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Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov’s Legacy. A Liber Amicorum to Professor Godunov
Springer, 2020.
Under the general editorship: G. Demidenko, E. Romenski, E. Toro, M. Dumbser
We propose an efficient algorithm based on boundary operator equations
for the numerical simulation of time-dependent waves in 3D. The algorithm employs
the method of difference potentials combined with the (strong) Huygens’ principle
(lacunae of the solution). It can handle nonconforming boundaries on regular structured
grids with no loss of accuracy and offers sublinear computational complexity.
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
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Petropavlovsky S., Turkel E., Journal of Computational Physics 2026 Vol. 558 Article 114880
We propose a method for the numerical computation of the 3D time-harmonic scattering about objects of complex shape. Our approach relies on the method of difference potentials combined with the lacunae-based integration of the Helmholtz equation. The former allows to handle curvilinear boundaries of scattering shapes on regular Cartesian grids with no loss of accuracy. ...
Added: April 6, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 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
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...
Added: December 3, 2025
Bogomolov F. A., Schrandt S., / Series arXiv "math". 2025.
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree. ...
Added: December 1, 2025
Deviatov R., Baek S., / Series arXiv "math". 2025.
The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for the torsion index of half-spin groups, the only remaining case in the calculation of ...
Added: December 1, 2025
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Prokhorov Y., / Series arXiv "math". 2025.
A $\mathbf{Q}$-conic bundle is a contraction $f: X\to Z$ of a three-dimensional algebraic variety $X$ to a surface~$Z$ such that the variety~$X$ has only terminal $\mathbf{Q}$-factorial singularities, the anticanonical divisor $-K_X$ is~$f$-ample, and $\uprho(X/Z)=1$. We provide an algorithm to transform a $\mathbf{Q}$-conic bundle to its standard form. ...
Added: December 1, 2025
Amerik E., Verbitsky M., Soldatenkov A., / Series arXiv "math". 2025.
Wierzba and Wisniewski proved that in dimension 4, every bimeromorphic map of hyperkahler manifolds is represented as a composition of Mukai flops. Hu and Yau conjectured that this result can be generalized to arbitrary dimension. They defined ``Mukai's elementary transformation'' as the blow-up of a subvariety ruled by complex projective spaces, composed with the contraction ...
Added: December 1, 2025
Kuznetsova A., / Series arXiv "math". 2025.
We study birational automorphisms of algebraic varieties of bounded growth, i.e. such that the norms of the inverse images ${(f^n)}^* \colon \mathrm{NS}(X)\to \mathrm{NS}(X)$ of the powers of the automorphism $f\in\mathrm{Bir}(X)$ are bounded above for $n\geqslant 0$. We prove that some power of an infinite order automorphism of a variety $X$ with such property factors either ...
Added: December 1, 2025
Petropavlovsky S., Tsynkov S., Turkel E., Journal of Computational Physics 2024 Vol. 498 Article 112705
We extend the previously developed high-order accurate method for acoustic scattering to electro-magnetic scattering, i.e., from the scalar setting to a vector setting. First, the governing Maxwell’s equations are reduced from their original first-order form to a system of second-order wave equa-tions for the individual Cartesian components of electromagnetic field. In free space, these wave ...
Added: December 12, 2023
Калужский печатный двор, 2021.
conference proceedings ...
Added: October 22, 2021
Petropavlovsky S., Tsynkov S., Turkel E., SIAM Journal of Scientific Computing 2020 Vol. 42 No. 5 P. A3462–A3488
We propose a boundary method for the numerical simulation of time-dependent
waves in three-dimensional (3D) exterior regions. The order of accuracy can be either second or
fourth in both space and time. The method reduces a given initial boundary value problem for
the wave equation to a set of operator equations at the boundary of the original domain. ...
Added: October 31, 2020
Petropavlovsky S., Цынков С. В., Журнал вычислительной математики и математической физики 2020 Т. 60 № 4 С. 725–737
A boundary method for simulation of wave propagation in 3D is proposed. The approach relies on the method of difference potentials and Huygens'principle allowing for an update of the solution only on the boundaries of a scatterer/ ...
Added: April 13, 2020