We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterization is given for the infinite family of triangles with sides in arithmetic progression. We show that there are no triangles with sides in geometric progression. We also show that apart from the square there are no cyclic quadrilaterals whose si...

The atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are two well-studied topological indices, which are useful tools in QSPR and QSAR investigations. In this paper, we first obtain explicit formulae for the expected values of ABC and GA indices in random spiro chains, which are graphs of a class of unbranched polycyclic aromatic hydrocarbons. Based on these formulae, we t...

A real-number to molecular structure mapping is a topological index. It graph invariant method for describing physico-chemical properties of structures specific substances. In that article, We examined pentacene’s chemical composition. The research on the subsequent indices reflected in our paper, we conducted an analysis several including general randic connectivity index, first zagreb sum-con...

The nervous system is the major target of the toxic effect of manganese (Mn) and its compounds. Nowadays, neurological diagnostics is directed towards early detection of symptoms and abortive forms, and the cases of serious damage of the nervous system are no longer reported. The aim of the present study was to assess the effects of manganese on the functions of the nervous system in workers ex...

This paper rst recalls by some examples the damages that the numerical inaccuracy of the oating-point arithmetic can cause during geometric computations, and it intends to explain why damages for geometric computations diier from those met in numerical computations. Then it surveys the various approaches proposed to overcome inaccuracy diiculties; conservative approaches use classical geometric...

Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n × n matrices F. In the case k = n, we exhibit an n 2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries.

The paper discusses the asymptotic behavior of generalizations of the Gauss’s arithmetic-geometric mean, associated with the names Meissel (1875) and Borchardt (1876). The "hapless computer experiment" in the title refers to the fact that the author at an earlier stage thought that one had genuine asymptotic formulae but it is now shown that in general "fluctuations" are present. However, no ve...