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Approximation of the Objective Function of Single-Machine Scheduling Problem
Mathematics. 2024. Vol. 12. No. 5. Article 699.
Alexander Lazarev, Nikolay Pravdivets, Barashov E.
The problem of the approximation of the coefficients of the objective function of a scheduling problem for a single machine is considered. It is necessary to minimize the total weighted completion times of jobs with unknown weight coefficients when a set of problem instances with known optimal schedules is given. It is shown that the approximation problem can be reduced to finding a solution to a system of linear inequalities for weight coefficients. For the case of simultaneous job release times, a method for solving the corresponding system of inequalities has been developed. Based on it, a polynomial algorithm for finding values of weight coefficients that satisfy the given optimal schedules was constructed. The complexity of the algorithm is O(n2(N + n)) operations, where n is the number of jobs and N is the number of given instances with known optimal schedules. The accuracy of the algorithm is estimated by experimentally measuring the function ε(N, n) = 1 ∑n |wj −w0j | , which is n j=1 w0j an indicator of the average modulus of the relative deviation of the found values wj from the true values w0j . An analysis of the results shows a high correlation between the dependence ε(N, n) and a function of the form α(n)/N, where α(n) is a decreasing function of n.
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
ООО "Издательство Юрайт ", 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
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
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
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
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
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
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
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Rozenblum G., Shirokov N. A., Israel Journal of Mathematics 2026 Vol. 274 P. 89–118
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Anton Karamyshev, Artem Krasilov, Evgeny Khorov, IEEE Transactions on Network Science and Engineering 2026 P. 1–18
Modern communication networks shall support mission-critical and real-time applications that demand high data rates, low latency, and ultra-high reliability, which is known as Ultra-reliable Low-latency Communications (URLLC). In URLLC systems, the effective capacity, i.e., the maximum traffic rate at which latency and reliability constraints are satisfied, is a key metric for resource management. Its estimations ...
Added: April 17, 2026
Alexeeva T., Shirokov N. A., St Petersburg Mathematical Journal 2025 Vol. 36 No. 1 P. 25–39
Let L be a chord-arc curve in R3. We introduce a functional class Hr+ω(L) where a modulus of continuity ω satisfies the Dini condition and r≥1. We define neighborhoods of L Ωδ(L)=⋃M∈LBδ(M), Bδ(M)={X∈R3:∥XM∥<δ} and set HarmΩδ(L) for harmonic functions in Ωδ(L). The Theorem 1 states that if f∈Hω+r(L) then there exist functions vδ∈HarmΩδ(L) such that ∣∣f(X)−vδ(M)∣∣≤cfδrω(δ), M∈L, and ∣∣∂αvδ(M)∣∣≤cfω(δ)δ, M∈Ωδ(L), |α|=r+1. The Theorem 2 states that if a function f defined on L satisfies claim of Theorem 1 then f∈Hω+r(L). ...
Added: March 16, 2026
Сильванович О. В., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 Т. 545 С. 179–205
Let ak < bk < ak+1, k ∈ Z, Ik = (ak, bk), Jk = [bk, ak+1]. We assume that |Ik| |Jk|, ak −−−−−→ k→+∞ ∞, ak −−−−−→ k→−∞ −∞ and |Jk| 1 |ak|α , |k| → ∞, α > 0. The distribution of {Jk} satisfies some regularity conditions, E = S k∈Z ...
Added: March 16, 2026
Медведев А. Н., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 № 545 С. 157–167
Let D be a bounded domain on the complex plain C with sufficiently smooth boundary. We denote by Λ αpDq, 0 α 1, the class of analytic functions in D satisfying the α-H¨older condition in D . Each function f P Λ αpDq can be factored as f F I with F ...
Added: March 16, 2026
Шагай М. А., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2023 Т. 527 С. 242–255
Let sk, 1 6 k 6 m, m > 2, be disjoint segments lying in a parallelogram Q. We denote by ℘(z) a doubly periodic Weierstrass function with the fundamental parallelogram Q. Let fk : sk → C be functions, and let f 0 k ∈ L pk (sk), 1 6 k 6 m, 1 ...
Added: February 10, 2024
Sintsova K. A., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2023 Vol. 56 No. 1 P. 46–56
The approximation-theory problem to describe classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, and splines arose over 100 years ago; it still remains topical. Among many problems related to approximation, we consider the two-variable polynomial approximation problem for a function defined on the continuum of an ...
Added: February 10, 2024