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Комбинаторный анализ схемы размещения различимых частиц по различимым ячейкам без пустых ячеек
Труды Карельского научного центра Российской академии наук. 2020. № 7. С. 120–126.
Enatskaya N.
The problems of the scheme analysis here consist in arranging the procedure
for enumerating the outcomes of the scheme, determining their number, solving
the problem of numbering these outcomes, and their modelling using the results
obtained here through similar studies of the same scheme but without restrictions.
Keywords: distinguishable particles; combination scheme; minimal elements in
cells.
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
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 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
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
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
Enatskaya N., , in: APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’20): Proceedings of the 46th International Conference “Applications of Mathematics in Engineering and Economics”Vol. 2333. Issue 3.: AIP Publishing LLC, 2021. Ch. 2333 P. 150012-1–150012-7.
Added: October 15, 2021
Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2021 № 6 С. 85–90
The article deals with a permutation scheme of size n with r successive series of
increasing elements. I solve the problems of finding the number of outcomes of the
scheme, and design the procedure for their enumeration using r successive schemes
of combinations of an array of different compositions of series of increasing serial
numbers of permutation elements. The ...
Added: October 14, 2021
Enatskaya N., Промышленные АСУ и контроллеры 2018 № 1 С. 58–61
The direct enumeration of the outcomes by the graph method fulfils and their number is find, the probability of outcomes of the scheme in the general combination scheme. The enumeration is solved for outcomes of the scheme and on this base the algorithm of their quick modelling is suggested. ...
Added: February 8, 2018
Enatskaya N., Труды Карельского научного центра Российской академии наук 2016 № 8 С. 136–140
Outputs of thecircuit are enumerated directly by the graph method, their number and probability in the general combinations circuit are determined, the problem of enumeration of outputs is solved and the algorithm of their rapid modeling is suggestrd on this basis. ...
Added: September 19, 2016
Н.Ю.Энатская, Промышленные АСУ и контроллеры 2015 № 8 С. 33–38
We consider procedures to numbers all outcomes of a combination scheme, establish a one-to-one correspondence between the outcomes and its numbers generated in numbering procedure, and give some methods to simulate the outcomes. ...
Added: November 9, 2015
Н. Ю. Энатская, Промышленные АСУ и контроллеры 2015 № 10 С. 28–31
The notion of the range R of outcomes of a combination scheme is Introduced as the maximal difference between the chosen elements. The number of outcomes of the scheme with limited range R not grater t is defined, their enumeration isfulfilled and the problem of numeration (theproblem of finding one-to-one correspondence between the number of ...
Added: November 9, 2015
Энатская Н. Ю., Колчин В. Ф., Колчин А. В., В кн.: Третий российско-финский симпозиум по дискретной математике.: Petrozavodsk: -, 2014. С. 61–63.
В схеме размещения различимых частиц по неразличимым ячейкам задается вид исхода, производится явное перечисление исходов, решаются прямая и обратная задачи их нумерации, находится их вероятностное распределение, приводится рекуррента для чисел исходов схемы и их вероятностей с фиксированными числами непустых ячеек, выводится явная формула общего числа всех исходов схемы, изучается распределение статистики пустых ячеек, разработан численный ...
Added: March 13, 2015