Small ball probabilities for a Wiener process under weighted sup-norms,with an application to the supremum of bessel local times

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup_0<11(t ^–p R(t)) and sup _t 0(e ^–1 R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.     

Bifurcation of controllability regions in a plane by separatrix splitting

For a nonlinear controlled dynamic system of the form where u(t) is a bounded piecewise-continuous control and m u(t) n, the article studies bifurcations (qualitative changes) of controllability (reachability) regions due to merging and subsequent splitting of separatrices of the equilibrium states of auxiliary autonomous systems. Conditions for continuous and discontinuous changes of the controllability (reachability) regions are established. Bifurcations of controllability regions of Duffing equations are considered as an illustration.Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 70–81, 1993.     

A -functional and the rate of convergence of some linear polynomial operators

We show that the -functional

where , is equivalent to the rate of convergence of a certain linear polynomial operator. This operator stems from a Riesz-type summability process of expansion by Legendre polynomials. We use the operator above to obtain a linear polynomial approximation operator with a rate comparable to that of the best polynomial approximation.

     

Alkaloids ofAnabasis aphylla and their cholinergic activities

A comparative study has been made of the anticholinesterase activities of the methiodides and hydrochlorides of anabasine, lupinine, anabasamine, and methyl aphyllinate, which have proved to be reversible inhibitors of two types of cholinesterases.The materials of this paper were presented at the IInd International Symposium on the Chemistry of Natural Compounds, Eskiehir, Turkey, 1996.A. S. Sadykov Institute of Bioorganic Chemistry, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (371) 162 70 71. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 327–330, May–June, 1998.     

Spectrophotometric determination of some aromatic amines

A method for spectrophotometric determination of four aromatic amines is described. The method is based on the reaction between the amine and the colorless Fe(III)-ferrozine complex. The amine reduces iron from Fe(III) to Fe(II) which forms a violet colored complex with ferrozine. The method is suitable for to the determination of 1,4-phenylenediamine, 2,4-diaminotoluene, 8-aminoquinoline and 2-amino-3-hydroxypyridine. The effect of different factors such as; pH, stability of the complex, temperature, ferrozine concentration, Fe(III) concentration and methanol concentration have been studied. The composition of the complex as well as the tolerance amount of other amines have been reported. Maximum absorbance is at 562 nm and Beer's law is obeyed over the ranges 0.17-1.6 ppm for 1,4-phenylenediamine, 0.45-3.7 ppm for 2,4-diaminotoluene, 0.51-3.4 ppm for 8-aminoquinoline and 0.53-4.4 ppm for 2-amino-3-hydroxypyridine. The obtained molar absorbtivities were 4.7x10(4), 2.0x10(4), 1.6x10(4), 1.5x10(3) l mol(-1) cm(-1) respectively.     

Synthesis of substituted 2-amino-1-arylidenaminoimidazoles and 1-arylidenaminoimidazo[1,2-a]imidazoles

A new method is proposed for the preparation of 2-amino-l-arylidenaminoimidazoles, which react with-haloketones to give a series of 1-arylidenamino-3-acylmethyl-2-iminoimidazolines and 1-arylidenaminoimidazo [1, 2-a]imidazoles depending on the conditions.Institute of Chemistry of the Republic of Moldova, 277028 Kishinev.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1209–1213, September, 1996. Original article submitted May 24, 1946.