Strong converse inequality for Kantorovich polynomials

For the Kantorovich polynomial approximationK _n (f, t), 1<p≤∞, we prove that, for somem, This equivalence includes a strong converse inequality of type B.     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

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.     

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.     

On two methods of determining the ellipses and ellipsoids of positioning accuracy of robot manipulators

Summary When analysing the problem of the positioning accuracy of robot manipulators it is important to know how far random deviations of the hand may be from the desired position if the joint positioning errors possess a normal distribution. Two methods of determining the ellipses and ellipsoids of probability concentration are compared. The first of them is based on the standard procedure of the probability calculus. The second approximate method consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid with principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. Examples of application demonstrate that these two methods give very close results.

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Zwei Methoden zur Bestimmung der Ellipsen und Ellipsoide der Positioniergenauigkeit von Handhabungsrobotern

Übersicht Bei der Untersuchung der Positioniergenauigkeit von Handhabungsrobotern ist es wichtig, die Größe zufälliger Abweichungen des Greifers von der erstrebten Position zu kennen, wenn die Lagefehler der Verbindungen eine Normalverteilung besitzen. Es werden zwei Methoden zur Bestimmung der Ellipsen bzw. Ellipsoide der Wahrscheinlichkeitsdichte verglichen. Die erste beruht auf dem Standardverfahren der Wahrscheinlichkeitsrechnung. Die zweite Näherungsmethode besteht darin, daß zunächst das Polygon bzw. Polyeder der Positioniergenauigkeit bestimmt wird und danach die Ellipse bzw. das Ellipsoid mit den Hauptachsen und Momenten zweiter Ordnung wie das Polygon oder Polyeder. Beispiele zeigen, daß beide Methoden zu sehr ähnlichen Ergebnissen führen.

     

Quinaldine derivatives with fluorine-containing substituents and cyanine dyes based on them

Condensation of fluorine-containing anilines with paraldehyde gave quinaldine derivatives with CF₃, CF₃S, and CF₃SO₂ groups in the 6 position, from which carbocyanine, merocyanine, and styryl dyes were synthesized. Fluorine-containing groups lower the basicity of quinaldine by 0.7–2.0 pK_a units and lead to deepening of the color of the dyes.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 76–78, January, 1978.     

Unusual coordination of the in(3+) atom in the decahydrated complex Na3{In[N(CH2COO)3]2}·9H2O

All-Union Scientific-Research Institute of Chemical Reagents and Ultrapure Chemical Substances. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 2, pp. 163–166, March–April, 1991.