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Congruences for the Apéry numbers modulo p³ [PDF]
Notes on Number Theory and Discrete MathematicsLet {Aₙ'} be the Apéry numbers given by Aₙ'=\Σⁿₖ₌ₒ$binom{n}{k}$²$binom{n+k}{k}$. For any prime p≡3 (mod 4) we show that A'_{(p-1)/2}≡p²/3$binom{(p-3)/2}{(p-3)/4}$² (mod p³). Let {tₙ} be given by t₀=1, t₁=5 and tₙ₊₁=(8n²+12n+5)tₙ-4n²(2n+1)²tₙ₋₁ (n≥1).
Zhi-Hong Sun
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Petrographic structures and Hardy – Weinberg equilibrium
Записки Горного института, 2020 The article is devoted to the most narrative side of modern petrography – the definition, classification and nomenclature of petrographic structures. We suggest a mathematical formalism using the theory of quadratic forms (with a promising extension to ...
Yury L. VOYTEKHOVSKY, Alena A. ZAKHAROVA
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Rings and ideals parametrized by binary n-ic forms [PDF]
, 2010 The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to binary quadratic forms, and found that ideal classes of quadratic rings ...
Wood, Melanie Matchett
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Quantum-inspired optimization for wavelength assignment
Frontiers in Physics, 2023 Problems related to wavelength assignment (WA) in optical communications networks involve allocating transmission wavelengths for known transmission paths between nodes that minimize a certain objective function, for example, the total number of ...
Aleksey S. Boev +7 more
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A QUBO Model for the Traveling Salesman Problem with Time Windows
Algorithms, 2019 This work focuses on expressing the TSP with Time Windows (TSPTW for short) as a quadratic unconstrained binary optimization (QUBO) problem. The time windows impose time constraints that a feasible solution must satisfy. These take the form of inequality
Christos Papalitsas +4 more
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Predictive‐based optimal automatic formation control of mobile vehicles
IET Cyber-systems and Robotics, 2021 In recent years, formation control has received a great deal of attention as one of the most interesting issues in multiple mobile robots systems. In variable formation control systems, multiple mobile vehicles can form an appropriate formation from a ...
Tadanao Zanma +3 more
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Quaternions and binary quadratic forms [PDF]
Proceedings of the American Mathematical Society, 1971 Methods are discussed for studying binary quadratic forms by use of quaternions derived from the ternary quadratic form f = x 2 − y z f = {x^2} - yz .
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Binary matrix factorization on special purpose hardware.
PLoS ONE, 2021 Many fundamental problems in data mining can be reduced to one or more NP-hard combinatorial optimization problems. Recent advances in novel technologies such as quantum and quantum-inspired hardware promise a substantial speedup for solving these ...
Osman Asif Malik +4 more
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Quadratic involutions on binary forms
Michigan Mathematical Journal, 2012 There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using compound transvectant formulae. We also study the associated varieties of forms which are preserved by such involutions.
Abdesselam, Abdelmalek +1 more
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Hilbert polynomials of the algebras of $SL_ 2$-invariants
Karpatsʹkì Matematičnì Publìkacìï, 2018 We consider one of the fundamental problems of classical invariant theory, the research of Hilbert polynomials for an algebra of invariants of Lie group $SL_2$.
N.B. Ilash
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