Polyethylene/poly(styrene-co-divinylbenzene) sodium sulphonate membranes : Part 1. Synthesis and properties

Transport properties of cation-exchange membranes have been studied. The self-diffusion coefficients of sodium and chloride ions, the transport numbers of sodium ions and water, and the conductivities were measured in 0.1 M sodium chloride at 25°C. The concentration potentials were determined in the system 0.05/0.15 M sodium chloride.The membranes were prepared by sulphonation of oriented polyethylene (PE) film modified with 30 wt % of styrene—divinylbenzene copolymer (poly(St-co-DVB)). The copolymer was introduced by interpolymerization of the monomers within the film without its dissolution. A sequence of membranes having similar ion-exchange capacity but differing in water content was then obtained from sheets of normal PE/poly(St-co-DVB)SO₃Na membranes by expanding them by heating in water followed by a thermal treatment in air.The deviations of the measured transport properties from the behaviour of homogeneous membranes and the analysis of the Kedem—Katchalsky relationships for composite membranes have led to the conclusion that in PE/poly(St-co-DVB)SO₃Na membranes a structure prevails with a series arrangement of layers with different properties.     

Minimal infeasible constraint sets in convex integer programs

In this paper we investigate certain aspects of infeasibility in convex integer programs, where the constraint functions are defined either as a composition of a convex increasing function with a convex integer valued function of n variables or the sum of similar functions. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining the model. We prove that for the considered class of functions, every infeasible system of inequality constraints in the convex integer program contains an inconsistent subsystem of cardinality not greater than 2 ⁿ , this way generalizing the well known theorem of Scarf and Bell for linear systems. The latter result allows us to demonstrate that if the considered convex integer problem is bounded below, then there exists a subset of at most 2 ⁿ −1 constraints in the system, such that the minimum of the objective function subject to the inequalities in the reduced subsystem, equals to the minimum of the objective function over the entire system of constraints.     

The structure of Valdivia compact lines

We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ₁, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.     

Discriminating multipartite entangled states

The variety of multipartite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view, classifications have been introduced. Accordingly, here we derive criteria and demonstrate how to experimentally discriminate an observed state against the ones of certain other classes of multipartite entangled states. Our method, originating in Bell inequalities, adds an important tool for the characterization of multiparty entanglement.     

On ideals and congruences in bcc-algebras

We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.     

Poset algebras over well quasi-ordered posets

A new class of partial order-types, class is defined and investigated here. A poset P is in the class iff the poset algebra F(P) is generated by a better quasi-order G that is included in L(P). The free Boolean algebra F(P) and its free distributive lattice L(P) have been defined in [ABKR]. The free Boolean algebra F(P) contains the partial order P and is generated by it: F(P) has the following universal property. If B is any Boolean algebra and f is any order-preserving map from P into a Boolean algebra B, then f can be extended to a homomorphism of F(P) into B. We also define L(P) as the sublattice of F(P) generated by P. We prove that if P is any well quasi-ordering, then L(P) is well founded, and is a countable union of well quasi-orderings. We prove that the class is contained in the class of well quasi-ordered sets. We prove that is preserved under homomorphic image, finite products, and lexicographic sum over better quasi-ordered index sets. We prove also that every countable well quasi-ordered set is in . We do not know, however if the class of well quasi-ordered sets is contained in . Additional results concern homomorphic images of posets algebras. The third author was supported by the following institutions: Israel Science Foundation (postdoctoral positions at Ben Gurion University 2000–2002), The Fields Institute (Toronto 2002–2004), and by The Nato Science Fellowship (University Paris VII, CNRS-UMR 7056, 2004).     

Highly stereoselective synthesis of para-substituted (E)-N-styrylcarbazoles via sequential silylative coupling-Hiyama coupling reaction

A series of new para-substituted (E)-(N)-styrylcarbazoles, i.e., eight (E)-9-[2-(aryl)ethenyl]-9H-carbazoles (5-12) and 1,4-bis[(E)-2-(9H-carbazol-9-yl)vinyl]benzene (13), have been synthesized in high yield and stereoselectively by a sequential silylative coupling-Hiyama coupling reaction, i.e., coupling of commercially available 9-vinylcarbazole with vinyltriethoxysilane or divinyltetramethyldisiloxane in the presence of [RuHCl(CO)(PCy₃)₂] (I), followed by Pd (II) catalyzed cross-coupling with para-substituted iodobenzenes.The tandem procedure has facilitated the synthesis of 13. X-ray structures of the intermediate silylvinylcarbazole (4), as well as products 12 and 13 have been obtained.     

Synthesis and photophysical properties of a new amino acid possessing a BODIPY moiety

The synthesis of a new amino acid possessing a BODIPY fluorophore, which is of use in peptide synthesis, is described. The influence of the amino acid as well as of benzoxazole moieties on the BODIPY spectral and photophysical properties is discussed. The photophysical properties of this fluorophore were modified only to a small extent compared to those of the parent compound.     

SAW hydrogen gas sensor based on WO3 and Pd nanostructures

Bi-layer nanostructures of WO₃ (～100 nm and 150 nm) with a very thin film of palladium (Pd～10 nm) on the top, have been studied for hydrogen gas-sensing application at ～700C and medium hydrogen concentrations (1 – 4%) in air. The structures were obtained by vacuum deposition (first the WO₃ and then the Pd film) onto a LiNbO₃ Y- cut Z-propagating substrate and were tested by means of Surface Acoustic Wave method in a three channel delay line configuration. Very repeatable results have been observed for these two nanostructures with changes in frequency on the level of 500 to 1800 Hz for hydrogen concentration from 1 to 4 % in air. The absolute response value depends on the WO₃ film thickness and hydrogen gas concentration and is greater for the nanostructure with a thicker WO₃ film.     

Detection of changes in cracked aluminium plate determinism by recurrence analysis

The paper investigates changes in determinism of undamaged and cracked aluminium plates with respect to excitation frequencies. Harmonic excitation of frequencies corresponding to structural resonances has been used to vibrate the plates. Vibration responses have been analysed using recurrence plots and recurrence quantification analysis. The smallest sufficient embedding dimension has been estimated using the false nearest neighbour??s algorithm. Mutual information analysis has been applied to determine the relevant time delays. The results demonstrate that performed analysis indicates changes in dynamic behaviour of the plates with respect to various excitation frequencies and crack modes.