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    On the number of representations of positive integers by quadratic forms as the basis of the space S4(Γ0(47),1) by Ahmet Tekcan, Osman Bızım

    Published 2004-01-01
    “…Moreover, a basis for the space S4(Γ0(47),1) are constructed, and the formulas for r(n;F4), r(n;G4), r(n;F3⊕G1), r(n;F2⊕G2), and r(n;F1⊕G3) are derived.…”
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  15. 55

    Hamiltonian paths passing through matchings in hypercubes with faulty edges by Shenyang Zhao, Fan Wang

    Published 2024-11-01
    “…If all vertices in $ Q_n-F $ have a degree of at least $ 2 $, then there exists a Hamiltonian path joining $ x $ and $ y $ passing through $ M $ in $ Q_n-F $, with the exception of two cases: (1) there exist two neighbors $ v $ and $ t $ of $ x $ (or $ y $) satisfying $ d_{Q_n-F}(v) = 2 $ and $ xt\in M $ (or $ yt\in M $); (2) there exists a path $ xvuy $ of length 3 satisfying $ d_{Q_n-F}(v) = 2 $ and $ uy\in M $ or $ d_{Q_n-F}(u) = 2 $ and $ xv\in M $.…”
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    One-dimensional QCD at finite density and its ’t Hooft-Veneziano limit by O. Borisenko, V. Chelnokov, S. Voloshyn, P. Yefanov

    Published 2025-01-01
    “…In the case of N f degenerate flavors we also calculate 1) the large N limit, 2) the large N f limit and 3) the ’t Hooft-Veneziano limit of all models. …”
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