On the number of (r,r+1)‐ factors in an (r,r+1)‐factorization of a simple graph

For integers d≥0, s≥0, a (d, d+s)‐graph is a graph in which the degrees of all the vertices lie in the set {d, d+1, …, d+s}. For an integer r≥0, an (r, r+1)‐factor of a graph G is a spanning (r, r+1)‐subgraph of G. An (r, r+1)‐factorization of a graph G is the expression of G as the edge‐disjoint union of (r, r+1)‐factors. For integers r, s≥0, t≥1, let f(r, s, t) be the smallest integer such that, for each integer d≥f(r, s, t), each simple (d, d+s) ‐graph has an (r, r+1) ‐factorization with x (r, r+1) ‐factors for at least t different values of x. In this note we evaluate f(r, s, t). © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 257‐268, 2009     

Flexible N,N,N-chelates as supports for iron and cobalt chloride complexes; synthesis, structures, DFT calculations and ethylene oligomerisation studies

The aryl-substituted N-picolylethylenediamine and diethylenetriamine ligands, (ArNHCH(2)CH(2))[(2-C(5)H(4)N)CH(2)]NH and (ArNHCH(2)CH(2))(2)NH (Ar = 2,6-Me(2)C(6)H(3), 2,4,6-Me(3)C(6)H(2)), have been prepared by employing palladium-catalysed N-C(aryl) coupling reactions of the corresponding primary amines with aryl bromide. Treatment of MCl(2) with (ArNHCH(2)CH(2))[(2-C(5)H(4)N)CH(2)]NH affords [[(ArNHCH(2)CH(2))((2-C(5)H(4)N)CH(2))NH]CoCl(2)](Ar = 2,6-Me(2)C(6)H(3) 1a; 2,4,6-Me(3)C(6)H(2)) 1b and [[(ArNHCH(2)CH(2))((2-C(5)H(4)N)CH(2))NH]FeCl(2)](n)(n= 1, Ar = 2,6-Me(2)C(6)H(3) 2a; n= 2, 2,4,6-Me(3)C(6)H(2) 2b) in high yield. The X-ray structures of 1a and 1b are isostructural and reveal the metal centres to adopt distorted trigonal bipyramidal geometries with the N,N,N-chelates adopting fac-structures. A facial coordination mode of the ligand is also observed in bimetallic 2b, however, in 2a the N,N,N-chelate adopts a mer-configuration with the metal centre adopting a geometry best described as square pyramidal. Solution studies indicate that mer-fac isomerisation is a facile process for these systems at room temperature. Quantum mechanical calculations (DFT) have been performed on 1a and 2a, in which the ligands employed are identical, and show the fac- to be marginally more stable than the mer-configuration for cobalt (1a) while for iron (2a) the converse is evident. Reaction of (ArNHCH(2)CH(2))(2)NH with CoCl(2) gave the five-coordinate complexes [[(ArNHCH(2)CH(2))(2)NH]CoCl(2)](Ar = 2,6-Me(2)C(6)H(3) 3a, 2,4,6-Me(3)C(6)H(2) 3b), in which the ligand adopts a mer-configuration; no reaction occurred with FeCl(2). All complexes 1-3 act as modest ethylene oligomerisation catalysts on activation with excess methylaluminoxane (MAO); the iron systems giving linear alpha-olefins while the cobalt systems give mixtures of linear and branched products.     

Dielectrophoretic force microscopy of aqueous interfaces

A novel scanning probe microscopy technique has allowed dielectrophoretic force imaging with nanoscale spatial resolution. Dielectrophoresis (DEP) traditionally describes the mobility of polarizable particles in inhomogeneous alternating current (ac) electric fields. Integrating DEP with atomic force microscopy allows for noncontact imaging with the image contrast related to the local electric polarizability. By tuning the ac frequency, dielectric spectroscopy can be performed at solid/liquid interfaces with high spatial resolution. In studies of cells, the frequency-dependent dielectrophoretic force is sensitive to biologically relevant electrical properties, including local membrane capacitance and ion mobility. Consequently, dielectrophoretic force microscopy is well suited for in vitro noncontact scanning probe microscopy of biological systems.     

Growth of thin Fe(0 0 1) films for terahertz emission experiments

The electrical and magnetic properties of thin iron (Fe) films have sparked significant scientific interest. Our interest, however, is in the fundamental interactions between light and matter. We have discovered a novel application for thin Fe films. These films are sources of terahertz (THz) radiation when stimulated by an incident laser pulse. After intense femtosecond pulse excitation by a Ti:sapphire laser, these films emit picosecond, broadband THz frequencies. The terahertz emission provides a direct measure of the induced ultrafast change in magnetization within the Fe film. The THz generation experiments and the growth of appropriate thin Fe films for these experiments are discussed. Several criteria are used to select the substrate and film growth conditions, including that the substrate must permit the epitaxial growth of a continuous, monocrystalline or single crystal film, yet must also be transparent to the emitted THz radiation. An Fe(0 0 1) film grown on the (0 0 1) surface of a magnesium oxide (MgO) substrate makes an ideal sample. The Fe films are grown by physical vapor deposition (PVD) in an ultrahigh vacuum (UHV) system. Low energy electron diffraction (LEED) and Auger electron spectroscopy (AES) are used to characterize the Fe(0 0 1) films. Two substrate surface preparation methods are investigated. Fe(0 0 1) films grown on MgO(0 0 1) substrates that are used as-received and films grown on MgO(0 0 1) substrates that have been UV/ozone-cleaned ex vacuo and annealed in vacuo produce the same results in the THz generation experiments. Either substrate preparation method permits the growth of samples suitable for the THz emission experiments.     

Non-random fluctuations and multi-scale dynamics regulation of human activity

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses dynamic patterns characterized by robust scale-invariant and nonlinear features. These patterns remain stable from one subject to another and are unaffected by changes in the average activity level that occur within individual subjects throughout the day and on different days of the week, since they persist during daily routine and when the same subjects undergo time-isolation laboratory experiments designed to account for the circadian phase and to control the known extrinsic factors. Further, by modeling the scheduled events imposed throughout the laboratory protocols, we demonstrate that they cannot account for the observed scaling patterns in activity fluctuations. We attribute these patterns to a previously unrecognized intrinsic nonlinear multi-scale control mechanism of human activity that is independent of known extrinsic factors such as random and scheduled events, as well as the known intrinsic factors which possess a single characteristic time scale such as circadian and ultradian rhythms.     

ALS-associated mutant SOD1<Superscript>G93A</Superscript> causes mitochondrial vacuolation by expansion of the intermembrane space and by involvement of SOD1 aggregation and peroxisomes

Background  

Amyotrophic lateral sclerosis (ALS) is an age-dependent neurodegenerative disease that causes motor neuron degeneration, paralysis and death. Mutations in Cu, Zn superoxide dismutase (SOD1) are one cause for the familial form of this disease. Transgenic mice expressing mutant SOD1 develop age-dependent motor neuron degeneration, skeletal muscle weakness, paralysis and death similar to humans. The mechanism whereby mutant SOD1 induces motor neuron degeneration is not understood but widespread mitochondrial vacuolation has been observed during early phases of motor neuron degeneration. How this vacuolation develops is not clear, but could involve autophagic vacuolation, mitochondrial permeability transition (MPT) or uncharacterized mechanisms. To determine which of these possibilities are true, we examined the vacuolar patterns in detail in transgenic mice expressing mutant SOD1^G93A.     

Dichlorocarbene Addition to

In contrast to the terminal phosphinidene complex PhPW(CO)(5) (2), which adds to [5]metacyclophane (1) in a 1,4-fashion, dichlorocarbene preferentially adds in a 1,2-fashion to the formal "anti-Bredt" type double bond of the aromatic ring of 1 to afford the norcaradiene 11b, which immediately rearranges to the bridged cycloheptatriene 12b and further by a [1,5] sigmatropic chlorine migration to the isomeric 13b as the first observable product. More slowly, the latter isomerizes via a dissociative mechanism to give 15b. A computational study supports the notion that the [1,5] chlorine migration in the rearrangement 12b --> 13b, for which an activation barrier of 70.2 kJ mol(-)(1) was calculated, is essentially concerted with minor charge separation. In contrast, the analogous [1,5] chlorine migration in the flat model compound 7,7-dichlorocycloheptatriene (12a) displays features of a dissociative pathway.     

Aza-polycyclic aromatic hydrocarbons: 1—Elucidation of the regiochemistry of 1,2,3,4-tetrahydroazabenz-[a]anthracene-7,12-diones by long-range carbon–proton coupling constants

The ¹³C NMR spectra of 5,8-quinolinedione, 6-chloro-5,8-quinolinedione and 7-chloro-5,8-quinolinedione have been examined in detail. Utilization of long-range proton-carbon coupling constants have allowed the unambiguous identification of the regioisomeric 8-aza-1,2,3,4-tetrahydrobenz[a]anthracene-7,12-dione and 11-aza-1,2,3,4-tetrahydrobenz[a]anthracene-7,12-dione.