Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Terekhov L.S.  

Toward the constructing an analogue of the derivative for interval values

L.S.Terekhov
Shown that the real number as a tool of mathematics does not always correspond to the solution of problems in physics. It turns out that these field measurements more in line with the interval value. Based on the uncertainty relation was proposed an algorithm for calculating ratio of the differences of field measurement data.
Ratio of the differences of field measurements is constructed as the ratio of the factors of the generalized uncertainty relation (UR). Generalization of UR was carried out on the basis of its radar shape differs from that of classical physics, the most common: take into account the ratio of signal to noise power and signal shape. Range of applicability of radar forms UR - the phenomenon of macroscopic scale.
The requirement to minimize a function representing the measurement error, for example, such as frequency, is performed only when the quantization factors of a generalized UR, which leads to a generalized UR quantized interval form.
Range of applicability of generalized UR unlike microphysics is limited by the "proper" quantization parameters during a particular macroscopic physical process. If a microcosm of the quantization can be called a fundamental "layout" parameters of the physical object constants of physics, for example, the energy levels of hydrogen atom, then the macroscopic quantization is the "marking" a transient, bounded by the limits of private macroscopic process. As a result, we can say that the numerical parameters of the physical phenomena in both macro and micro-world are of the nature of interval values. Summarizes the results of testing the approach on the example of numerical integration.
 
 

Abstracts file: LSTerekhov-annotation.doc
Full text file: ДОКЛАД-ЛСТерехов.pdf


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