114,699 research outputs found

    Binding numbers and f-factors of graphs

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    AbstractLet G be a connected graph of order n, a and b be integers such that 1 ≤ a ≤ b and 2 ≤ b, and f: V(G) → {a, a + 1, …, b} be a function such that Σ(f(x); x ∈ V(G)) ≡ 0 (mod 2). We prove the following two results: (i) If the binding number of G is greater than (a + b −1)(n−1)(an−(a + b) + 3) and n ≥(a + b)2a, then G has an f-factor; (ii) If the minimum degree of G is greater than (bn − 2)(a + b), and n ≥(a + b)2a, then G has an f-factor

    A Survey of Best Monotone Degree Conditions for Graph Properties

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    We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.Comment: 25 page

    Many-body Fock sectors in Wick-Cutkosky model

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    In the model where two massive scalar particles interact by the ladder exchanges of massless scalar particles (Wick-Cutkosky model), we study in light-front dynamics the contributions of different Fock sectors (with increasing number of exchanged particles) to full normalization integral and electromagnetic form factor. It turns out that two-body sector always dominates. At small coupling constant α≪1\alpha\ll 1, its contribution is close to 100%. It decreases with increase of α\alpha. For maximal value α=2π\alpha=2\pi, corresponding to the zero bound state mass, two-body sector contributes to the normalization integral 64%, whereas the three-body contribution is 26% and the sum of all higher contributions from four- to infinite-body sectors is 10%. Contributions to the form factor from different Fock sectors fall off faster for asymptotically large Q2Q^2, when the number of particles in the Fock sectors becomes larger. So, asymptotic behavior of the form factor is determined by the two-body Fock sector.Comment: 36 pages, 16 figure

    Follistatin-like 3 (FSTL3) mediated silencing of transforming growth factor (TGF ) signaling is essential for testicular aging and regulating testis size

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    Follistatin-like 3 (FSTL3) is a glycoprotein that binds and inhibits the action of TGFβ ligands such as activin. The roles played by FSTL3 and activin signaling in organ development and homeostasis are not fully understood. The authors show mice deficient in FSTL3 develop markedly enlarged testes that are also delayed in their age-related regression. These FSTL3 knockout mice exhibit increased Sertoli cell numbers, allowing for increased spermatogenesis but otherwise showing normal testicular function. The data show that FSTL3 deletion leads to increased AKT signaling and SIRT1 expression in the testis. This demonstrates a cross-talk between TGFβ ligand and AKT signaling and leads to a potential mechanism for increased cellular survival and antiaging. The findings identify crucial roles for FSTL3 in limiting testis organ size and promoting age-related testicular regression
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