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Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which is inspired by the Hindley-Rosen technique for confluence.
Accattoli, Beniamino +2 more
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A method of factoring and the factorization of đčâ [PDF]
The continued fraction method for factoring integers, which was introduced by D. H. Lehmer and R. E. Powers, is discussed along with its computer implementation. The power of the method is demonstrated by the factorization of the seventh Fermat number
Morrison, Michael A., Brillhart, John
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Golnaz Badkobeh +7 more
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Complete-factors and f-factors
Let \(G\) be a graph and \(F\) a spanning subgraph of \(G\) with at least two components and with all components complete. Let \(f\) be an integer-valued function defined on \(V(G)\) with \(\sum_{x \in V(G)} f(x)\) even. If for each component \(C\) of \(F\), \(G - V(C)\) has an \(f\)-factor (that is, a spanning subgraph \(H\) in which \(\deg_H(x) = f(x)
Hikoe Enomoto, Taro Tokuda
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We introduce and investigate the category of factorization of a multiplicative, commutative, cancellative, pre-ordered monoid $A$, which we denote $\mathcal{F}(A)$. The objects of $\mathcal{F}(A)$ are factorizations of elements of $A$, and the morphisms in $\mathcal{F}(A)$ encode combinatorial similarities and differences between the factorizations. We
Brandon Goodell, Sean Sather-Wagstaff
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The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually.
Yingzhou Li +4 more
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Abstract We introduce a new approach to (deterministic) integer factorisation, which could be described in the cryptographically fashionable term of âfactoring with hintsâ: we prove that, for any Ï” > 0, given the knowledge of the factorisations of O
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The Biopsychosocial Factor [PDF]
medical practice; rather in significant part it is engaged in special interest advocacy, pursuing and preserving social powerâ [ 5 , p. 11]. How could Engel and Holman identify the dangers of special interest groups, as they are sadly known these days [6] , in the 1970s is astonishing. Biomedical reductionism is the key to the success of pharmaceutical
FAVA, GIOVANNI ANDREA +3 more
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ABSTRACT Primary lung carcinomas and bronchial carcinoid tumors (BC) are very rare malignancies in childhood. While typical BC and mucoepidermoid carcinomas are mostly lowâgrade, localized tumors with a more favorable prognosis than in adults, necessitating avoidance of overtreatment, adenocarcinomas of the lung are often diagnosed at advanced disease ...
Michael Abele +19 more
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