Near-perfect matrices

A 0, 1 matrixA isnear-perfect if the integer hull of the polyhedron {x0: Ax } can be obtained by adding one extra (rank) constraint. We show that in general, such matrices arise as the cliquenode incidence matrices of graphs. We give a colouring-like characterization of the corresponding class of near-perfect graphs which shows that one need only check integrality of a certain linear program for each 0, 1, 2-valued objective function. This in contrast with perfect matrices where it is sufficient to check 0, 1-valued objective functions. We also make the following conjecture: a graph is near-perfect if and only if sequentially lifting any rank inequality associated with a minimally imperfect graph results in the rank inequality for the whole graph. We show that the conjecture is implied by the Strong Perfect Graph Conjecture. (It is also shown to hold for graphs with no stable set of size eleven.) Our results are used to strengthen (and give a new proof of) a theorem of Padberg. This results in a new characterization of minimally imperfect graphs: a graph is minimally imperfect if and only if both the graph and its complement are near-perfect.The research has partially been done when the author visited Mathematic Centrum, CWI, Amsterdam, The Netherlands.     

On quadratic forms of height two and a theorem of Wadsworth

Let and be anisotropic quadratic forms over a field of characteristic not . Their function fields and are said to be equivalent (over ) if and are isotropic. We consider the case where and is divisible by an -fold Pfister form. We determine those forms for which becomes isotropic over if , and provide partial results for . These results imply that if and are equivalent and , then is similar to over . This together with already known results yields that if is of height and degree or , and if , then and are equivalent iff and are isomorphic over .

     

乙烯系单体自由基聚合的阻聚效应──XIX．取代哌啶羟胺和二叔丁基羟胺及其稳定自由基对苯乙烯－丙烯腈共聚合的影响

研究了二叔丁基羟胺（ＤＴＢＨＡ），二叔丁基氮氧自由基（ＤＴＢＮＯ·），２，２，６，６－四甲基－４－羟基哌啶羟胺（ＴＭＨＰＨＡ）和２，２，６，６－四甲基－４－羟基哌啶－１－氧自由基（ＴＭＨＰＯ·）对过氧化苯甲酰（ＢＰＯ）６０℃引发的苯乙烯（Ｍ１）－丙烯腈（Ｍ２）共聚合的阻聚行为．结果表明，这些阻聚剂对Ｓｔ－ＡＮ共聚均表现良好的阻聚行为，其中氮氧自由基优于相应羟胺．同时观察到Ｓｔ—ＡＮ竞聚率的改变，羟胺使ｒ１有所降低，ｒ２略有增大．但相应的氮氧自由基是相反结果．阻聚剂为２００ｐｐｍ时，共聚物中的恒比共聚点由对照实验的０．６１９变化为０．５３３，０．６４５，０．５８９和０．６９８相对于ＤＴＢＨＡ，ＤＴＢＮＯ·，ＴＭＨＰＨＡ和ＴＭＨＰＯ·．     

Structural Features of Solid Phases and Topology of Phase Diagrams

The paper considers model phase diagrams of binary and ternary systems involving transformations (transitions) of phase equilibria. The relationship between the type of structural solidstate transformation and the type of phase diagram is shown. Topological series of phase diagrams of systems with continuous and limited types of solid solutions are considered, including phase diagrams with polymorphic transitions between intermediate solid phases of variable composition.     

Substituent control in the diastereoselectivity of dipolar cycloadditions of nitrones and their Zn(II) complexes with N-arylmaleimides

The π-π stacking interactions between maleimide's and nitrone's aromatic rings during the 1,3-dipolar cycloaddition were assumed to control the exo-endo selectivity of the reaction. The exo-endo ratios change during the reactions until they reach a constant value, which depends on the substituent. Electron-withdrawing groups favour the exo adduct while electron-donating groups favour the endo adduct. The nitrone ZnBr₂ complexes react much more slowly than the free nitrone and the cycloaddition is exo selective in all cases independent of the substituents on the maleimide's aromatic ring. Thermal retrocycloaddition of the cycloadducts produce the corresponding nitrones. The ring opening in the presence of secondary amines did not induce imine formation. endo Adducts were shown for the first time to be the stable paramagnetic compounds.     

β-Tricarbonyl compounds. I. 2,4-Disubstituted 1,3-cyclopentanediones

Summary Stable enolic isomers of 2-aroyl-4-aracyl-1,3-cyclopentanediones such as3 and4 were prepared by condensation of aryl methyl ketones and diethyl maleate using an excess of sodium ethoxide (Aryl=C₆H₅, 4-C₆H₄CH₃, 4-C₆H₄Br and 4-C₆H₄Cl).

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-Tricarbonyl Verbindungen. I. 2,4-Disubstituierte 1,3-Cyclopentandione

Zusammenfassung Stabile Enol-Isomere von 2-Aroyl-4-aracyl-1,3-cyclopentandionen wie3 und4 wurden durch Kondensation von Arylmethylketonen und Diethylmaleat mit einem Überschuß von Natriumethoxid dargestellt (Aryl=C₆H₅, 4-C₆H₄CH₃, 4-C₆H₄Br und 4-C₆H₄Cl).

     

Study of isomorphism in fluorine-containing antimony(III) complexes

The mutual influence of the atoms on the composition of solid fluorine-containing antimony(iii) complexes formed in aqueous solutions in the (MF) _x −(M′F) _n−x −SbF₃ (M, M′=Na, K, Rb, Cs, and NH₄;n=1, 2;x=0 to 2), (KNO₂) _n −(KY) _n −SbF₃ (Y=F, Cl, SO₄;n=0.5, 1), and K₂SbF₅−K₂SbCl₅ systems was investigated by elemental, X-ray, and thermogravimetric analyses and by IR and^121,123Sb NQR spectroscopy. The isomorphism conditions for fluorine-containing antimony(iii) compounds resulting in the formation of complexes NaM′SbF₅·1.5H₂O (M′=K and Rb), K₂SbF₅·1.5H₂O, NaCs₃Sb₄F₁₆·H₂O, KsbF₃Cl, K₂SbF₂Cl₃ with constant compositions, continuous M _x M′_2−x SbF₅ (0<x<2) and limited M _x M′_1−x SbF₄ (0.25<x<0.75; M, M′=K, Rb, Cs, and NH₄) solid solutions or LiF+MSbF₄ (M=Na, K, Rb, and Cs), M₂SbF₅+Cs₂SbF₅ (M=Na and K) and MSbF₄+NaSbF₄ (M=Rb and NH₄) mechanical mixtures were determined. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 103–108, January, 1999.     

15-甲基-双环[10,3,0]十五碳-1(12)-烯-13-酮的晶体结构及分子稳定构象

15-甲基-双环[10,3,0]十五碳-1(12)-烯-13-酮的单晶属空间群P2_1/n,晶胞参数:a=0.4838(1)nm,b=1.3949(2)nm,c=2.1645(4)nm,β=92.07(1)°,Z=4.其中平面五员环呈刚性。另一个含烯十二员环的实际构象与分子力学计算的最稳定构象一致。     

Classification of extensions of torus algebra II

We use extension theory and algebraic methods to give a complete characterization of extensions of torus algebra by stable Cuntz algebras,and prove certain classification theorems of these extension algebras.