منابع مشابه
Improving the Chen and Chen Result for Odd Perfect Numbers
If qα is the Euler factor of an odd perfect number N, then we prove that its so-called index σ(N/qα) � qα ≥ 32 × 5× 7 = 315. It follows that for any odd perfect number, the ratio of the non-Euler part to the Euler part is greater than 32 × 5× 7/2.
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Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We provide improved lower bounds for the rank of a symmetric tensor (i.e., a homogeneous polynomial) obtained by considering the singularities of the hypersurface defined by the polynomial. We obtain normal forms for po...
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Bajijiasu is an oligosaccharide extracted from the traditional Chinese medicine Radix Morindae Officinalis (Morinda officinalis F.C. How) used for disease about intelligence and memory. The effects of Bajijiasu on learning and non-cognitive disturbances have been confirmed. However, its potential to protect against Alzheimer’s disease was not clearly studied. In this work, we want to study the ...
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The terminology and notation used here have been introduced in the following articles: [9], [8], [7], [3], [4], [6], [5], [2], and [1]. For simplicity we adopt the following rules: W , X, Y , Z will denote sets, D will denote a non-empty set, f will denote a function, and x, y will be arbitrary. Let B be a set. We say that B is a Tarski-Class if and only if: for all X, Y such that X ∈ B and Y ⊆...
متن کاملResonance, Linear Syzygies, Chen Groups, and the Bernstein-gelfand-gelfand Correspondence
If A is a complex hyperplane arrangement, with complement X, we show that the Chen ranks of G = π1(X) are equal to the graded Betti numbers of the linear strand in a minimal, free resolution of the cohomology ring A = H(X, k), viewed as a module over the exterior algebra E on A: θk(G) = dimk Tor E k−1(A, k)k , for k ≥ 2, where k is a field of characteristic 0. The Chen ranks conjecture asserts ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.07.023