Analysis of Electrical Circuits with Variable Load Regime Parameters

Пенин, А.

doi:10.1007/978-3-319-28451-4

Cited by 3 publications

(1 citation statement)

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“…In "The Encyclopedia of Mathematics" [4], the special role of geometry is characterized in the following way: "Developments of geometry and its applications, advances in geometric perception of abstract objects in various areas of mathematics and natural science provide solid evidence of the importance of geometry as one of the most profound and fruitful means for cognizing reality" [5,6].…”

Section: Introductionmentioning

confidence: 99%

Measurements and geometry

Mazin

2021

ACTA IMEKO

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The paper is aimed at demonstrating the points of contact between measurements and geometry, which is done by modelling the main elements of the measurement process by the elements of geometry. It is shown that the basic equation for measurements can be established from the expression of projective metric and represents its particular case. Commonly occurring groups of functional transformations of the measured value are listed. Nearly all of them are projective transformations, which have invariants and are useful if greater accuracy of measurements is desired. Some examples are given to demonstrate that real measurement transformations can be dealt with via fractional-linear approximations. It is shown that basic metrological and geometrical categories are related, and a concept of seeing a multitude of physical values as elements of an abstract geometric space is introduced. A system of units can be reasonably used as the basis of this space. Two tensors are introduced in the space. One of them (the affinor) describes the interactions within the physical object, the other (the metric tensor) establishes the summation rule on account of the random nature of components.

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Section: Introductionmentioning

confidence: 99%