Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight

The Banach algebra generated by one-dimensional linear singular integral operators with matrix valued piecewise continuous coefficients in the spaceL _p (,) with an arbitrary weight is studied. The contour consists of a finite number of closed curves and open arcs with satisfy the Carleson condition. The contour may have a finite number of points of selfintersection. The symbol calculus in this algebra is the main result of the paper.     

First synthesis of 1,9-dideoxyforskolin from ptychantin A

1,9-Dideoxyforskolin 2 has been synthesized starting from ptychantin A 3.     

About the ratio of the size of a maximum antichain to the size of a maximum level in finite partially ordered sets

LetP be a finite partially ordered set. The lengthl(x) of an elementx ofP is defined by the maximal number of elements, which lie in a chain withx at the top, reduced by one. Letw(P) (d(P)) be the maximal number of elements ofP which have the same length (which form an antichain). Further let . The numbers and as well as all partially ordered sets for which these maxima are attained are determined.     

The erdös-dushnik-miller theorem for topological graphs and orders

A topological graph is a graph G=(V, E) on a topological space V such that the edge set E is a closed subset of the product space V x V. If the graph contains no infinite independent set then, by a well-known theorem of Erdös, Dushnik and Miller, for any infinite set LV, there is a subset LL of the same oardinality |L| = |L| such that the restriction G L is a complete graph. We investigate the question of whether the same conclusion holds if we weaken the hypothesis and assume only that some dense subset AV does not contain an infinite independent set. If the cofinality cf (|L|)>|A|, then there is an L as before, but if cf (|L|)<-|A|, then some additional hypothesis seems to be required. We prove that, if the graph GA is a comparability graph and A is a dense subset, then for any set LV such that cf (|L|)>, there is a subset LL of size |L|=|L| such that GL is complete. The condition cf (|L|)> is needed.Research supported by NSERC grant #A5198.     

Posets isomorphic to their extensions

A standard extension for a poset P is a system Q of lower ends (descending subsets) of P containing all principal ideals of P. An isomorphism between P and Q is called recycling if [Y]Q for all YQ. The existence of such an isomorphism has rather restrictive consequences for the system Q in question. For example, if Q contains all lower ends generated by chains then a recycling isomorphism between P and Q forces Q to be precisely the system of all principal ideals. For certain standard extensions Q, it turns out that every isomorphism between P and Q (if there is any) must be recycling. Our results include the well-known fact that a poset cannot be isomorphic to the system of all lower ends, as well as the fact that a poset is isomorphic to the system of all ideals (i.e., directed lower ends) only if every ideal is principal.     

Fluorinated triazinones from hexafluoroacetone ethoxycarbonylimine

The behavior of hexafluoroacetone ethoxycarbonylimine in cyclocondensation with different binucleophiles of the amidine type, viz., amino derivatives of N- and N,S-heterocycles, was studied. A preparative method for the synthesis of previously unknown annelated 2,2-bis(trifluoromethyl)-1,3,5-triazinones was developed.     

苯胺气相N－烷基化反应研究Ⅱ．苯胺和乙醇常压催化合成N－乙基苯胺的工业应用

苯胺气相Ｎ－烷基化反应研究Ⅱ．苯胺和乙醇常压催化合成Ｎ－乙基苯胺的工业应用陈骏如，李瑞祥，韩银仙，李贤均（四川大学化学系成都６１００６４）Ｎ－乙基苯胺是制造染料、塑料、炸药和医药等许多化工产品的重要中间体，其合成方法过去多采用无机酸催化剂，如Ｈ＿２Ｓ...     

用动力学方法研究8,9-苯并-2-亚甲基-1,4,6-三氧螺[4,4]壬烷的聚合反应机理

根据在自由基引发剂存在下,8,9-苯并-2-亚甲基-1,4,6-三氧螺(4,4)壬烷(Ⅰ)可能存在的竞争反应,推导了动力学方程式。用红外光谱法测定了单体的消失速率和苯酞的生成速率。实验结果与推导动力学方程式相符。进一步证明了单体(Ⅰ)的增长反应由加成聚合和开环—异构化—加成这两个反应组成。这两个反应对总速率的相对贡献与单体浓度有关。得到了共聚物的结构。     

Chiral separation of N-(trans-4-isopropylcyclohexylcarbonyl)-D,L-phenylalanine isomers by high performance liquid chromatography

Summary A high-performance liquid chromatographic method was developed for the chiral separation of a new anti-diabetic agent, N-(trans-4-isopropylcyclohexylcarbonyl)-D-phenylalanine, and its L-enantiomer. The separation was performed on a Sumichiral OA-3300 column. Optimized mobile phase was 0.025 mol.L⁻¹ ammonium acetate in methanol solution. UV detection was at 210 nm. Baseline chiral separation was obtained within 12 minutes. The detection limits are 80 pg for the D-enantiomer and 120 pg for the L-enantiomer. RSD of the method was below 1% (n=5).