Syntheses and structures of two NiIICoIINiII complexes of macrocyclic ligands

Two new linear trinuclear complexes, [Co(NiL¹)₂(SCN)₂] (1) and [Co(NiL²)₂(H₂O)₂](ClO₄)₂?·?2C₂H₅OH (2), have been prepared by using Co(ClO₄)₂?·?6H₂O and two macrocyclic complex ligands NiL¹ and NiL². L¹ and L² are the doubly deprotonated forms of dimethyl 5,6,7,8,15,16-hexahydro-6,7-dioxodibenzo[1,4,8,11]tetraazabicyclo[12.4.0^15,16]13,18-dicarboxylate and dimethyl 5,6,7,8,15,16-hexahydro-15-methyl-6,7-dioxodibenzo[1,4,8,11]tetraazacyclotetradecine-13,18-dicarboxylate, respectively. X-ray single crystal analyses reveal the coordination geometries around Ni(II) in both 1 and 2 are identical and slightly distorted square planar with N₄ donors; all Ni–N bonds in the two complexes are very short. The Co(II) ions are at the centers of the trinuclear complexes and have distorted octahedral coordination geometries of O₄N₂ donors in 1 and an O₆ in 2. π?···?π interactions involving aromatic and non-aromatic π-systems join the trinuclear entities to form 2-D layers in the crystals of 1 and 2.     

Dipheno-silyliminoquinones - A 14π-system

Lithium salts of 2.6-dialkylanilines react with di-tert-butylfluorosilanes to give mono (1-3) - and bis (7, 8)-(2.6-dialkylphenylamino)silanes. Amino-2.6-dimethylphenyl-(di-tert-butylfluoro)silane (1) forms with BuLi a dimeric lithium salt (4) containing an eight-membered (LiFNSi)₂ ring system. Thermally, 4 loses LiF and a bicyclic compound (9) via iminosilenes is obtained. The lithium salt of the bulkier amino-2.6-diisopropylphenyl-(di-tert-butylfluorosilanes) (5-7) thermally loses LiH and iminosilanes (10-12) with a 14π-system are isolated. The reaction mechanisms and crystal structures are discussed.     

Formation of metal-lustrous organic crystals from 2-aryl-1-(4-methoxyphenyl)-5-(5-tricyanoethenyl-2-thienyl)pyrroles

Various 2-aryl-1-(4-methoxyphenyl)-5-(5-tricyanoethenyl-2-thienyl)pyrroles (3) were synthesized. When the 2-aryl group of 3 is phenyl, 4-tolyl, and 4-methoxyphenyl, organic crystals with greenish yellow metallic luster are formed. In contrast, a 2-(4-fluorophenyl) derivative of 3 gives gold-like lustrous crystals. The relation of their crystal structures with the appearance of metallic color is mentioned.     

Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion

Let A = d/dθ denote the generator of the rotation group in the space C(Γ), where Γ denotes the unit circle. We show that the stochastic Cauchy problem

Series representations for some mathematical constants

The authors apply a classical series identity involving the psi (or digamma) function with a view to deriving series representations for a number of known mathematical constants. Several closely-related consequences and results are also considered.     

Synthesis of metal complexes with a novel ethyldioxolane pendant-arm hexaazamacrocyclic ligand

The coordination capability of a pendant-arm azamacrocyclic ligand L with four ethyldioxolane pendant groups towards transition, post-transition and lanthanide metal ions was achieved. In all cases, complexes with a 2:1 metal:ligand molar ratio were obtained. The complexes were characterized by elemental analysis, MS-FAB, IR, conductivity measurements, ¹H and ¹³C NMR spectroscopy. Crystal structures of [CoL][CoBr_0.5(NO₃)_3.5] and [(H₂O)H₂L][Nd(NO₃)₄(H₂O)₃]NO₃·3.5H₂O have been determined. The [CoL]²⁺ cation contains the Co(II) ion endomacrocyclicly coordinated in a distorted octahedral geometry with a N₆ core. The Nd(III) complex presents a mononuclear exomacrocyclic structure with an 11 coordination environment. π,π-Stacking interactions have been observed between the pyridine rings of the protonated ligand [(H₂O)H₂L]²⁺, and the [Nd(NO₃)₄(H₂O)₃]²⁻ anion.     

On Hua-Tuan’s conjecture

Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1 + p, 1 + p + p2 or 1 + p + 2p2 (mod p3). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold.     

二（2-吡啶基）甲二醇·亚氨基二乙酸根合镍（Ⅱ）配合物的合成与表征

合成了一个单核镍配合物Ni（H2bpd）[NH（CH2COO）2]（H2O）2（H2bpd=bis（2-pyridyl）methanediol,二（2-吡啶基）甲二醇）,并用IR和X射线单晶衍射进行结构测定.该化合物属单斜晶系,P2（1）/c空间群,晶胞参数：a=1.031 05（3）,b=1.003 52（3）,c=1.747 270（10）nm,β=106.232（2）°,Z=4,Dc=1.638 g/cm3,μ=1.169 mm-1,F（000）=888,R=0.087 4,wR2=0.172 8.此化合物中金属镍原子与两个配体中的三个氮原子和三个氧原子螯合,形成扭曲的八面体构型.在氢键,π-π堆积和CH-π作用下,化合物形成了3D结构.     

Brauer pairs of Camina p-groups of nilpotence class 2

In this paper, we find a condition that characterizes when two Camina p-groups of nilpotence class 2 form a Brauer pair. Received: 26 September 2008     

The hyperelliptic integrals and π

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A class of hyperelliptic integrals are expressed through hypergeometric functions, like those of Gauss, Lauricella and Appell, namely multiple power series. Whenever they can on their own be reduced to elliptic integrals through an algebraic transformation, we obtain a two-fold representation of the same mathematical object, and then several completely new π determinations through the above special functions and/or Euler integrals. All our π formulae have been successfully tested by means of convenient Mathematica_®'s packages and enter in a wide historical/sound context of π-formulae quite far from being exhausted. Due to their structure, the formulae's practical value does not lie in computing π, but in allowing, through π, a benchmark for computing the involved special functions, particularly those less elementary.

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