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Automorphisms of the total digraph for the ring of square matrices over a field
Linear Algebra and its Applications. 2023. Vol. 666. P. 129-143.
Costara C., A. E. Guterman, A. M. Maksaev, V. V. Promyslov
In this paper, we characterize the automorphisms of the total graph for the ring M_n of matrices of order n≥2 over any field with at least 3 elements. To do this, we apply the technique of maps preserving matrix invariants; in particular, as an intermediate step, we characterize pairs of surjective maps φ_1,φ_2:M_n →M_n such that A+B is singular if and only if φ_1(A)+φ_2(B) is singular.
A.E. Guterman, A.M. Maksaev, V.V. Promyslov, Linear Algebra and its Applications 2022 Vol. 644 P. 1-27
Let F be an algebraically closed field and Mn be the n × n matrix algebra over F. A total graph of the full matrix
algebra is the graph with Mn as vertices, and two distinct matrices A, B are adjacent if and only if A+B is singular. The
characterization of all the automorphisms of the total ...
Added: June 13, 2022
Burman Y. M., Ploskonosov A., Trofimova A., / Cornell University. Series math "arxiv.org". 2011. No. 1109.6625.
We calculate determinants of weighted sums of reflections and of (nested) commutators of reflections. The results obtained generalize the matrix-tree theorem by Kirchhoff and the Pfaffian-hypertree theorem by Massbaum and Vaintrob. ...
Added: November 7, 2012
Burman Y. M., Journal of Algebraic Combinatorics 2019 Vol. 50 No. 4 P. 427-446
The classical matrix-tree theorem discovered by G.Kirchhoff in 1847
expresses the principal minor of the (n x n) Laplace matrix as a
sum of monomials of matrix elements indexed by directed trees with n
vertices. We prove, for any k >= n, a three-parameter family of
identities between degree k polynomials of matrix elements of the
Laplace matrix. For k=n and special values of ...
Added: October 18, 2018
Shirokov D., Computational and Applied Mathematics 2021 Vol. 40 P. 1-29
In this paper, we solve the problem of computing the inverse in Clifford algebras of arbitrary dimension. We present basis-free formulas of different types (explicit and recursive) for the determinant, other characteristic polynomial coefficients, adjugate, and inverse in real Clifford algebras (or geometric algebras) over vector spaces of arbitrary dimension $n$. The formulas involve only ...
Added: July 15, 2021
Shitov Y., Linear Algebra and its Applications 2018 Vol. 554 P. 49-50
We prove that the determinant of an n-by-n 0-1 matrix with at most n + k non-zero entries does not exceed α^k with α ≈ 1.316074. ...
Added: September 26, 2018
Shitov Y., Linear Algebra and its Applications 2018 Vol. 554 P. 49-50
We prove that the determinant of an n x n 01-matrix with at most n+k non-zero entries does not exceed α^k with α=4^(1/3)≈1.316074. ...
Added: January 30, 2019
Guterman A. E., Spiridonov I.A., Linear Algebra and its Applications 2020 Vol. 599 P. 140-155
Let $M_{n}(\mathbb{F})$ denote the set of square matrices of size $n$ over a field $\mathbb{F}$ with characteristics different from two. We say that the map $f: M_{n}(\mathbb{F}) \rightarrow M_{n}(\mathbb{F})$ is additive if $f(A+B) = f(A) + f(B)$ for all $A, B \in M_{n}(\mathbb{F})$. The main goal of this paper is to prove that for $n>2$ ...
Added: November 9, 2020
Logvenkov S. A., Samovol V. S., М. : МЦНМО, 2017
Наряду с разделами линейной алгебры, традиционно включаемыми в подобные учебные издания, в данном учебнике представлены некоторые специальные темы, связанные прежде всего с теорией матриц, в том числе, многочленные матрицы и их преобразования, жордановы матрицы, методы приведения матриц к нормальной жордановой форме и др. В книге также нашли отражение такие вопросы, имеющие важное прикладное значение, как ...
Added: December 31, 2017
Rotmistrov A., Popova P., Социология: методология, методы, математическое моделирование 2016 № 43 С. 63-99
The focus of this article is the methodological aspect of political activism determinants identifying; specifically variants of handling with categorical predictors which hypothetically explain the level of activism. When using regression for explaining the issue, one may transform such predictors into dummy variables. Such a popular solution makes the model bulky and causes troubles with ...
Added: March 15, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
Added: December 22, 2016
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.
We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...
Added: September 29, 2019
Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.
We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...
Added: March 9, 2014
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016
The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...
Added: November 2, 2016
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293
Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...
Added: September 29, 2014
Турунцева М., Астафьева Е., Баева М. et al., Научный вестник ИЭП им. Гайдара.ру (электронный журнал) 2015 № 3(85) С. 3-33
В статье представлены расчеты прогнозных значений различных экономических показателей Российской Федерации во II–III кварталах 2015 г., построенные на основе моделей временных рядов, структурных эконометрических уравнений и моделей, построенных с использованием результатов конъюнктурных опросов. ...
Added: June 18, 2015
Nelyubin A. P., Podinovskiy V. V., Журнал вычислительной математики и математической физики 2023 Т. 63 № 5 С. 717-730
Развит новый подход к оцениванию параметров аппроксимации, при котором удаленность аппроксимирующей функции от заданного конечного множества точек оценивается векторным критерием, компонентами которого являются модули невязок во всех точках. При помощи этого критерия задается отношение предпочтения в удаленности и лучшей считается аппроксимирующая функция, недоминируемая по такому отношению. Изучена аппроксимация для нескольких отношений предпочтения, в том числе ...
Added: July 3, 2023
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291
The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...
Added: December 7, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020