Forcing highly connected subgraphs

A theorem of Mader states that highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. We extend this result to infinite graphs. Here, it is necessary to require not only high degree for the vertices but also high vertex‐degree (or multiplicity) for the ends of the graph, that is, a large number of disjoint rays in each end. We give a lower bound on the degree of vertices and the vertex‐degree of the ends which is quadratic in k, the connectedness of the desired subgraph. In fact, this is not far from best possible: we exhibit a family of graphs with a degree of order 2^k at the vertices and a vertex‐degree of order k log k at the ends which have no k‐connected subgraphs. Furthermore, if in addition to the high degrees at the vertices, we only require high edge‐degree for the ends (which is defined as the maximum number of edge‐disjoint rays in an end), Mader's theorem does not extend to infinite graphs, not even to locally finite ones. We give a counterexample in this respect. But, assuming a lower bound of at least 2k for the edge‐degree at the ends and the degree at the vertices does suffice to ensure the existence (k + 1)‐edge‐connected subgraphs in arbitrary graphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 331–349, 2007     

Coexistence of self-organized criticality and intermittent turbulence in the solar corona

An extended data set of extreme ultraviolet images of the solar corona provided by the SOHO spacecraft is analyzed using statistical methods common to studies of self-organized criticality (SOC) and intermittent turbulence (IT). The data exhibit simultaneous hallmarks of both regimes: namely, power-law avalanche statistics as well as multiscaling of structure functions for spatial activity. This implies that both SOC and IT may be manifestations of a single complex dynamical process entangling avalanches of magnetic energy dissipation with turbulent particle flows.     

Textile/Metal–Organic‐Framework Composites as Self‐Detoxifying Filters for Chemical‐Warfare Agents

The current technology of air‐filtration materials for protection against highly toxic chemicals, that is, chemical‐warfare agents, is mainly based on the broad and effective adsorptive properties of hydrophobic activated carbons. However, adsorption does not prevent these materials from behaving as secondary emitters once they are contaminated. Thus, the development of efficient self‐cleaning filters is of high interest. Herein, we report how we can take advantage of the improved phosphotriesterase catalytic activity of lithium alkoxide doped zirconium(IV) metal–organic framework (MOF) materials to develop advanced self‐detoxifying adsorbents of chemical‐warfare agents containing hydrolysable P? F, P? O, and C? Cl bonds. Moreover, we also show that it is possible to integrate these materials onto textiles, thereby combining air‐permeation properties of the textiles with the self‐detoxifying properties of the MOF material.     

Electrochemistry and spectroelectrochemistry of bismanganese porphyrin-corrole dyads

A series of homobimetallic manganese cofacial porphyrin-corrole dyads were synthesized and investigated as to their electrochemistry, spectroelectrochemistry, and ligand binding properties in nonaqueous media. Four dyads were investigated, each of which contained a Mn(III) corrole linked in a face-to-face arrangement with a Mn(III) porphyrin. The main difference between compounds in the series is the type of spacer, 9,9-dimethylxanthene, anthracene, dibenzofuran, or diphenylether, which determines the distance and interaction between the metallomacrocycles. Each redox process of the porphyrin-corrole dyads was assigned on the basis of spectroscopic and electrochemical data and by comparison with reactions and properties of the monocorrole and the monoporphyrin which were examined under the same solution conditions. The Mn(III) porphyrin part of the dyad undergoes two major one-electron reductions in pyridine and benzonitrile, the first of which involves a Mn(III)/Mn(II) process and the second the addition of an electron to the conjugated π-ring system of the macrocycle. The Mn(III) corrole part of the dyads also exhibits two major redox processes, one involving Mn(III)/Mn(II) and the other Mn(III) to Mn(IV) under the same solution conditions. The potentials and reversibility of each electron transfer reaction were shown to depend upon the solvent, type of spacer separating the two macrocycles, and the presence or absence of axial ligation, the latter of which was investigated in detail for the case of acetate ion which was found to bind within the cavity of the dyad to both manganese centers, both before and after the stepwise electroreduction to the Mn(II) forms of the two macrocycles. An intramolecular chloride ion exchange between the porphyrin part of the dyads which contain Mn(III)Cl and the singly oxidized corrole in the dyad is observed after the Mn(III)/Mn(IV) reaction of the corrole, suggesting that chloride is coordinated inside the cavity in the neutral compound.     

Metal ion complexing properties of dipyridoacridine, a highly preorganized tridentate homologue of 1,10-phenanthroline

DPA (dipyrido[4,3-b;5,6-b]acridine) may be considered as a tridentate homologue of phen (1,10-phenanthroline). In this paper some of the metal ion complexing properties of DPA in aqueous solution are reported. Using UV-visible spectroscopy to follow the intense π-π* transitions of DPA as a function of pH gave protonation constants at ionic strength (μ) = 0 and 25 °C of pK(1) = 4.57(3) and pK(2) = 2.90(3). Titration of 10(-5) M solutions of DPA with a variety of metal ions gave log K(1) values as follows: Zn(II), 7.9(1); Cd(II), 8.1(1); Pb(II), 8.3(1); La(III), 5.23(7); Gd(III), 5.7(1); Ca(II), 3.68; all at 25 °C and μ = 0. Log K(1) values at μ = 0.1 were obtained for Mg(II), 0.7(1); Sr(II), 2.20(1); Ba(II), 1.5(1). The log K(1) values show that the high level of preorganization of DPA leads to complexes 3 log units more stable than the corresponding terpyridyl complexes for large metal ions such as La(III) or Ca(II), but that for small metal ions such as Mg(II) and Zn(II) such stabilization is minimal. Molecular mechanics calculations (MM) are used to show that the best-fit M-N length for coordination with DPA is 2.60 ?, accounting for the high stability of Ca(II) or La(III) complexes of DPA, which are found to have close to this M-N bond length in their phen complexes.     

Alkoxyamine-cyanoborane adducts: efficient cyanoborane transfer agents

We report the synthesis of the hitherto unknown zwitterionic alkoxyamino cyanoboranes by reduction of O-alkyloximes with sodium cyanoborohydride; unprecedented cyanoboronated N-alkoxyformamidines were also isolated as by-products. Boronated alkoxyamines were found to be efficient cyanoborane transfer agents towards more basic amines, including aminosugars; they were also successfully transformed into neoglycoconjugates by the neoglycorandomization reaction with reducing sugars.     

Potent 5-nitrofuran derivatives inhibitors of Trypanosoma cruzi growth: electrochemical, spectroscopic and biological studies

Cyclic voltammetry and electron spin resonance techniques were used in the investigation of several potential antiprotozoal containing thiosemicarbazone and carbamate nitrofurans. In the electrochemical behaviour, a self-protonation process involving the nitro group was observed. The reactivity of the nitro anion radical for these derivatives with glutathione, a biological relevant thiol, was also studied in means of cyclic voltammetry. These studies demonstrated that glutathione could react with radical species from 5-nitrofuryl system. Furthermore, from the voltammetric results, some parameters of biological significance as E(7)(1) (indicative of the biological nitro anion radical formation), and [Formula: see text] (thermodynamic indicator the of oxygen redox cycling) have been calculated. We also evaluated the stability of the nitro anion radical in terms of the dimerization constant (k(d)). The nitrofuran-free radicals from cyclic voltammetry were characterized by electron spin resonance. A clear dependence between both the thiosemicarbazone or carbamate substructure and the length of the linker, furyl- or furylpropenyl-spacer, and the delocalization of the unpaired electron was observed. Through of biological assays we obtained important parameters that account for the selective anti-trypanosomal activity of these derivatives. The trypomastigote viability study showed that all derivatives are as active as in the epimastigote form of the parasite in a doses dependent manner.     

A Raman microprobe study of melt inclusions in kimberlites from Siberia, Canada, SW Greenland and South Africa

The geometries, energies and vibrational frequencies of various polyborates in both gaseous and aqueous phase were calculated at the B3LYP/aug-cc-pVDZ level. The calculated total symmetrical stretching Raman shifts of B(OH)(3), B(OH)(4)(-), B(2)O(OH)(4), B(2)O(OH)(5)(-), B(2)O(OH)(6)(2-), B(3)O(3)(OH)(3), B(3)O(3)(OH)(4)(-), B(3)O(3)(OH)(5)(2-), B(3)O(3)(OH)(6)(3-), B(4)O(5)(OH)(4)(2-) and B(5)O(6)(OH)(4)(-) were assigned to 877.40, 735.33, 785.22, 792.90, 696.79, 587.72, 599.06, 740.16, 705.01, 551.67 and 521.04cm(-1), respectively. The results can be used as the characteristic frequency for polyborates in aqueous phase at room temperature. At least six types of polyborates B(OH)(3), B(OH)(4)(-), B(3)O(3)(OH)(4)(-), B(3)O(3)(OH)(5)(2-), B(4)O(5)(OH)(4)(2-) and B(5)O(6)(OH)(4)(-), occur in aqueous solutions at ambient temperature. The chemical species distribution and the relevant interaction mechanisms among polyborates in the solutions were also suggested.     

Cocrystals of 6‐propyl‐2‐thiouracil: N—H...O versus N—H...S hydrogen bonds

In order to investigate the relative stability of N—H...O and N—H...S hydrogen bonds, we cocrystallized the antithyroid drug 6‐propyl‐2‐thiouracil with two complementary heterocycles. In the cocrystal pyrimidin‐2‐amine–6‐propyl‐2‐thiouracil (1/2), C₄H₅N₃·2C₇H₁₀N₂OS, (I), the `base pair' is connected by one N—H...S and one N—H...N hydrogen bond. Homodimers of 6‐propyl‐2‐thiouracil linked by two N—H...S hydrogen bonds are observed in the cocrystal N‐(6‐acetamidopyridin‐2‐yl)acetamide–6‐propyl‐2‐thiouracil (1/2), C₉H₁₁N₃O₂·2C₇H₁₀N₂OS, (II). The crystal structure of 6‐propyl‐2‐thiouracil itself, C₇H₁₀N₂OS, (III), is stabilized by pairwise N—H...O and N—H...S hydrogen bonds. In all three structures, N—H...S hydrogen bonds occur only within R₂²(8) patterns, whereas N—H...O hydrogen bonds tend to connect the homo‐ and heterodimers into extended networks. In agreement with related structures, the hydrogen‐bonding capability of C=O and C=S groups seems to be comparable.