A sharp inequality for the variance with respect to the Ewens sampling formula

Lithuanian Mathematical Journal - We examine the variance of a linear statistic defined on the symmetric group endowed with the Ewens probability. Despite the dependence of the summands, it can be...     

Local probabilities and total variation distance for random permutations

We are concerned with permutations taken uniformly at random from the symmetric group. Firstly, we study the probability of a permutation missing short cycles. Secondly, the result is employed to establish a formula for total variation distance between the process of multiplicities of cycle lengths in a random permutation and a process of independent Poisson random variables. We apply an analytic approach originated in number theory (K. Gyory et al. (Eds.) in Number Theory in Progress, 1999).     

Triphosphane formation from the terminal zirconium phosphinidene complex [Cp2Zr=PDmp(PMe3)] (Dmp=2,6-Mes2C6H3) and crystal structure of DmpP(PPh2)2

The new terminal phosphinidene complex [Cp₂Zr=PDmp(PMe₃)] (Dmp=2,6-Mes₂C₆H₃; 1) was prepared in 81% yield by the reaction of [Li(Et₂O)][P(H)Dmp] with [Cp₂Zr(Me)Cl] in the presence of excess PMe₃. Compound 1 reacts with Ph₂PCl to produce selectively the sterically congested triphosphane DmpP(PPh₂)₂ (2) and [Cp₂ZrCl₂] in high yields. The structure of 2 obtained by X-ray diffraction analysis of a single crystal reveals phosphorus–phosphorus bond lengths of 2.251(2) and 2.234(2) Å and a PPP bond angle of 105.46(6)°.     

On a certain class of infinite products with an application to arithmetical semigroups

This work was done while the second author held a visiting professorship at the University of Paderborn. Financial support has been provided by DFG.     

1,4-Bis(phosphine)-2,5-difluoro-3,6-dihydroxybenzenes and their P-oxides: Syntheses, structures, ligating and electronic properties

Reactions of 1,4-difluoro-2,5-dimethoxybenzene with LDA (1:2) at low temperatures generated organodilithio intermediates; quenching the reaction mixtures with chlorophosphines ClPR₂ produced 1,4-bis(phosphino)-2,5-difluoro-3,6-dimethoxybenzenes 1a (R = Ph) and 1b (R = iPr). Demethylation of 1a–b was accomplished by BBr₃, yielding bis(phosphino)hydroquinones 2a–b. Treating 2a–b with excess hydrogen peroxide produced bis(phosphinyl)hydroquinones 3a–b. The binucleating properties of 2a were established by the formation of a bimetallic nickel complex upon reaction with Ph₂Ni(PMe₃)₂. Electrochemical activity of hydroquinones 2a–b and 3a–b was examined by cyclic voltammetry. In addition, compounds 2a, 3a and 3b were obtained in crystalline form and characterized by single-crystal X-ray diffraction. The influence of the fluorine substituents on the composition of the frontier orbitals of 2a and 3a was examined by computational methods.     

2-Methyl-1,4-naphthoquinones containing 3-[N-(ω-mercaptoalkyl)alkanamide] chains: synthesis, self-assembling, and electrochemical properties

2-Methyl-1,4-naphthoquinone derivatives containing 3-[N-(ω-mercaptoalkyl)alkanamide] chains were synthesized from ω-bromoalkylamine salts of 2-methyl-3-carboxyalkyl-1,4-naphthoquinones in the presence of N,N′-dicyclohexylcarbodiimide at ambient temperature, and then transformed into the corresponding mercapto derivatives. Their self-assembling and electrochemical properties on gold were studied. The influence of an intrachain amide group on the structure and electron transfer properties of self-assembled monolayers were evaluated by comparison with analogous ester and alkyl chain-containing 2-methyl-1,4-naphthoquinones.     

Discrete damage traces from filamentation of Gauss-Bessel pulses

Filamentation of Bessel-Gauss pulses propagating in borosilicate glass is found to produce damage lines extending over hundreds of micrometers and consisting of discrete, equidistant damage spots. These discrete damage traces are explained by self-regeneration of Gauss-Bessel beams during propagation and are potentially applicable in laser microfabrication of transparent materials.     

An unusual equilibrium chlorine atom transfer process and its potential for assessment of steric pressure by bulky aryls

An unusually facile intermolecular chlorine atom transfer process has been discovered between the phospha-Wittig reagents ArP=PMe3 and ArPCl2 (Ar is a sterically hindered aryl group). The atom transfer process is catalyzed by added PMe3. A mechanism is forwarded that is based upon a Me3P/Me3PCl2 couple that allows shuttling of chlorine atoms between ArP groups. This unique transfer process is exploited to evaluate the steric properties of aryl groups via an equilibrium process.