A Berry-Esséen bound for student's statistic in the non-I.I.D. case

We establish a Berry-Esséen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esséen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.Research supported by the SFB 343 in Bielefeld.     

Analysis ofAllium sulfur amino acids by HPLC after derivatization

Summary Two pre-column derivatization procedures coupled with reversed phase HPLC have been compared for the analysis ofS-Alk(en)yl0L-cysteine sulfoxides in variousAllium species. In order to establish external standards some (+/-) sulfoxides were synthesized, using a new method to enhance asymmetric synthesis of the diastereoisomers. The first derivatization method is the formation ofo-phthaldialdehyde/tert.-butylthiol derivatives which can be analyzed using UV detection. The second, presently used for amino acid analysis, is the Waters Pico-Tag method, which employs phenylisothiocyanate as derivatization reagent. As the Pico-Tag method was found to be the most efficient for determination ofS-alk(en)yl-L-cysteine sulfoxides it was used to determine the alliin content of various samples of garlic.     

固相配位化学反应研究ⅩⅩⅩⅩⅢ.[Co(NH_3)_4CO_3]Cl、[Co(en)_2CO_3]Cl与NH_4SCN的固相取代反应

本文研究了[Co(NH_3)_4CO_3]Cl、[Co(en)_2CO_3]C1分别与NH_4SCN在100℃发生的固相取代反应.[Co(NH_3)_4CO_3]Cl与NH_4SCN反应生成trans-[Co(NH_3)_4(NCS)_2]~+;[Co(en)_2CO_3]Cl与NH_4SCN反应先生成cis-[Co(en)_2(NCS)_2]~+,然后转化成trans-(Co(en)_2(NCS)_2]~+。采用气相色谱、红外光谱、X粉末衍射和核磁共振法对相应反应体系及其产物进行了测试,推测反应按S_(N~2)机理进行。     

Partial molar volumes and partial molar adiabatic compressibilities of ethylenediamine complexes in water

Densities and ultrasonic propagating velocities of aqueous solutions of ethylenediamine complexes [Co(en)₃]Cl₃, [Cr(en)₃]Cl₃, [Ni(en)₃]Cl₂, and [Cu(en)₂]Cl₂ (en=ethylenediamine), as well as the ligand ethylenediamine were measured at 25°C. The infinite dilution values of the partial molar volume V ₂ ⁰ and partial molar adiabatic compressibility K _s ⁰ were evaluated. The value of K _s ⁰ of the ligand ethylenediamine is nearly zero. The values of V ₂ ⁰ and K _s ⁰ are combined with other interaction parameters, such as the Stokes radii and the viscosity B-coefficients, and their dependece upon the charge number and the stereochemistry of the complex ions is discussed.     

A Berry-Esséen Theorem for Serial Rank Statistics

Berry-Esséen bounds of the optimal O(n-1/2) order are obtained, under the null hypothesis of randomness, for serial linear rank statistics, of the form a1 (Rt)a2(Rt-k). Such statistics play an essential role in distribution-free methods for time-series analysis, where they provide nonparametric analogues to classical (Gaussian) correlogram-based methods. Berry-Esséen inequalities are established under mild conditions on the score-generating functions, allowing for normal (van der Waerden) scores. They extend to the serial case the earlier result of Does (1982, Ann. Probab., 10, 982-991) on (nonserial) linear rank statistics, and to the context of nonparametric rank-based statistics the parametric results of Taniguchi (1991, Higher Order Asymptotics for Time Series Analysis, Springer, New York) on quadratic forms of Gaussian stationary processes.     

Design of single chain magnets through cyanide-bearing six-coordinate complexes

The design and preparation of stable cyanide-bearing six-coordinate complexes of formula [M^III(L)(CN)_x]^{(x + l − m)−} (M = trivalent transition metal ion and L = polydentate blocking ligand) are summarized here. Their use as ligands towards either fully hydrated metal ions or coordinatively unsaturated preformed species, to afford a wide variety of low-dimensional metal assemblies whose nuclearity, dimensionality and magnetic properties can be tuned, is also reviewed. Special emphasis is put on the appropriate choice of the end-cap ligand L whose denticity determines the number of coordinated cyanide groups in the mononuclear precursors. Among the different new spin topologies obtained through this rational synthetic strategy, ferromagnetically coupled 4,2-ribbon like bimetallic chains which exhibit slow magnetic relaxation and hysteresis effects (chain as magnets) are one of the most appealing and constitute the heart of the present contribution.