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## Classification of invariant algebraic curves and nonexistence of algebraic limit cycles in quadratic systems from family (I) of the Chinese classification

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 2020. Vol. 30. No. 4. P. 2050056-1-2050056-9.

Demina M.V., Valls C.

We give the complete classication of irreducible invariant algebraic curves in family (I) of the

Chinese classication. In addition, we provide a complete and correct proof of the non{existence of

algebraic limit cycles for these equations.

Demina M.V., Valls C., Proceedings of the Royal Society of Edinburgh: Section A 2020 Vol. 150 No. 6 P. 3231-3251

We give the complete classification of irreducible invariant algebraic curves of quadratic Lienard differential equations.
We prove that these equations have irreducible invariant algebraic curves of unbounded degrees, in contrast with what is wrongly claimed in the literature. In addition, we classify all the quadratic Lienard differential equations that admit a Liouvillian first integral. ...

Added: October 22, 2019

Demina M.V., Physics Letters A 2018 Vol. 382 No. 20 P. 1353-1360

The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C^2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing–van der Pol oscillators possess Liouvillian first integrals are obtained. New exact ...

Added: September 29, 2018

Demina M.V., Communications in Contemporary Mathematics 2022 Vol. 24 No. 3 Article 2150007

An explicit expression for the cofactor related to an irreducible invariant
algebraic curve of a polynomial dynamical system in the plane is derived. A
sufficient condition for a polynomial dynamical system in the plane to have a
finite number of irreducible invariant algebraic curves is obtained. All
these results are applied to Lienard dynamical systems $x_t=y$,
$y_t=-f(x)y-g(x)$ with $\deg f<\deg ...

Added: June 15, 2021

Demina M.V., Studies in Applied Mathematics 2023 Vol. 150 No. 3 P. 755-817

We provide the necessary and sufficient conditions of Liouvillian integrability for Liénard differential systems describing nonlinear oscillators with a polynomial damping and a polynomial restoring force. We prove that Liénard differential systems are not Darboux integrable excluding subfamilies with certain restrictions on the degrees of the polynomials arising in the systems. We demonstrate that if ...

Added: May 12, 2023

Demina M.V., Applied Mathematics Letters 2018 Vol. 84 P. 42-48

A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in $\mathbb{C}^2$ is introduced. The structure of irreducible invariant algebraic curves for Li\'{e}nard dynamical systems $x_t=y$, $y_t=-g(x)y-f(x)$ with $\text{deg} f=\text{deg} g+1$ is obtained. It is shown that there exist Li\'{e}nard systems that possess more complicated invariant algebraic curves than it was ...

Added: September 29, 2018

Demina M.V., Kuznetsov N.S., Journal of Dynamical and Control Systems 2021 Vol. 27 No. 2 P. 403-415

The upper bound on the degrees of irreducible Darboux polynomials associated
to the ordinary differential equations $ x_{tt}+\varepsilon {x_t}^2+\eta
x_t+f(x)=0 $ with $ f(x)\in\mathbb{C}[x]\setminus\mathbb{C} $ and $
\varepsilon\neq0 $ is derived. The availability of this bound provides the
solution of the Poincar\'{e} problem. Results on uniqueness and existence of
Darboux polynomials are presented. The problem of Liouvillian integrability
for related dynamical ...

Added: September 23, 2020

Demina M.V., Analysis and Mathematical Physics 2021 Vol. 11 No. 1 P. 25

The problem of Liouvillian integrability for the classical force-free generalized Duffing
oscillators is solved completely. All the cases when the generalized Duffing oscillators
possess Liouvillian first integrals are classified. It is shown that the general solutions
in integrable cases are expressible via elliptic and hyperelliptic functions. The relationship
between the generalized Duffing systems and the Newell–Whitehead–Segel
equation is used to ...

Added: January 4, 2021

Danilov V., Rakhel M., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 179-187

In this paper, we show how to construct an asymptotic representation of the fundamental solution to the Cauchy problem for degenerate linear parabolic equations. ...

Added: June 6, 2021

Malyshev D., Alekseev V., Дискретный анализ и исследование операций 2008 Т. 15 № 1 С. 3-10

Доказывается полиномиальная разрешимость задачи о независимом множестве для бесконечного семейства подмножеств класса планарных графов. ...

Added: August 31, 2012

Lanham : University Press of America, 2012

The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...

Added: February 13, 2013

P. : Université Paris 13 - Paris Sorbonne Cité, 2013

In this workshop we will bring together participants who have solutions for one or more of the following problems: How can mutual understanding be optimized with the help of technology in hospitals where both patients and professionals have varying language skills, cultural backgrounds and cognitive capacities? Can domain ontologies, natural language processing tools, multilingual knowledge-based ...

Added: December 18, 2014

Akopov A. S., Beklaryan L. A., Saghatelyan A. K., Environmental Modelling and Software 2019 Vol. 116 P. 7-25

Urban greenery such as trees can effectively reduce air pollution in a natural and eco-friendly way. However, how to spatially locate and arrange greenery in an optimal way remains as a challenging task. We developed an agent-based model of air pollution dynamics to support the optimal allocation and configuration of tree clusters in a city. The Pareto ...

Added: February 24, 2019

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

Malyshev D., Journal of Applied and Industrial Mathematics 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021

Malyshev D., Discrete Mathematics 2015 Vol. 338 No. 11 P. 1860-1865

We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. ...

Added: April 7, 2014

Nicol R., Chapman S., Vertes P. et al., Journal of Neurophysiology (США) 2012 Vol. 107 No. 5 P. 1421-1430

How do human brain networks react to dynamic changes in the sensory environment? We measured rapid changes in brain network organization in response to brief, discrete, salient auditory stimuli. We estimated network topology and distance parameters in the immediate central response period, <1 s following auditory presentation of standard tones interspersed with occasional deviant tones ...

Added: October 23, 2014

Николаев М. В., Nikitin A. A., Дифференциальные уравнения 2019 Т. 55 № 9 С. 1209-1217

В работе изучается нелинейное интегральное уравнение, возникающее в результате параметрического замыкания третьего пространственного момента в модели У. Дикмана и Р. Лоу. Исследуется вопрос о существовании неподвижной точки интегрального оператора, задаваемого данным уравнением. Доказывается некомпактность полученного оператора. Формулируются условия, при которых уравнение имеет нетривиальное решение. ...

Added: November 7, 2019

Красноярск : ИВМ СО РАН, 2013

Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...

Added: November 18, 2013

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014

Skoptsov K. A., Sheshenin S., Galatenko V. V. et al., International Journal of Applied Mechanics 2016 Vol. 8 No. 2 P. 1650016-01-1650016-18

We present a method for evaluating elastic properties of a composite material produced by molding a resin filled with short elastic fibers. A flow of the filled resin is simulated numerically using a mesh-free method. After that, assuming that spatial distribution and orientation of fibers are not significantly changed during polymerization, effective elastic moduli of ...

Added: May 22, 2016

Decrouez G. G., Robinson A., Risk Analysis: An International Journal 2013 Vol. 33 No. 12 P. 2142-2153

We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, ...

Added: September 29, 2014

Chernyshev S. V., Cherepanov E. A., Pankratiev E. V. et al., Journal of Mathematical Sciences 2005 Vol. 128 No. 6 P. 3487-3495

Added: January 27, 2014

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

Bliznets Ivan, Cygan M., Komosa P. et al., ACM Transactions on Computation Theory 2018 Vol. 10 No. 2 P. 1-32

The H-free Edge Deletion problem asks, for a given graph G and integer k, whether it is possible to delete at most k edges from G to make it H-free—that is, not containing H as an induced subgraph. The H-free Edge Completion problem is defined similarly, but we add edges instead of deleting them. The study of these two problem families has recently been the subject of intensive studies from the point of ...

Added: October 30, 2018