Results 11 to 20 of about 261,453 (169)
Matrix-Free Proof of a Regularity Characterization [PDF]
The Electronic Journal of Combinatorics, 2003 The central concept in Szemerédi's powerful regularity lemma is the so-called $\epsilon$-regular pair. A useful statement of Alon et al. essentially equates the notion of an $\epsilon$-regular pair with degree uniformity of vertices and pairs of vertices. The known proof of this characterization uses a clever matrix argument.
Andrzej Czygrinow, Brendan Nagle
openaire +2 more sources
Proceedings of the Institute for System Programming of the RAS, 2022 The paper investigates the problem of analyzing the regularity of multidimensional matrices based on the repetition of significant (non-empty) characters in the matrix cells. Such a repetition means that when the matrix is shifted along one or more of its coordinates, some significant characters are preserved.
Igor Borisovich Burdonov +1 more
openaire +1 more source
Statistical weighted A-summability with application to Korovkin’s type approximation theorem
Journal of Inequalities and Applications, 2016 We introduce the notion of statistical weighted A-summability of a sequence and establish its relation with weighted A-statistical convergence. We also define weighted regular matrix and obtain necessary and sufficient conditions for the matrix A to be ...
Syed Abdul Mohiuddine
doaj +1 more source
Weighted almost convergence and related infinite matrices
Journal of Inequalities and Applications, 2018 The purpose of this paper is to introduce the notion of weighted almost convergence of a sequence and prove that this sequence endowed with the sup-norm ∥ ⋅ ∥ ∞ ${\Vert \cdot \Vert } _{\infty}$ is a BK-space. We also define the notions of weighted almost
Syed Abdul Mohiuddine, Abdullah Alotaibi
doaj +1 more source
A New Paranormed Sequence Space Defined by Regular Bell Matrix
Dera Natung Government College Research Journal, 2023 This paper aims to construct a new paranormed sequence space by the aid of a regular matrix of Bell numbers. As well, its special duals such as α−,β−,γ− duals are presented and Schauder basis is determined.
Murat Karakaş, Muhammet Cihat Dağlı
doaj +1 more source
Binary matrix completion with nonconvex regularizers [PDF]
CoRR, 2019 Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case of BMC problem, in which only a subset of positive elements can be observed.
Chunsheng Liu 0003, Hong Shan
openaire +4 more sources
International Journal of Mathematics and Mathematical Sciences, 1999 In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences.
Richard F. Patterson
doaj +1 more source
An Application On The Lucas Numbers And Infinite Toeplitz Matrices
Cumhuriyet Science Journal, 2017 In this paper, we firstly establish the regular matrix by using Lucas numbers. Then, byintroducing the sequence space with the help of the matrix , we show that this space is a BK-space and isomorphic to the space . Also, we give some inclusion relations
Murat Karakaş, Hasan Karabudak
doaj +1 more source
Submatrices of summability matrices
International Journal of Mathematics and Mathematical Sciences, 1978 It is proved that a matrix that maps ℓ1 into ℓ1 can be obtained from any regular matrix by the deletion of rows. Similarly, a conservative matrix can be obtained by deletion of rows from a matrix that preserves boundedness. These techniques are also used
J. A. Fridy
doaj +1 more source
Journal of Mathematics, 2021 In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂℂ2 of the complex matrix algebra M4,ℂ. We exhibit regular functions defined on a domain in ℂ4 but taking values in ℂℂ2.
Ji Eun Kim
doaj +1 more source