The Multilevel Finite Element Discretizations Based on Local Defect-Correction for Nonsymmetric Eigenvalue Problems

Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that the schemes are simple and easy to carry out, and can be used to solve singular nonsymmetric eigenvalue problems efficiently. We also discuss the local error estimates of finite element approximations; it's a new feature here that the estimates apply to the local domains containing corner points

Does High-tech Export Cause More Technology Spillover? Evidence from Contemporary China

This paper attempts to investigate whether high-tech product export causes more technology spillover compared with traditionally primary manufactured goods export.A generalized multi-sector spillover model is presented to involve the causations of export composition and technology spillover, which is based on two distinctive approaches of measuring technology spillover: “between-spillover” and “within-spillover”. The empirical estimation is conducted with a panel analysis involving 31 provinces in China over the period of 1998-2005. Although high-tech export sectors involve a higher productivity compared with other sectors, this productivity advantage in high-tech export sectors does not cause technology spillover towards both domestic sectors and other export sectors. Therefore, this paper suggests that technology spillover of export mainly takes place in traditional export sectors rather than high-tech export sectors.Export Composition; High-tech Export; Technology Spillover; Multi-sector Spillover Model

A Class of Spectral Element Methods and Its A Priori/A Posteriori Error Estimates for 2nd-Order Elliptic Eigenvalue Problems

This paper discusses spectral and spectral element methods with Legendre-Gauss-Lobatto nodal basis for general 2nd-order elliptic eigenvalue problems. The special work of this paper is as follows. (1) We prove a priori and a posteriori error estimates for spectral and spectral element methods. (2) We compare between spectral methods, spectral element methods, finite element methods and their derived p-version, h-version, and hp-version methods from accuracy, degree of freedom, and stability and verify that spectral methods and spectral element methods are highly efficient computational methods

Stereo Matching in Time: 100+ FPS Video Stereo Matching for Extended Reality

Real-time Stereo Matching is a cornerstone algorithm for many Extended Reality (XR) applications, such as indoor 3D understanding, video pass-through, and mixed-reality games. Despite significant advancements in deep stereo methods, achieving real-time depth inference with high accuracy on a low-power device remains a major challenge. One of the major difficulties is the lack of high-quality indoor video stereo training datasets captured by head-mounted VR/AR glasses. To address this issue, we introduce a novel video stereo synthetic dataset that comprises photorealistic renderings of various indoor scenes and realistic camera motion captured by a 6-DoF moving VR/AR head-mounted display (HMD). This facilitates the evaluation of existing approaches and promotes further research on indoor augmented reality scenarios. Our newly proposed dataset enables us to develop a novel framework for continuous video-rate stereo matching. As another contribution, our dataset enables us to proposed a new video-based stereo matching approach tailored for XR applications, which achieves real-time inference at an impressive 134fps on a standard desktop computer, or 30fps on a battery-powered HMD. Our key insight is that disparity and contextual information are highly correlated and redundant between consecutive stereo frames. By unrolling an iterative cost aggregation in time (i.e. in the temporal dimension), we are able to distribute and reuse the aggregated features over time. This approach leads to a substantial reduction in computation without sacrificing accuracy. We conducted extensive evaluations and comparisons and demonstrated that our method achieves superior performance compared to the current state-of-the-art, making it a strong contender for real-time stereo matching in VR/AR applications

Terahertz imaging with sub-wavelength resolution by femtosecond laser filament in air

Terahertz (THz) imaging provides cutting edge technique in biology, medical sciences and non-destructive evaluation. However, due to the long wavelength of the THz wave, the obtained resolution of THz imaging is normally a few hundred microns and is much lower than that of the traditional optical imaging. We introduce a sub-wavelength resolution THz imaging technique which uses the THz radiation generated by a femtosecond laser filament in air as the probe. This method is based on the fact that the femtosecond laser filament forms a waveguide for the THz wave in air. The diameter of the THz beam, which propagates inside the filament, varies from 20 {\mu}m to 50 {\mu}m, which is significantly smaller than the wavelength of the THz wave. Using this highly spatially confined THz beam as the probe, THz imaging with resolution as high as 20 {\mu}m (~{\lambda}/38) can be realized.Comment: 10 pages, 7 figure