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Approximation for attraction field of irregular celestial bodies using four massive points
Acta Astronautica. 2019. Vol. 157. P. 225–232.
Burov A. A., Guerman A., Nikonova Ekaterina, Nikonov V.
Approximation of the gravitational field of an irregular celestial body by the gravitational attraction field of four massive points is studied here in the framework of K-means method, known from the theory of pattern recognition. Using this approach, the simplified models for gravitational fields of asteroid (1620) Geographos and comet (67P) Churyumov-Gerasimenko are constructed. For asteroid (1620) Geographos, the proposed model is compared with the previously used one when this asteroid is represented by four cotangent spheres with co-planar centers.
Priority areas:
mathematics
Language:
English
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Ozhegov R., Махлуф М., Goltsman G. et al., Инженерная физика 2026 № 8 С. 27–39
This paper investigates the theoretical limits of object detection within isotropic scattering media using single-photon lidar. Within a simplified model, we derive the fundamental relationship between the maximum attainable detection range and the required photon count per pulse. Two distinct limiting regimes are analyzed: the ballistic photon regime, which maintains high spatial resolution but necessitates ...
Added: October 8, 2026
Didenkulova E., Chugunov V., Didenkulova I., Wave Motion 2026 Vol. 147 Article 103787
This work presents a new analytical solution of the shallow water theory for cylindrical propagation of long tsunami-like waves in the basin of variable depth. Considered model cases are related to tsunami wave propagation from an asteroid fallen into the sea, or from underwater volcanic eruptions. The corresponding bottom geometries represent radially symmetric obstacles such ...
Added: October 8, 2026
Flamarion M., Didenkulova E., Pelinovsky E., Physics Letters A 2026 Vol. 598 Article 132218
In this letter, bipolar solitary wave interactions in the Schamel equation are revisited numerically. Two simulation settings are considered: repeated collisions in a periodic domain, and the interaction of a positive solitary wave with a train of negative polarity solitary waves of equal amplitude. In the first case, when the amplitudes are comparable, the larger ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Isaev T. F., Шаров А. Н., Журнал вычислительной математики и математической физики 2026 Т. 66 № 1 С. 83–93
Исследуются свойства оптических покрытий на основе использования упрощенного симулятора ошибок в толщинах слоев покрытий при их напылении. Обосновывается возможность такого подхода. Выводятся аналитические оценки среднеквадратичного значения нормы вектора ошибок и степени коррелированности ошибок в толщинах слоев покрытия. Изучается зависимость среднеквадратичного значения нормы вектора ошибок и свойств покрытия от уровня случайных ошибок в слоях. ...
Added: October 5, 2026
Осипова А. М., Пилипенко С. В., Novikov D. I. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 063522
We investigate the prospects for observing a specific spectral distortion of the cosmic microwave
background, which occurs due to the anisotropy of the radiation when it is scattered by hot plasma of
galaxy clusters. Detection of this anisotropic Sunyaev-Zel’dovich effect would enable an independent
measurement of the CMB anisotropy multipoles with l 1⁄4 1, 2, 3, allow the ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Gribova N. I., Osmanov S. V., Lyashko S. D. et al., Journal of Magnetism and Magnetic Materials 2025 No. 614 P. 1–8
Here we demonstrate nanometer thick iron garnet films with high specific Faraday rotation suitable for
the magneto-optical applications. Bismuth-substituted iron garnet films of compositions Bi1Y2Fe5O12 and
Bi1Tm2Fe5O12 deposited on gadolinium gallium garnet substrate are fabricated and characterized. Their
thicknesses range from 2 to 10 nm, which corresponds to just a few crystal lattice constants. Spectacularly,
Faraday rotation of the ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Seleznev G., Fominov Yakov V., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 7 Article 074505
Dirty superconducting films with magnetic impurities can exhibit nontrivial behavior in a magnetic field that
polarizes the impurity spins. As predicted by Kharitonov and Feigelman (KF) [JETP Lett. 82, 421 (2005)],
this polarization reduces the exchange scattering rate. Consequently, a parallel magnetic field can enhance
the critical temperature Tc when magnetic-field pair breaking is weak, as realized for ...
Added: October 2, 2026
Zhukov A., Chen F., Zeng Y. et al., Nanoscale 2026 Vol. 18 No. 36 P. 19223–19253
Colloidal semiconductor nanocrystals have emerged as promising materials for next-generation light-emitting diodes (LEDs) owing to their solution processability, tunable emission wavelengths, narrow emission linewidths, and high photoluminescence quantum yields. Among them, anisotropic nanocrystals, including one-dimensional nanorods (NRs) and two-dimensional nanoplatelets (NPLs), offer additional opportunities for controlling transition dipole moment orientation and light out-coupling efficiency. These ...
Added: October 2, 2026
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
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
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026