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The width and integer optimization on simplices with bounded minors of the constraint matrices
Optimization Letters. 2016. Vol. 10. No. 6. P. 1179–1189.
Gribanov D., Chirkov A. Y.
In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some quasi-polynomial-time and polynomial-time algorithms to solve the integer linear optimization problem defined on simplices minus all their integer vertices assuming that some minors of the constraint matrices of the simplices are bounded.
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Glutsyuk A., / Series arXiv "math". 2026.
A planar dual billiard is a planar curve γ equipped with a family (σP)|P∈γ of projective involutions of the projective lines LP tangent to γ at P that fix P. A dual billiard is called rationally integrable, if there exists a rational function R(x,y) of two variables (called first integral) whose restriction to each tangent ...
Added: September 8, 2026
Alexandrov A., Glutsyuk A., Journal of Differential Equations 2026 Vol. 465 Article 114178
The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on ...
Added: September 8, 2026
Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058
A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conjecture, studied by many mathematicians, states that if the billiard boundary has an inner neighborhood foliated by closed caustics, then it is an ellipse. In the paper we study ...
Added: September 8, 2026
Вохминцев И. В., Вестник международных организаций: образование, наука, новая экономика 2026 Т. 21 № 2
The EAEU and the CSTO are Russia’s principal regional international organisations. Understanding, assessing, and analysing the foreign-policy positions of the countries that belong to them is a matter of the state’s national interests. This determines the purpose of the study: to identify the level and the form of cohesion in the voting of EAEU and ...
Added: September 7, 2026
Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438
In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...
Added: September 7, 2026
Ismailov A., Constructive Approximation 2026
The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f is bounded from below by the Motzkin density.
We generalize the bound to polynomials in several variables and almost periodic functions.
We then use these generalizations to extend known results on Taikov’s problem. ...
Added: September 7, 2026
Alshanskaia E., Portnova G., Liaukovich K. et al., Frontiers in Neuroscience 2024 Vol. 18
Added: September 7, 2026
Зуенко Д. О., Trofimova E., Хайдарова И., IEEE Access 2026 Vol. 14 P. 121339–121357
Oil spill segmentation in Synthetic Aperture Radar (SAR) images is limited by noisy annotations in publicly available datasets and by architectural choices that interact with label quality in opposing directions. First, we introduce a manually refined version of the Deep-SAR Oil Spill (SOS) dataset, in which 36.25% of masks are corrected for false positives, missed ...
Added: September 7, 2026
Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401
В работе изучаются перестановки, возникающие при упорядочивании по возрастанию дробных долей произведений элементов фиксированной целочисленной последовательности на вещественный параметр. Исследуется количество различных перестановок, которые можно получить таким образом при изменении этого параметра от нуля до единицы. ...
Added: September 7, 2026
Неверов В. Д., Красавин А. В., Vagov A. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 113 P. 1–6
We develop a neural network approach to solve the self-consistent Bogoliubov-de Gennes equations in strongly disordered s-wave superconductors. The method accurately reproduces inhomogeneous gap distributions and generalizes to system sizes far larger than those used in training. It reduces computational scaling from O(N6 ) to O(N2), enabling quantitative analysis of percolation phenomena and the superconductor-insulator ...
Added: September 5, 2026
Sheshukova M., Durmus A., Khusainov M. et al., Statistics 2026 P. 1–25
In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant stepsize and study the explicit dependence of the convergence rate on the problem dimension d and quantities related to the design matrix. When the number of iterations n is known in advance, ...
Added: September 4, 2026
Proceedings of Machine Learning Research , 2026.
Added: September 4, 2026
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Springer, 2025.
This book celebrates the remarkable contributions of Panos M. Pardalos, offering a comprehensive collection of 20 rigorously peer-reviewed articles that span the breadth of his research interests. From deterministic and stochastic global optimization to combinatorial optimization, this volume provides insights into solving modern applied problems in planning theory, support vector machines, data mining, supply chain ...
Added: April 29, 2025
Spiridonov I., Mathematical notes 2019 Vol. 106 No. 1-2 P. 146 – 150
Added: April 27, 2025
Kaimakov K., Malyshev D., Математические заметки 2025 Т. 117 № 5 С. 672–679
В данной работе рассматривается задача о минимальном остовном дереве (кратко, ЗМОД) на произвольном множестве $n$ точек $d$-мерного пространства в $l_1$-норме. Для этой задачи при каждом фиксированном $d\geq 2$ известен алгоритм сложности $O\big(n\cdot (\log\,n + \log^{r_d}\,n\cdot \log\log\,n)\big)$, где $r_d\in \{0,1,2,4\}$ при $d\in \{2,3,4,5\}$ и $r_d=d$ при $d\geq 6$. Для $d=3$ известно улучшение этого результата до сложности ...
Added: January 18, 2025
Guo Z., Jiang T., Wang G. et al., Journal of Computational and Applied Mathematics 2025 Vol. 463
The introduction of quaternions in the quantum chemistry framework provides new ideas for solving some of the difficulties encountered in traditional approaches and is expected to expand the scope of quantum chemistry research. This paper investigates the eigenvalue problem of a Hermitian quaternion matrix by means of the complex representation of a quaternion matrix. This ...
Added: December 16, 2024
Kirill V. Kaymakov, Dmitry S. Malyshev, Optimization Letters 2025 Vol. 19 P. 1441–1454
The tolerance of an element of a combinatorial optimization problem with respect to a given optimal solution is the maximum change, i.e., decrease or increase, of its cost, such that this solution remains optimal. The bottleneck path problem, for given an edge-capacitated graph, a source, and a target, is to find the max-min value of ...
Added: November 5, 2024
E. A. Morozov, Siberian Electronic Mathematical Reports 2020 Vol. 17 No. n/a P. 1580–1587
We consider an interesting class of combinatorial symmetries of polytopes which we call edge-length preserving combinatorial symmetries. These symmetries not only preserve the combinatorial structure of a polytope but also map each edge of the polytope to an edge of the same length. We prove a simple sucient condition for a polytope to realize all ...
Added: September 27, 2024
Kruglov V., Pochinka O., Современная математика. Фундаментальные направления 2022 Т. 68 № 3 С. 467–487
Gradient-like flows on surfaces have simple dynamics, which inspired many mathematicians
to search for invariants of their topological equivalence. Under assumptions of different generality
on the class of gradient-like flows under consideration, such classical invariants as the Leontovich–
Mayer scheme, the Peixoto graph, the equipped Peixoto graph, the two-color Wang graph, the threecolor Oshemkov–Sharko graph, the Fleitas circular ...
Added: October 17, 2022
Omrani H., Oveysi Z., Emrouznejad A. et al., Journal of the Operational Research Society 2023 Vol. 74 No. 4 P. 1150–1165
Conventional DEA performs like a “black box” and provides no information about sub-processes. In some cases, such as banks, providing services is made up of interactive and interdependent processes. Also, in real world applications, inputs could be shared among these sub-processes. Moreover, due to the characteristics of some variables, such as number of employees, only integer values could be assigned to ...
Added: September 3, 2022
Gribanov D., Zolotykh N., Optimization Letters 2022 Vol. 16 No. 7 P. 1991–2018
Let a polyhedron $P$ be defined by one of the following ways:
\begin{enumerate}
\item[(i)] $P = \{x \in \RR^n \colon A x \leq b\}$, where $A \in \ZZ^{(n+k) \times n}$, $b \in \ZZ^{(n+k)}$ and $\rank A = n$,
\item[(ii)] $P = \{x \in \RR_+^n \colon A x = b\}$, where $A \in \ZZ^{k \times n}$, $b \in \ZZ^{k}$ ...
Added: October 29, 2021
Gribanov D., , in: Mathematical Optimization Theory and Operations Research: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Proceedings.: Cham: Springer, 2021. P. 79–95.
Added: October 29, 2021