Synthesis of the C11-C29 fragment of amphidinolide F

[reaction: see text] An efficient synthesis of the C(11)-C(29) fragment 31 of amphidinolide F has been accomplished via a diastereoselective [3 + 2]-annulation reaction of allylsilane 5 and ethyl glyoxylate to prepare the key tetrahydrofuran 15 and a highly stereoselective methyl ketone aldol reaction to generate the C(11)-C(16) segment.     

Synthesis and structural characterization of five new coordination polymer chain structures using a new,Z-shaped ligand, 2,2′-bis-(4-pyridylethynyl)tolane

Using the new ligand, 2,2-bis-(4-pyridylethynyl)tolane we have synthesized five new coordination polymers: HgBr₂[2,2-bis-(4-pyridylethynyl)tolane] (1), HgI₂[2,2-bis-(4-pyridylethynyl)tolane] (2), Ni(acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane] (3), Zn(acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane] (4), and Cu(hexafluoro acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane]CHCl₃ (5). 2,2-Bis-(4-pyridyl ethynyl)tolane is a rigid ligand with a Z-shape that promotes the formation of zig-zag chains. Compounds 1– 5 were characterized by single crystal X-ray diffraction; and compounds 1– 3 were additionally characterized by IR, elemental analysis, and thermogravimetric analysis. Compound 1 crystallizes in the monoclinic space group C2/c with a = 29.761(3) Å, b = 5.0531(5) Å, c = 16.7823(15) Å, = 104.090(2), V = 2447.9(4) ų, Z = 4. Each mercury is bound to two tolane ligands and two bromine anions, resulting in a tetrahedral coordination environment. Compound 2 crystallizes in the monoclinic space group P2/c, with a = 20.3061(17) Å, b = 5.6303(5) Å, c = 24.5459(19) Å, = 110.338(2), V = 2631.4(4) ų, Z = 4. Here also, each mercury is bound to two tolane ligands and two iodine anions in a tetrahedral coordination environment. The ligand orientation differs in compounds 1 and 2 being trans oriented in 1 and cis oriented in 2. Compound 3 crystallizes in the monoclinic space group P2₁/c with a = 14.5947(14) Å, b = 6.3082(6) Å, c = 18.3939(18) Å, = 112.112(2), V = 1568.9(3) ų, Z = 2. Each nickel is bound to two tolane ligands and two bidentate AcAc anions, resulting in an octahedral coordination environment. Compound 4, which is isostructural with 3, also crystallizes in the monoclinic space group P2₁/c with a = 14.6990(9) Å, b = 6.2724(4) Å, c = 18.6433(11) Å, = 112.8610(10), V = 1583.86(17) ų, Z = 2. Compound 5 crystallizes in the triclinic space group P-1 with a = 6.5487(4) Å, b = 11.6471(7) Å, c = 14.3225(9) Å, = 70.1360(10), = 89.3990(10), = 88.7680(10), V = 1027.18(11) ų, Z = 1. Each copper in 5 is bound to two tolane ligands and two bidentate hfAcAc anions, resulting in an octahedral coordination environment identical to that found in 3 and 4.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

Efficient protiodesilylation of unactivated C(sp3)-SiMe2Ph bonds using tetrabutylammonium fluoride

[reaction: see text] The protiodesilylation of unactivated C(sp3)-SiMe2Ph bonds proceeds efficiently by treatment with tetrabutylammonium fluoride in wet DMF or THF via isolable dimethylsilanol intermediates.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

Coordination dimers constructed from metal(II) halides and the organic ligand 1,2-dimethoxy- 4,5-bis(2-pyridylethynyl)benzene

A series of new coordination compounds has been synthesized using the organic ligand 1,2-dimethoxy-4,5-bis(2-pyridylethynyl)benzene (dmpeb). The compounds all form dimers consisting of two metal cations bridged by two ligand molecules. Charge balance is provided by halide ligands, and the four-coordinate metal centers are distorted from the ideal tetrahedral environment. [CoCl₂(dmpeb)]₂ (1) crystallizes in the monoclinic space group P2₁/n with a = 8.5272(6) Å, b = 18.3653(13) Å, c = 13.3493(9) Å, β = 103.574(2)^°, V = 2032.2(2) ų, Z = 2. [ZnCl₂(dmpeb)]₂ (2) is isostructural to 1 and has the cell parameters a = 8.5495(4) Å, b = 18.4049(8) Å, c = 13.3692(6) Å, β = 103.4460(10)^°, V = 2046.01(16) ų, Z = 2. [ZnBr₂(dmpeb)]₂ (3) is also isostructural to 1 with a = 8.7882(5) Å, b = 18.7260(12) Å, c = 13.3857(8) Å, β = 102.5990(10)^°, V = 2149.8(2) ų, Z = 2. Additionally, the compounds [ZnI₂(dmpeb)]₂ (4, cell parameters: a = 8.9650(5) Å, b = 19.1251(10) Å, c = 13.4160(7) Å, β = 101.1660(10)^°, V = 2256.7(2) ų, Z = 2), [HgCl₂(dmpeb)]₂ (5, cell parameters: a = 8.8457(7) Å, b = 18.4030(15) Å, c = 13.3711(11) Å, β = 104.246(2)^°, V = 2109.7(3) ų, Z = 2), and [HgBr₂(dmpeb)]₂ (6, cell parameters: a = 9.0576(5) Å, b = 18.8634(11) Å, c = 13.4535(8) Å, β = 102.9780(10)^°, V = 2239.9(2) ų, Z = 2) are also isostructural to 1. A seventh dimeric compound, [HgI₂(dmpeb)]₂, not isostructural to the others was also characterized by X-ray crystallography. [HgI₂(dmpeb)]₂ (7) crystallizes in the triclinic space group P-1 with a = 8.8028(5) Å, b = 12.0990(7) Å, c = 12.4082(7) Å, α = 109.7240(10)^°, β = 107.3680(10)^°, γ = 93.0880(10)^°, V = 1169.57(12) ų, Z = 1.