Regio- and stereoselective nucleophilic additions of amines, thiols and aminophosphanes to the CC bond of P,P-diphenyl-P-(2-phenylethynyl)-λ-phosphazenes

Nitrogen and sulfur nucleophiles, such as amines, thiophenols, and aminophosphanes, add to the triple bond of P-ethynyl-λ⁵-phosphazenes to give regio and diastereoselectively P-ethenyl-λ⁵-phosphazenes. An equally selective substitution reaction, occurring by an addition-elimination pathway, on bis(iminophosphoranyl)ethenes has been also achieved.     

一种单分子操纵DNA组蛋白复合物的新方法

介绍了在云母表面一种拉直λ-DNA-组蛋白复合物的新方法.借助原子力显微成像表明,该方法不但对裸λ-DNA的拉直效果较好,而且可以拉直不同浓度的DNA-组蛋白的复合物.利用此方法可以在单分子水平上研究DNA的复制、转录过程以及DNA-蛋白质相互作用.     

Weighted integral inequalities for solutions of the A-harmonic equation

We prove the parametric versions of -weighted integral inequalities for differential forms satisfying the A-harmonic equation. These results can be considered as extensions of the classical inequalities for Sobolev functions.     

Turán's theorem for pseudo-random graphs

The generalized Turán number ex(G,H) of two graphs G and H is the maximum number of edges in a subgraph of G not containing H. When G is the complete graph Km on m vertices, the value of ex(Km,H) is , where o(1)→0 as m→∞, by the Erd?s-Stone-Simonovits theorem.In this paper we give an analogous result for triangle-free graphs H and pseudo-random graphs G. Our concept of pseudo-randomness is inspired by the jumbled graphs introduced by Thomason [A. Thomason, Pseudorandom graphs, in: Random Graphs '85, Poznań, 1985, North-Holland, Amsterdam, 1987, pp. 307-331. MR 89d:05158]. A graph G is (q,β)-bi-jumbled if

     

VERBINDUNGEN MIT DEM 1,3-DIMETHYL-1,3- DIAZA-2-PHOSPHETIDIN-4-ON GRUNDGERüST: SYNTHESE VON 1,3-DIMETHYL-2-PHENYLIMINO- 1,3-DIAZA-2λ4-PHOSPHETIDIN-4-ON-DERIVATEN. RÖNTGENSTRUKTURANALYSE VON 4,6- DIMETHOXY -5,10-DIPHENYL-1,3,7,9- TETRAMETHYL-l,3,5,7,9,10-HEXAAZA- 4λ5,6λ55-DIPHOSPHADISPIRO[3.1.3.1]DECAN-2,8-DION

Abstract

Die Umsetzung einer Reihe von λ³P-Diazaphosphetidinonen, MeNC(:O)N(Me)PY (Y [dbnd] NEt₂: 1, N(CH₂)₄; 2, NPh₂; 3, OMe; 4, N(cyc)₂; 5), mit Phenylazid wird beschrieben. Die dabei primär entstandenen 2-Phenylimino-λ⁴P-diazaphosphetidinone, MeNC(:O)N(Me)P(:NPh)Y sind mit Ausnahme des sterisch anspruchsvollen Dicyclohexylderivats, Y [dbnd] N(cyc)₂; 12, unbeständig und dimerisieren rasch zu den entsprechenden Diazadiphosphetidinen, 7 und 9–11. Aus 7 bildet sich in Lösung unter Abspaltung von MeN[dbnd]C[dbnd]NMe das A4P, λ⁴P,λ⁵P-Diazadiphosphetidin 8. Die neuen Verbindungen 8–12 wurden analytisch, ₁H-, ₁₃C- und ³¹P-NMR-spektroskopisch sowie durch ihre Massenspektren charakterisiert. Darüber hinaus wurde von Verbindung 11 eine Röntgenstrukturanalyse durchgeführt. Das Molekül besitzt kristallographische zweizählige Symmetric. Die Geometrie am Phosphor ist verzerrt trigonal bipyramidal, mit P—N-Bindungslängen 173.9. 179.2 pm (axial) sowie 168.3, 168.7 pm (äquatorial).

Compounds involving the 1,3-dimethyl-1,3-diaza-2-phosphetidin-4-one framework: Synthesis of 1,3- dimethyl-2-phenylimino-l,3-diaza-2λ⁴-phosphetidin-4-one derivatives. X-ray crystal structure analysis of 4,6-dimethoxy-5,10-diphenyl-l,3,7,9-tetramethyl- 1,3,5,7,9,10-hexaaza-4λ⁵,6λ⁵-diphosphadispiro- [3.1.3.l]decan-2,8-dione.

The reactions of a series of λ³P-diazaphosphetidinones MeNC(:O)N(Me)PY (Y [dbnd] NEt₂,; ₁, N(CH₂)₄; 2, NPh2,; 3, OMe; 4, N(cyc)₂; 5), with phenyl azide are described. The initially formed 2-phenylimino-λ⁴P-diazaphosphetidinones, MeNC(:O)N(Me)P(:NPh)Y, are. except for the bulky dicyclohexyl derivative 12, unstable and dimerize rapidly to the corresponding diazadiphosphetidines, 7 and 9–11. The λ⁴P,λ⁴P-diazadiphosphetidine 8 is formed from 7 in solution by elimination of MeN[dbnd]C[dbnd]NMe. The novel compounds 8–12 were characterized by analysis, n.m.r. and mass spectroscopy; additionally, an X-ray crystal structure analysis of 11 was carried out. The molecule possesses crystallographic twofold symmetry. The P-N bond lengths are 173.9, 179.2 pm (axial) and 168.3, 168.7 pm (equatorial).     

N(2,2,0)代数的(∈,∈∨q_(λ,μ))-模糊关联理想

从以下几个方面对N(2,2,0)代数(∈,∈∨q_((λ,μ)))-模糊关联理想进行了详细的研究.首先,给出N(2,2,0)代数广义模糊关联理想概念和点态化(∈,∈∨q_((λ,μ)))-模糊关联理想概念,研究了两者之间的等价关系;其次,给出了(∈,∈∨q_((λ,μ)))-模糊关联理想若干等价刻画;再次,讨论了(∈,∈∨q_((λ,μ)))-模糊关联理想与(∈,∈∨q_((λ,μ)))-模糊理想之间的关系;最后,获得了(∈,∈∨q_((λ,μ)))-模糊关联理想交与并的相关性质.     

Absolutely convergent Fourier series and function classes. II

We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs to one of the Zygmund classes Λ_∗(α) and λ_∗(α) for some 0<α?2. This paper is a natural supplement to our earlier one [F. Móricz, Absolutely convergent Fourier series and function classes, J. Math. Anal. Appl. 324 (2) (2006) 1168-1177] under the same title, and we keep its notations.     

δJordan-李三系上带有权λ的k-阶广义导子

本文研究了δJordan-李三系上带有权λ的k-阶广义导子的相关问题.通过计算,得到了每一个δJordan-李三系上带有权λ的k-阶Jordan三角θ-导子都是一个带有权λ的k-阶θ-导子.在定义下,给出了带有权λ的k-阶Jordan三角θ-导子的另一种等价形式.同时,建立了带有权λ的k-阶广义(θ,ϕ)-导子和Rota-BaxterδJordan-李三系上带有权λ的Rota-Baxter算子的遗传性质,得到了每一个Rota-BaxterδJordan-李代数能看成一个Rota-BaxterδJordan-李三系的结论.     

含参数线性方程组解的判别方法注记

当线性方程组中含有未知参数时,线性方程组解的情况往往需要进行讨论.本文给出了在非齐次线性方程组系数矩阵中含有未知参数且系数行列式等于零的情况下,判定对应参数值下方程组的解是无解还是有无穷多解的两个判定定理.和以前的方法比较,本文提出的讨论方法更直接.     

半群的(∈,∈ ∨q(λ,μ))-模糊k-理想(英文)

本文研究了半群中的广义模糊k-理想和(∈,∈∨q(λ,μ))-模糊k-理想.利用模糊集的截集及模糊集的性质,获得了(∈,∈∨q(λ,μ))-模糊k-理想的等价刻画,广义模糊特征化及广义模糊k-理想直积的基本性质.最后还给出了半群S是左k-诺特的充要条件是对于S的任意广义模糊左k-理想A,Im(A)是[λ,μ]上的良序子集.这些结果有重要的理论价值.