COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OF △（3, 3, k）

Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.     

Generalizations of M-matrices which may not have a nonnegative inverse

Generalizations of M-matrices are studied, including the new class of GM-matrices. The matrices studied are of the form sI-B with B having the Perron-Frobenius property, but not necessarily being nonnegative. Results for these classes of matrices are shown, which are analogous to those known for M-matrices. Also, various splittings of a GM-matrix are studied along with conditions for their convergence.     

Synthesis of 99mTc-cationic steroid antimicrobial-107 and in vitro evaluation

Ceragenins/cationic steroid antimicrobials (CSAs) are a group of cholic acid derivatives with many properties that make them favourable for application as anti-infective agents. CSA-107 is also a member of this group that was labelled with ^99mTc by using SnCl₂·2H₂O as reducing agent and Na–K tartrate as transchelating agent. Labelling efficiency was optimized by varying the amount of reducing agent, pH, and time of incubation. Labelling efficiency and the stability of ^99mTc-CSA-107 in human serum was determined by paper and thin layer chromatography, which were >95 and >90 % respectively. In vitro binding of ^99mTc-CSA-107 was >95 % determined by using Staphylococcus aureus bacteria.     

CuCN catalyzed one pot synthesis of γ-keto diesters: domino double Michael addition followed by Nef reaction

An efficient one pot synthesis of γ-keto diesters through double Michael addition coupled with Nef reaction in the presence of CuCN catalyst and Cs₂CO₃ base is described. The reaction proceeds rapidly in DCM to give the products in good yields. A plausible mechanism is proposed.     

Evaluation of highly loaded low specific activity 99Mo on alumina column as 99mTc generator

Adsorption behavior of molybdate on acidic alumina was studied at boiling water bath temperature (~100 °C). Various parameters affecting the adsorption of molybdenum, such as pH, amount of molybdenum, incubation period, etc., were determined. A ^99mTc generator was prepared by adsorbing low specific activity ⁹⁹Mo (150 mg) on 1 g alumina. Elutions were carried out with saline. Performance of the generator such as ⁹⁹Mo breakthrough, aluminum contents, pH, elution profile, radiochemical purity, and labeling efficiency of kits were checked.     

Self-focusing in transformer oil with external electric field

We report a pioneer observation of self-focusing in transformer oil with external electric field. The experiments were conducted at variable powers (5?C15 mW) of red He-Ne laser at various adjustable external electric field intensities (0?C15 kV/cm). Self-defocusing in transformer oil is observed in the absence of electric field. While with the applied electric field, self-focusing is witnessed that became excessively strong at high electric field. It is further observed that beam divergence decreases with the increase of electric field and it reduces by about 70% at 15 kV/cm. Self-focusing has been observed with both polarized and unpolarized laser light.     

Effective stability for slow time-dependent near-integrable Hamiltonians and application

The aim of this note is to prove a result of effective stability for a non-autonomous perturbation of an integrable Hamiltonian system, provided that the perturbation depends slowly on time. Then we use this result to clarify and extend a stability result of Giorgilli and Zehnder for a mechanical system with an arbitrary time-dependent potential.     

Linear relationships in α,β-unsaturated carbonyl compounds between the half-wave reduction potentials, the frontier orbital energies and the Hammett σp values

A linear relationship between the half-wave reduction potentials of α,β-unsaturated carbonyl compounds R–CHCH–COX and the Hammett σ_p values of R and X is proposed: E_1/2=−1.341σ_p(X)σ_p(R)+1.123σ_p(X)+1.746σ_p(R)−1.694. A linear relationship is also observed for the LUMO's energy values, the absolute chemical hardness η, the chemical potential μ, the electrophilicity power ω, or the polarisation of the ethylenic double bond with the Hammett σ_p values of R and X.     

The reaction of tertiary phosphines with (Ph2Se2I2)2--the influence of steric and electronic effects

The reaction of (Ph(2)Se(2)I(2))(2) with a wide variety of tertiary phosphines possessing different steric and electronic properties has been studied, leading in most cases to R(3)PSe(Ph)I adducts; [R(3)P = (p-CH(3)C(6)H(4))(3)P (1), (m-CH(3)C(6)H(4))(3)P (2), (o-OCH(3)C(6)H(4))(3)P (4), Ph(2)MeP (6), Me(2)PhP (7), Me(3)P (8), Cy(3)P (9)]. All of the products formed were characterised by elemental analysis, Raman and multinuclear NMR spectroscopy. Both steric and electronic factors are important in determining the structural motif (CT vs. ionic) observed in the solid-state. In general, highly basic phosphines result in a lengthening of the Se-I interaction, and a preference for an ionic structure. The reaction with (o-CH(3)C(6)H(4))(3)P does not yield a stable R(3)PSe(Ph)I adduct, and instead (o-CH(3)C(6)H(4))(3)PI(2) (3) is formed. The unusually long P-I bond, [2.5523(12) A], and short I-I bond, [3.0724(4) A], exhibited by is a result of the high steric requirements of this phosphine. The similarly bulky (o-SCH(3)C(6)H(4))(3)P yields a mixture of (o-SCH(3)C(6)H(4))(3)PSe(Ph)I (5a) and [(o-SCH(3)C(6)H(4))(3)PSePh]I(3) (5b). The crystal structures of (m-CH(3)C(6)H(4))(3)PSe(Ph)I, 2, (o-CH(3)C(6)H(4))(3)PI(2), 3, [(o-OCH(3)C(6)H(4))(3)PSePh]I.CH(2)Cl(2), 4, [(o-SCH(3)C(6)H(4))(3)PSePh]I(3), 5b, two pseudo-polymorphs of Ph(2)MePSe(Ph)I, 6a/6b, and [Me(3)PSe(Ph)I](2).CH(2)Cl(2), 8, are reported. The R(3)PSe(Ph)I adducts formed exhibit one of four types of behaviour. Type I products, (such as 2) are CT in the solid-state and display fluxionality in solution. Type II products (such as 6a/6b) lie close to the CT/ionic structural borderline, displaying long Se-I bonds, and are more appropriately classified as [R(3)PSePh] (acceptor)/I(-) (donor) CT complexes. Type II complexes ionise in solution to [R(3)PSePh]I. Type III products, such as 8, are ionic in solution, but frequently show cation-anion, or cation-solvent interactions in the solid-state, although these interactions are weak and the linear P-Se-I motif is lost. Type IV products (such as 4) are ionic and feature bulky phosphines. They display no short cation-anion interactions in the solid-state.     

Reactions of Ph4Se4Br4 with tertiary phosphines. Structural isomerism within a series of R3PSe(Ph)Br compounds

The synthesis and characterisation of Ph(4)Se(4)Br(4) (1) directly from the reaction of Ph(2)Se(2) with dibromine is reported. The solid-state structure of 1 consists of four PhSeBr units linked by weak selenium-selenium bonds [3.004(2)-3.051(2) A] into a Se(4) square, and is structurally analogous to the previously reported Ph(4)Te(4)I(4). The reactions of Ph(4)Se(4)Br(4) with a variety of tertiary phosphines have been undertaken, resulting in the formation of compounds of formula R(3)PSe(Ph)Br. X-Ray crystallographic analysis of three of the compounds reveals different structural isomers. Ph(3)PSe(Ph)Br (2) is a charge-transfer (CT) compound [Se-Br 3.0020(8) A], with an essentially linear P-Se-Br bond angle, 172.15(4) degrees and T-shaped geometry at selenium. Me(3)PSe(Ph)Br (5) also contains the selenium atom in a T-shaped geometry, consistent with a CT formulation, although the Se-Br distance of 3.327(3) A is considerably longer than observed for 2. In contrast, Cy(3)PSe(Ph)Br (6) is an ionic phosphonium salt, [Cy(3)PSePh]Br with no short Se-Br interactions. Geometry at selenium is bent, as expected for an ionic compound. These results are discussed with reference to the previously reported iodo-compounds Ph(3)PSe(Ph)I and [(Me(2)N)(3)PSe(Ph)]I.