A point cloud as an information-intensive 3D representation usually requires a large amount of transmission, storage and computing resources, which seriously hinder its usage in many emerging fields. In this paper, we propose novel simplification method, Approximate Intrinsic Voxel Structure (AIVS), to meet the diverse demands real-world application scenarios. The method includes pre-processing...

We investigate the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement-type controllers for single-input singleoutput linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled Diophantine equations of polynomials. An extra complexity...

In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.

We give necessary and sufficient conditions for a Banach space operator with the single valued extension property (SVEP) to satisfy Weyl’s theorem and a-Weyl’s theorem. We show that if T or T ∗ has SVEP and T is transaloid, then Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )). When T ∗ has SVEP, T is transaloid and T is a-isoloid, then a-Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T ...

The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely dense and the eigenfunctions become concentrated in the vicinity of the intermittent fixed point. Analytical considerations generalize the results to a broad...

We give necessary and sufficient conditions for a Banach space operator with the single valued extension property (SVEP) to satisfy Weyl’s theorem and a-Weyl’s theorem. We show that if T or T ∗ has SVEP and T is transaloid, then Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )). When T ∗ has SVEP, T is transaloid and T is a-isoloid, then a-Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T ...

Gravitational waves (GWs) induced by scalar curvature fluctuations are an important source of the cosmological GW background and a crucial counterpart primordial black hole scenario. However, doubts have been cast on theoretically predicted spectrum due to its seeming gauge dependence. In this paper, we shed light dependence issue in general backgrounds. First, inspired Hamiltonian formalism pr...