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## On Asymptotic Series Expansions of Solutions to the Riccati Equation

Mathematical notes. 2021. Vol. 110. No. 1. P. 135-144.

Scalar real Riccati equations with coefficients expanding in convergent power series in a neighborhood of infinity is considered. Continued solutions of such equations are studied. Power geometry methods are used to obtain conditions for expanding these solutions in asymptotic series.

V.S.Samovol, Mathematical notes 2019 Vol. 105 No. 4 P. 592-603

The Riccati equation with coefficients expandable in convergent power series in a neigh- borhood of infinity are considered. Extendable solutions of such equations are studied. Methods of power geometry are used to obtain conditions for convergent series expansions of these solutions. An algorithm for deriving such series is given. ...

Added: April 10, 2019

V.S.Samovol, Doklady Mathematics 2020 Vol. 101 No. 1 P. 49-52

Scalar real Riccati equations with coefficients expandable in convergent power series in a neighborhood
of infinity are considered. Extendable solutions to equations of this kind are studied. Methods of
power geometry are used to obtain conditions for asymptotic series expansions of these solutions. ...

Added: October 10, 2020

V.S. Samovol, Asymptotic Analysis 2019 Vol. 115 P. 223-239

The Riccaty equation with coefficients having power asymptotic in a neighbourhood of infinity is studied. We examine the solutions to these equations and describe their asymptotic form ...

Added: November 24, 2019

Palamarchuk E. S., Automation and Remote Control 2018 Vol. 79 No. 2 P. 289-299

We consider the problem of modeling anomalous diffusions with the Ornstein–Uhlenbeck process with time-varying coefficients. An anomalous diffusion is defined as a process whose mean-squared displacement non-linearly grows in time which is nonlinearly growing in time. We classify diffusions into types (subdiffusion, normal diffusion, or superdiffusion) depending on the parameters of the underlying process. We ...

Added: June 1, 2018

Anastasia V. Parusnikova, Opuscula Mathematica 2014 Vol. 34 No. 3 P. 591-599

The question under consideration is Gevrey summability of formal power series solutions to the third and fifth Painlevй equations near infinity. We consider the fifth Painleve equation in two cases: when αβγδ \neq 0 and when αβγ \neq 0, δ = 0 and the third Painlevé equation when all the parameters of the equation are ...

Added: February 28, 2014

Parusnikova A., Andrey Vasilyev, Journal of Mathematical Sciences 2019 Vol. 241 No. 3 P. 318-326

We examine asymptotic expansions of the third Painlevé transcendents for αδ ≠ 0 and γ = 0 in the neighborhood of infinity in a sector of aperture <2π by the method of dominant balance). We compare intermediate results with results obtained by methods of three-dimensional power geometry. We find possible asymptotics in terms of elliptic ...

Added: October 26, 2019

V. S. Samovol, Qualitative Theory of Dynamical Systems 2022 Vol. 21 Article 47

We consider a nonlinear ordinary differential equation of arbitrary order
with coefficients in the form of power series that converge in a neighborhood
of the origin. The methods created in power geometry in recent
years make it possible to compute formal solutions to that equation in the
form of Dulac series. We describe the corresponding algorithm and prove
a sufficient ...

Added: April 10, 2022

V.S. Samovol, Doklady Mathematics 2018 Vol. 97 No. 3 P. 250-253

A Riccati equation with coefficients expandable into convergent power series in a neighborhood of
infinity is considered. Continuable solutions to equations of this type are studied. Conditions for the expansion
of these solutions into convergent series in a neighborhood of infinity are obtained by methods of power
geometry. ...

Added: July 6, 2018

Afanasiev V., Semion A., Проблемы управления 2021 № 1 С. 24-35

A differential game of several players is considered as follows. One player (attacker) penetrates some space, and several other players (pursuers) appear simultaneously to intercept the attacker. Upon detecting the pursuers, the attacker tries to evade them. The dynamics of each player are described by a time-invariant linear system of a general type with scalar ...

Added: April 6, 2021

V. S. Samovol, Moscow Mathematical Journal 2018 Vol. 18 No. 2 P. 387-402

In the article the solutions of Emden–Fowler-type equa- tions of any order are studied using methods of power geometry. It is shown that these methods can be successfully applied in the study of asymptotic behaviour of the solutions. Also, we find conditions for the existence (nonexistence) of solutions of new types having non- power (power-logarithmic) asymptotics. ...

Added: July 25, 2018

Palamarchuk E. S., Automation and Remote Control 2019 Vol. 80 No. 2 P. 250-261

We consider a control problem over an infinite time horizon with a linear stochastic system with an unstable asymptotically unbounded state matrix. We extend the notion of anti-stability of a matrix to the case of non-exponential anti-stability, and introduce an antistability rate function as a characteristic of the rate of growth for the norm of ...

Added: April 28, 2019

Furmanov K. K., I. M. Nikol'skii, Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Arzhantsev I., Journal of Lie Theory 2000 Vol. 10 No. 2 P. 345-357

Added: July 8, 2014

Litvin Y. V., Игорь Вячеслвович Абрамов, 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

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

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

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

Beklemishev L. D., Анастасия Александровна Оноприенко, Математический сборник 2015 Т. 206 № 9 С. 3-20

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...

Added: March 13, 2016

A.N. Bagrov, Gordin V. A., Ph.L. Bykov, 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

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

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

Decrouez G. G., Peter Hall, 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

Min Namkung, Kwon Younghun, 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

Турунцева М., Астафьева Е., М. Баева 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