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Application of imaging postprocessing of spiral CT in the staging of lung cancer 认领 引用 被引量：1
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作者 Zhiming Xiang Fang Huang +2 位作者 Cuimei Liang Xiangdong Xu Lilian Tan 《The Chinese-German Journal of Clinical Oncology》 2008年第5期254-258,共5页
Objective： To evaluate the role of spiral CT imaging postprocessing techniques in preoperative TNM staging of lung cancer. Methods： 106 patients with pathologically confirmed lung cancer received spiral CT examinati... Objective： To evaluate the role of spiral CT imaging postprocessing techniques in preoperative TNM staging of lung cancer. Methods： 106 patients with pathologically confirmed lung cancer received spiral CT examinations with a new revised TNM staging method of lung cancer which was taken as criterion of diagnosis. The images were reconstructed by using different postprocessing techniques such as MPR, MIP, SSD, VR, and their TNM staging capabilities were assessed by using postprocessing imaging and the results with axial CT images were compared. Results： In T staging, the accurate rates of axial CT images in T1-T4 staging were 77.3%, 60.6%, 60.7%, and 60.3% respectively; for postprocessing images, the accurate rates were 86.4%, 90.9%, 89.3%, and 87.0% respectively, In N staging, the accurate rates of axial CT images were 84.6%, 68.1%, 63.6%, and 64.2% in N0-N3 staging, respectively; but they were 92.3%, 90.9%, 90.9%, and 85.7% in postprocessing images, respectively. The postprocessing images were superior to axial CT images in T1-T3 and N1-N3 staging of lung cancer but there were no significant differences in T1 and NO staging. For metastasis, the postprocessing images may be helpful for the TNM staging of lung cancer. Conclusion： The postprocessing techniques of the spiral CT could improve the accurate rates of TNM staging of lung cancer, and represent a useful complement to the axial CT. 展开更多
关键词 spiral CT imaging postprocessing lung cancer TNM staging
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Research on postprocessing of seven-axis linkage parallel kinematics machine with complicated surfaces 认领 引用
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作者 魏永庚 石勇 赵坤 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2007年第2期244-247,共4页
Because of restriction of workspace of parallel kinematics Machine (PKM), 6 DOF PKM can’t finish machining of workpiece with complicated surfaces under only once locating. It is necessary to fit workpiece beyond twic... Because of restriction of workspace of parallel kinematics Machine (PKM), 6 DOF PKM can’t finish machining of workpiece with complicated surfaces under only once locating. It is necessary to fit workpiece beyond twice and to lead to low machining precision. Therefore the seven-axis linkage PKM is implemented by fixing a turntable on the worktable of the six-axis linkage PKM. However, the turntable angle decomposing problem from the CL file should be well considered. If the traditional decomposing methods are adopted, the nutation angle usually goes beyond the workspace of the machine. Therefore, according to the relation of the machine coordinate system and the workpiece coordinate system, the turntable angle decomposition algorithmic of the consistent coordinate system and the turntable angle decomposition algorithmic of the non-consistent coordinate system are developed to resolve the problem mentioned above. The turntable angle decomposition of the non-consistent coordinate system processes the decomposition which is based on the consistent coordinate system again. It calculates the initial angle of the locating workpiece, and the decomposed angle of the turntable at the machine coordinate system results in the nutation angle not going beyond workspace of the machine, thereby the decomposition process can be simplified. 展开更多
关键词 parallel kinematics machine （PKM） complicated surfaces postprocessing
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Postprocessing treatments to improve the laser damage resistance of fused silica optical surfaces and SiO_2 coatings 认领 引用 被引量：4
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作者 刘文文 魏朝阳 +1 位作者 易葵 邵建达 《Chinese Optics Letters》 SCIE EI CAS CSCD 2015年第4期62-66,共5页
The combination of deep wet etching and a magneto-rheological finishing （MRF） process is investigated to simultaneously improve laser damage resistance of a fused-silica surface at 355 nm. The subsequently deposited... The combination of deep wet etching and a magneto-rheological finishing （MRF） process is investigated to simultaneously improve laser damage resistance of a fused-silica surface at 355 nm. The subsequently deposited SiO2 coatings are researched to clarify the impact of substrate finishing technology on the coatings. It is revealed that a deep removal proceeding from the single side or double side had a significant impact on the laser-induced damage threshold （LIDT） of the fused silica, especially for the rear surface. After the deep etching, the MRF process that followed does not actually increase the LIDT, but it does ameliorate the surface qualities without additional LIDT degradation. The combination guarantee both the integrity of the surface＇s finish and the laser damage resistance of the fused silica and subsequent SiO2 coatings. 展开更多
关键词 deep Postprocessing treatments to improve the laser damage resistance of fused silica optical surfaces and SiO2 coatings SiO MRF
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Accuracy Enhancement Using Spectral Postprocessing for Differential Equations and Integral Equations 认领 引用 被引量：8
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作者 Tao Tang Xiang Xu 《Communications in Computational Physics》 SCIE 2009年第2期779-792,共14页
It is demonstrated that spectral methods can be used to improve the accuracy of numerical solutions obtained by some lower order methods.More precisely,we can use spectral methods to postprocess numerical solutions of... It is demonstrated that spectral methods can be used to improve the accuracy of numerical solutions obtained by some lower order methods.More precisely,we can use spectral methods to postprocess numerical solutions of initial value differential equations.After a few number of iterations(say 3 to 4),the errors can decrease to a few orders of magnitude less.The iteration uses the Gauss-Seidel type strategy,which gives an explicit way of postprocessing.Numerical examples for ODEs,Hamiltonian system and integral equations are provided.They all indicate that the spectral processing technique can be a very useful way in improving the accuracy of the numerical solutions.In particular,for a Hamiltonian system accuracy is only one of the issues;some other conservative properties are even more important for large time simulations.The spectral postprocessing with the coarse-mesh symplectic initial guess can not only produce high accurate approximations but can also save a significant amount of computational time over the standard symplectic schemes. 展开更多
关键词 Postprocessing spectral methods rate of convergence Hamiltonian system integral equations
A SUPERONVERGENCE ANALYISIS FOR FINITE ELEMENT SOLUTION BY THE INTERPOLANT POSTPROCESSING ON IRREGULAR MESHES FOR SMOOTH PROBLEM 认领 引用
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作者 Qi-ding Zhu Qun Lin 《Journal of Computational Mathematics》 SCIE EI 2001年第3期323-326,共4页
The post-processing procedure is given by a interpolant postprocessing of the finit element solution by appropriately-define finite dimensional subspaces, The corresponding superconvergence are established on general ... The post-processing procedure is given by a interpolant postprocessing of the finit element solution by appropriately-define finite dimensional subspaces, The corresponding superconvergence are established on general quasi-regular finite element partitions. 展开更多
关键词 finite element superconvergence interpolant postprocessing
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Postprocessing Techniques of High-Order Galerkin Approximations to Nonlinear Second-Order Initial Value Problems with Applications to Wave Equations 认领 引用
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作者 Mingzhu Zhang Lijun Yi 《Communications in Computational Physics》 SCIE 2024年第3期816-858,共43页
The aim of this paper is to propose and analyze two postprocessing techniques for improving the accuracy of the C1-and C0-continuous Galerkin(CG)time stepping methods for nonlinear second-order initial value pro... The aim of this paper is to propose and analyze two postprocessing techniques for improving the accuracy of the C1-and C0-continuous Galerkin(CG)time stepping methods for nonlinear second-order initial value problems,respectively.We first derive several optimal a priori error estimates and nodal superconvergent estimates for the C1-and C0-CG methods.Then we propose two simple but efficient local postprocessing techniques for the C1-and C0-CG methods,respectively.The key idea of the postprocessing techniques is to add a certain higher order generalized Jacobi polynomial of degree k+1 to the C1-or C0-CG approximation of degree k on each local time step.We prove that,for problems with regular solutions,such postprocessing techniques improve the global convergence rates for the L2-,H1-and L∞-error estimates of the C1-and C0-CG methods with quasi-uniform meshes by one order.As applications,we apply the superconvergent postprocessing techniques to the C1-and C0-CG time discretization of nonlinear wave equations.Several numerical examples are presented to verify the theoretical results. 展开更多
关键词 Galerkin time stepping second-order initial value problem superconvergent postprocessing
End-to-end algorithm research in PACT—from signal processing to reconstruction solution to image processing:A review 认领 引用 被引量：3
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作者 JinJin Cheng Shuilin Wang +12 位作者 Shirui Dong Yang Wang Xuyu Fu Jichao Zhang Wenkai Li Siyu Chen Silue Zeng Yaguang Ren Xiaohui Ma Jinhai Liu Mingjian Sun Rongkang Gao Chengbo Liu 《Journal of Innovative Optical Health Sciences》 SCIE EI CSCD 2025年第4期19-61,共43页
Photoacoustic computed tomography(PACT)is an innovative biomedical imaging technique that has gained significant application in the field of biomedicine due to its ability to visualize optical contrast with high resol... Photoacoustic computed tomography(PACT)is an innovative biomedical imaging technique that has gained significant application in the field of biomedicine due to its ability to visualize optical contrast with high resolution and deep tissue penetration.However,the inherent challenges associated with photoacoustic signal excitation,propagation and detection often result in suboptimal image quality.To overcome these limitations,researchers have developed various advanced algorithms that span the entire image reconstruction pipeline.This review paper aims to present a detailed analysis of the latest advancements in PACT algorithms and synthesize these algorithms into a coherent framework.We provide tripartite analysis—from signal processing to reconstruction solution to image processing,covering a spectrum of techniques.The principles and methodologies,as well as their applicability and limitations,are thoroughly discussed.The primary objective of this study is to provide a thorough review of advanced algorithms applicable to PACT,offering both theoretical foundations and practical guidance for enhancing the imaging effect of PACT. 展开更多
关键词 Photoacoustic computed tomography pre-processing main transformation postprocessing deep learning
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Impact of different sampling rates on precise point positioning performance using online processing service 认领 引用 被引量：3
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作者 Serdar Erol Reha Metin Alkan +1 位作者 İ.Murat Ozulu Veli Ilçi 《Geo-Spatial Information Science》 SCIE EI CSCD 2021年第2期302-312,I0008,共11页
In this study,the effect of different sampling rates(i.e.observation recording interval)on the Precise Point Positioning(PPP)solutions in terms of accuracy was investigated.For this purpose,a field test was carried ou... In this study,the effect of different sampling rates(i.e.observation recording interval)on the Precise Point Positioning(PPP)solutions in terms of accuracy was investigated.For this purpose,a field test was carried out inÇorum province,Turkey,on 11 September 2019.Within this context,a Geodetic Point(GP)was established and precisely coordinated.A static GNSS measurement was occupied on the GP for about 4-hour time at 0.10 second(s)/10 Hz measurement intervals with the Trimble R10 geodetic grade GNSS receiver.The original observation file was converted to RINEX format and then decimated into the different data sampling rates as 0.2 s,0.5 s,1 s,5 s,10 s,30 s,60 s,and 120 s.All these RINEX observation files were submitted to the Canadian Spatial Reference System-Precise Point Positioning(CSRS-PPP)online processing service the day after the data collection date by choosing both static and kinematic processing options.In this way,PPP-derived static coordinates,and the kinematic coordinates of each measurement epoch were calculated.The PPP-derived coordinates obtained from each decimated sampling intervals were compared to known coordinates of the GP for northing,easting,2D position,and height components.According to the static and kinematic processing results,high data sampling rates did not change the PPP solutions in terms of accuracy when compared to the results obtained using lower sampling rates.The results of this study imply that it was not necessary to collect GNSS data with high-rate intervals for many surveying projects requiring cm-level accuracy. 展开更多
关键词 Precise Point Positioning(PPP) online GNSS postprocessing service high-rate GNSS sampling rate monitoring structure behavior
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Superconvergence analysis of lower order anisotropic finite element 认领 引用 被引量：1
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作者 朱国庆 石东洋 陈绍春 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第8期1119-1130,共12页
The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. ... The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpo- lation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis. 展开更多
关键词 nonconforming finite element anisotropic error estimate interpolation postprocessing superconvergence
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Superconvergence analysis of the finite element method for nonlinear hyperbolic equations with nonlinear boundary condition 认领 引用 被引量：1
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作者 SHI Dong-yang LI Zhi-yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2008年第4期455-462,共8页
This paper discusses the semidiscrete finite element method for nonlinear hyperbolic equations with nonlinear boundary condition. The superclose property is derived through interpolation instead of the nonlinear H^1 p... This paper discusses the semidiscrete finite element method for nonlinear hyperbolic equations with nonlinear boundary condition. The superclose property is derived through interpolation instead of the nonlinear H^1 projection and integral identity technique. Meanwhile, the global superconvergence is obtained based on the interpolated postprocessing techniques. 展开更多
关键词 nonlinear hyperbolic equation nonlinear boundary condition superconvergence postprocessing technique
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Approximation and Superconvergence Analysis for a New Higher Order Wilson Element to Sobolev Type Equations 认领 引用
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作者 石东洋 郝晓斌 《Chinese Quarterly Journal of Mathematics》 北大核心 2008年第1期127-134,共8页
In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate ... In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations. 展开更多
关键词 Sobolev type equations higher order Wilson element interpolation postprocessing technique superconvergence
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Fused monochromatic imaging acquired by single source dual energy CT in hepatocellular carcinoma during arterial phase: an initial experience 认领 引用 被引量：4
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作者 Shun-Yu Gao Xiao-Peng Zhang +5 位作者 Yong Cui Ying-Shi Sun Lei Tang Xiao-Ting Li Xiao-Yan Zhang Jun Shan 《Chinese Journal of Cancer Research》 SCIE CAS CSCD 2014年第4期437-443,共7页
Objective： To explore whether single and fused monochromatic images can improve liver tumor detection and delineation by single source dual energy CT （ssDECT） in patients with hepatocellular carcinoma （HCC） durin... Objective： To explore whether single and fused monochromatic images can improve liver tumor detection and delineation by single source dual energy CT （ssDECT） in patients with hepatocellular carcinoma （HCC） during arterial phase. Methods： Fifty-seven patients with HCC who underwent ssDECT scanning at Beijing Cancer Hospital were enrolled retrospectively. Twenty-one sets of monochromatic images from 40 to 140 keV were reconstructed at 5 keV intervals in arterial phase. The optimal contrast-noise ratio （CNR） monochromatic images of the liver tumor and the lowest-noise monochromatic images were selected for image fusion. We evaluated the image quality of the optimal-CNR monochromatic images, the lowest-noise monochromatic images and the fused monochromatic images, respectively. The evaluation indicators included the spatial resolution of the anatomical structure, the noise level, the contrast and CNR of the tumor. Results： In arterial phase, the anatomical structure of the liver can be displayed most clearly in the 65-keV monochromatic images, with the lowest image noise. The optimal-CNR monochromatic images of HCC tumor were 50-keV monochromatic images in which the internal structural features of the liver tumors were displayed most clearly and meticulously. For tumor detection, the fused monochromatic images and the 50-keV monochromatic images had similar performances, and were more sensitive than 65-keV monochromatic images. Conclusions： We achieved good arterial phase images by fusing the optimal-CNR monochromatic images of the HCC tumor and the lowest-noise monochromatic images. The fused images displayed liver tumors and anatomical structures more clearly, which is potentially helpful for identifying more and smaller HCC tumors. 展开更多
关键词 Computed tomography （CT） dual energy hepatocellular carcinoma （HCC） image postprocessing comparative study
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Contact-Stress-Based Stress Recovery Methods for Discontinuous Deformation Analysis 认领 引用 被引量：1
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作者 Ruoyu Guan Shean Bie 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2020年第4期508-520,共13页
Discontinuous deformation analysis(DDA)has been widely applied for the simulation of block systems that have many discontinuous surfaces.The penalty method is utilized to ensure that there are no penetrations between ... Discontinuous deformation analysis(DDA)has been widely applied for the simulation of block systems that have many discontinuous surfaces.The penalty method is utilized to ensure that there are no penetrations between blocks.A linear polynomial function for displacement leads to a constant stress for a block,which cannot precisely describe the stress field within the block.Therefore,a high-order polynomial displacement function and a flue mesh are always used to improve the precision of the stress field.However,these means are not practical for simulating block systems that have many contacts.In this paper,the contact-stress-based stress recovery methods are proposed for DDA.High-precision solutions for the contact stresses on the boundaries of the blocks are utilized.The first-order Gaussian point of a block is the block's centroid,where the constant stress obtained via DDA is of higher precision.The high-precision solutions for the stresses are utilized in the least squares method to recover a single block's inner stress field.The proposed methods enhance the resolution of the stress field inside a single block without increasing the computational effort in the main iterative process for displacement in DDA.Numerical examples are simulated using both the finite element method(FEM)with a fine mesh and the proposed DDA program.The recovered DDA results can accurately describe the distribution of the stresses in a single block and,in some areas,have the same precision as the FEM results.Moreover,the precision of the proposed methods improves as the gradient of the contact stress on the boundary decreases. 展开更多
关键词 Contact stress Postprocessing Stress recovery method Discontinuous deformation analysis
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Mobile mini-fluorimeter for antibiotic aptasensing based on surface-plasmonic effect of burlike nanogolds enhanced by digitized imaging diagnosis 认领 引用
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作者 Tiantian Man Fulin Zhu +4 位作者 Yaqi Huang Yuhao Piao Yan Su Shengyuan Deng Ying Wan 《Chinese Chemical Letters》 SCIE CAS CSCD 2024年第5期418-422,共5页
Antibiotic abuse now poses a grave threat to global ecology and bestirs public concerns about the residue issue in daily necessities.The traceability measurements along supply chain or logistic circulation have become... Antibiotic abuse now poses a grave threat to global ecology and bestirs public concerns about the residue issue in daily necessities.The traceability measurements along supply chain or logistic circulation have become increasingly essential given the labile nature of diverse synthetic residuals on site.In an attempt to answer this urgency,here a miniaturized fluorometric aptasensor prototype was contrived that catered to the point-of-care screening norm for two typical additives:chloramphenicol and enrofloxacin.The key target-indicating module worked in vitro based on the competitive binding-induced fluorescence recovery of fluorescein-labeled aptamers,which were photobleached beforehand in the format of double helix on burlike nanogold carriers.The“prickly”geometry of the latter not just enriched the capture probes at preferentially substrate-accessible spires;but also contributed to a tip-enhanced surface plasmon effect,sensitizing the signal-on during the duplex dissociation even at nanomolar threshold of the analytes.On the other hand,to encompass a full portable,a set of optical devices were mounted within a 3D-printed cartridge(adaptor)to converge the light beam and route it towards the detector,for which the smartphone camera came up in handy with a home-developed App for calibrating the emissive brightness.Enlightened by the high-dynamic-range compression,an imaging diagnostic algorithm was built in to grid and digitize each slide in the album for augmented detection performance.Thus,a novel bio-to-silico integration was invented that capable of in situ rapid reporting on the antibiotic presence with high sensitivity and selectivity.Further field practices in spiked milk on sales proved the precision and rudimentary feasibility of the well-assembled model of appliance,thus holding nice prospects in nonexpert(e.g.,family and local community)utilities for foodborne antibiotic identification. 展开更多
关键词 Chloramphenicol and enrofloxacin Aptasensor Gold nanoburs Smartphone fluorimetric suite Digitized image postprocessing
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On the Numerical Solutions of One and Two-Stage Model of Carcinogenesis Mutations with Time Delay and Diffusion 认领 引用
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作者 Ishtiaq Ali 《Applied Mathematics》 2013年第10期118-124,共7页
In this paper, we focused on numerical solutions of carcinogenesis mutations models that are based on reaction-diffusion systems and Lotka-Volterra food chains. We consider the case with one and two-stages of mutation... In this paper, we focused on numerical solutions of carcinogenesis mutations models that are based on reaction-diffusion systems and Lotka-Volterra food chains. We consider the case with one and two-stages of mutations with appropriate initial conditions and the zero-flux boundary conditions. The main purpose is to construct a stable discretization scheme, which allows much accuracy than those of a standard approach. To this end, we use the spectral method to postprocess numerical solutions for the proposed model by using some classical methods for solving differential equations. The implementation of the algorithm is simple and it does not need to solve the linear or nonlinear system (in case the model is nonlinear). We simulate the one and two-stage carcinogenesis mutations model and compared the results with previously published ones. 展开更多
关键词 Carcinogenesis Mutations Delay and Diffusion Spectral Postprocessing Numerical Simulations
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Pressure Angle Effect of Concave Cylinder Surface on Motion Characteristics of Fiber Placement Machine 认领 引用 被引量：1
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作者 WANG Xianfeng GAO Tiancheng 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2020年第6期898-902,共5页
There are amounts of issues to be resolved in the process of designing the fiber placement trajectory of the cylindrical component,such as the interference between the machine and the component and the over-travel of ... There are amounts of issues to be resolved in the process of designing the fiber placement trajectory of the cylindrical component,such as the interference between the machine and the component and the over-travel of the axis of rotation on the fiber placement head.When the pressure on the cylinder surface inclines in a certain direction or at an angle within the normal plane,the motion characteristics of the rotation axis will be different.This paper analyzes the pressure angle effect of the concave cylinder surface on the motion features of a fiber placement machine.The placement area is enlarged by tilting pressure with the same lifting stroke,which is significant in preventing interference and selecting post-processing algorithm. 展开更多
关键词 composite materials fiber placement inclination angle pressure cylinder postprocess
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End-to-end design of multicolor scintillators for enhanced energy resolution in X-ray imaging 认领 引用 被引量：3
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作者 Seokhwan Min Seou Choi +5 位作者 Simo Pajovic Sachin Vaidya Nicholas Rivera Shanhui Fan Marin Soljačić Charles Roques-Carmes 《Light: Science & Applications》 SCIE EI CAS CSCD 2025年第6期1606-1617,共12页
Scintillators have been widely used in X-ray imaging due to their ability to convert high-energy radiation into visible light,making them essential for applications such as medical imaging and high-energy physics.Rece... Scintillators have been widely used in X-ray imaging due to their ability to convert high-energy radiation into visible light,making them essential for applications such as medical imaging and high-energy physics.Recent advances in the artificial structuring of scintillators offer new opportunities for improving the energy resolution of scintillator-based X-ray detectors.Here,we present a three-bin energy-resolved X-ray imaging framework based on a three-layer multicolor scintillator used in conjunction with a physics-aware image postprocessing algorithm.The multicolor scintillator is able to preserve X-ray energy information through the combination of emission wavelength multiplexing and energy-dependent isolation of X-ray absorption in specific layers.The dominant emission color and the radius of the spot measured by the detector are used to infer the incident X-ray energy based on prior knowledge of the energy-dependent absorption profiles of the scintillator stack.Through ab initio Monte Carlo simulations,we show that our approach can achieve an energy reconstruction accuracy of 49.7%,which is only 2%below the maximum accuracy achievable with realistic scintillators.We apply our framework to medical phantom imaging simulations where we demonstrate that it can effectively differentiate iodine and gadolinium-based contrast agents from bone,muscle,and soft tissue. 展开更多
关键词 x ray imaging physics aware image postprocessing energy reconstruction multicolor scintillators Monte Carlo simulations improving energy resolution artificial structuring scintillators energy resolution
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Computing the lower and upper bounds of Laplace eigenvalue problem:by combining conforming and nonconforming finite element methods 认领 引用 被引量：10
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作者 LUO FuSheng LIN Qun XIE HeHu 《Science China Mathematics》 SCIE 2012年第5期1069-1082,共14页
We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the l... We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the eigenvalue.Additionally,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented.Thus,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once.Some numerical results are also presented to demonstrate our theoretical analysis. 展开更多
关键词 lower bound upper bound ECR EQ1ro t eigenvalue problem postprocessing
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HIGH ACCURACY ANALYSIS OF ELLIPTIC EIGENVALUE PROBLEM FOR THE WILSON NONCONFORMING FINITE ELEMENT 认领 引用 被引量：2
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作者 吴冬生 《Acta Mathematicae Applicatae Sinica》 2001年第2期200-206,共7页
In this paper, the Wilson nonconforming finite element is considered for solving elliptic eigenvalue problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfunction and eigenvalue ... In this paper, the Wilson nonconforming finite element is considered for solving elliptic eigenvalue problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfunction and eigenvalue are obtained. 展开更多
关键词 Eigenvalue problems high accuracy analysis interpolation postprocessing Wilson nonconforming finite element
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Two-scale sparse finite element approximations 认领 引用 被引量：1
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作者 LIU Fang ZHU JinWei 《Science China Mathematics》 SCIE CSCD 2016年第4期789-808,共20页
To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d... To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper approximations.As applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation. 展开更多
关键词 combination discretization eigenvalue finite element postprocessing two-scale
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