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Consider the functions \(\exp (-\zeta x^2)p_j(x)\) with \(p_j(x)= \sin [\pi/2 (x+1) (j+1/2)]\) and \(\text{Re} \zeta>0\). It is shown in this note that the family \(h_{j,k} (x)=h_j(x-2k)\), \(j=0,1, \dots, k\in Z\) is an unconditional basis for \(L^2(R)\). Also the dual basis for this is constructed. When \(\zeta>0\), this result is implicit in \textit{
Coifman, R.R., Meyer, Y.
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GS-SLAM: Dense Visual SLAM with 3D Gaussian Splatting [PDF]
In this paper, we introduce GS-SLAM that first utilizes 3D Gaussian representation in the Simultaneous Localization and Mapping (SLAM) system. It facilitates a better bal-ance between efficiency and accuracy.
Chi Yan +6 more
semanticscholar +1 more source
AbstractAs the standard method for solving systems of linear equations, Gaussian elimination (GE) is one of the most important and ubiquitous numerical algorithms. However, its successful use relies on understanding its numerical stability properties and how to organize its computations for efficient execution on modern computers.
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Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions
We have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions.
Ayşe Zeynep Azak
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Finn Lindgren +2 more
exaly +2 more sources
Conformations of Steroid Hormones: Infrared and Vibrational Circular Dichroism Spectroscopy
Steroid hormone molecules may exhibit very different functionalities based on the associated functional groups and their 3D arrangements in space, i.e., absolute configurations and conformations.
Yanqing Yang +6 more
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PGSR: Planar-Based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction [PDF]
Recently, 3D Gaussian Splatting (3DGS) has attracted widespread attention due to its high-quality rendering, and ultra-fast training and rendering speed.
Danpeng Chen +9 more
semanticscholar +1 more source
Analyses and Modeling Impulse Noise Generated by Household Appliances
This paper describes analysis of impulse noise generated by small household appliances. Furthermore we propose a new model of impulse noise based on the averaged power spectrum and the random phase generation with various phase distributions.
Jaroslav Krejci, Tomas Zeman
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Learned Image Compression With Discretized Gaussian Mixture Likelihoods and Attention Modules [PDF]
Image compression is a fundamental research field and many well-known compression standards have been developed for many decades. Recently, learned compression methods exhibit a fast development trend with promising results.
Zhengxue Cheng +3 more
semanticscholar +1 more source
This paper proposes a curvature demodulation of Mach-Zehnder interferometer (MZI) sensors based on complete spectral information. An MZI sensor composed of two waist-enlarged single mode fibers (SMFs) was fabricated.
Mingyao Liu +9 more
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