Metal ion complexes with native cyclodextrins. An overview

The review presents a survey of the metal complexing properties of native cyclodextrins (including deprotonation in alkaline medium) and a report on some recent results on composition and stability of metal–cyclodextrin complexes.     

Limit Processes with Independent Increments for the Ewens Sampling Formula

The Ewens sampling formula in population genetics can be viewed as a probability measure on the group of permutations of a finite set of integers. Functional limit theory for processes defined through partial sums of dependent variables with respect to the Ewens sampling formula is developed. Techniques from probabilistic number theory are used to establish necessary and sufficient conditions for weak convergence of the associated dependent process to a process with independent increments. Not many results on the necessity part are known in the literature.     

Zerovalent titanium-sulfur complexes. Novel dithiocarbamato derivatives of Ti(CO)6: [Ti(CO)4(S2CNR2)]-

Oxidation of [Ti(CO)(6)](2-) by thiuram disulfides, (R(2)NCS(2))(2), affords the first isolable mononuclear six-coordinate titanium(0) carbonyls, [Ti(CO)(4)(S(2)CNR(2))](-), which have unusual trigonal prismatic geometries and chemical and spectral properties that are remarkably similar to those of the 18-electron and seven-coordinate anion [Ti(CO)(4)(eta(5)-C(5)H(5))](-).     

Interaction of pyridine‐2,5‐dicarboxylic acid with heavy metal ions in aqueous solutions

Interactions between pyridine‐2,5‐dicarboxylic acid and Zn(II), Ni(II), Pb(II), Cd(II), and Cu(II) were characterized in aqueous solutions (20°C; I = 0.4 (KNO₃)) by means of d.c.‐polarography, spectrophotometry, and ¹H NMR spectroscopy. Polarography was used to determine the concentration of free metal ions in the presence of 10‐fold excess ligand in weakly alkaline solutions, and to determine stability constants for the Zn(II), Cd(II), and Cu(II) complexes with pyridine‐2,5‐dicarboxylic acid. ¹H NMR spectroscopy was used to further characterize complex formation. © 2005 Wiley Periodicals, Inc. 16:285–291, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20123     

A limit theorem for additive functions defined on the symmetric group

We are concerned with the value distribution problem of additive functions defined on the symmetric group endowed with the uniform (Haar) measure. For such a function, normalized by a slowly varying sequence, we establish necessary and sufficient conditions for the weak convergence of its distribution to a limit law.     

Strong convergence on weakly logarithmic combinatorial assemblies

We deal with the random combinatorial structures called assemblies. Instead of the traditional logarithmic condition which assures asymptotic regularity of the number of components of a given order, we assume only lower and upper bounds of this number. Using the author’s analytic approach, we generalize the independent process approximation in the total variation distance of the component structure of an assembly. To evaluate the influence of strongly dependent large components, we obtain estimates of the appropriate conditional probabilities by unconditioned ones. The estimates are applied to examine additive functions defined on a new class of structures, called weakly logarithmic. Some analogs of Major’s and Feller’s theorems which concern almost sure behavior of sums of independent random variables are proved.     

Variance of additive functions defined on random assemblies

We establish an inequality for the variance of an additive function defined on random decomposable structures called assemblies. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set into itself. It is analogous to the Turán–Kubilius inequality for additive number-theoretic functions.     

Total variation approximation for random assemblies and a functional limit theorem

A class of random weakly logarithmic combinatorial assemblies is explored in the paper. We extend total variation approximations for the distribution of component vector of a random structure. That leads to the probabilistic approach suitable to examine the asymptotic value distribution of additive functions defined on such assemblies with the component sizes restricted to a given set. The results generalize several investigations of random Λ-permutations and their extensions to other structures obtained mainly by the Russian mathematicians. Instead of the most popular approach based upon the Tauber type theorems, we develop a comparative asymptotical analysis of coefficients of two Taylor series. Demonstrating possible applications, we obtain necessary and sufficient conditions for the weak convergence of processes defined via partial sums of an additive function to the Brownian motion.