An ore-type condition for the existence ofk-factors in graphs

Letk be a positive integer, and letG be a graph of ordern withn 4k – 5,kn even and minimum degree at leastk. We prove that if the degree sum of each pair of nonadjacent vertices is at leastn, thenG has ak-factor.     

Determination of saccharides in sake by high-performance liquid chromatography with polarized photometric detection

A high-performance liquid chromatographic method has been developed for the determination of saccharides in sake, an alcoholic beverage brewed from rice. Saccharides in sake were separated on a normal phase (carbamoyl bonded silica) column using a linear gradient elution of water in acetonitrile. Seven saccharides, glucose, maltose, isomaltose, maltotriose, panose, isomaltotriose and ethyl alpha-D-glucoside, were determined by a polarized photometric detector. Unidentified peaks suggesting saccharides with polymerization degrees over 4 were also observed. The proposed method did not require any sample clean-up treatment. As an application, saccharide compositions in various kinds of sake were compared.     

Synthesis and photoluminescence properties of BF2 complexes with 1,3-diketone ligands

BF₂ complexes with 1,3-diketone ligands were synthesized, and their optical and electrochemical properties were studied. The colors of the complexes varied depending on the structures of the 1,3-diketone ligands. The absorption and emission maxima of the complexes with 1,3-diaryl-1,3-diketone ligands were considerably red shifted as compared to those of the complexes with 1-aryl-3-trifluoromethyl-1,3-diketone ligands, suggesting an extended π-conjugation of the 1,3-diaryl-1,3-diketone moieties. The molar absorption coefficients and quantum yields of the complexes with 1,3-diaryl-1,3-diketone ligands were larger than those of the complexes with 1-aryl-3-trifluoromethyl-1,3-diketone ligands. Cyclic voltammetry measurements revealed that the reduction potentials of the BF₂ complexes were higher than those of the free ligands. These complexes exhibited various emission colors in the solid states due to the intermolecular interactions.     

Synthesis, Characterization, and Crystal Structure of a (&mgr;-Oxo)bis(&mgr;-acetato)diiron(III) Complex with a Dinucleating Hexapyridine Ligand, 1,2-Bis[2-(bis(2-pyridyl)methyl)-6-pyridyl]ethane. The First Example of a Discrete (&mgr;-Oxo)bis(&mgr;-acetato)diiron(III) Complex with a Dinucleating Ligand

A mononucleating tripyridine ligand, 2-(bis(2-pyridyl)methyl)-6-methylpyridine (L(1)), and a dinucleating hexapyridine ligand, 1,2-bis[2-(bis(2-pyridyl)methyl)-6-pyridyl]ethane (L(2)), have been prepared. The reaction of a carbanion of 2,6-lutidine with 2-bromopyridine affords L(1) which is converted to L(2) quantitatively by treating with tert-butyllithium and 1,2-dibromoethane. (&mgr;-Oxo)bis(&mgr;-acetato)diiron(III) complexes [Fe(2)(O)(OAc)(2)(L(1))(2)](ClO(4))(2) (1) and [Fe(2)(O)(OAc)(2)L(2)](ClO(4))(2) (2) have been synthesized and characterized by means of infrared, UV/vis, mass, and M?ssbauer spectroscopies and by measuring magnetic susceptibility and cyclic voltammograms. All the spectral data are consistent with the (&mgr;-oxo)bis(&mgr;-acetato)diiron(III) core structure in both 1 and 2. A relatively strong molecular ion peak at m/z 865 corresponding to [{Fe(2)O(OAc)(2)L(2)}(ClO(4))](+) in a FAB mass spectrum of 2 suggests the stabilization of the (&mgr;-oxo)bis(&mgr;-acetato)diiron(III) core structure by L(2) in a solution state. The compound 2.DMF.2-PrOH.H(2)O, chemical formula C(44)Cl(2)Fe(2)H(51)N(7)O(16), crystallizes in the monoclinic space group C2/c with a = 22.034(6) ?, b = 12.595(5) ?, c = 20.651(7) ?, beta = 121.49(2) degrees, and Z = 4. The cation has 2-fold symmetry with the bridging oxygen atom on the 2-fold axis: Fe-(&mgr;-O) = 1.782(5) ?, Fe-O-Fe = 123.6(6) degrees, and Fe.Fe = 3.142(3) ?. The diiron(III) core structure of 2 seems to be stabilized by encapsulation of the ligand. Compound 2 is the first example of a discrete (&mgr;-oxo)bis(&mgr;-acetato)diiron(III) complex with a dinucleating ligand.     

Preparation of Metallaiminophosphoranes and Their Reactivity

Treatment of [Cp*(CO) 2 M{P(NHPh)(OMe) 2 }]PF 6 (M = Fe and Ru) with NaNH 2 gives metallaiminophosphoranes, Cp*(CO) 2 M{P(NPh)(OMe) 2 }. The x-ray structures and reactivity of the complexes are reported.     

One‐Pot Stereoselective Synthesis of 2‐Acylaziridines and 2‐Acylpyrrolidines from N‐(Propargylic)hydroxylamines

The stereoselective direct transformation of N‐(propargylic)hydroxylamines into cis‐2‐acylaziridines was achieved by the combined use of AgBF₄ and CuCl. Copper salts were found to promote the transformation of the intermediary 4‐isoxazolines into 2‐acylaziridines and both 3‐aryl‐ and 3‐alkyl‐substituted 2‐acylaziridines could be prepared by using this method. Furthermore, subsequent 1,3‐dipolar cycloaddition of azomethine ylides that were generated in situ from the intermediary 2‐acylaziridines with maleimides was achieved in a stereoselective one‐pot procedure to afford the corresponding 2‐acylpyrrolidines, which consisted of an octahydropyrrolo[3,4‐c]pyrrole skeleton.