We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across th...We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.展开更多
The movement principle of sidewalls and floor of extraction opening is analyzed, it is found that floor heave not only has something to do with the floor strata, but sidewalls. The effect of sidewall anchor and corner...The movement principle of sidewalls and floor of extraction opening is analyzed, it is found that floor heave not only has something to do with the floor strata, but sidewalls. The effect of sidewall anchor and corner anchor is studied, the mechanical principle of reinforcing sidewalls and corners is put forward and applied in engineering practice.展开更多
With the increasing necessities for reliable printed circuit board(PCB) product, there has been a considerable demand for high speed and high precision vision positioning system. To locate a rectangular lead component...With the increasing necessities for reliable printed circuit board(PCB) product, there has been a considerable demand for high speed and high precision vision positioning system. To locate a rectangular lead component with high accuracy and reliability, a new visual positioning method was introduced. Considering the limitations of Ghosal sub-pixel edge detection algorithm, an improved algorithm was proposed, in which Harris corner features were used to coarsely detect the edge points and Zernike moments were adopted to accurately detect the edge points. Besides, two formulas were developed to determine the edge intersections whose sub-pixel coordinates were calculated with bilinear interpolation and conjugate gradient method. The last experimental results show that the proposed method can detect the deflection and offset, and the detection errors are less than 0.04° and 0.02 pixels.展开更多
1.Introduction We are all familiar with the word"integrity"and have:some common understanding of it.It is generally accepted that honesty and reliability are two important aspects of integrity.Specifc to sci...1.Introduction We are all familiar with the word"integrity"and have:some common understanding of it.It is generally accepted that honesty and reliability are two important aspects of integrity.Specifc to scientific research,what is research integrity?Why does it matter?Is it just the responsibility of researchers themselves or a shared responsibility of the entire research community?展开更多
Due to the continuous rising demand of handheld devices like iPods, mobile, tablets;specific applications like biomedical applications like pacemakers, hearing aid machines and space applications which require stable ...Due to the continuous rising demand of handheld devices like iPods, mobile, tablets;specific applications like biomedical applications like pacemakers, hearing aid machines and space applications which require stable digital systems with low power consumptions are required. As a main part in digital system the SRAM (Static Random Access Memory) should have low power consumption and stability. As we are continuously moving towards scaling for the last two decades the effect of this is process variations which have severe effect on stability, performance. Reducing the supply voltage to sub-threshold region, which helps in reducing the power consumption to an extent but side by side it raises the issue of the stability of the memory. Static Noise Margin of SRAM cell enforces great challenges to the sub threshold SRAM design. In this paper we have analyzed the cell stability of 9T SRAM Cell at various processes. The cell stability is checked at deep submicron (DSM) technology. In this paper we have analyzed the effect of temperature and supply voltage (Vdd) on the stability parameters of SRAM which is Static Noise Margin (SNM), Write Margin (WM) and Read Current. The effect has been observed at various process corners at 45 nm technology. The temperature has a significant effect on stability along with the Vdd. The Cell has been working efficiently at all process corners and has 50% more SNM from conventional 6T SRAM and 30% more WM from conventional 6T SRAM cell.展开更多
In Present scenario battery-powered hand-held multimedia systems become popular. The power consumption in these devices is a major concern these days for its long operational life. Although various techniques to reduc...In Present scenario battery-powered hand-held multimedia systems become popular. The power consumption in these devices is a major concern these days for its long operational life. Although various techniques to reduce the power dissipation has been developed. The most adopted method is to lower the supply voltage. But lowering the Vdd reduces the gate current much more rapidly than the sub-threshold current and degrades the SNM. This degraded SNM further limits the voltage scaling. To improve the stability of the SRAM cell topology of the conventional 6T Static Random Access Memory (SRAM) cell has been changed and revised to 8T and 10T cell, the topologies. This work has analyzed the SRAM’s Static Noise Margin (SNM) at 8T for various process corners at 65nm technology. It evaluates the SNM along with the write margins of the cell along with the cell size of 8T SRAM bit-cell operating in sub-threshold voltage at various process corners. It is observed that an 8T cell has 13 % better write margin than conventional 6T SRAM cell. This paper analyses the dependence of SNM of SRAM memory cell on supply voltage, temperature, transistor sizing in 65nm technology at various process corners (TT, SS, FF, FS, and SF).展开更多
As China moves to fundamentally improve its virus response by downgrading COVID-19 management to Class B from top-level Class A,one sector that has remained crucial yet bruised by the three-year battle against the dis...As China moves to fundamentally improve its virus response by downgrading COVID-19 management to Class B from top-level Class A,one sector that has remained crucial yet bruised by the three-year battle against the disease finally released a sigh of relief.展开更多
Monocular vision-based navigation is a considerable ability for a home mobile robot. However, due to diverse disturbances, helping robots avoid obstacles, especially nonManhattan obstacles, remains a big challenge. In...Monocular vision-based navigation is a considerable ability for a home mobile robot. However, due to diverse disturbances, helping robots avoid obstacles, especially nonManhattan obstacles, remains a big challenge. In indoor environments, there are many spatial right-corners that are projected into two dimensional projections with special geometric configurations. These projections, which consist of three lines,might enable us to estimate their position and orientation in 3 D scenes. In this paper, we present a method for home robots to avoid non-Manhattan obstacles in indoor environments from a monocular camera. The approach first detects non-Manhattan obstacles. Through analyzing geometric features and constraints,it is possible to estimate posture differences between orientation of the robot and non-Manhattan obstacles. Finally according to the convergence of posture differences, the robot can adjust its orientation to keep pace with the pose of detected non-Manhattan obstacles, making it possible avoid these obstacles by itself. Based on geometric inferences, the proposed approach requires no prior training or any knowledge of the camera’s internal parameters,making it practical for robots navigation. Furthermore, the method is robust to errors in calibration and image noise. We compared the errors from corners of estimated non-Manhattan obstacles against the ground truth. Furthermore, we evaluate the validity of convergence of differences between the robot orientation and the posture of non-Manhattan obstacles. The experimental results showed that our method is capable of avoiding non-Manhattan obstacles, meeting the requirements for indoor robot navigation.展开更多
In this note we prove that the corner cutting procedure preserves continuityproperties,i.e.,a sequence of polygons obtained in this way belongs to the Lipschitz classof the same constant and exponent.As a consequence ...In this note we prove that the corner cutting procedure preserves continuityproperties,i.e.,a sequence of polygons obtained in this way belongs to the Lipschitz classof the same constant and exponent.As a consequence this also holds for all functions orcurves obtained as the limit of this procedure, such as the Bernstein polynomials,Bezierand spline parametric curves,etc.展开更多
The etching characteristics of concave and convex corners formed in a microstructure by the intersection of {111} planes in wet anisotropic etchant are exactly opposite to each other. The convex corners are severely a...The etching characteristics of concave and convex corners formed in a microstructure by the intersection of {111} planes in wet anisotropic etchant are exactly opposite to each other. The convex corners are severely attacked by anisotropic Fetchant, while the concave corners remain unaffected. In this paper, we present a new model which explains the root cause of the initiation and advancement of undercutting phenomenon at convex corners and its absence at concave corners on {110} silicon wafers. This contrary etching characteristics of convex and concave corners is explained by utilizing the role of dangling bond in etching process and the etching behavior of the tangent plane at the convex corner. The silicon atoms at the convex edge/ridge belong to a high etch rate tangent plane as compared to {111} sidewalls, which leads to the initiation of undercutting at the convex corner. On the other hand, all the bonds of silicon atoms pertaining to concave edges/ridge are engaged with neighboring atoms and consequently contain no dangling bond, thus resulting in no-undercutting at concave edges/corners.展开更多
During both daily operation and emergency evacuation,the corners of walking facilities in subway stations play an important role in efficient circulation.However,the effectiveness of the corner is difficult to assess....During both daily operation and emergency evacuation,the corners of walking facilities in subway stations play an important role in efficient circulation.However,the effectiveness of the corner is difficult to assess.In this paper,a method of passenger gathering and scattering analysis based on queueing models was proposed to investigate the corner performance in subway stations.Firstly,we constructed a set of state spaces of passenger flow according to passenger density and proposed the state transition model of passenger flow.Moreover,the model of passenger flow blocking and unblocking probability were also presented.Then,to illustrate the validity of the method and model,several passenger gathering-scattering scenarios and were simulated to verify the influence of passenger distribution and facility width on passenger walking,and the blocking probability,throughput,and expected time were also analyzed under various widths of the target corridor and arrival rates.Results showed that the proposed model can reproduce the trend of walking parameters changing and the self-organizing phenomenon of'faster is lower'.With the increase of arrival rates of passengers,walking speeds of passengers decrease and the expected walking time is prolonged,and the blocking probability sharply increased when the arrival rate exceeded 7 peds/s.In addition,with change of width of the target facility,efficiency of capacity of walking circulation facility fluctuated.With the width of the target corridor enlarged by 10%,the steady state of passenger flow was less crowded.Therefore,corridor width is critical to the circulation efficiency of passengers in subway stations.The conclusions will help to develop reasonable passenger flow control plans to ease the jam and keep passengers walking safely.展开更多
Increasing evidence supports the notion that pattern-recognition-receptor-mediated immunity goes beyond plasma membrane-to-nucleus signaling.With the findings of the pathways linking plasma membrane and chloroplasts a...Increasing evidence supports the notion that pattern-recognition-receptor-mediated immunity goes beyond plasma membrane-to-nucleus signaling.With the findings of the pathways linking plasma membrane and chloroplasts and the functions of stromules and perinuclear chloroplast clustering(PCC)in plant defense,chloroplast immunity has emerged as a cornerstone of plant defense and a target of plant pathogens.展开更多
The appropriate use of animal models is one of the most important steps for a successful translational research project.For scientists working in basic biomaterials research and development,the problem is the uncertai...The appropriate use of animal models is one of the most important steps for a successful translational research project.For scientists working in basic biomaterials research and development,the problem is the uncertainty in selecting the most suitable models for a particular research question.Because of the complexity of translational research,the choice of animal model must be a thorough and clearly-defined process in order to provide relevant,reliable and translatable scientific data,ensure the most beneficial use of the animals,and to be accepted by peers.As stated by Bernard Rollin,1“The most brilliant design,the most elegant procedures,the purest reagents,along with investigator talent,public money,and animal life are all wasted if the choice of animal is incorrect.”To design a successful animal experiment,many questions need to be addressed.展开更多
Isaw an advertisement for a 30-foot by 30-foot silk Persian carpet in a pan-Middle Eastern newspaperrecently with the punch line "Ifyour palace needs it, contactus." Palaces and carpet weavers are synonymous...Isaw an advertisement for a 30-foot by 30-foot silk Persian carpet in a pan-Middle Eastern newspaperrecently with the punch line "Ifyour palace needs it, contactus." Palaces and carpet weavers are synonymous with the oil-soaked Middle East. As an occasional collector of展开更多
Everyone has a unique idea of what Wuhan looks like.Designer Li Lanlan is inclined to record the minutiae of its daily life.In Li's eyes,the life of local people is becoming more colorful as the city develops.Peop...Everyone has a unique idea of what Wuhan looks like.Designer Li Lanlan is inclined to record the minutiae of its daily life.In Li's eyes,the life of local people is becoming more colorful as the city develops.People are more willing to experience life outside instead of staying at home.Activities such as enjoying a slow life in a cafe on Lihuangpi Road and tasting night snacks at sidewalk stalls are popular with locals.These scenes are common themes in Li's photographs.展开更多
印度是一个相对性保守之国,最近,一些影院老板在影院中开设了“情侣座”,效果很好。“情侣座”被本文称为Close-Up Corners/romantic corners。别具情趣。本文虽短,语言却很精彩。第一句的Lovers have it tough就可咀嚼一番。英语有have...印度是一个相对性保守之国,最近,一些影院老板在影院中开设了“情侣座”,效果很好。“情侣座”被本文称为Close-Up Corners/romantic corners。别具情趣。本文虽短,语言却很精彩。第一句的Lovers have it tough就可咀嚼一番。英语有have it good/have it easy/have it soft之说,其含义大同小异:[口]生活过得优裕。而略作推断,Lovers have it tough的意思就是“情侣们日子不好过”,为什么?prying eyes两个词就说明了问题。展开更多
This paper studies the multi-degree reduction of tensor product B(?)zier surfaces with any degree interpolation conditions of four corners, which is urgently to be resolved in many CAD/CAM systems. For the given condi...This paper studies the multi-degree reduction of tensor product B(?)zier surfaces with any degree interpolation conditions of four corners, which is urgently to be resolved in many CAD/CAM systems. For the given conditions of corners interpolation, this paper presents one intuitive method of degree reduction of parametric surfaces. Another new approximation algorithm of multi-degree reduction is also presented with the degree elevation of surfaces and the Chebyshev polynomial approximation theory. It obtains the good approximate effect and the boundaries of degree reduced surface can preserve the prescribed continuities. The degree reduction error of the latter algorithm is much smaller than that of the first algorithm. The error bounds of degree reduction of two algorithms are also presented .展开更多
Finite element approximation of the elliptic operator on a non-convexdomain composed of rectangles is considered using a graded mesh.Some errorestimates and error expansion are presented.
Considering the acoustic source scattering problems,when the sour-ce is non-radiating/invisible,we investigate the geometrical characterization for the underlying sources at polyhedral and conical corner.It is reveale...Considering the acoustic source scattering problems,when the sour-ce is non-radiating/invisible,we investigate the geometrical characterization for the underlying sources at polyhedral and conical corner.It is revealed that the non-radiating source with Holder continuous regularity must vanish at the corner.Using this kind of geometrical characterization of non-radiating sources,we establish local and global unique determination for a source with the polyhedral or corona shape support by a single far field measurement.Uniqueness by a single far field measurement constitutes of a long standing problem in inverse scattering problems.展开更多
基金supported by National Natural Science Foundation of China(12061080,12161087 and 12261093)the Science and Technology Project of the Education Department of Jiangxi Province(GJJ211601)supported by National Natural Science Foundation of China(11871305).
文摘We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
文摘The movement principle of sidewalls and floor of extraction opening is analyzed, it is found that floor heave not only has something to do with the floor strata, but sidewalls. The effect of sidewall anchor and corner anchor is studied, the mechanical principle of reinforcing sidewalls and corners is put forward and applied in engineering practice.
基金Project(51175242)supported by the National Natural Science Foundation of ChinaProject(BA2012031)supported by the Jiangsu Province Science and Technology Foundation of China
文摘With the increasing necessities for reliable printed circuit board(PCB) product, there has been a considerable demand for high speed and high precision vision positioning system. To locate a rectangular lead component with high accuracy and reliability, a new visual positioning method was introduced. Considering the limitations of Ghosal sub-pixel edge detection algorithm, an improved algorithm was proposed, in which Harris corner features were used to coarsely detect the edge points and Zernike moments were adopted to accurately detect the edge points. Besides, two formulas were developed to determine the edge intersections whose sub-pixel coordinates were calculated with bilinear interpolation and conjugate gradient method. The last experimental results show that the proposed method can detect the deflection and offset, and the detection errors are less than 0.04° and 0.02 pixels.
文摘1.Introduction We are all familiar with the word"integrity"and have:some common understanding of it.It is generally accepted that honesty and reliability are two important aspects of integrity.Specifc to scientific research,what is research integrity?Why does it matter?Is it just the responsibility of researchers themselves or a shared responsibility of the entire research community?
文摘Due to the continuous rising demand of handheld devices like iPods, mobile, tablets;specific applications like biomedical applications like pacemakers, hearing aid machines and space applications which require stable digital systems with low power consumptions are required. As a main part in digital system the SRAM (Static Random Access Memory) should have low power consumption and stability. As we are continuously moving towards scaling for the last two decades the effect of this is process variations which have severe effect on stability, performance. Reducing the supply voltage to sub-threshold region, which helps in reducing the power consumption to an extent but side by side it raises the issue of the stability of the memory. Static Noise Margin of SRAM cell enforces great challenges to the sub threshold SRAM design. In this paper we have analyzed the cell stability of 9T SRAM Cell at various processes. The cell stability is checked at deep submicron (DSM) technology. In this paper we have analyzed the effect of temperature and supply voltage (Vdd) on the stability parameters of SRAM which is Static Noise Margin (SNM), Write Margin (WM) and Read Current. The effect has been observed at various process corners at 45 nm technology. The temperature has a significant effect on stability along with the Vdd. The Cell has been working efficiently at all process corners and has 50% more SNM from conventional 6T SRAM and 30% more WM from conventional 6T SRAM cell.
文摘In Present scenario battery-powered hand-held multimedia systems become popular. The power consumption in these devices is a major concern these days for its long operational life. Although various techniques to reduce the power dissipation has been developed. The most adopted method is to lower the supply voltage. But lowering the Vdd reduces the gate current much more rapidly than the sub-threshold current and degrades the SNM. This degraded SNM further limits the voltage scaling. To improve the stability of the SRAM cell topology of the conventional 6T Static Random Access Memory (SRAM) cell has been changed and revised to 8T and 10T cell, the topologies. This work has analyzed the SRAM’s Static Noise Margin (SNM) at 8T for various process corners at 65nm technology. It evaluates the SNM along with the write margins of the cell along with the cell size of 8T SRAM bit-cell operating in sub-threshold voltage at various process corners. It is observed that an 8T cell has 13 % better write margin than conventional 6T SRAM cell. This paper analyses the dependence of SNM of SRAM memory cell on supply voltage, temperature, transistor sizing in 65nm technology at various process corners (TT, SS, FF, FS, and SF).
文摘As China moves to fundamentally improve its virus response by downgrading COVID-19 management to Class B from top-level Class A,one sector that has remained crucial yet bruised by the three-year battle against the disease finally released a sigh of relief.
基金supported by the National Natural Science Foundation of China(61771146,61375122)the National Thirteen 5-Year Plan for Science and Technology(2017YFC1703303)in part by Shanghai Science and Technology Development Funds(13dz2260200,13511504300)。
文摘Monocular vision-based navigation is a considerable ability for a home mobile robot. However, due to diverse disturbances, helping robots avoid obstacles, especially nonManhattan obstacles, remains a big challenge. In indoor environments, there are many spatial right-corners that are projected into two dimensional projections with special geometric configurations. These projections, which consist of three lines,might enable us to estimate their position and orientation in 3 D scenes. In this paper, we present a method for home robots to avoid non-Manhattan obstacles in indoor environments from a monocular camera. The approach first detects non-Manhattan obstacles. Through analyzing geometric features and constraints,it is possible to estimate posture differences between orientation of the robot and non-Manhattan obstacles. Finally according to the convergence of posture differences, the robot can adjust its orientation to keep pace with the pose of detected non-Manhattan obstacles, making it possible avoid these obstacles by itself. Based on geometric inferences, the proposed approach requires no prior training or any knowledge of the camera’s internal parameters,making it practical for robots navigation. Furthermore, the method is robust to errors in calibration and image noise. We compared the errors from corners of estimated non-Manhattan obstacles against the ground truth. Furthermore, we evaluate the validity of convergence of differences between the robot orientation and the posture of non-Manhattan obstacles. The experimental results showed that our method is capable of avoiding non-Manhattan obstacles, meeting the requirements for indoor robot navigation.
文摘In this note we prove that the corner cutting procedure preserves continuityproperties,i.e.,a sequence of polygons obtained in this way belongs to the Lipschitz classof the same constant and exponent.As a consequence this also holds for all functions orcurves obtained as the limit of this procedure, such as the Bernstein polynomials,Bezierand spline parametric curves,etc.
文摘The etching characteristics of concave and convex corners formed in a microstructure by the intersection of {111} planes in wet anisotropic etchant are exactly opposite to each other. The convex corners are severely attacked by anisotropic Fetchant, while the concave corners remain unaffected. In this paper, we present a new model which explains the root cause of the initiation and advancement of undercutting phenomenon at convex corners and its absence at concave corners on {110} silicon wafers. This contrary etching characteristics of convex and concave corners is explained by utilizing the role of dangling bond in etching process and the etching behavior of the tangent plane at the convex corner. The silicon atoms at the convex edge/ridge belong to a high etch rate tangent plane as compared to {111} sidewalls, which leads to the initiation of undercutting at the convex corner. On the other hand, all the bonds of silicon atoms pertaining to concave edges/ridge are engaged with neighboring atoms and consequently contain no dangling bond, thus resulting in no-undercutting at concave edges/corners.
基金supported by the National Key R&D Program of China(No.2020YFB1600701).
文摘During both daily operation and emergency evacuation,the corners of walking facilities in subway stations play an important role in efficient circulation.However,the effectiveness of the corner is difficult to assess.In this paper,a method of passenger gathering and scattering analysis based on queueing models was proposed to investigate the corner performance in subway stations.Firstly,we constructed a set of state spaces of passenger flow according to passenger density and proposed the state transition model of passenger flow.Moreover,the model of passenger flow blocking and unblocking probability were also presented.Then,to illustrate the validity of the method and model,several passenger gathering-scattering scenarios and were simulated to verify the influence of passenger distribution and facility width on passenger walking,and the blocking probability,throughput,and expected time were also analyzed under various widths of the target corridor and arrival rates.Results showed that the proposed model can reproduce the trend of walking parameters changing and the self-organizing phenomenon of'faster is lower'.With the increase of arrival rates of passengers,walking speeds of passengers decrease and the expected walking time is prolonged,and the blocking probability sharply increased when the arrival rate exceeded 7 peds/s.In addition,with change of width of the target facility,efficiency of capacity of walking circulation facility fluctuated.With the width of the target corridor enlarged by 10%,the steady state of passenger flow was less crowded.Therefore,corridor width is critical to the circulation efficiency of passengers in subway stations.The conclusions will help to develop reasonable passenger flow control plans to ease the jam and keep passengers walking safely.
基金supported by grants from the National Key Research and Development Program of China(2021YFD1400400)the Natural Science Foundation of China(32320103010,32172385,and 31930089).
文摘Increasing evidence supports the notion that pattern-recognition-receptor-mediated immunity goes beyond plasma membrane-to-nucleus signaling.With the findings of the pathways linking plasma membrane and chloroplasts and the functions of stromules and perinuclear chloroplast clustering(PCC)in plant defense,chloroplast immunity has emerged as a cornerstone of plant defense and a target of plant pathogens.
文摘The appropriate use of animal models is one of the most important steps for a successful translational research project.For scientists working in basic biomaterials research and development,the problem is the uncertainty in selecting the most suitable models for a particular research question.Because of the complexity of translational research,the choice of animal model must be a thorough and clearly-defined process in order to provide relevant,reliable and translatable scientific data,ensure the most beneficial use of the animals,and to be accepted by peers.As stated by Bernard Rollin,1“The most brilliant design,the most elegant procedures,the purest reagents,along with investigator talent,public money,and animal life are all wasted if the choice of animal is incorrect.”To design a successful animal experiment,many questions need to be addressed.
文摘Isaw an advertisement for a 30-foot by 30-foot silk Persian carpet in a pan-Middle Eastern newspaperrecently with the punch line "Ifyour palace needs it, contactus." Palaces and carpet weavers are synonymous with the oil-soaked Middle East. As an occasional collector of
文摘Everyone has a unique idea of what Wuhan looks like.Designer Li Lanlan is inclined to record the minutiae of its daily life.In Li's eyes,the life of local people is becoming more colorful as the city develops.People are more willing to experience life outside instead of staying at home.Activities such as enjoying a slow life in a cafe on Lihuangpi Road and tasting night snacks at sidewalk stalls are popular with locals.These scenes are common themes in Li's photographs.
文摘印度是一个相对性保守之国,最近,一些影院老板在影院中开设了“情侣座”,效果很好。“情侣座”被本文称为Close-Up Corners/romantic corners。别具情趣。本文虽短,语言却很精彩。第一句的Lovers have it tough就可咀嚼一番。英语有have it good/have it easy/have it soft之说,其含义大同小异:[口]生活过得优裕。而略作推断,Lovers have it tough的意思就是“情侣们日子不好过”,为什么?prying eyes两个词就说明了问题。
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69973041) Natural Science Foundation of Zhejiang Province (Grant No. 698025) and the Foundation of State Key Basic Research 973 Project (Grant No. G1998030600).
文摘This paper studies the multi-degree reduction of tensor product B(?)zier surfaces with any degree interpolation conditions of four corners, which is urgently to be resolved in many CAD/CAM systems. For the given conditions of corners interpolation, this paper presents one intuitive method of degree reduction of parametric surfaces. Another new approximation algorithm of multi-degree reduction is also presented with the degree elevation of surfaces and the Chebyshev polynomial approximation theory. It obtains the good approximate effect and the boundaries of degree reduced surface can preserve the prescribed continuities. The degree reduction error of the latter algorithm is much smaller than that of the first algorithm. The error bounds of degree reduction of two algorithms are also presented .
基金supported by the Deutsche Forschungsgemeinschaft(DFG),SFB 123."Stochatistische Mathematische Modelle",Universitat Heidelberg
文摘Finite element approximation of the elliptic operator on a non-convexdomain composed of rectangles is considered using a graded mesh.Some errorestimates and error expansion are presented.
基金the National Natural Science Foundation of China(Grant No.12371422)the Fundamental Research Funds for the Central Universities,JLU(Grant No.93Z172023Z01)+3 种基金The work of Y.Geng is supported by the Graduate Innovation Fund of Jilin University(Grant No.2023Cx276)the Hong Kong RGC General Research Funds(Projects 12302919,12301420 and 11300821)the NSFC/RGC Joint Research Fund(Project N.City U101/21)the France-Hong Kong ANR/RGCJoint Research(Grant No.A-HKBU 203/19).
文摘Considering the acoustic source scattering problems,when the sour-ce is non-radiating/invisible,we investigate the geometrical characterization for the underlying sources at polyhedral and conical corner.It is revealed that the non-radiating source with Holder continuous regularity must vanish at the corner.Using this kind of geometrical characterization of non-radiating sources,we establish local and global unique determination for a source with the polyhedral or corona shape support by a single far field measurement.Uniqueness by a single far field measurement constitutes of a long standing problem in inverse scattering problems.