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On the solutions of ordinary differential equations in the form of Dulac series
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 convergence condition for such formal solutions.
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., V. N. Sivkin, Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
N. Belousov, L. Cherepanov, Derkachov S. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Gontsov R., Goryuchkina I., Asymptotic Analysis 2015 Vol. 93 No. 4 P. 311–325
Added: December 28, 2024
Gontsov R., Goryuchkina I., Manuscripta Mathematica 2018 Vol. 156 No. 1 P. 171–185
Added: December 20, 2024
N.V. Gaianov, A.V. Parusnikova, Siberian Mathematical Journal 2024 Vol. 65 No. 5 P. 1062–1073
We derive a special form of the q-difference equations whose solutions exist in the form of a Dulac series. We find the coefficients of the Dulac series from some algebraic difference equations having a polynomial solution under appropriate conditions. An example is given of a q-difference equation which demonstrates the lack of upper bounds for the degrees of ...
Added: September 25, 2024
Karakaya E., Sedat Alataş, Yılmaz B., Energy Efficiency 2020 Vol. 13 No. 7 P. 1457–1472
Recent studies investigating convergence in energy consumption at the sectoral level within a country suggest that aggregate energy consumption could mask considerable differential impacts that might be observed at the sectoral level. This study aims to contribute and complement the existing convergence literature with an attempt to analyze sectoral convergence in energy consumption from the ...
Added: September 23, 2022
Karakaya E., Yılmaz B., Alatas S., Environmental Science and Pollution Research 2019 Vol. 26 No. 16 P. 16682–16694
Much of the existing research analyses on emissions and climate policy are dominantly based on emissions data provided by production-based accounting (PBA) system. However, PBA provides an incomplete picture of driving forces behind these emission changes and impact of global trade on emissions, simply by neglecting the environmental impacts of consumption. To remedy this problem, ...
Added: September 23, 2022
Karakaya E., Sedat Alataş, Yılmaz B., Energy Economics 2019 Vol. 82 P. 135–138
Strazicich and List (Are CO2 Emission Levels Converging among Industrial Countries? Environmental and Resource Economics 2003; 24: 263–271) examine whether CO2 emissions converge among the twenty-one industrial countries from 1960 to 1997. This study replicates their main results and performs a similar analysis on a more recent dataset and a new econometric method. Their findings are confirmed to a large ...
Added: September 23, 2022
Anoshin V.I., Beketova A.D., Parusnikova A., , in: Computer Algebra. 4th International Conference Materials.: M.: Max press, 2021. P. 27–29.
Added: March 30, 2022
Samovol V., 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. ...
Added: September 21, 2021
Smirnykh L. I., Woergoetter A., / Series ECON WPS "Working Papers in Economic Theory and Policy". 2021. No. 3.
In this study we analyze the convergence of GDP per capita from 2000 to2013 (current prices and euro exchange rates) for eight countries (Czech Republic, Slovakia, Slovenia, Hungary, Poland, Estonia, Latvia, and Lithuania) of the European Union (CEE8). Some convergence indicators are also calculated for the CEE8 as a whole. The main purpose of this ...
Added: May 3, 2021