An Extremal Characterization of the Incidence Graphs of Projective Planes

Let G be a 4-cycle free, bipartite graph on 2n vertices with partitions of equal cardinality n. Let c₆(G) denote the number of cycles of length 6 in G. We prove that for n 3, c₆(G) , where , with equality if and only if G is the incidence point-line graph of a projective plane.     

Transport properties of copper-doped carbon aerogels

The magnetic susceptibility, conductivity, magnetoresistance (MR) and Hall effect of copper-doped carbon aerogels are measured and compared with corresponding results from the original carbon aerogels. The experimental results indicate that the temperature-dependent magnetic susceptibility of the copper-doped and of the original carbon aerogels is well fit by a Curie function at low temperatures. The copper-doped carbon aerogels show a higher susceptibility and spin concentration than the original carbon aerogel. After doping by copper, the materials exhibit a more linear current-voltage curve than the original carbon aerogel under the same measurement conditions. The electrical resistance of the copper-doped carbon aerogels is strikingly lower than that of the original carbon aerogels, and decreases with increasing copper content in the samples. The temperature-dependent resistivity ρ(T) of all of the copper-doped and original carbon aerogels can be fitted by an exp(T^−1/2) dependence for T<100 K. The copper-doped and pristine carbon aerogels follow a quadratic MR behavior Δρ/ρ=AB² in the magnetic field range B investigated (up to 5 T), except at very low temperatures (T<4 K).     

Unprecedented Homoleptic Bis‐Tridentate Iridium(III) Phosphors: Facile,Scaled‐Up Production,and Superior Chemical Stability

Bis‐tridentate Ir(III) metal complexes are expected to show great potential in organic light‐emitting diode (OLED) applications due to the anticipated, superb chemical and photochemical stability. Unfortunately, their exploitation has long been hampered by lack of adequate methodology and with inferior synthetic yields. This hurdle can be overcome by design of the first homoleptic, bis‐tridentate Ir(III) complex [Ir(pzpyph)(pz^Hpyph)] ( 1 ), for which the abbreviation (pzpyph)H (or pz^Hpyph) stands for the parent 2‐pyrazolyl‐6‐phenyl pyridine chelate. After that, methylation and double methylation of 1 afford the charge‐neutral Ir(III) complex [Ir(pzpyph)(pz^Mepyph)] ( 2 ) and cationic complex [Ir(pz^Mepyph)₂][PF₆] ( 3 ), while deprotonation of 1 gives formation of anionic [Ir(pzpyph)₂][NBu₄] ( 4 ), all in high yields. These bis‐tridentate Ir(III) complexes 2 – 4 are highly emitted in solution and solid states, while the charge‐neutral 2 and corresponding t ‐butyl substituted derivative [Ir(pzpy^Buph)(pz^Mepy^Buph)] ( 5 ) exhibit superior photostability versus the tris‐bidentate references [Ir(ppy)₂(acac)] and [Ir(ppy)₃] in toluene under argon, making them ideal OLED emitters. For the track record, phosphor 5 gives very small efficiency roll‐off and excellent overall efficiencies of 20.7%, 66.8 cd A^?1, and 52.8 lm W^?1 at high brightness of 1000 cd m^?2. These results are expected to inspire further studies on the bis‐tridentate Ir(III) complexes, which are judged to be more stable than their tris‐bidentate counterparts from the entropic point of view.     

Separation of chitosan oligomers by immobilized metal affinity chromatography

A novel approach for chitosan oligosaccharide (COS) separation by immobilized metal affinity chromatography (IMAC) based on the differences in the interactions of chelated copper (II) ions with various COS (dimers, trimers, tetramers) is described. Polyhydroxylic chromatographic supports (agarose CL-6B and silica) were functionalized with various chelating functions such as iminodiacetate (IDA), carboxymethyl-aspartate (CM-Asp) and tris(carboxymethyl)ethylenediamine (TED). The COS retention capacities of the columns were between 2 and 6 mg/cm(3), depending on the chelating group. The COS were separated and/or enriched up to 95% for dimer and trimer and 90% for the tetramer, with yields of 60-95%.     

Variational approach to wetting problems: Calculation of a shape of sessile liquid drop deposited on a solid substrate in external field

Analysis of the shape of sessile drops pinned to a solid substrate and exposed to the external potential is presented. Explicit expressions describing the drops’ shape are obtained with a calculus of variations for 2D and 3D wetting problems. The presented approach is applicable for analysis of electrowetting problems, the study of vibrated and centrifuged drops.     

Introduction of a New Devices for Sampling Organic Pollutants

A new mimic biological sampling devices, which consisted of lipid-containing semipermeable-membrane (SPMD) for sampling organic pollutants has been introduced.     

Novel mechanism for the formation of long-chain branching in polyethylene

Polyethylene produced by a vanadium-based polymerization catalyst contains long-chain branching as determined by NMR and rheology, even though the polymer has very low levels of vinyl unsaturation. A new mechanism is proposed for the formation of the long-chain branching, which involves C H bond activation of the polyethylene backbone through a σ-bond metathesis reaction, followed by ethylene insertion at the new V C bond. Consistent with the proposed C H bond activation mechanism, the polymerization catalyst was also found to insert ethylene into the C H bonds of alkanes such as heptane. A bridged metallocene catalyst was also found to activate C H bonds of alkanes suggesting this new mechanism may explain the formation of long-chain branching in some metallocene-produced polyethylene. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2889–2898, 1998     

Evaluating partially observed survival histories: retrospective projection of covariate trajectories

The use of maximum likelihood methods in analysing times to failure in the presence of unobserved randomly changing covariates requires constrained optimization procedures. An alternative approach using a generalized version of the EM-algorithm requires smoothed estimates of covariate values. Similar estimates are needed in evaluating past exposures to hazardous chemicals, radiation or other toxic materials when health effects only become evident long after their use. In this paper, two kinds of equation for smoothing estimates of unobserved covariates in survival problems are derived. The first shows how new information may be used to update past estimates of the covariates' values. The second can be used to project the covariates' trajectory from the present to the past. If the hazard function is quadratic in form, both types of smoothing equation can be derived in a closed analytical form. Examples of both types of equation are presented. Use of these equations in the extended EM-algorithm, and in estimating past exposures to hazardous materials, are discussed. © 1997 by John Wiley & Sons, Ltd.