This paper is a brief review and development of a part of the plenary report in the Moscow Institute of Physics and Technology. Two existing tools of sub-interval analysis (the sub-interval arithmetic, including incomplete data analysis, and sub-interval images) are reviewed and elements of two...

A forbidden zones theorem, mathematical approach and model are proposed in the present article. In particular, the approach supposes that people decide as if there were some biases of the expectations of measurement data. The article is motivated by the need of a theoretical support for the...

This article reviews and improves the theorems of the existence of restrictions near the boundaries of finite numerical segments and of the probability scale in the presence of non-zero dispersion. The non-zero dispersion may be caused, for example, by the influence of observation noises....

In this post the contents of the book "Introduction to Sub-Interval Analysis and its Applications" are briefly reviewed in the Russian language, for the convenience of Russian and Russian-speaking readers.

The article represents a brief review and development of the plenary report in the Moscow Institute of Physics and Technology. Three existing tools of sub-interval analysis (sub-interval arithmetic, incomplete data analysis and images) are reviewed and elements of two new tools (sub-interval...

В настоящей заметке, для удобства российских и русскоговорящих читателей, на русском языке кратко рассмотрено содержание книги "Введение в Суб-Интервальный...

The proof of the theorem of existence of the ruptures, namely the proof of maximality, is improved. The theorem may be used in economics and explain the well-known problems such as Allais’ paradox. Illustrated examples of ruptures are presented.

An introduction to interval analysis of distributions, as a new direction of interval analysis, is presented, including illustrated examples. New formulas and additional restrictions for intervals of moments, including mean value, are obtained. Among them are Novoselov formulas for moments and...

The theorem of existence of the ruptures in the probability scale was proved in 2010. The theorem is used to analyze and to partially answer to the basic questions of insurance. The question is “To insure or not”. The goal of this paper is to reveal pure mathematical aspects of insurance...

The article raises the question of possible existence of gaps, ruptures in the probability scale and of possible values of these ruptures. The calculations give 1/3 of the standard deviation as the minimal value of these ruptures for a number of standard distributions.