Synthese und thermische Eigenschaften von molekularen Clusterverbindungen zusammengesetzt aus Elementen der Gruppen 11‐13‐16

Syntheses and Thermal Properties of Cluster Molecules, formed from Groups 11‐13‐16 Elements In the presence of PPh₃, CuX (X = Cl, CH₃COO) or AgOC(O)C₆H₅ and GaCl₃ react in THF with S(SiMe₃)₂ or Se(SiMe₃)₂ to yield [Cu₆Ga₈Cl₄S₁₃(PPh₃)₆] ( 1 ), [Cu₆Ga₈Cl₄Se₁₃(PPh₃)₆] ( 2 ), [Ag₆Ga₈Cl₄S₁₃(PPh₃)₆] ( 4 ) and [Ag₆Ga₈Cl₄Se₁₃(PPh₃)₆] ( 5 ). The use of PⁿPr₂Ph instead of PPh₃ and subsequent layering with n‐hexane leads to the formation of the cluster [Cu₆Ga₈Cl₄Se₁₃(PⁿPr₂Ph)₁₂] ( 3a , 3b ). Reaction of CuCl, GaCl₃ and PⁿPr₃ with Se(SiMe₃)₂ in THF results in the crystallisation of the ionic cluster (HPⁿPr₃)₂[Cu₂Ga₄Cl₄Se₆(PⁿPr₃)₄] ( 6 ). The structures of 1 — 6 were determined by X‐ray single crystal structure analysis. Thermogravimetric measurements of the cluster molecules and powder diffraction patterns of the remaining powders reveal the potential use of them as single source precursor compounds for the synthesis of the related ternary solid state materials.     

Cyclic organohydroborate complexes of metallocenes: VIII. Triphenylsiloxy derivatives of Group IV organometallic systems, Cp2M(OSiPh3)X (M=Ti, Zr, Hf; X=Cl, {(μ-H)2BC8H14})

Group IV metallocene triphenylsiloxy chlorides, Cp₂MCl(OSiPh₃) (1, M=Ti; 2, M=Zr; 3, M=Hf), and cyclic organohydroborates, Cp₂M(OSiPh₃){(μ-H)₂BC₈H₁₄} (4, M=Zr; 5, M=Hf), were synthesized and characterized. The new hafnocene chloride derivative 3 was obtained by treating Cp₂HfCl₂ with triphenylsilanol and piperidine. The 18-electron cyclic organohydroborates 4 and 5 were afforded by reacting 2 and 3 with K[H₂BC₈H₁₄], the potassium salt of the 9-BBN dimer. Reaction of 1 with K[H₂BC₈H₁₄] causes reduction of the Ti(IV) center and produces the well-known Ti(III), 17-electron, paramagnetic dimer [Cp₂Ti(μ-Cl)₂TiCp₂] (6). Single-crystal X-ray diffraction structures of 3, 4, 5, and 6 were determined.     

乙二醛双缩(2-羟基苯胺)(GBHA)在稀土离子分析中的应用

利用乙二醛双缩（2－羟基苯胺）（GBHA）对Ln^3 系离子进行分组分析，同时以GBHA为显色剂，用分光光度法分别测定了Ho^3 ,Yb^3 ,Er^3 ,Dy^3 和Tb^3五种离子，其检出限为10^-6mol/L，工作曲线线性范围为10^-5－－10^-3mol/L。     

丙烯酸酯和甲基丙烯酸酯基团转移共聚研究

研究了三种丙烯酸酯分别和四种甲基丙烯酸酯的基团转移共聚，用１Ｈ ＮＭＲ法测定共聚物组成，扩展的Ｋｅｌｅｎ Ｔｕｄｏｓ法测定竞聚率，结果为γＭＡ＝９２３、γＭＭＡ＝００６；γＥＡ＝１４１５、γＭＭＡ＝００１；γＢＡ＝７５１、γＭＭＡ＝００２；γＭＡ＝１４４１、γＥＭＡ＝００１；γＭＡ＝１３９６、γＢＭＡ＝０２３；γＭＡ＝８６６、γｉ ＢＭＡ＝００８，表明基团转移聚合同阴离子聚合有明显的相似之处．     

Wilson's functional equations on groups

We study properties of solutionsf, g, h C(G) of the functional equation

Degree of approximation of analytic functions by “near-best” polynomial approximants

We study the rate of approximation of a functionfA(K) in the interior of the compact setK by polynomials, that are close to best polynomial approximants on the whole setK. Lower and upper estimates of possible improvement of convergence (depending on the geometry ofK) are obtained.Communicated by Vilmos Totik.     

Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights

A classic 1970 paper of B. Muckenhoupt established necessary and sufficient conditions for weightedL _p convergence of Hermite series, that is, orthogonal expansions corresponding to the Hermite weight. We generalize these to orthogonal expansions for a class of Freud weightsW ²:=e ^–2Q , by first proving a bound for the difference of the orthonormal polynomials of degreen+1 andn–1 of the weightW ². Our identical necessary and sufficient conditions close a slight gap in Muckenhoupt's conditions for the Hermite weight at least forp>1. Moreover, our necessary conditions apply whenQ(x)=|x|, >1 while our sufficient conditions apply at least for =2,4,6,....Communicated by Vilmos Totik.     

A counterexample to subexponential growth of orthogonal polynomials

We construct an example of polynomialsp _n orthonormal with respect to a measure such that the sequencep _n (x) has an exponential lower bound for a pointx in the support of .Communicated by Paul Nevai.     

On Lipschitz property of solutions of functional equations

In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :