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An Effective Method for Studying Extremal Problems [PDF]
Современные информационные технологии и IT-образование, 2022 The homotopy method (or the parameter continuation method) first appeared in the middle of the 19th century and is being actively developed at the present time.
Vladimir V. Nefedov +1 more
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Extremal problems of double stars [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 In a generalized Tur\'an problem, two graphs $H$ and $F$ are given and the question is the maximum number of copies of $H$ in an $F$-free graph of order $n$. In this paper, we study the number of double stars $S_{k,l}$ in triangle-free graphs.
Ervin Győri +2 more
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Extremal problems for multigraphs [PDF]
Journal of Combinatorial Theory, Series B, 2022 An $(n,s,q)$-graph is an $n$-vertex multigraph in which every $s$-set of vertices spans at most $q$ edges. Turán-type questions on the maximum of the sum of the edge multiplicities in such multigraphs have been studied since the 1990s. More recently, Mubayi and Terry [An extremal problem with a transcendental solution, Combinatorics Probability and ...
A. Nicholas Day +2 more
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On Extremal Problems on Multigraphs
Graphs and Combinatorics, 2023 An $(n,s,q)$-graph is an $n$-vertex multigraph in which every $s$-set of vertices spans at most $q$ edges. Erdős initiated the study of maximum number of edges of $(n,s,q)$-graphs, and the extremal problem on multigraphs has been considered since the 1990s.
Ran Gu, Shuaichao Wang
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Extremal length and Dirichlet problem on Klein surfaces [PDF]
Opuscula Mathematica, 2019 The object of this paper is to extend the method of extremal length to Klein surfaces by solving conformally invariant extremal problems on the complex double.
Monica Roşiu
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Extremal problems for GCDs [PDF]
Combinatorics, Probability and Computing, 2021 AbstractWe prove that if $A \subseteq [X,\,2X]$ and $B \subseteq [Y,\,2Y]$ are sets of integers such that gcd (a, b) ⩾ D for at least δ|A||B| pairs (a, b) ε A × B then $|A||B|{ \ll _{\rm{\varepsilon }}}{\delta ^{ - 2 - \varepsilon }}XY/{D^2}$ . This is a new result even when δ = 1.
Green, B, Walker, A
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Energies, 2022 A brief review of the development of ideas on extremal principles in the theory of heat and mass transfer processes (including those in reacting media) is given. The extremal principles of non-equilibrium thermodynamics are critically examined.
Igor Donskoy
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Improving Lagrange Dual Bounds for Quadratic Extremal Problems
Кібернетика та комп'ютерні технології, 2020 Introduction. Due to the fact that quadratic extremal problems are generally NP-hard, various convex relaxations to find bounds for their global extrema are used: Lagrangian relaxation, SDP-relaxation, SOCP-relaxation, LP-relaxation, and others.
Oleg Berezovskyi
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ON SOME SHARP THEOREMS ON DISTANCE FUNCTION IN HARDY TYPE, BERGMAN TYPE AND HERZ TYPE ANALYTIC CLASSES [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2017 We present some new sharp estimates concerning distance function in some new mixed norm and Lizorkin-Triebel type spaces in the unit ball.This leads at the same time to direct generalizations of our recent results on extremal problems in such Bergman ...
R. F. Shamoyan, S.P. Maksakov
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Application network programming method – knapsack problem and it’s modification [PDF]
E3S Web of Conferences, 2023 New method of multi-extremal optimization has been developed - a network programming method, which is based on the possibility to represent a complex function as a superposition of simpler functions. The paper deals with network (dichotomous) programming
Burkova Irina +2 more
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