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Wigner function dynamics with boundaries expressed as convolution
Journal of Physics A: Mathematical and Theoretical. 2023. Vol. 56. No. 32.
Seidov S.
E. M. Novikova, Mathematical notes 2025 Vol. 118 No. 4 P. 794–810
For each integer nonnegative n, in some Hilbert space, we introduce an integral
transform H_n. It is similar to the well-known Hankel (Fourier–Bessel) transform of nth order due
to the fact that it is related to the Fourier transform and its integral kernel is expressed in terms of
the Bessel function J_n. But, unlike the Hankel transform, intended ...
Added: November 25, 2025
Lotonina K., Fedorenko Sergei Valentinovich, Olshevskaia O., , in: 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), 5-7 Nov. 2025.: IEEE, 2025. P. 1–4.
A novel method of construction of the discrete Fourier transform (DFT) over the finite field has been proposed. The method is based on a polynomial representation of the DFT computation. We choose to minimize the sum of the number of operations (multiplications and additions) over a finite field as the optimization criterion. The presented method ...
Added: November 10, 2025
S S Seidov, D G Bezymiannykh, Journal of Physics A: Mathematical and Theoretical 2025 Vol. 58 No. 2 Article 025301
In the present paper we derive the Wigner current of the particle in a multidimensional billiard - the compact region of space in which the particle moves freely. The calculation is based on proposed by us previously method of imposing boundary conditions by convolution of the free particle Wigner function with some time independent function, ...
Added: October 24, 2024
D. V. Gribanov, Shumilov I. A., D. S. Malyshev, Optimization Letters 2024 Vol. 18 P. 73–103
In this work we consider the problem of computing the (min,+)-convolution of two sequences a and b of lengths n and m, respectively, where n≥m. We assume that a is arbitrary, but b_i=f(i), where f(x):[0,m)→R is a function with one of the following properties: f is linear, f is monotone, f is convex, f is concave, f is piece-wise linear, f is a polynomial function of a fixed degree. To the best of our knowledge, the concave, piece-wise linear and polynomial ...
Added: May 28, 2023
Magnus J. R., Peresetsky A., Frontiers in Psychology 2022 Vol. 13 Article 840180
An explanation of the Dunning–Kruger effect is provided which does not require any psychological explanation, because it is derived as a statistical artifact. This is achieved by specifying a simple statistical model which explicitly takes the (random) boundary constraints into account. The model fits the data almost perfectly ...
Added: March 25, 2022
Magnus J. R., Peresetsky A., / Series TI "Tinbergen Institute Discussion Paper". 2021. No. 2021-092/III.
Added: November 3, 2021
Sergei Valentinovich Fedorenko, IEEE Access 2021 Vol. 9 P. 38673–38686
A novel method for finding roots of polynomials over finite fields has been proposed.
This method is based on the cyclotomic discrete Fourier transform algorithm.
The improvement is achieved by using the normalized cyclic convolutions,
which have a small complexity and allow matrix decomposition,
as well as methods of adapting the truncated normalized cyclic convolutions calculation.
For small values of ...
Added: April 15, 2021
Kurakin D., Социологическое обозрение 2020 Т. 19 № 3 С. 167–231
Inequality is amongst the most fundamental and formidable social problems of modernity. It thus does not come as a surprise that it is a major theme that cuts through multiple areas of sociology. However, the major limitation of most social research on inequality is that its focus is often limited to the redistribution of resources, ...
Added: October 16, 2020
Gordin V. A., Shemendyuk A., Applied Mathematical Modelling 2020 Vol. 88 P. 550–572
Local perturbations of an infinitely long rod travel to infinity. On the contrary, in the case of a finite length of the rod, the perturbations reach its boundary and are reflected. The boundary conditions constructed here for the implicit difference scheme imitate the Cauchy problem and provide almost no reflection. These boundary conditions are non- ...
Added: September 20, 2020
Fedorenko Sergei Valentinovich, IEEE Transactions on Signal Processing 2020 Vol. 68 P. 4813–4823
The new method for the discrete Fourier transform computation over a finite field is introduced.
This method is a nontrivial generalization of the Duhamel-Hollmann algorithm with replacement
of the Toeplitz convolution calculation by the normalized cyclic convolution calculation.
Both algorithms have the smallest multiplicative complexity. ...
Added: September 12, 2020
Jabir J. M., Profeta C., Stochastic Processes and their Applications 2019 Vol. 129 No. 11 P. 4269–4293
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In this note, we consider the construction of a one-dimensional stable Langevin type process confined in the upper half-plane and submitted to diffusive-reflective boundary conditions whenever the particle position hits 0. We show that two main different regimes appear according to the values of the chosen parameters. We then use this study to ...
Added: November 15, 2019
Kurakin D., American Journal of Cultural Sociology 2020 Vol. 8 No. 1 P. 63–89
Cultural sociology must catch up in taking seriously recent initiatives in the sociology of culture and cognition, represented by the works of Omar Lizardo, John Levi Martin, Stephen Vaisey, and others. However, aiming at progress in cultural analysis, these theories are partly driven by an epistemic logic alien to cultural theorizing, making the very concept ...
Added: October 14, 2019
Sergei Valentinovich Fedorenko, IEEE Transactions on Signal Processing 2015 Vol. 63 No. 20 P. 5307–5317
A normalized cyclic convolution is a cyclic convolution when one of its factors is a fixed polynomial. Herein, a novel method for constructing a normalized cyclic convolution over a finite field is introduced. This novel method is the first constructive and best known method for even lengths. This method can be applied for computing discrete ...
Added: February 3, 2018
Vyugin I. V., Solodkova E. V., Shkredov I. D., Mathematical notes 2017 Vol. 101 No. 1 P. 58–70
A new upper bound for the additive energy of the Heilbronn subgroup is found. Several applications to the distribution of Fermat quotients are obtained. ...
Added: May 22, 2017
Lavrinenko Y. S., Morozov I.V., Valuev I. A., Contributions to Plasma Physics 2016 Vol. 56 P. 448–458
The influence of boundary conditions for the classical and wave packet molecular dynamics (MD) simulations of nonideal electron-ion plasma is studied. We start with the classical MD and perform a comprehensive study of convergence of the per-particle potential energy and pressure with the number of particles using both the nearest image method (periodic boundaries) and ...
Added: June 28, 2016
Gordin V. A., Tsymbalov E. A., , in: Numerical Algebra with Applications. Proceedings of Fourth China-Russia Conference.: Rostov-on-Don: Southern Federal University Publishing, 2015. P. 110–113.
Added: March 9, 2016
Yasnitsky L., Вестник Пермского университета. Серия: Математика. Механика. Информатика 2012 № 3(11) С. 73–79
Излагается точка зрения автора на некоторые приоритетные вопросы в области развития и применения метода конечных элементов. Излагается алгоритм применения метода конечных элементов с диагонализированными матрицами разрешающих СЛАУ в задачах термогравитационной конвекции жидкости. Приводится пример применения алгоритма для решения технической проблемы получения высококачественных стальных отливок методом математического моделирования. ...
Added: December 6, 2012
Finkelberg M. V., Braverman A., Advances in Mathematics 2012 No. 230 P. 414–432
This is the second paper of the series, started by Braverman-Finkelberg (2010) which describes a conjectural analogue of the affine Grassmannian for affine Kac-Moody groups (also known as double affine Grassmannian). The current paper is dedicated to describing a conjectural analogue of the convolution diagram for the double affine Grassmannian. In case our group is ...
Added: December 3, 2012