Copointed Hopf algebras over S4

We study the realizations of certain braided vector spaces of rack type as Yetter–Drinfeld modules over a cosemisimple Hopf algebra H. We apply the strategy developed in [1] to compute their liftings and use these results to obtain the classification of finite-dimensional copointed Hopf algebras over ${\mathbb{S}}_4$.     

Global solutions and asymptotic behavior for a parabolic degenerate coupled system arising from biology

In this paper we will focus on a parabolic degenerate system with respect to unknown functions u and w on a bounded domain of the two dimensional Euclidean space. This system appears as a mathematical model for some biological processes. Global existence and uniqueness of a nonnegative classical Hölder continuous solution are proved. The last part of the paper is devoted to the study of the asymptotic behavior of the solutions.     

Hopf Algebras of Dimension 16

We complete the classification of Hopf algebras of dimension 16 over an algebraically closed field of characteristic zero. We show that a non-semisimple Hopf algebra of dimension 16, has either the Chevalley property or its dual is pointed.     

Language-theoretic complexity of disjunctive sequences

A sequence over an alphabet ∑ is called disjunctive if it contains all possible finite strings over ∑ as its substrings. Disjunctive sequences have been recently studied in various contexts. They abound in both category and measure senses. In this paper we measure the complexity of a sequence x by the complexity of the language P(x) consisting of all prefixes of x. The languages P(x) associated to disjunctive sequences can be arbitrarily complex. We show that for some disjunctive numbers x the language P(x) is context-sensitive, but no language P(x) associated to a disjunctive number can be context-free. We also show that computing a disjunctive number x by rationals corresponding to an infinite subset of P(x) does not decrease the complexity of the procedure, i.e. if x is disjunctive, then P(x) does not have an infinite context-free subset. This result reinforces, in a way, Chaitin's thesis (1969) according to which perfect sets, i.e. sets for which there is no way to compute infinitely many of its members essentially better (simpler/quicker) than computing the whole set, do exist. Finally we prove the existence of the following language-theoretic complexity gap: There is no x ε ∑^w such that P(x) is context-free but not regular. If S(x), the set of all finite substrings of a sequence x ε ∑^w, is slender, then the set of all prefixes of x is regular, that is P(x) is regular if and only if S(x) is slender.     

Synthesis,structural characterization and in vitro antitumour properties of triorganoantimony(V) disalicylates: Crystal and molecular structures of [5-Y-2-(ho)-C6H3COO]2SbMe3 (YH,Me, MeO)

Triorganoantimony(V) salicylates, [5-Y-2-(HO)-C₆H₃COO]₂SbR₃ (R=Me, Ph; Y=H, Me, MeO), were obtained by reacting R₃SbCl₂ with the appropriate sodium salt. The compounds have been characterized by IR, MS, ¹H and ¹³C NMR spectroscopy. The molecular structure of the three substituted trimethylantimony(V) disalicylates has been determined by X-ray diffraction. The salicylate ligands are mono-coordinated to antimony through an oxygen atom of each carboxylate, leading to a trigonal bipyramidal geometry, with the antimony-methyl groups in equatorial positions and the oxygen atoms in axial positions. The trimethylantimony compounds tested in vitro against a series of human tumour cell lines were found to be inactive.     

Synthesis and Characterization of Alumina R Chemically Modified with n-Octyl for Use as a Stationary Phase in TLC

JPC – Journal of Planar Chromatography – Modern TLC - A stationary phase for thin-layer chromatography has been prepared by attaching 1-octene to alumina R. This stationary phase has...     

Synthesis and thermal behaviour of new poly(azomethine-ether)

A new poly(azomethine-ether) was synthesized by the reaction of bisphenol A with a thermotropic azomethine monomer, namely 4,4′-oxy-bis(4-chlorobenzylideneimino phenylene). In order to understand the influence of the molecular weight on the thermal properties, four fractions were isolated from the initial polymer. They were investigated by elemental analysis and spectroscopic methods (IR, UV, ¹H NMR) and their thermal behaviour was studied by differential scanning calorimetry, optical microscopy, thermogravimetrical analysis. An increase of the thermal transition temperatures and mesophase order with increasing molecular weight was noticed.     

Simulating the relaxation dynamics of microwave-driven zeolites

We have performed equilibrium and nonequilibrium molecular dynamics simulations to study how microwave (MW)-heated zeolite systems relax to thermal equilibrium. We have simulated the relaxation of both ionic and dipolar phases in FAU-type zeolites, finding biexponential relaxation in all cases studied. Fast-decay times were uniformly below 1 ps, while slow-decay times were found to be as long as 14 ps. Fast-decay times increase with an increase in the initial temperature difference between MW-heated ions/dipoles and the equilibrium system. Slow-decay times were found to be relatively insensitive to the details of the MW-heated nonequilibrium state. Velocity, force, and orientational correlation functions, calculated at equilibrium to explore the natural dynamics of energy transfer, decay well before 1 ps and show little evidence of biexponential decay. In contrast, kinetic energy correlation functions show strong biexponential behavior with slow-decay times as long as 14 ps. We suggest a two-step mechanism involving initial, efficient energy transfer mediated by strongly anharmonic zeolite-guest forces, followed by a slower process mediated by weakly anharmonic couplings among normal modes of the zeolite framework. In addition to elucidating relaxation from MW-heated states, we expect that these studies will shed light on energy transfer in other contexts, such as adsorption and reaction in zeolites, which often involve significant heat release.     

The effect of hydration/dehydration on the AC electrical conductivity of H4PVMo11O40 and some of its cesium salts used as catalysts

Changes in AC electrical conductance G of vanadium substituted 12-molybdophosphoric acid and of its (mono)-acid and neutral cesium salts were studied. Depending on the environment, the electrical conductivity is a combination of protonic and electronic conduction, the protonic one dominating at low temperature.     

On-chip cell lysis by local hydroxide generation

We present a novel method for on-chip cell lysis based on local hydroxide electro-generation. Hydroxide ions porate the cell membrane, leading to cell lysis. After lysis occurs, hydrogen ions, also generated on chip, react with excess hydroxide, creating a neutral pH lysate and eliminating the need for a wash step. Three different cell types are shown to be effectively lysed by this method: red blood cells, HeLa (human tumor line) and Chinese Hamster Ovary (CHO) cell lines. The release of cytoplasmic molecules from HeLa and CHO cells is demonstrated by monitoring the escape of a membrane impermeant dye from the cytoplasm. In the vicinity of the cathode, the hydroxide concentration is predicted by finite element simulations and shown to fit the lysis rates at different distances from the generating cathode. For flow-through experiments, a second device integrating a mechanical filter with hydroxide generation is fabricated and tested. The purpose of the filter is to trap whole cells and only allow lysate to pass through. The flow rate dependence of hydroxide concentration at the lysis filter is modeled and lysis efficiency is experimentally determined to be proportional to the hydroxide concentration for flow rates from 15 to 30 microl min(-1).