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Minimizing Total Weighted Tardiness for Scheduling Equal-Length Jobs on a Single Machine
Automation and Remote Control. 2020. Vol. 81. No. 5. P. 853–868.
Gafarov E., Lazarev A. A., Werner F.
In this paper, we consider the problem of minimizing total weighted tardiness for equal-length jobs with arbitrary release dates on a single machine. This problem is mentioned as a minimal open problem, see http://www2.informatik.uni osnabrueck.de/knust/class/dateien/classes/ein_ma/ein_ma, i.e., its complexity status is still open. The latest results on this problem were presented in the years 2000 and 2005, namely solution algorithms for special cases. We present some properties of this problem and discuss possible ways for future research.
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
Eduard Sopin, Nazarin A., Begishev V. et al., IEEE Transactions on Vehicular Technology 2026 Vol. 75 No. 6 P. 10995–11007
Aimed at rate-greedy applications having extreme requirements for the data rate at the air interface, 5G New Radio (NR) systems may experience problems when the number of user equipment (UE) in the coverage of the cell increases due to limited capacity of the physical downlink control channel (PDCCH).The aim of this study is to explore ...
Added: August 26, 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
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
Makogon A., Oleg Sukhoroslov, , in: Supercomputing. 10th Russian Supercomputing Days, RuSCDays 2024, Moscow, Russia, September 23–24, 2024, Revised Selected Papers, Part I* 1.: Springer, 2025. P. 300–318.
Resource allocation and scheduling algorithms play a crucial role in operation of modern computing clusters. The algorithms used and their settings can significantly impact cluster utilization, application performance, and user experience. This area of research requires the use of simulators to quickly test a hypothesis or conduct comparative testing of different algorithms. This paper presents ...
Added: February 22, 2025
A. Lazarev, N. Pravdivets, Grishin E. et al., , in: 13th Multiconference on Control Problems (MCCP 2020) 6-8 October 2020, Saint Petersburg, RussiaVol. 1864.: IOP Publishing, 2021. Ch. 012057.
Added: December 16, 2022
Lazarev A. A., Lemtyuzhnikova D. V., Tyunyatkin A. A. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 10 P. 2881–2886
This research extends the interpolation approach to approximating the objective function value for the minimization maximum lateness problem. The interpolation approach is defined using a special objective function Lmax(α), which is proven to be continuous and depends only on α transform coefficient. Such a function is proven to be monotonically increasing, and this property is ...
Added: December 5, 2022
Oleg Sukhoroslov, Maxim Gorokhovskii, Roman Ilgovskiy et al., , in: Материалы IV Международного семинара по информационным, вычислительным и управляющим системам для распределенных сред (ICCS-DE 2022).: Иркутск: ИДСТУ СО РАН, 2022. P. 79–96.
Resource management is a critical part of modern large-scale distributed systems and an active area of research. The diversity of systems, workloads and requirements have lead to many domain-specific problem statements, solutions and simulation tools proposed by researchers, which are hard to compare and reuse. In this paper, an overview of related resource management problems ...
Added: October 30, 2022
Mukosey A., Semenov A., Lobachevskii Journal of Mathematics 2022 Vol. 43 P. 873–881
In this paper we address the problem of node allocation for high performance computer systems based on the Angara interconnect with the torus topology. Most allocation strategies for the torus topologies assume redundancy, i.e. for a user job it is possible to allocate more nodes than required. We propose the new node allocation algorithm for ...
Added: October 26, 2022
Mylnikov L., Computers & Industrial Engineering 2022 Vol. 163 Article 107807
The problem investigated in the paper is very timely due to the necessity to increase planning and management efficiency of production systems as new innovation products come to the market on a regular basis. This task may be achieved if we upgrade the formalization level by the description of processes which a production system performs to create a ...
Added: October 5, 2022
Sukhoroslov O. V., The Journal of Supercomputing 2021 No. 77 P. 7989–8012
Workflows that consume and produce large amounts of data are being widely used in modern scientific computing and data processing pipelines. Scheduling of data-intensive workflows requires a careful management of data transfers between tasks, since network contention can significantly impact the workflow execution time. The paper presents and evaluates several scheduling algorithms, data transfer strategies ...
Added: October 29, 2021
Sukhoroslov O. V., Voloshinov V., Smirnov S., , in: Supercomputing. RuSCDays 2020. Communications in Computer and Information ScienceVol. 1331: 6th Russian Supercomputing Days, RuSCDays 2020, Moscow, Russia, September 21–22, 2020, Revised Selected Papers.: Switzerland: Springer, 2020. P. 634–646.
Added: October 29, 2021