Darstellung und spektroskopische Charakterisierung von Carboxylatododecaboraten

Preparation and Spectroscopic Characterization of Carboxylatododecaborates The tetrabutylammonium salt (TBA)₂[B₁₂H₁₂]^2? reacts with formic, acetic, cyanoacetic, phenylacetic, propionic, butyric, and thioacetic acid at temperatures between 80 and 150°C forming the carboxylatododecaborates [(RC(O)O)_n? B₁₂H_{12? n}]^2?, n = 1, 2, [CH₃C(O)S? B₁₂H₁₁]^2?. The isolation of the pure compounds is achieved by ion exchange chromatography on diethylaminoethyl cellulose. In case of the dicarboxylatododecaborates beside the 1,7-isomer predominantly the 1,2-isomer, while 1,2-[(OH)C₆H₅CH₂C(O)O? B₁₂H₁₀]^2? is formed exclusively. The alcaline hydrolysis of [RC(O)O? B₁₂H₁₁]^2? and 1,2-[(OH)C₆H₅CH₂C(O)O? B₁₂H₁₀]^2? results in [(OH)? B₁₂H₁₁]^2? and 1,2-[(OH)₂? B₁₂H₁₀]^2?. All compounds are characterized by their ¹¹B-nmr, ¹³C-nmr and IR spectra. The ¹¹B-nmr signals are assigned by a sheme allowing to establish expected spectra.     

源内裂解液相色谱-质谱鉴别人参皂甙砒和拟人参皂甙F11

研究了利用源内碰撞诱导解离（in-source collision—induced dissociation）的高效液相色谱-大气压化学电离质谱（HPLC—APCI／MS）获取人参和西洋参的化学标志物——人参皂甙Rf和拟人参皂甙F11的特征结构信息及鉴别人参和西洋参的方法。在乙腈-水梯度洗脱反相液相色谱及源内碰撞诱导解离条件下，能获得人参皂甙Rf和拟人参皂甙F11的母核离子及去糖基离子的源内碰撞诱导解离谱，从其差别能清楚区分这对同分异构体。本方法对人参皂甙Rf和拟人参皂甙F11的检出限能达到10^-7g柱上样量，简单、快速，单次质谱实验就能鉴别人参和西洋参。     

CoAPO-11分子筛的合成、表征和催化性能： 1-己烯异构化反应

水热法合成了钴取代磷铝酸盐分子筛CoAPO-11，并采用了X射线衍射、扫描电子显微镜、红外光谱、紫外可见光谱以及氮气吸脱附等表征手段对合成的样品进行表征，并在合成的分子筛上进行1-己烯异构化反应评价，并考查了温度和空速对反应的影响。结果表明，在反应温度300℃及空速为2.4h－1CoAPO-11分子筛对1-己烯异构化反应具有较好的催化性能。     

Cyclotomic units over finite fields

Let ζ be a primitivesp-th root of unity for a primep>2, and consider the group Ω(ζ) of cyclotomic units in the ringR(ζ)=ℒ[ζ+ζ^-1]. This paper deals with the image of Ω(ζ) in the unit group ofR(ζ)/qR(ζ), whereq is a prime ≠p. In particular, it obtains criteria for this image to be essentially everything, and a lower bound on the density of primesp (withq fixed) for which it cannot be. These results have a direct bearing on previous work about units in integral group rings for cyclic groups of orderpq. Work supported in part by an operating grant from NSERC (Canada).     

Frobenius-Perron operators and approximation of invariant measures for set-valued dynamical systems

A set-valued dynamical systemF on a Borel spaceX induces a set-valued operatorF onM(X) — the set of probability measures onX. We define arepresentation ofF, each of which induces an explicitly defined selection ofF; and use this to extend the notions of invariant measure and Frobenius-Perron operators to set-valued maps. We also extend a method ofS. Ulam to Markov finite approximations of invariant measures to the set-valued case and show how this leads to the approximation ofT-invariant measures for transformations , whereT corresponds to the closure of the graph of .     

Interactions between octyl-β-D-glucoside and α-amino acids or small peptides

The interactions between octyl--D-glucoside and glycine in water have been investigated by surface tension, viscosity, and density measurements. The results show that the -amino acid causes an unexpected lowering of the critical micellar concentration of octyl--D-glucoside. Such a finding has been interpreted in temss of dipole-dipole interactions between the hydrophilic site of the surfactant and the peptidic cosluttes. From three to seven amino acid molecules have been estimated to be coordinated with each glucoside unity in the micellar state. The research has been extended to glycine oligopeptides and L-lysine. The latter compound has effects similar to those observed with glycine whereas diglycine and triglycine show weaker effects on the micellization process.     

The distribution of square-full integers

Let , wheref(n) is the characteristic function of square-full integers. A formula is proved that can be used to obtain better upper bound estimate for (x). We get (x)=O(x ^5/33+), which improves the exponent 11/72 obtained by R. Blasubramania and K. Ramachandra.     

An indexed set of density bounds on lattice packings

It has long been known that the admissibility of a lattice with respect to a symmetric convex bodyB is equivalent to being a packing lattice for 1/2B. This fact is the basis of the interplay between the classical theory of the arithmetic minima of positive definite quadratic forms, on the one hand, and the dense lattice packing of spheres inR ⁿ , on the other.We give an indexed set of bounds _L (B) a _j , where 0 j n/2, on the lattice packing density ofB. The casej=0 reduces to the aforementioned long-known fact, andj=1 was proved by Elkies, Odlyzko, and Rush, and was used to obtain record high packing densities for various superballs. The new cases make possible the use of smaller primes in the construction of these dense packings.Supported by National Science Foundation grant DMS-9103233.     

McMullen's conditions and some lower bounds for general convex polytopes

We give a lower bound for the number of vertices of a generald-dimensional polytope with a given numberm ofi-faces for eachi = 0,..., d/2 – 1. The tightness of those bounds is proved using McMullen's conditions. Form greater than a small constant, those lower bounds are attained by simpliciali-neighbourly polytopes.     

Über lineare Unabhängigkeit

It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w ₁ + ... + w _m over , wherew ₁,...,w _m are given real numbers. In particular, if this dimension ism, i.e. ifw ₁,...,w _m are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade.