Emanuel Grinberg - outstanding achievements in applied mathematics: radio filters, hulls of tankers, graphs and integrated circuits

Manfred Sneps-Sneppe


The paper is dedicated to the 50th anniversary of the Grinberg theorem. The main works of Emanuel Grinberg (1911-1982) in applied mathematics are described, following the stages of his life path, namely: the design of radio receivers and the calculation of radio filters (1949-1959), hull of tanker calculations (1962-1964), the study of graph theory and the proof of the Grinberg theorem (1968), designing of integrated circuits (1968-1980).

Calculations of radio filters are associated with the expansion of the use of continued fractions for the analysis of linear electric circuits (the Kauer model) and the developing of new tools – the Grinberg brackets (as an extension of the Euler brackets), as well as the application of Chebyshev polynomials. Calculations of tanker hulls go back to the beginning of the theory of splines. The Grinberg theorem is a fundamental result of graph theory: it determines the necessary condition for a planar graph to contain the Hamiltonian cycle, that is, a closed path that passes through each vertex of a given graph exactly once. The Grinberg theorem is a generalization of Euler's problem (1736) about the seven bridges of Koenigsberg. The design of integrated circuits develops the Linvill model for semiconductors and the Ebers-Moll model for mathematical description of transistors and diodes.

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