We study the growth of the rank of elliptic curves and, more generally, Abelian varieties upon extensions of number fields. First, we show that if L/K is a finite Galois extension of number fields such that Gal(L/K) does not have an index 2 subgroup and A/K is an Abelian variety, then rkA(L)− rkA(K) can never be 1. We obtain more precise results when Gal(L/K) is of odd order, alternating, SL2(F...

Distributed dynamic channel allocation techniques are becoming important with the tremendous growth in mobile cellular communication and demand for wireless multimedia applications. These techniques can be categorized as search based or update based. Search based techniques have low messaging complexity and are suited for high system load and low request rates. On the other hand update based sc...

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given m × n matrix A by a matrix B of rank at most k which is much smaller than m and n. The best rank k approximation can be determined via the singular value decomposition which, however, has prohibitively high computational complexity and storage requirements for very large m and...

In this article we introduce a full-rank representation of the Drazin inverse AD of a given complex matrix A, which is based on an arbitrary full-rank decomposition of Al, l ≥ k, where k is the index of A. We show that the known representation of the Drazin inverse of A, devised in [7], represents a partial case of this result. Using this general representation, we introduce a determinantal rep...

Tutte associates a V by V skew-symmetric matrix T , having indeterminate entries, with a graph G=(V,E). This matrix, called the Tutte matrix, has rank exactly twice the size of a maximum cardinality matching of G. Thus, to find the size of a maximum matching it suffices to compute the rank of T . We consider the more general problem of computing the rank of T +K where K is a real V by V skew-sy...

Abstract. It is known that the i-th order laminated microstructures can be resolved by the k-th order rank-one convex envelopes with k ≥ i. So the requirement of establishing an efficient numerical scheme for the computation of the finite order rank-one convex envelopes arises. In this paper, we develop an iterative scheme for such a purpose. The 1-st order rank-one convex envelope R1f is appro...

A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. Kruskal has previously shown that the three component matrices involved are essentially unique when the sum of their k-ranks is at least twice the rank of the decomposition plus 2. It was proved that Kruskal’s sufficient condition is also necessary when the rank of ...

We review the status of rare kaon decays, concentrating on modes with sensitivity to short-distance flavour physics. Invited Talk presented at the 3rd Workshop on Physics and Detectors for Daphne (DAΦNE 99), Frascati, 16-19 Nov. 1999

ENWEndNote BIBJabRef, Mendeley RISPapers, Reference Manager, RefWorks, Zotero AMA Chyl-Surdacka K, Borzęcki A, Latifa J, Turska-Kozłowska M, Majchrzycka M. Keratosis follicularis (Darier disease) – clinical characteristics and treatment a review update. Postępy Dermatologii i Alergologii/Advances in Dermatology Allergology. 2023. doi:10.5114/ada.2022.124344. APA Chyl-Surdacka, K., Borzęcki, A.,...

We present the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights. Given a dynamic directed graph G such that each edge can assume at most S different real values, we show how to support updates in O(n2.5 √ S log n ) amortized time and queries in optimal worst-case time. No previous fully dynamic algorithm was known for this p...