Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Diastereoselective preparation of 2,4,6-trisubstituted-2'-cyanopiperidines: application to the construction of the carbon framework of perhydrohistrionicotoxin

The anodic cyanation of methanolic solutions of the 2-alkyl-N-phenylpiperidines 6b-d was performed in a flow cell equipped with a graphite felt anode. The reaction led to the formation of the 2-cyano-6-alkyl-N-phenylpiperidines 2b-d and proceeded with a high degree of regioselectivity. The 1H NMR spectra of the aminonitriles 2b-d showed an epimeric mixture at C-6. The major isomer has a trans configuration in which the cyano group is axial and the alkyl substituent is equatorial. Conversely, electrochemical oxidation of the 4-methyl-6-pentyl-N-phenylpiperidine 6e afforded the trisubstituted aminonitrile 2e as a single diastereomer (> 98% de). The 4-cyanobutyl side chain was incorporated in a two-step procedure to yield dinitrile 4e. This latter compound was directly converted into spiropiperidine 5e by using the Thorpe-Ziegler annulation procedure. The overall sequence (4 steps, 43%) allows the construction of the basic carbon framework of perhydrohistrionicotoxin.     

Versatile reactions of a para-bromophenylacetylide iron(II) derivative and X-ray structure of the fluoro analogue. Synthesis of new redox-active organoiron(II) synthons

The synthesis of the new (η²-dppe)(η⁵-C₅Me₅)Fe---CC---1,3-(C₆H₄X) (m-2a/2b; X=F/Br) and (η²-dppe)(η⁵-C₅Me₅)Fe---CC---1,4-(C₆H₄I) (2c) complexes, as well as the solid-state structure of the known (η²-dppe)(η⁵-C₅Me₅)Fe---CC---1,4-(C₆H₄F) (2a) complex are described. The catalytic coupling reactions of the bromo complexes with various alkynes were next investigated. Starting from the known (η²-dppe)(η⁵-C₅Me₅)Fe---CC---1,4-(C₆H₄Br) complex (2b), the synthesis of the (η²-dppe)(η⁵-C₅Me₅)Fe---CC---1,4-(C₆H₄)---CC---H complex (6d) and of the corresponding silyl-protected precursors (η²-dppe)(η⁵-C₅Me₅)Fe---CC---1,4-(C₆H₄)CC---SiR₃ (6b/6c; R=ⁱPr/Me) are reported. By use of lithium---bromine exchange reactions on 2b, the silyl- (7a; E=Si; R=Me) and tin- (7b–7d; E=Sn; R=Me, Bu, Ph) substituted analogues (η²-dppe)(η⁵-C₅Me₅)Fe---CC---1,4-(C₆H₄)ER₃ are also isolated. The spectroscopic and electrochemical characterisations of all these new Fe(II)/Fe(III) redox-active building blocks are presented and the electronic substituent parameters for the “(η²-dppe)(η⁵-C₅Me₅)Fe---CC” group are determined by means of ¹⁹F-NMR.     

Molecular structure of simple mono- and diphenyl meso-substituted porphyrin diacids: influence of protonation and substitution on the distorsion

The crystal and molecular structures of three simple porphyrin diacids have been determined from X-ray diffraction data to delineate how the peripheral substituents of the porphyrin affect the overall molecular flexibility. Di-meso-substituted [DPPH₄]²⁺(CF₃CO₂⁻)₂ and, mono-meso-substituted [MPPH₄]²⁺(CF₃CO₂⁻)₂ and [dedmMPPH₄]²⁺(CF₃CO₂⁻)₂ porphyrin diacids show increasingly saddled core conformation. Some of the spectroscopic properties (NMR and UV-visible) of the porphyrin diacids are also discussed in terms of the observed structures.     

A Convenient,Large-Scale Preparation of 2,4-Dichlorophenyl-4-bromomethyl-phenoxyacetate Suitable for Resin Anchorage of the First Fmoc Amino Acid

2,4-dichlorophenyl-4-bromomethyl-phenoxyacetate 3 was prepared by NBS treatement of 2,4-dichlorophenyl-4-methylphenoxyacetate 2. This ester is a key intermediate in the preparation of 2,4-dichlorophenyl-N^α-Fmoc-aminoacyl-4-oxymethylphenoxy-acetates suitable for anchorage of the first amino acid on amine-functionalized polymers.     

Optical image asymmetric cryptosystem using fingerprint based on iterative fraction Fourier transform

A novel asymmetric cryptosystem for optical image is proposed using fingerprint based on iterative fractional Fourier transform. To enhance the security, a hyperchaotic phase generated by a 4D Lorenz system is considered as the public key in the proposed encryption system, while the private key is emerged by the retrieved phase and fingerprint. In the encryption process, the secret information is hid into the hyperchaotic phase. Subsequently, the private key can be obtained by a reversible operation. To decrypt the original image, the ciphertext and private key are imported into the input plane of fractional Fourier system. This system is also applicable for information authentication because the fingerprint is used both in encryption and decryption approach. Some numerical simulations have been done to test the validity and capability of the encryption system.     

Synthesis,Photophysics and Nonlinear Optical Properties of Stilbenoid Pyrimidine‐Based Dyes Bearing Methylenepyran Donor Groups

The nonlinear properties and the photophysical behavior of two π‐conjugated chromophores that incorporate an electron‐deficient pyrimidine core (A) and γ‐methylenepyrans as terminal donor (D) groups have been thoroughly investigated. Both dipolar and quadrupolar branching strategies are explored and rationalized on the basis of the Frenkel exciton model. Even though a cooperative effect is clearly observed if the dimensionality is increased, the nonlinear optical (NLO) response of this series is moderate if one considers the nature of the D/A couple and the size of the chromophores (as measured by the number of π electrons). This effect was attributed to a disruption in the electronic conjugation within the dyes’ scaffold for which the geometry deviates from planarity owing to a noticeable twisting of the pyranylidene end‐groups. This latter structural parameter also has a strong influence on the excited‐state dynamics, which leads to a very efficient fluorescence quenching.     

Spatial updating, spatial transients, and regularities of a complex automaton with nonperiodic architecture

We study the dynamics of patterns exhibited by rule 52, a totalistic cellular automaton displaying intricate behaviors and wide regions of active/inactive synchronization patches. Systematic computer simulations involving 2(30) initial configurations reveal that all complexity in this automaton originates from random juxtaposition of a very small number of interfaces delimiting active/inactive patches. Such interfaces are studied with a sidewise spatial updating algorithm. This novel tool allows us to prove that the interfaces found empirically are the only interfaces possible for these periods, independently of the size of the automata. The spatial updating algorithm provides an alternative way to determine the dynamics of automata of arbitrary size, a way of taking into account the complexity of the connections in the lattice.     

Spin‐State Ordering on One Sub‐lattice of a Mononuclear Iron(III) Spin Crossover Complex Exhibiting LIESST and TIESST

The two‐step spin crossover in mononuclear iron(III) complex [Fe(salpm)₂]ClO₄ ? 0.5 EtOH ( 1 ) is shown to be accompanied by a structural phase transition as concluded from ⁵⁷Fe Mössbauer spectroscopy and single crystal X‐ray diffraction, with spin‐state ordering on just one of two sub‐lattices in the intermediate magnetic and structural phase. The complex also exhibits thermal‐ and light‐induced spin‐state trapping (TIESST and LIESST), and relaxation from the LIESST and TIESST excited states occurs via the broken symmetry intermediate phase. Two relaxation events are evident in both experiments, that is, two T(LIESST) and two T(TIESST) values are recorded. The change in symmetry which accompanies the TIESST effect was followed in real time using single crystal diffraction. After flash freezing at 15 K the crystal was warmed to 40 K at which temperature superstructure reflections were observed to appear and disappear within a 10 000 s time range. In the frame of the international year of crystallography, these results illustrate how X‐ray diffraction makes it possible to understand complex ordering phenomena.     

A new approach to A,B-difunctionalisation of cyclodextrins using bulky 1,3-bis[bis(aryl)chloromethyl]benzenes as capping reagents

1,3-Bis[bis(4-tert-butylphenyl)chloromethyl]benzene and 1,3-bis[bis(4-anisyl)chloromethyl]benzene were employed as regioselective capping reagents for the preparation of C-6A,C-6B-bridged, permethylated alpha- and beta-CD derivatives; isolated yields up to 55% of proximally capped, methylated CDs were obtained, thus opening the way to the straightforward preparation of a wide range of A,B-functionalised CDs. As revealed by a single crystal X-ray diffraction study, the benzene-1,3-bis[bis(4-tert-butylphenyl)methyl] spacer is perfectly suited for A,B-capping of beta-cyclodextrin.