We investigate the validity of Taylor's Hypothesis (TH) in analysis Alfv\'enic fluctuations velocity and magnetic fields solar wind streams measured by Parker Solar Probe (PSP)~during first four encounters. use PSP field measurements from 24 h intervals selected each The applicability TH is investigated measuring parameter $\epsilon=\delta u_0/\sqrt{2}V_\perp$, which quantifies ratio between ty...

In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...

We give a $(1+\epsilon)$-approximate distance oracle with $O(1)$ query time for an undirected planar graph $G$ with $n$ vertices and non-negative edge lengths. For $\epsilon>0$ and any two vertices $u$ and $v$ in $G$, our oracle gives a distance $\tilde{d}(u,v)$ with stretch $(1+\epsilon)$ in $O(1)$ time. The oracle has size $O(n\log n ((\log n)/\epsilon+f(\epsilon)))$ and pre-processing time $...

We establish a correspondence between class of Wilson-'t Hooft lines in four-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. compute the vacuum expectation values twisted product space $S^1 \times_\epsilon \mathbb{R}^2 \times \mathbb{R}$ localizati...

Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic second-order operators, as well higher-order such Bilaplacian, have been discretized specialized applications. this paper, we study a class of that generalizes four...

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...