We give a classification of all linear natural operators transforming p-vectors (i.e., skew-symmetric tensor fields of type (p, 0)) on n-dimensional manifolds M to tensor fields of type (q, 0) on TAM, where TA is a Weil bundle, under the condition that p ≥ 1, n ≥ p and n ≥ q. The main result of the paper states that, roughly speaking, each linear natural operator lifting p-vectors to tensor fields of type (q, 0) on TA is a sum of operators obtained by permuting the indices of the tensor products of linear natural operators lifting p-vectors to tensor fields of type (p, 0) on TA and canonical tensor fields of type (q − p, 0) on TA., Jacek Dębecki., and Obsahuje seznam literatury
Let M_{m,n} be the set of all m × n real matrices. A matrix A \in M_{m,n} is said to be row-dense if there are no zeros between two nonzero entries for every row of this matrix. We find the structure of linear functions T: M_{m,n} \rightarrow M_{m,n} that preserve or strongly preserve row-dense matrices, i.e., T(A) is row-dense whenever A is row-dense or T(A) is row-dense if and only if A is row-dense, respectively. Similarly, a matrix A \in M_{m,n} is called a column-dense matrix if every column of A is a column-dense vector. At the end, the structure of linear preservers (strong linear preservers) of column-dense matrices is found., Sara M. Motlaghian, Ali Armandnejad, Frank J. Hall., and Obsahuje seznam literatury
We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix A. The result exploits the Frobenius inner product between A and a given rank-one landmark matrix X. Different choices for X may be used, depending on the problem under investigation. In particular, we show that the choice where X is the all-ones matrix allows to estimate the signature of the leading eigenvector of A, generalizing previous results on Perron-Frobenius properties of matrices with some negative entries. As another application we consider the problem of community detection in graphs and networks. The problem is solved by means of modularity-based spectral techniques, following the ideas pioneered by Miroslav Fiedler in mid-’70s. We show that a suitable choice of X can be used to provide new quality guarantees of those techniques, when the network follows a stochastic block model., Dario Fasino, Francesco Tudisco., and Obsahuje seznam literatury
Consider the n×n matrix with (i, j)’th entry gcd (i, j). Its largest eigenvalue \lambda _{n} and sum of entries s_{n} satisfy \lambda _{n} > s_{n}/n. Because sn cannot be expressed algebraically as a function of n, we underestimate it in several ways. In examples, we compare the bounds so obtained with one another and with a bound from S.Hong, R.Loewy (2004). We also conjecture that \lambda _{n} > 6\Pi ^{-2}n log n for all n. If n is large enough, this follows from F.Balatoni (1969)., Jorma K. Merikoski., and Obsahuje seznam literatury
Consider $\mathcal T_n(F)$ - the ring of all $n\times n$ upper triangular matrices defined over some field $F$. A map $\phi$ is called a zero product preserver on ${\mathcal T}_n(F)$ in both directions if for all $x,y\in{\mathcal T}_n(F)$ the condition $xy=0$ is satisfied if and only if $\phi(x)\phi(y)=0$. In the present paper such maps are investigated. The full description of bijective zero product preservers is given. Namely, on the set of the matrices that are invertible, the map $\phi$ may act in any bijective way, whereas for the zero divisors and zero matrix one can write $\phi$ as a composition of three types of maps. The first of them is a conjugacy, the second one is an automorphism induced by some field automorphism, and the third one transforms every matrix $x$ into a matrix $x'$ such that $\{y\in\mathcal T_n(F) xy=0\}=\{y\in\mathcal T_n(F) x'y=0\}$, $\{y\in\mathcal T_n(F) yx=0\}=\{y\in\mathcal T_n(F) yx'=0\}$., Roksana Słowik., and Obsahuje bibliografii
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal L^{p} regularity of the periodic Laplace and Stokes operators and a local-intime existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group G: = \mathbb{R}^{n - 1} \times \mathbb{R}/L\mathbb{Z} to obtain an R-bound for the resolvent estimate. Then, Weis’ theorem connecting R-boundedness of the resolvent with maximal L^{p} regularity of a sectorial operator applies., Jonas Sauer., and Obsahuje seznam literatury
A necessary and sufficient condition for the Reeb vector field of a three dimensional non-Kenmotsu almost Kenmotsu manifold to be minimal is obtained. Using this result, we obtain some classifications of some types of (k, μ, v)-almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of (k, μ, v)-almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal., Yaning Wang., and Obsahuje bibliografii
Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajłasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness of the Hardy-Littlewood maximal operator, we establish a generalization of Sobolev’s inequality for Sobolev functions in Musielak-Orlicz-Hajłasz-Sobolev spaces., Takao Ohno, Tetsu Shimomura., and Obsahuje seznam literatury