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Interval-based Q-analysis: Probability-Theoretical Approach to the Analysis of System’s Structure
P. 45–55.
Translator: E. Levshenkova
In press
In this paper we propose probability-theoretic approach to compare intervals with rigorous bounds which opens a door to more adequate forms of representation and processing of expert estimates uncertainty
In book
Kaufering: b-Quadrat Verlag, 2015.
Smirnov E., Тутубалина А. А., Успехи математических наук 2020 Т. 75 № 6(456) С. 177–178
В работе рассматривается подразбиение комплексов подслов, определенных Кнутсоном и Миллером, на слайд-комплексы; показано, что эти комплексы являются шеллинговыми и гомеоморфны шару или сфере. ...
Added: October 28, 2020
Smirnov E., Тутубалина А. А., / Series math "arxiv.org". 2020. No. 2006.16995.
Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gröbner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the corresponding Schubert polynomial. In 2017 S.Assaf and D.Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and ...
Added: July 6, 2020
Smirnov E., В кн.: Тезисы докладов седьмой школы-конференции "Алгебры Ли, алгебраические группы и теория инвариантов".: Самара: Инсома-пресс, 2018. С. 43–44.
We define simplicial complexes for slide polynomials and show that they are always homeomorphic to balls or spheres. ...
Added: October 7, 2019
Madera A. G., Kandalov P. I., Computer Research and Modeling 2016 Vol. 8 No. 3 P. 501–520
The currently performed mathematical and computer modeling of thermal processes in technical systems is based on an assumption that all the parameters determining thermal processes are fully and unambiguously known and identified (i.e., determined). Meanwhile, experience has shown that parameters determining the thermal processes are of undefined interval-stochastic character, which in turn is responsible for ...
Added: October 29, 2018
Madera A. G., Kandalov P., Applied Mathematical Modelling 2017 No. 42 P. 257–268
As the practice shows, the parameters of electronic systems that determine the thermal processes are not unambiguously known and identified, but they are indeterminate and interval stochastic, which, in its turn, causes the intevally stochastic character of the thermal processes. This article develops a method that allows modelling unsteady interval stochastic thermal processes in an ...
Added: October 29, 2018
Zaev D., Записки научных семинаров ПОМИ РАН 2015 Т. 437 С. 100–130
Пусть X – польское топологическое пространство. P(X) – множество вероятностных борелевских мер на нем, T:X→X – гомеоморфизм. Мы доказываем, что для симплекса Dom⊆P инвариантных относительно T мер значение метрики Канторовича на Dom можно полностью восстановить, зная только ее значения на крайних точках. Этот факт тесно связан со следующим результатом: инвариантный оптимальный транспортный план может быть представлен как смесь инвариантных оптимальных транспортных планов между крайними точками ...
Added: March 9, 2016
Volk D., Kleptsyn V., Nonlinearity 2014 Vol. 27 No. 7 P. 1595–1601
In this paper we consider a class of skew products over transitive subshifts of finite type with interval fibres. For a natural class of 1-parameter families we prove that for all but countably many parameter values the nonwandering set (in particular, the union of all attractors and repellers) has zero measure. As a consequence, the ...
Added: December 22, 2015
Sheldon K. M., Osin E. N., Gordeeva T. O. et al., Personality and Social Psychology Bulletin 2017 Vol. 43 No. 9 P. 1215–1238
We conducted a theoretical and psychometric evaluation of Self-determination theory’s "relative autonomy continuum," an important aspect of the theory whose validity has recently been questioned. We first derived a comprehensive relative autonomy index (C-RAI) containing six subscales and 24 items, by conducting a paired paraphrase content analysis of existing RAI measures. We administered the C-RAI ...
Added: December 21, 2015
Gribanov D., Veselov S. I., Optimization Letters 2016 Vol. 10 No. 6 P. 1169–1177
Let A be an \((m \times n)\) integral matrix, and let \(P=\{ x :A x \le b\}\) be an n-dimensional polytope. The width of P is defined as \( w(P)=min\{ x\in \mathbb {Z}^n{\setminus }\{0\} :max_{x \in P} x^\top u - min_{x \in P} x^\top v \}\). Let \(\varDelta (A)\) and \(\delta (A)\) denote the greatest ...
Added: October 12, 2015
Madera A. G., International Journal of the Analytic Hierarchy Process 2015 Vol. 7 No. 2 P. 337–348
In this article, we propose a method of decision making in multi-criteria problems given an interval uncertainty of the estimates given by the subject in reference to the importance of one criterion over another and various alternatives for each criterion. The method is the development of the deterministic process of the Analytic Hierarchy Process, which ...
Added: August 17, 2015
Degtyarev K. Y., , in: Proceedings of the 10th International Conference on Application of Fuzzy Systems and Soft Computing (ICAFS-2012).: Kaufering: b-Quadrat Verlag, 2012. P. 27–37.
The material of the present paper is grounded on the holist algebraic method (Q-analysis) proposed by English mathematician and physicist R.H.Atkin. At its core, the approach is aimed at both analysis of systems structures (in the form of simplicial complexes K, which is formed by a set of properly adjoined objects called simplexes) and calculation ...
Added: October 31, 2012