Solutions of nonlinear difference equations in the domain of $(\zeta _{n})$-Cesàro matrix in $\ell _{t(\cdot)}$ of nonabsolute type, and its pre-quasi ideal

We have constructed the sequence space $(\Xi (\zeta ,t) )_{\upsilon }$ ( Ξ ( ζ , t ) ) υ , where $\zeta =(\zeta _{l})$ ζ = ( ζ l ) is a strictly increasing sequence of positive reals tending to infinity and $t=(t_{l})$ t = ( t l ) is a sequence of positive reals with $1\leq t_{l}<\infty $ 1 ≤ t l < ∞ , by the domain of $(\zeta _{l})$ ( ζ l ) -Cesàro matrix in the Nakano sequence space $\ell _{(t_{l})}$ ℓ ( t l ) equipped with the function $\upsilon (f)=\sum^{\infty }_{l=0} ( \frac{ \vert \sum^{l}_{z=0}f_{z}\Delta \zeta _{z} \vert }{\zeta _{l}} )^{t_{l}}$ υ ( f ) = ∑ l = 0 ∞ ( | ∑ z = 0 l f z Δ ζ z | ζ l ) t l for all $f=(f_{z})\in \Xi (\zeta ,t)$ f = ( f z ) ∈ Ξ ( ζ , t ) . Some geometric and topological properties of this sequence space, the multiplication mappings defined on it, and the eigenvalues distribution of operator ideal with s-numbers belonging to this sequence space have been investigated. The existence of a fixed point of a Kannan pre-quasi norm contraction mapping on this sequence space and on its pre-quasi operator ideal formed by $(\Xi (\zeta ,t) )_{\upsilon }$ ( Ξ ( ζ , t ) ) υ and s-numbers is presented. Finally, we explain our results by some illustrative examples and applications to the existence of solutions of nonlinear difference equations.

Kannan Contraction Operator on the Domain of r . -Cesàro Matrix in ℓ t . and Related Prequasi Ideal with an Application of Nonlinear Difference Equations

In this article, the sequence space Ξ r , t υ has been built by the domain of r l -Cesàro matrix in Nakano sequence space ℓ t l , where t = t l and r = r l are sequences of positive reals with 1 ≤ t l < ∞ , and υ f = ∑ l = 0 ∞ ∑ z = 0 l r z f z / ∑ z = 0 l r z t l , with f = f z ∈ Ξ r , t . Some topological and geometric behavior of Ξ r , t υ , the multiplication maps acting on Ξ r , t υ , and the eigenvalues distribution of operator ideal constructed by Ξ r , t υ and s -numbers have been examined. The existence of a fixed point of Kannan prequasi norm contraction mapping on this sequence space and on its prequasi operator ideal are investigated. Moreover, we indicate our results by some explanative examples and actions to the existence of solutions of nonlinear difference equations.

Characterizing the long-period seismicity of Teide volcano in Tenerife (Canary Islands, Spain)

&lt;p&gt;The volcanic long-period seismicity, composed of long-period events and volcanic tremors, constitutes an important attribute of volcanic unrest. Its detection and characterization is therefore a key aspect of volcano monitoring. In the present work, a method based on the seismic network covariance matrix, the equivalent in the frequency domain of the cross-correlation matrix, is used to automatically detect and locate long-period events of the Teide volcano on the island of Tenerife (Canary Islands, Spain). The method is based on the analysis of eigenvalues and eigenvectors of the network covariance matrix.&lt;/p&gt;&lt;p&gt;Long-period events are detected through the time evolution of the width of the network covariance matrix eigenvalues distribution, which is a proxy of the number of sources acting in the wavefield. Each detected long-period event is then located using the moveout information of the corresponding first eigenvector. Three years of seismic data (from 2017 to 2019) continuously recorded by the Red S&amp;#237;smica Canaria (C7), a permanent monitoring network composed of 17 broadband stations operated by the Instituto Volcanol&amp;#243;gico de Canarias (INVOLCAN), are analysed. The obtained locations are compared with potential locations from INVOLCAN&amp;#8217;s catalog, obtained by a standard approach based on manual phases picking.&lt;/p&gt;