New global stability conditions for a class of difference equations

In this paper we consider some classes of difference equations, including the well-known Clark model, and study the stability of their solutions. In order to do that we introduce a property, namely semicontractivity, and study relations between ‘semi-contractive’ functions and sufficient conditions for the solution of the difference equation to be globally asymptotically stable. Moreover, we establish new sufficient conditions for the solution to be globally asymptotically stable, and we improve the ‘3/2 criteria’ type stability conditions.      

Electro-optic transparent frequency conversion of a continuous light wave based on multistage phase modulation

Frequency conversion of a continuous light wave based on multistage phase modulation has been investigated both analytically and numerically. The proposed frequency-conversion process consists of three stages: (i) phase modulation and chirp compression to generate a pulse train, (ii) Doppler shift of the pulse center frequency in a second phase modulation, and (iii) demodulation of the pulse train. By controlling the modulation power we can select the destination frequency from an equally spaced grid separated by the modulation frequency. A conversion efficiency of approximately 40% has been numerically confirmed with respect to a destination frequency of +/- 50 channels. Carrier frequency conversion of an analog data stream is numerically demonstrated.     

In-Line Reactions and Ionizations of Vaporized Diphenylchloroarsine and Diphenylcyanoarsine in Atmospheric Pressure Chemical Ionization Mass Spectrometry

We propose detecting a fragment ion (Ph₂As⁺) using counter-flow introduction atmospheric pressure chemical ionization ion trap mass spectrometry for sensitive air monitoring of chemical warfare vomiting agents diphenylchloroarsine (DA) and diphenylcyanoarsine (DC). The liquid sample containing of DA, DC, and bis(diphenylarsine)oxide (BDPAO) was heated in a dry air line, and the generated vapor was mixed into the humidified air flowing through the sampling line of a mass spectrometer. Humidity effect on the air monitoring was investigated by varying the humidity of the analyzed air sample. Evidence of the in-line conversion of DA and DC to diphenylarsine hydroxide (DPAH) and then BDPAO was obtained by comparing the chronograms of various ions from the beginning of heating. Multiple-stage mass spectrometry revealed that the protonated molecule (MH⁺) of DA, DC, DPAH, and BDPAO could produce Ph₂As⁺ through their in-source fragmentation. Among the signals of the ions that were investigated, the Ph₂As⁺ signal was the most intense and increased to reach a plateau with the increased air humidity, whereas the MH⁺ signal of DA decreased. It was suggested that DA and DC were converted in-line into BDPAO, which was a major source of Ph₂As⁺.

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Double-Gyroid Nanostructure Formation by Aggregation-Induced Atropisomerization and Co-Assembly of Ionic Liquid-Crystalline Amphiphiles

We report a new molecular-design principle for creating double-gyroid nanostructured molecular assemblies based on atropisomerization. Ionic amphiphiles containing two imidazolium rings close to each other were designed and synthesized. NMR data revealed that the rotation of the imidazolium rings is restricted, with an activation energy as high as 63 kJ mol⁻¹ in DMSO-d₆ solution (DFT prediction for a model compound in the vacuum: 90–100 kJ mol⁻¹). Due to the restricted rotation, the amphiphiles feature “double” atropisomeric axes in their ionic segments and form three stable atropisomers: meso, R, and S. These isomers co-organize into -type bicontinuous cubic liquid-crystalline mesophases through nanosegregation of the ionic and non-ionic parts. Considering the intrinsic characteristic of -type bicontinuous cubic structures that they are composed of intertwined right- and left-handed single gyroids, we propose that the simultaneous presence of both R- and S-atropisomers is an important contributor to the formation of double-gyroid structures.     

Synthesis and evaluation of α-helix mimetics based on a trans-fused polycyclic ether: sequence-selective binding to aspartate pairs in α-helical peptides

Inspired by the topological similarity between ladder-like cyclic ether skeletons and α-helical peptides, a trans-fused 6/6/6/6 tetracyclic ether containing two hydroxyl groups separated by a distance of 4.8 Å was designed as a scaffold for a nonpeptidic α-helix mimetic. Two alkyl guanidinium groups were attached to the hydroxyl groups to develop a synthetic receptor for the specific recognition of i + 4 spaced aspartate pairs on the surface of an α-helical peptide. A circular dichroism (CD) titration showed that this mode of molecular recognition stabilizes α-helical structures of peptides containing i + 4 spaced aspartate pairs.     

Characterization of the benzene-insoluble fraction of the hydrolyzate of phenyltrimethoxysilanes in the presence of benzyltrimethylammonium hydroxide

The insoluble fraction obtained from the hydrolysis and condensation of (4-dimethylamino-, 2-methyl-, and nonsubstituted)phenyltrimethoxysilanes in the presence of benzyltrimethylammonium hydroxide in benzene was characterized. IR, ¹H NMR, and ²⁹Si NMR suggested that the insoluble fraction was composed of RSi(O )₃, that is, a T³ structure. X-ray diffraction indicated the presence of a long-range ordered structure composed of a mixture of crystals. Raman spectroscopy strongly suggested a cage structure by the presence of a ring-opening vibration assignable to a cubic structure at 475–482 cm⁻¹. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4587–4597, 2004     

Supramolecular hydrogel formation based on inclusion complexation between poly(ethylene glycol)-modified chitosan and alpha-cyclodextrin

Supramolecular hydrogels have been prepared on the basis of polymer inclusion complex (PIC) formation between poly(ethylene glycol) (PEG)-modified chitosans and alpha-cyclodextrin (alpha-CD). A series of PEG-modified chitosans were synthesized by coupling reactions between chitosan and monocarboxylated PEG using water-soluble carbodiimide (EDC) as coupling agent. With simple mixing, the resultant supramolecular assembly of the polymers and alpha-CD molecules led to hydrogel formation in aqueous media. The supramolecular structure of the PIC hydrogels was confirmed by differential scanning calorimetry (DSC), X-ray diffraction, and (13)C cross-polarized/magic-angle spinning (CP/MAS) NMR characterization. The PEG side-chains on the chitosan backbones were found to form inclusion complexes (ICs) with alpha-CD molecules, resulting in the formation of channel-type crystalline micro-domains. The IC domains play an important role in holding together hydrated chitosan chains as physical junctions. The gelation property was affected by several factors including the PEG content in the polymers, the solution concentration, the mixing ratio of host and guest molecules, temperature, pH, etc. All the hydrogels in acidic conditions exhibited thermo-reversible gel-sol transitions under appropriate conditions of mixing ratio and PEG content in the mixing process. The transitions were induced by supramolecular association and dissociation. These supramolecular hydrogels were found to have phase-separated structures that consist of hydrophobic crystalline PIC domains, which were formed by the host-guest interaction between alpha-CD and PEG, and hydrated chitosan matrices below the pK(a).The formation of inclusion complexes between alpha-cyclodextrin and PEG-modified chitosan leads to the formation of hydrogels that can undergo thermo-reversible supramolecular dissociation.