49 research outputs found

    Does fault matter?

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    Duress is no excuse

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    Memories of My Father: The Early Years (1918—1934)

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    Serum gangliosides as endogenous immunomodulators

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    Some ergodic theorems over kk-full numbers

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    In 2022, Bergelson and Richter established a new dynamical generalization of the prime number theorem. Later, Loyd showed a disjoint form with the Erdős-Kac theorem. Recently, the author and his coauthors proved some ergodic theorems over squarefree numbers related to these results. In this paper, building on the previous work, we will derive the analogues of Bergelson-Richter\u27s theorem, Erdős-Kac theorem and Loyd\u27s theorem over kk-full numbers for any integer k2k\geq2.10 page

    Abundance of arithmetic progressions in CR\mathcal{CR}-sets

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    H.Furstenberg and E.Glasner proved that for an arbitrary kNk\in\mathbb{N}, any piecewise syndetic set of integers contains a kk-term arithmetic progression and the collection of such progressions is itself piecewise syndetic in Z.\mathbb{Z}. The above result was extended for arbitrary semigroups by V. Bergelson and N. Hindman, using the algebra of the Stone-Čech compactification of discrete semigroups. However, they provided an abundance for various types of large sets. In \cite{DHS}, the first author, Neil Hindman and Dona Strauss introduced two notions of large sets, namely, JJ-set and CC-set. In \cite{BG}, V. Bergelson and D. Glasscock introduced another notion of largeness, which is analogous to the notion of JJ-set, namely CR\mathcal{CR}- set. All these sets contain arithmetic progressions of arbitrary length. In \cite{DG}, the second author and S. Goswami proved that for any JJ-set, ANA\subseteq\mathbb{N}, the collection {(a,b):{a,a+b,a+2b,,a+lb}A}\{(a,b):\,\{a,a+b,a+2b,\ldots,a+lb\}\subset A\} is a JJ-set in (N×N,+)(\mathbb{N\times\mathbb{N}},+). In this article, we prove the same for CR\mathcal{CR}-sets.8 pages. arXiv admin note: substantial text overlap with arXiv:2108.0520

    The binding of the B-chain of ricin to Burkitt lymphoma cells A new approach to ligand-receptor interaction studies

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    AbstractIt is shown that conformational changes of receptor proteins brought about by binding of a ligand induce changes in the lipid environment of the receptor that can be monitored by fluorescent lipid probes. On this basis a new approach to studies of ligand-receptor binding is proposed. Using the interaction of the ricin B-chain with Burkitt lymphoma cells as an example and fluorescent labelled sphingomyelin as a probe, the ligand-induced changes of fluorescence anisotropy were shown to be concentration-dependent and to permit determination of the binding constant and the number of receptor-binding sites. The method was found to be specific and highly sensitive, allowing detection of the action of one RB molecule per cell. Scatchard analysis of the binding of 125I-RB demonstrated the presence on the cell surface of two binding sites with Kd ~ 10−10 and ~ 10−8 M, respectively. Only the high-affinity sites were detected by the fluorescence technique. Saturation of these sites resulted in maximum inhibition of protein synthesis
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