Synthesis of 1-hydroxy-2-(N-substituted) azatwistanes

The reductive amination of bicyclo[3.3.1]nonane-2,6-dione with benzylamine or isopropylamine in the presence of sodium borohydride proceeds with the formation of 1-hydroxy-2-(N-substituted)azatwistanes. When 1-hydroxy-2-benzyl-2-azatwistane is refluxed with acetic anhydride, the ring is opened to give 2-acetoxy-6-acetylbenzylaminobicyclo[3.3.1] nonane. The structures of the synthesized compounds were proved by means of the IR and PMR spectra and the results of elementary analysis.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 940–942, July, 1980.     

High-efficiency parametric oscillation and spectral control in the red spectral region with periodically poled KTiOPO(4)

Narrow-linewidth optical pulses at wavelengths near 630 nm with 2.2-mJ energy were generated with 61% efficiency in a periodically poled KTiOPO(4) parametric oscillator pumped by a frequency-doubled Q -switched Nd:YAG laser. The tuning range was extended to 30 nm by a noncollinear elliptical pumping geometry. We demonstrate that by angular dispersion a noncollinear optical parametric oscillator can be used to control the spectral and spatial characteristics of the output signal beam.     

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).     

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.     

Computation of <Emphasis Type="BoldItalic">p</Emphasis>-variation

A code for computing the p-variation of a piecewise monotone function is introduced. The code is publicly available in the R environment package under the name pvar. The algorithm is based on some properties of the p-variation of a piecewise monotone function proved in this paper. The mathematical results may have their own interest.     

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...     

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.