [4+2] cycloaddition with both aromatic and aliphatic α,β‐unsaturated aldehydes. The generality of the process is demonstrated by approaching 6,6‐, 5,6‐, 7,6‐, 6,6,6‐, and 6,5,6‐fused ring systems, as well as biorelevant steroid‐like 6,6,6,6,5‐ and 6,6,6,5,6‐rings. A stepwise reaction mechanism for the key [4+2] addition is proposed as a domino bis‐vinylogous Michael/Michael/retro‐Michael reaction cascade. The utility of the malononitrile moiety as traceless activating group of the dicyano nucleophilic substrates is demonstrated.     

pH-controlled dispersive liquid–liquid microextraction for the analysis of ionisable compounds in complex matrices: Case study of ochratoxin A in cereals

A new sample preparation procedure, termed pH-controlled dispersive liquid–liquid microextraction (pH-DLLME), has been developed for the analysis of ionisable compounds in highly complex matrices. This DLLME mode, intended to improve the selectivity and to expand the application range of DLLME, is based on two successive DLLMEs conducted at opposite pH values. pH-DLLME was applied to determination of ochratoxin A (OTA) in cereals. The hydrophobic matrix interferences in the raw methanol extract (disperser, 1 mL) were removed by a first DLLME (I DLLME) performed at pH 8 to reduce the solubility of OTA in the extractant (CCl₄, 400 μL). The pH of the aqueous phase was then adjusted to 2, and the analyte was extracted and concentrated by a second DLLME (extractant, 150 μL C₂H₄Br₂). The main factors influencing the efficiency of pH-DLLME including type and volume of I DLLME extractant, as well as the parameters affecting the OTA extraction by II DLLME, were studied in detail. Under optimum conditions, the method has detection and quantification limits of 0.019 and 0.062 μg kg⁻¹, respectively, with OTA recoveries in the range of 81.2–90.1% (n = 3). The accuracy of the analytical procedure, evaluated with a reference material (cereal naturally contaminated with OTA), is acceptable (accuracy of 85.6% ± 1.7, n = 5).     

Organocatalytic asymmetric direct alpha-alkynylation of cyclic beta-ketoesters

The first organocatalytic enantioselective direct alpha-alkynylation of beta-ketoesters and 3-acyl oxindoles is described. It is demonstrated that activated beta-halo-alkynes undergo nucleophilic acetylenic substitution catalyzed by chiral phase-transfer compounds to afford the alkynylated products in high yields and excellent enantioselectivities. The potential of the reaction is first demonstrated for various alkynylating reagents having chloride and bromide as the leaving groups and substituents such as allyl and alkyl esters, amides, ketones, and sulfones. These reactions proceed with 74-99% yield and 88-97% ee. Then the scope in nucleophile is demonstrated for a large number of cyclic beta-ketoesters with various ring-sizes and for oxindoles as well. The corresponding optically active products are formed in high yields and with enantioselectivities up to 98% ee. The procedure allows for the stereocontrolled attachment of an ethynyl unit in the alpha-position to the carbonyl compound by facile removal of the activating group, and this has been demonstrated for a number of the optically active allyl esters. Furthermore, the synthesis of optically active 1,4-enynes is also shown. The isolation and characterization by X-ray analysis of the catalyst with p-nitrophenolate as the counterion allowed us to propose a model of the catalyst-substrate intermediate which might account for the observed enantioselectivity of the organocatalytic enantioselective alpha-alkynylation reaction. Furthermore, it is suggested that this intermediate is also the reactive species for a number of other electrophiles adding to beta-ketoesters giving enantioselectivities in the range of 90-98% ee.     

Spin–rotation couplings: spinning test particles and Dirac field

The hypothesis of coupling between spin and rotation introduced long ago by Mashhoon is examined in the context of “1 + 3” and “3 + 1” space-time splitting techniques, either in special or in general relativity. Its content is discussed in terms of classical (Mathisson–Papapetrou–Dixon–Souriou model) as well as quantum physics (Foldy–Wouthuysen transformation for the Dirac field in an external field), reviewing and discussing all the relevant theoretical literature concerning the existence of such effect. Some original contributions are also included. Dedicated to Bahram Mashhoon for his 60th birthday.     

Coordination chemistry of 1,3,5-triaza-7-phosphaadamantane (PTA) and derivatives. Part II. The quest for tailored ligands,complexes and related applications

This review paper covers the recent developments (2004–2009) on the tailored synthetic modifications and related coordination chemistry of the water-soluble cage-like aminophosphine ligand 1,3,5-triaza-7-phosphatricyclo-[3.3.1.1]decane (PTA), together with the new applications in the fields of catalysis, material science and medicinal chemistry.