A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the v...A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.展开更多
Consider L<sup>2</sup>-projection u<sub>h</sub> of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for const...Consider L<sup>2</sup>-projection u<sub>h</sub> of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for constructing a superclose to function u<sub>h</sub> are proposed and then superconvergence for both u<sub>h</sub> and Du<sub>h</sub> are proved. When n is odd and no boundary conditions are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order Gauss points G<sub>n+1</sub> in each element. When n is even and function values on the boundary are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order points Z<sub>n+1</sub> in each element. If the other boundary conditions are given, then the conclusions are valid in all elements that its distance from the boundary≥ch|lnh|. The above conclusions are also valid. for n-dergree rectangular element Q<sub>1</sub> （n）.展开更多
In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^...In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.展开更多
There have been numerous works proposed to merge augmented reality/mixed reality(AR/MR)and Internet of Things(IoT)in various ways.However,they have focused on their specific target applications and have limitations on...There have been numerous works proposed to merge augmented reality/mixed reality(AR/MR)and Internet of Things(IoT)in various ways.However,they have focused on their specific target applications and have limitations on interoperability or reusability when utilizing them to different domains or adding other devices to the system.This paper proposes a novel architecture of a convergence platform for AR/MR and IoT systems and services.The proposed architecture adopts the oneM2M IoT standard as the basic framework that converges AR/MR and IoT systems and enables the development of application services used in general-purpose environments without being subordinate to specific systems,domains,and device manufacturers.We implement the proposed architecture utilizing the open-source oneM2M-based IoT server and device platforms released by the open alliance for IoT standards(OCEAN)and Microsoft HoloLens as an MR device platform.We also suggest and demonstrate the practical use cases and discuss the advantages of the proposed architecture.展开更多
[Objectives]To establish an ultra performance convergence chromatography(UPC2)method to determine the content of enantiomers in(R)-2-methoxyethyl1-(1-phenylethyl)-1H-imidazole-5-carboxylate hydrochloride(ET-26 HCl).[M...[Objectives]To establish an ultra performance convergence chromatography(UPC2)method to determine the content of enantiomers in(R)-2-methoxyethyl1-(1-phenylethyl)-1H-imidazole-5-carboxylate hydrochloride(ET-26 HCl).[Methods]ChiralpakAD-3 chromatographic column(4.6 mm×100 mm,3μm)was used,with 0.1%diethylamine methanol solution-supercritical carbon dioxide(1∶9)as mobile phase;flow rate 2.0 mL/min;back pressure 2000 psi,detection wavelength 240 nm,and column temperature 35℃.[Results]ET-26-HCl was completely separated from the enantiomers,and the linear relationship was good;the detection limit was 1.5μg/mL.[Conclusions]This method is suitable for the determination of the content of enantiomers in ET-26-HCl.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10971203 and 11271340)the Research Fund for the Doctoral Program of Higher Education of China (No. 20094101110006)
文摘A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.
基金Supported by the National Natrual Science Funds of China
文摘Consider L<sup>2</sup>-projection u<sub>h</sub> of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for constructing a superclose to function u<sub>h</sub> are proposed and then superconvergence for both u<sub>h</sub> and Du<sub>h</sub> are proved. When n is odd and no boundary conditions are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order Gauss points G<sub>n+1</sub> in each element. When n is even and function values on the boundary are prescribed, then u<sub>h</sub> is of superconvergence at n+1 order points Z<sub>n+1</sub> in each element. If the other boundary conditions are given, then the conclusions are valid in all elements that its distance from the boundary≥ch|lnh|. The above conclusions are also valid. for n-dergree rectangular element Q<sub>1</sub> （n）.
基金S.Geng's research was supported in part by the National Natural Science Foundation of China(12071397)Excellent Youth Project of Hunan Education Department(21B0165)+1 种基金F.Huang's research was supported in part by the National Key R&D Program of China 2021YFA1000800the National Natural Science Foundation of China(12288201).
文摘In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.
基金This research was supported by MSIT(Ministry of Science and ICT),Korea,under the ITRC(Information Technology Research Center)support program(IITP-2021-2018-0-01431)the High-Potential Individuals Global Training Program(2019-0-01611)supervised by the IITP(Institute for Information&Communications Technology Planning&Evaluation).
文摘There have been numerous works proposed to merge augmented reality/mixed reality(AR/MR)and Internet of Things(IoT)in various ways.However,they have focused on their specific target applications and have limitations on interoperability or reusability when utilizing them to different domains or adding other devices to the system.This paper proposes a novel architecture of a convergence platform for AR/MR and IoT systems and services.The proposed architecture adopts the oneM2M IoT standard as the basic framework that converges AR/MR and IoT systems and enables the development of application services used in general-purpose environments without being subordinate to specific systems,domains,and device manufacturers.We implement the proposed architecture utilizing the open-source oneM2M-based IoT server and device platforms released by the open alliance for IoT standards(OCEAN)and Microsoft HoloLens as an MR device platform.We also suggest and demonstrate the practical use cases and discuss the advantages of the proposed architecture.
文摘[Objectives]To establish an ultra performance convergence chromatography(UPC2)method to determine the content of enantiomers in(R)-2-methoxyethyl1-(1-phenylethyl)-1H-imidazole-5-carboxylate hydrochloride(ET-26 HCl).[Methods]ChiralpakAD-3 chromatographic column(4.6 mm×100 mm,3μm)was used,with 0.1%diethylamine methanol solution-supercritical carbon dioxide(1∶9)as mobile phase;flow rate 2.0 mL/min;back pressure 2000 psi,detection wavelength 240 nm,and column temperature 35℃.[Results]ET-26-HCl was completely separated from the enantiomers,and the linear relationship was good;the detection limit was 1.5μg/mL.[Conclusions]This method is suitable for the determination of the content of enantiomers in ET-26-HCl.
