Complete characterization of almost Moore digraphs of degree three

It is well known that Moore digraphs do not exist except for trivial cases (degree 1 or diameter 1), but there are digraphs of diameter two and arbitrary degree which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. In this paper, we prove that digraphs of degree three and diameter k ≥ 3 which miss the Moore bound by one do not exist. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 112–126, 2005     

Supramolecular dimer formation through hydrogen bond extensions of carboxylate ligands – Path for magnetic exchange

A new complex of unusual composition [Cu(3-O₂Nbz)₂(nia)(H₂O)₂] (1) (nia = nicotinamide, 3-O₂Nbz = 3-nitrobenzoate) has been prepared and studied together with two other complexes of composition [Cu(4-O₂Nbz)₂(nia)₂(H₂O)₂] (2) and [Cu(4-O₂Nbz)₂(nia)₂]?(4-O₂NbzH)₂ (3) (4-O₂Nbz = 4-nitrobenzoate). The composition of all complexes has been determined by elemental analysis, the complexes have been studied by electronic, infrared and EPR spectroscopy, as well as by magnetization measurements over the temperature range 1.8–300 K, and their structures have been solved. The structure of complex (1) consists of molecules, where Cu(II) atom is monodentately coordinated by the pair of 3-nitrobenzoato anions in trans  -positions together with water and nicotinamide molecules, forming nearly tetragonal basal plane, and by another water molecule in axial position of tetragonal-pyramidal coordination polyhedron. The neighboring molecule coordination polyhedron basal planes are coplanar and allow formation of supramolecular dimers with strong H-bonds between hydrogen atoms from equatorially coordinated water molecules and uncoordinated carboxylate oxygen atoms thus giving the nearest Cu?$?$Cu distance of 4.886(2) Å. Magnetization measurements showed that complex (1) exhibits maximum of magnetic susceptibility at 6.5 K and a fit to Bleaney-Bowers equation gave singlet–triplet energy gap 2J = −6.25 cm⁻¹, and zJ′ = −0.03 cm⁻¹. This might be an experimental proof that the carboxylate bridges extended with hydrogen bonds are the pathway of the spin–spin interactions. The temperature dependence of changes in EPR spectra of (1) and the spectrum at 4.2 K have confirmed its hydrogen bonded dimeric structure. The calculated Cu?$?$Cu distance 4.8 Å is in very good agreement with the value obtained from crystal structure. The complexes (2) and (3) at 300 K exhibit magnetic moment μ_eff = 1.98 B.M. and μ_eff = 1.84 B.M., respectively. These values practically do not change with lowering the temperature up to 5 K and only small drops to μ_eff = 1.87 B.M. (for (2)) and μ_eff = 1.79 B.M. (for (3)) at 1.8 K have been observed. The EPR spectra of complex (2) at room temperature as well as at 77 K are of axial type with g_⊥ = 2.062 and g_|| = 2.285 and exhibit resolved parallel hyperfine splitting with A_|| = 160 Gauss. The EPR spectra of complex (3) at room temperature as well as at 77 K are of axial type with g_⊥ = 2.065 and g_|| = 2.235 and exhibit unresolved parallel hyperfine splitting. EPR spectra of (2) and (3) are consistent with the X-ray structure.     

Highly hydrated poly(allylamine)/silica magnetic resin

The creation of multifunctional nanomaterials by combining organic and inorganic components is a growing trend in nanoscience. The unique size-dependent properties of magnetic nanoparticles (MNPs) make them amenable to numerous applications such as carriers of expensive biological catalysts, in magnetically assisted chemical separation of heavy metals and radionuclides from contaminated water sources. The separation of minor actinides from high-level radionuclide waste requires a sorbent stable in acidic pH, with ease of surface functionalization, and a high capacity for binding the molecules of interest. For the described experiments, the MNPs with 50 nm average size were used (size distribution from 20 to 100 nm and an iron content of 80–90 w/w%). The MNPs that have been double coated with an initial silica coating for protection against iron solubilization and oxidation in nitric acid solution (pH 1) and a second silica/polymer composite coating incorporating partially imbedded poly(allylamine) (PA). The final product is magnetic, highly swelling, containing >95% water, with >0.5 mmol amines g^?1 available for functionalization. The amine groups of the magnetic resin were functionalized with the chelating molecules diethylenetriaminepentaacetic acid (DTPA) and N,N-dimethyl-3-oxa-glutaramic acid (DMOGA) for separation of minor actinides from used nuclear fuel.     

On some consequences of an external magnetic field applied to HTS coils

A computational model which enables to evaluate the distribution of the critical currents, electric fields and the voltage in the winding of a solenoidal high temperature superconducting (HTS) magnets subjected to an external magnetic field parallel with the magnet axis, was developed. The model comes out from the well-known power law between the electric field and the transport current of the HTS tape short sample. It allows to predict the voltage–current V(I) characteristics of both the pancake coils and the complete magnet. The model was applied to the magnet system consisting of 22 pancake coils made of multifilamentary Bi(2223)/Ag tape at 20 K, which is subjected to an external uniform magnetic field parallel with the coil axis. A rather unexpected behavior of the magnet at different operating conditions (operating current and external magnetic field strength) is predicted, analyzed and reported together with a theoretical explanation. On one hand, the external uniform magnetic field parallel with the coil axis increases the resulting magnetic field strength, however, on the other hand it simultaneously decreases the angle between the resulting magnetic field and the tape surface. Thus, the effect of higher magnetic loading caused by the presence of an external magnetic field strength which is acting on individual turns located close to the coil’s flanges is compensated by more favorable orientation of the tape with respect to the resulting magnetic field. As a result, increase in the critical currents of these turns is expected. Further, the results indicate, that in case of the high field HTS insert coils the anisotropy in the I_c(B) characteristic does not play a substantial role. As a consequence, the technology of the production of the tapes for high field insert HTS coils should concentrate rather on the tapes having the current carrying capacity as high as possible, than on the attempt how to decrease the anisotropy in the I_c(B) by changing the architecture of the filaments in the tape.     

Polysulfobetaine films prepared by electrografting technique for reduction of biofouling on electroconductive surfaces

The sulfobetaine films were prepared on stainless steel and golden surfaces. In the first step, the poly(2-(dimethylamino)ethyl methacrylate) film was created by employing the electrografting polymerization technique. In the second step, this film was modified to polysulfobetaine, i.e. the polymer film bearing the zwitterionic groups. The presence of the electrografted film and its modification were determined by contact angle measurements, infrared spectroscopy in reflectance mode and X-ray photoelectron spectroscopy. The prepared films were homogeneous with the thickness from about 5 to 26 nm as determined by X-ray photoelectron spectroscopy. The atomic force microscopy measurements showed the increase of surface roughness upon the surface coating. In vitro tests using adherent RAT-2 fibroblast cells and fluorescently labelled bovine serum albumin proteins showed that prepared polysulfobetaine films can be used in applications requiring the resistance against cell attachment and biofouling.     

Phase diagrams of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice

The ground-state and finite-temperature behavior of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice is investigated within the framework of two rigorous methods: the decoration-iteration transformation and exact recursion relations. The model under consideration describes a hybrid classical-quantum system consisting of the Ising and Heisenberg spins, which interact among themselves either through the Ising or XXZ Heisenberg nearest-neighbor interaction. Both sublattice magnetizations of the Ising and Heisenberg spins are exactly calculated with the aim to examine phase diagrams, thermal variations of the total and sublattice magnetizations. The finite-temperature phase diagrams form continuous (second-order) phase transition lines only, which exhibit a small reentrant region if the diamond-like decorated Bethe lattice with a sufficiently high coordination number is considered.     

Smallest Vertex‐Transitive Graphs of Given Degree and Diameter

For every d and k, we determine the smallest order of a vertex‐transitive graph of degree d and diameter k, and in each such case we show that this order is achieved by a Cayley graph.     

Diastereoselective ortho-lithiation of [5]ferrocenophanes

Planarly chiral ferrocene derivatives with bridged cyclopentadienyl rings are interesting ligands in asymmetric catalysis. A planar stereogenic unit is conveniently introduced by diastereoselective ortho-lithiation. The directed lithiation of several [5]ferrocenophane derivatives followed by quenching with chlorodiphenylphosphane led to planarly chiral ligands. The sense of diastereoselection was studied by computational methods. Absolute configuration of methoxy phosphane was determined by single crystal X-ray diffraction study.