A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some new results on superimposed codes

A (w,r) cover‐free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A (w,r) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as the concept of key distribution pattern. In the present paper, we give some new results on superimposed codes. First we construct superimposed codes from super‐simple designs which give us results better than superimposed codes constructed by other known methods. Next we prove the uniqueness of the (1,2) superimposed code of size 9 × 12, the (2,2) superimposed code of size 14 × 8, and the (2,3) superimposed code of size 30 × 10. Finally, we improve numerical values of upper bounds for the asymptotic rate of some (w,r) superimposed codes. © 2004 Wiley Periodicals, Inc.     

Hamiltonian N2‐locally connected claw‐free graphs

A graph G is N₂‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N₂‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005     

A lithium ethyl­ene­diphos­phon­ate containing lithium chains and symmetric hydrogen bonds

In the title compound, catena‐poly[lithium‐μ₃‐ethyl­ene­diphos­phon­ato], [Li(C₂H₇O₆P₂)]_n, the supra­molecular monoclinic (C2/c) structure consists of one‐dimensional lithium chains [Li⋯Li = 2.7036 (8) Å] that are embedded within ethyl­ene­diphosphon­ate anions linked by strong symmetric hydrogen bonds [O⋯O = 2.473 (3) Å]. The Li atoms and the H atom in the symmetric hydrogen bond reside on twofold rotation axes and there is an inversion center at the mid‐point of the C—C bond of the ethylenediphosphonate ligand.     

Elliptic equations with BMO coefficients in Reifenberg domains

The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are studied. Optimal regularity requirements on the coefficients and domains for the W^1,p theory, 1 < p < ∞, are obtained. The principal coefficients are supposed to be in the John‐Nirenberg space with small BMO seminorms. The domain is a Reifenberg domain. These conditions for the W^1,p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains. In fact, these domains might have fractal dimensions. © 2004 Wiley Periodicals, Inc.     

Evidence of a Photo‐Radical Pathway Responsible of the Rearrangement of a Manganese(III)‐Schiff Base Complex in Solution

A new Mn^III‐Schiff base complex, [MnL(OH₂)](ClO₄) ( 1 ) (H₂L = N, N′‐bis‐(3‐Br‐5‐Cl‐salicylidene)‐1, 2‐diimino‐2‐methylethane), an inorganic model of the catalytic center (OEC, Oxygen Evolving Complex) in photosystem II (PSII), has been synthesized and characterized by elemental analysis, IR and EPR spectroscopy, mass spectrometry, magnetic susceptibility measurement and the study of its redox properties by cyclic and normal pulse voltammetry. This complex mimics reactivity (showing a relevant photolytic activity), and also some structural characteristics (parallel‐mode Mn^III EPR signal from partially assembled OEC cluster) of the natural OEC. The complex 1 was found to rearrange in solution into a crystallographically solved square‐pyramidal complex, [MnLL′] ( 2 ) (HL′ = 6‐bromo‐4‐chloro‐2‐cyanophenol), through a process, which probably liberates radical species (detected by EPR), and provokes a C—N bond cleavage in the ligand. A photo‐radical mechanism is discussed to explain this rearrangement.     

Crystallization and morphology of poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) blends. I. Spherulitic morphology and growth by polarized microscopy

The development of the poly(3‐hydroxybutyrate) (PHB) morphology in the presence of already existent poly(vinylidene fluoride) (PVDF) spherulites was studied by two‐stage solidification with two separate crystallization temperatures. PVDF formed irregular dendrites at lower temperatures and regular, banded spherulites at elevated temperatures. The transition temperature of the spherulitic morphology from dendrites to regular, banded spherulites increased with increasing PVDF content. A remarkable amount of PHB was included in the PVDF dendrites, whereas PHB was rejected into the remaining melt from the banded spherulites. When PVDF crystallized as banded spherulites, PHB could consequently crystallize only around them, if at all. In contrast, PHB crystallized with a common growth front, starting from a defined site in the interfibrillar regions of volume‐filling PVDF dendrites. It formed by itself dendritic spherulites that included a large number of PVDF spherulites. For blends with a PHB content of more than 80 wt %, for which the PVDF dendrites were not volume‐filling, PHB first formed regular spherulites. Their growth started from outside the PVDF dendrites but could later interpenetrate them, and this made their own morphology dendritic. These PHB spherulites melted stepwise because the lamellae inside the PVDF dendrites melted at a lower temperature than those from outside. This reflected the regularity of the two fractions of the lamellae because that of those inside the dendrites of PVDF was controlled by the intraspherulitic order of PVDF, whereas that from outside was only controlled by the temperature and the melt composition. The described morphologies developed without mutual nucleating efficiency of the components. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 873–882, 2003     

Crystallographic report: catena‐Aqua(2,2′‐bipyrimidine)lithium(I) perchlorate

A lithium(I) coordination polymer has been formed from LiClO₄ and the 2,2′‐bipyrimidine (bpym) ligand in which each square pyramidal lithium(I) atom is coordinated in the basal plane by four nitrogen donor atoms derived from two bpym ligands and one water molecule at the apical position. These are connected into a layer structure via hydrogen‐bonding interactions involving the perchlorate anions. Copyright © 2004 John Wiley & Sons, Ltd.