On a conjecture of grant walker for the first occurrence of irreducible modular representations of general linear groups

Let GL _n = GL(n,F _p ) be the group of all n×ninvertible matrices over the field F _p of p elements, p a prime number. As well known, a complete set of irreducible GL _n -modules as submodules of the polynomial algebra was constructed by Stephen Doty and Grant Walker, Ton That Tri (see [1], [4]). Grant Walker has a conjecture that the occurence of these modules is the first occurence of these modules as submodules in the polynomial algebra. The aim of this paper is to give a proof of the above conjecture for p= 2.     

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     

Straightforward access to new vinca-alkaloids via selective reduction of a nitrile containing anhydrovinblastine derivative

A procedure to exclusively obtain 3′S-cyanoanhydrovinblastine 12 from two naturally occurring vinca-alkaloids (catharanthine and vindoline) in one step with good yield is described. Stereoselective reductions of 12, providing straightforward access to three new vinca-alkaloids, including two diastereomers 3′S-cyano-(4′R,5′-dihydro)-anhydrovinblastine and 3′S-cyano-(4′S,5′-dihydro)-anhydrovinblastine as well as (3′S-aminomethyl)-(4′S,5′-dihydro)-anhydrovinblastine in good yields is also reported.     

An oxacalix[2]arene[2]pyrimidine-bis(Zn-porphyrin) tweezer as a selective receptor towards fullerene C70

An oxacalix[2]arene[2]pyrimidine-bis(Zn^II-porphyrin) conjugate was readily prepared via nucleophilic aromatic substitution of a phenolic AB₃-Zn-porphyrin on the upper rim of a (1,3-alternate) 5,17-bis(methylsulfonyl)oxacalix[4]arene precursor. Efficient 1:1 complex formation between the ‘jaws’ bisporphyrin tweezer and fullerene C₇₀ was evidenced by ¹H NMR titrations (K = 3.0 × 10⁴ M⁻¹), while no detectable complexation could be observed with C₆₀. On the other hand, an analogous oxacalix[4]arene-bis(Cu-corrole) conjugate did not show any measurable (C₆₀ or C₇₀) fullerene binding.     

Radiolysis of 1-naphthol in aqueous solutions

The effects of absorbed doses, initial pH and 1-naphthol concentration onto its radiolysis in aqueous sulphuric and hydrochloric acids by gamma rays from ⁶⁰Co were investigated. Under the experimental conditions, 1-naphthol degradation yields increased with increasing the absorbed doses (0.3–3.0 kGy) and with decreasing the initial 1-naphthol concentration (20–1 ppm). It was found out that the hydrated electrons did not play any significant roles in 1-naphthol radiolysis, as the degradation yields were higher at pH₀ ~ 0.46 compared to those at pH₀ ~ 2.0–5.0. The corresponding radiolytic yields G(−1-naphthol) were (6.13 ± 1.00)) × 10⁻² and (5.11 ± 0.22) × 10⁻² μmol/J in sulphuric acids, (15.61 ± 3.85) × 10⁻² and (4.76 ± 0.48) × 10⁻² μmol/J in hydrochloric acids. 1-Naphthol degradation rates could be described by the kinetic equations of pseudo-first-order reactions. An empirical relation between the observed reaction constants k _D and the initial 1-naphthol concentrations was established, enabling to predict the absorbed doses required for a given treatment efficiency. Three products of 1-naphthol degradation were revealed using an HPLC/UV procedure.     

Determination of microelement distribution in different components of soil-plant systems

The leaves, stem, and roots of two types of shrubs (tea (Camellia sinensis) and sweet leaf (Sauropus androgynus)) and two types of herbs (vetiver grass (Vetiveria zizanioides L. Nash) and maize (Zea mays L)) and the Thucuc soil where the plants were growing were collected to be studied. The contents of 22 elements in the samples were determined by three methods: X-Ray fluorescence analysis (XRFA), gamma activation analysis (GAA), and the tracking method to study the distribution of these elements in plants and the soil-plant relationship. This study was carried out at the Flerov Laboratory of Nuclear Reactions (FLNR), Joint Institute for Nuclear Research (JINR), Dubna, Russia. The distribution of the elements in the soil-plant system was studied.     

The Role of Frozen Spins in the Exchange Anisotropy of Core-Shell Fe@Fe(3)O(4) Nanoparticles

Core-shell Fe@Fe(3)O(4) nanoparticles exhibit substantial exchange bias at low temperatures, mediated by unidirectionally aligned moments at the core-shell interface. These spins are frozen into magnetic alignment with field cooling, and are depinned in a temperature-dependent manner. The population of such frozen spins has a direct impact on both coercivity (H(C)) and the exchange-bias field (H(E)), which are modulated by external physical parameters such as the strength of the applied cooling field and the cycling history of magnetic field sweeps (training effect). Aging of the core-shell nanoparticles under ambient conditions results in a gradual decrease in magnetization but overall retention of H(C) and H(E), as well as a large increase in the population of frozen spins. These changes are accompanied by a structural evolution from well-defined core-shell structures to particles containing multiple voids, attributable to the Kirkendall effect. Energy-filtered and high-resolution transmission electron microscopy both indicate further oxidation of the shell layer, but the Fe core is remarkably well preserved. The increase in frozen spin population with age is responsible for the overall retention of exchange bias, despite void formation and other oxidation-dependent changes. The exchange-bias field becomes negligible upon deliberate oxidation of Fe@Fe(3)O(4) nanoparticles into yolk-shell particles, with a nearly complete physical separation of core and shell.     

Catalytic asymmetric hydrogenation of aromatic ketones in room temperature ionic liquids

Polar bisphosphonic acid-derived Ru(BINAP)(DPEN)Cl₂ precatalysts were synthesized and immobilized in room temperature ionic liquids (RTILs) for asymmetric hydrogenation of aromatic ketones with ee values of up to 98.7%. The performance of the Ru catalysts is highly dependent on the nature of imidazolium ILs. For the imidazolium ILs without acidic protons, both ILs and Ru catalysts were recycled by simple extraction and reused. Such a simple immobilization approach also prevented the leaching of Ru (and Ru catalysts) into the chiral secondary alcohol products, and should prove desirable for the production of pharmaceutical intermediates that are free from metal contaminants.