Non-Traditional Squares of Predication and Quantification

Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel. The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating in this way: losing the definability between the existence- and all-quantifier. Therefore, a combination of non-traditional predication and classical quantification is preferred here.      

On the independence complex of square grids

The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by Fendley et al., that for some rectangular grids, with toric boundary conditions, the alternating number of independent sets is extremely simple. More precisely, under a coprimality condition on the sides of the rectangle, the number of independent sets of even and odd cardinality always differ by 1. In physics terms, this means looking at the hard-particle model on these grids at activity −1. This conjecture was recently proved by Jonsson. Here we produce other families of grid graphs, with open or cylindric boundary conditions, for which similar properties hold without any size restriction: the number of independent sets of even and odd cardinality always differ by 0, ±1, or, in the cylindric case, by some power of 2. We show that these results reflect a stronger property of the independence complexes of our graphs. We determine the homotopy type of these complexes using Forman’s discrete Morse theory. We find that these complexes are either contractible, or homotopic to a sphere, or, in the cylindric case, to a wedge of spheres. Finally, we use our enumerative results to determine the spectra of certain transfer matrices describing the hard-particle model on our graphs at activity −1. These results parallel certain conjectures of Fendley et al., proved by Jonsson in the toric case.     

Isolation of lanthanides from spent nuclear fuel by means of high performance ion chromatography (HPIC) prior to mass spectrometric analysis

Pure and complete fractions of neodymium, samarium, europium, gadolinium and dysprosium were isolated by means of high performance ion chromatography, using a cation exchange column and gradient elution with alpha-hydroxyisobutyric acid solutions (α-HIBA). Intermediate precision and robustness of the isolation method was investigated, identifying eluent pH as the most important parameter. Investigation of the elution behaviour of the most important fission and activation products and actinides indicated that preventing the accumulation of cesium on the cation exchange column required further isocratic elution with a higher concentrated α-HIBA solution after elution of the lanthanides. A sample matrix free of carbon was achieved by means of acid digestion, followed by UV photo-oxidation, resulting in samples suitable for mass spectrometric analysis.

     

Single crystal EPR study of the dinuclear Cu(II) complex [Cu(tda)(phen)](2)·H(2)tda (tda = thiodiacetate, phen = phenanthroline): influence of weak interdimeric magnetic interactions

We report powder and single crystal EPR measurements of [Cu(tda)(phen)](2)·H(2)tda (tda = thiodiacetate, phen = phenanthroline) at 9.7 GHz. This compound consists of centrosymmetric copper(II) ion dimers, weakly ferromagnetically exchange-coupled (J = +3.2 cm(-1)), in which the dimeric units are linked by hydrophobic chemical paths involving the phen molecules. EPR revealed that the triplet spectra are collapsed by interdimeric exchange interactions mediated by that chemical path. Analysis and simulation of the single crystal EPR spectra were performed using Anderson's exchange narrowing model, together with statistical arguments. This approach allowed us to interpret the spectra modulated by the interdimeric interactions in situations of weak, intermediate, and strong exchange. We evaluated an interdimeric exchange constant J' = 0.0070(3) cm(-1), indicating that hydrophobic paths can transmit weak exchange interactions between centers at relatively long distances of the order of ～10 ?.     

Aqua(oxydiacetato‐κ3O,O′,O′′)(pyridine‐3‐carboxamide‐κN1)copper(II) sesquihydrate

In the monomeric title compound, [Cu(C₄H₄O₅)(C₆H₆N₂O)(H₂O)]·1.5H₂O, the Cu^II cation is bound in a square‐pyramidal coordination to a tridentate oxydiacetate (ODA) ligand, a monodentate pyridine‐3‐carboxamide (p3ca) ligand and one aqua ligand, where the two organic ligands form the basal plane and the water O atom occupies the unique apical site. The ODA ligand presents a slight out‐of‐plane puckering in its central ether O atom, while the p3ca ligand is essentially planar. The availability of efficient donors and acceptors for hydrogen bonding results in the formation of strongly linked hydrogen‐bonded bilayers parallel to (101), with an interplanar distance of 3.18 (1) Å and a stacking separation between the bilayers of 3.10 (1) Å, both of them governed by extended π–π interactions. The disordered nature of the solvent water molecules around inversion centres is discussed. The monoaqua compound is compared with the octahedral diaqua analogue, [Cu(C₄H₄O₅)(C₆H₆N₂O)(H₂O)₂], reported recently [Perec & Baggio (2009). Acta Cryst. C 65 , m296–m298].     

Triades et familles de courbes gauches

Sans résumé Received: 3 April 1998 / in final form: 16 December 1998     

Walks on the slit plane

 In the first part of this paper, we enumerate exactly walks on the square lattice that start from the origin, but otherwise avoid the half-line . We call them walks on the slit plane. We count them by their length, and by the coordinates of their endpoint. The corresponding three variable is algebraic of degree 8. Moreover, for any point (i, j), the length for walks of this type ending at (i, j) is also algebraic, of degree 2 or 4, and involves the famous Catalan numbers. Our method is based on the solution of a functional equation, established via a simple combinatorial argument. It actually works for more general models, in which walks take their steps in a finite subset of ℤ² satisfying two simple conditions. The corresponding are always algebraic. In the second part of the paper, we derive from our enumerative results a number of probabilistic corollaries. For instance, we can compute exactly the probability that an ordinary random walk starting from (i, j) hits for the first time the half-line at position (k, 0), for any triple (i, j, k). This generalizes a question raised by R. Kenyon, which was the starting point of this paper. Taking uniformly at random all n-step walks on the slit plane, we also compute the probability that they visit a given point (k, 0), and the average number of visits to this point. In other words, we quantify the transience of the walks. Finally, we derive an explicit limit law for the coordinates of their endpoint. Received: 22 December 2001 / Revised version: 19 February 2002 / Published online: 30 September 2002 Both authors were partially supported by the INRIA, via the cooperative research action Alcophys. Mathematics Subject Classification (2000): O5A15-60C05     

Highly hydrophilic surfaces from polyglycidol grafts with dual antifouling and specific protein recognition properties

Homopolymer grafts from α-tert-butoxy-ω-vinylbenzyl-polyglycidol (PGL) were prepared on gold and stainless steel (SS) substrates modified by 4-benzoyl-phenyl (BP) moieties derived from the electroreduction of the parent salt 4-benzoyl benzene diazonium tetrafluoroborate. The grafted BP aryl groups efficiently served to surface-initiate photopolymerization (SIPP) of PGL. In similar conditions, SIPP of hydroxyethyl methacrylate (HEMA) permitted the production of PHEMA grafts as model surfaces. Water contact angles were found to be 66°, 15°, and 0° for SS-BP, SS-PHEMA, and SS-PPGL, respectively. The spontaneous spreading of water drops on SS-PPGL was invariably observed with 1.5 μL water drops. PPGL thus appears as a superhydrophilic polymer. Resistance to nonspecific adsorption of proteins of PPGL and PHEMA grafts on gold was evaluated by surface plasmon resonance (SPR) using antibovine serum albumin (anti-BSA). The results conclusively show that PPGL-grafts exhibit enhanced resistance to anti-BSA adsorption compared to the well-known hydrophilic PHEMA. PPGL grafts were further modified with BSA through the carbonyldiimidazole activation of the OH groups providing immunosensing surfaces. The so-prepared PPGL-grafted BSA hybrids specifically interacted with anti-BSA in PBS as compared to antimyoglobin. It is clear that the superhydrophilic character of PPGL grafts opens new avenues for biomedical applications where surfaces with dual functionality, namely, specific protein grafting together with resistance to biofouling, are required.