The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functi...The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.展开更多
Geode, boudinage, and undulation structures are widely distributed in the siliceous beds of the Upper Cretaceous/Tertiary rocks in Jordan. Their formation was attributed to tectonic forces, syngenetic processes, organ...Geode, boudinage, and undulation structures are widely distributed in the siliceous beds of the Upper Cretaceous/Tertiary rocks in Jordan. Their formation was attributed to tectonic forces, syngenetic processes, organic disintegration processes, subaquatic gliding, compaction and settlement, and meteoritic impacts. In this work, the structural features in the siliceous beds of Jordan are attributed to an interplay of load and directed pressures, and mineralogical transformation processes (opal-A to opal-CT to quartz), governed by pH changes. Tectonic directed pressure was acting in an ESE-WSW direction and is common in the silicified limestone of Upper Cretaceous.展开更多
Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at th...Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity;however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.展开更多
In this paper, we generalize geodesic E-convex function and define geodesic γ-pre-E-convex and geodesic γ-E-convex functions on Riemannian manifolds. The sufficient condition of equivalence class of geodesic γ-pre-...In this paper, we generalize geodesic E-convex function and define geodesic γ-pre-E-convex and geodesic γ-E-convex functions on Riemannian manifolds. The sufficient condition of equivalence class of geodesic γ-pre-E-convexity and geodesic γ-E-convexity for differentiable function on Riemannian manifolds is studied. We discuss the sufficient condition for E-epigraph to be geodesic E-convex set. At the end, we establish some optimality results with the aid of geodesic γ-pre-E-convex and geodesic γ-E-convex functions and discuss the mean value inequality for geodesic γ-pre-E-convex function.展开更多
In this paper, we get necessary and sufficient conditions for a Finsler space en- dowed with an （α,β）-metric where its geodesic coefficients G^i （x, y） and the reverse of geodesic coefficients G^i（x,-y） have t...In this paper, we get necessary and sufficient conditions for a Finsler space en- dowed with an （α,β）-metric where its geodesic coefficients G^i （x, y） and the reverse of geodesic coefficients G^i（x,-y） have the same Douglas curvature. They are the conditions such that （α,β）-metrics have reversible geodesics.展开更多
It is shown to be a relevant study involving terrestrial methods of measurement, such as： forward and backward intersections, geometric leveling, trigonometric leveling with short distance targeted and spatial positi...It is shown to be a relevant study involving terrestrial methods of measurement, such as： forward and backward intersections, geometric leveling, trigonometric leveling with short distance targeted and spatial positioning GNSS methods, for the definition of field reference points and field-object points located in rough terrain. The geodesic structures were implemented in the Historic Site of Olinda employing GNSS （global navigation satellite system） receivers, total stations and digital level. The historical site of Olinda was recorded by UNESCO as Historical and Cultural Heritage of Humanity. The study area is located in the center of the busiest site with a quite roughly relief. This area has been studied since 2007 involving Research of Scientific Initiation and Pos-Graduation Course. This paper aims to present the realized experiments for the implementation and definition of geodesic structures in environments with very rough relief, including large old houses and historic monuments.展开更多
An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid...An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.展开更多
Computer-aided detection(CAD) for CT colonography refers to a scheme that automatically detects polyps in CT images of colon. Current CAD schemes already have a relatively high sensitivity and a low false positive rat...Computer-aided detection(CAD) for CT colonography refers to a scheme that automatically detects polyps in CT images of colon. Current CAD schemes already have a relatively high sensitivity and a low false positive rate. However, misdiagnosis and missed diagnosis are still common to happen, mainly due to the existence of haustral folds(HFs). An innovative idea of segmenting semilunar HFs from the smooth colonic wall and then using different methods to detect polyps on HFs and those on the smooth colonic wall is proposed in this paper to reduce the false positives and false negatives caused by HFs. For the polyps on HFs, a novel segmentation method is specially developed based on complementary geodesic distance transformation(CGDT). The proposed method is tested on four different models and real CT data. The property of CGDT is proved and our method turns out to be effective for HF segmentation and polyp segmentation. The encouraging experimental results primarily show the feasibility of the proposed method and its potential to improve the detection performance of CAD schemes.展开更多
Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT...Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m^＊ = 0 and m^＊ 〈〈 M, respectively.展开更多
Recently Malihe Heydari-Fard obtained a spherically symmetric exterior black hole solution in the brane-world scenario, which can be used to explain the galaxy rotation curves without postulating dark matter. By analy...Recently Malihe Heydari-Fard obtained a spherically symmetric exterior black hole solution in the brane-world scenario, which can be used to explain the galaxy rotation curves without postulating dark matter. By analysing the particle effective potential, we have investigated the time-like geodesic structure of the spherically symmetric black hole in the brane-world. We mainly take account of how the cosmological constant α and the stellar pressure β affect the time-like geodesic structure of the black hole. We find that the radial particle falls to the singularity from a finite distance or plunges into the singularity, depending on its initial conditions. But the non-radial time-like geodesic structure is more complex than the radial case. We find that the particle moves on the bound orbit or stable （unstable） circle orbit or plunges into the singularity, or reflects to infinity, depending on its energy and initial conditions. By comparing the particle effective potential curves for different values of the stellar pressureβ and the cosmological constant α, we find that the stellar pressure parameter β does not affect the time-like geodesic structure of the black hole, but the cosmological constant a has an impact on its time-like geodesic structure.展开更多
We present a new algorithm to compute a geodesic path over a triangle mesh. Based on Novotni＇s propagating wavefront method which is similar to the well known Dijkstra algorithm, we made some improvements which Novot...We present a new algorithm to compute a geodesic path over a triangle mesh. Based on Novotni＇s propagating wavefront method which is similar to the well known Dijkstra algorithm, we made some improvements which Novotni had missed and we also gave the method to find out the geodesic path which Novotni had not. It can handle both convex and non-convex surfaces or even with boundaries. Experiment results show that our method works very well both in efficiency and precision.展开更多
Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approxim...Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern.This search approach is very simple,and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method.Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information.Additionally,the geodesic cutting pattern saved about 21%of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.展开更多
The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at...The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as 10–100 ms-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.展开更多
Convolutional neural networks(CNNs)are prone to mis-segmenting image data of the liver when the background is complicated,which results in low segmentation accuracy and unsuitable results for clinical use.To address t...Convolutional neural networks(CNNs)are prone to mis-segmenting image data of the liver when the background is complicated,which results in low segmentation accuracy and unsuitable results for clinical use.To address this shortcoming,an interactive liver segmentation algorithm based on geodesic distance and V-net is proposed.The three-dimensional segmentation network V-net adequately considers the characteristics of the spatial context information to segment liver medical images and obtain preliminary segmentation results.An artificial algorithm based on geodesic distance is used to form artificial hard constraints to modify the image,and the superpixel piece created by the watershed algorithm is introduced as a sample point for operation,which significantly improves the efficiency of segmentation.Results from simulation of the liver tumor segmentation challenge(LiTS)dataset show that this algorithm can effectively refine the results of automatic liver segmentation,reduce user intervention,and enable a fast,interactive liver image segmentation that is convenient for doctors.展开更多
The purpose of this paper is to give a sufficient and necessary condition of totally geodesic on invariant submanifold of contact metric manifold and is to generalize the results in [3] and [4].
The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynami...The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection of 1-jet bundle. The dynamical flow concerning the non-autonomous case motion of an nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on 1-jet bundle, which is different from the case in an autonomous mechanical system.展开更多
This paper aims to determine the geodesic precession in Yu's (Ω, Aab)-field the- ory[1], and to compare the result with that of the Schwarzschild orbit.
Based on the theory of differential geometry, the geodesic equation of surfaces of rotation is derived and the mathematical model for geodesic winding of surfaces of rotation is established. It is the theoretical foun...Based on the theory of differential geometry, the geodesic equation of surfaces of rotation is derived and the mathematical model for geodesic winding of surfaces of rotation is established. It is the theoretical foundation of combination winding.展开更多
基金Supported by the National Natural Science Foundation of China（11074099）
文摘The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.
文摘Geode, boudinage, and undulation structures are widely distributed in the siliceous beds of the Upper Cretaceous/Tertiary rocks in Jordan. Their formation was attributed to tectonic forces, syngenetic processes, organic disintegration processes, subaquatic gliding, compaction and settlement, and meteoritic impacts. In this work, the structural features in the siliceous beds of Jordan are attributed to an interplay of load and directed pressures, and mineralogical transformation processes (opal-A to opal-CT to quartz), governed by pH changes. Tectonic directed pressure was acting in an ESE-WSW direction and is common in the silicified limestone of Upper Cretaceous.
文摘Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity;however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.
文摘In this paper, we generalize geodesic E-convex function and define geodesic γ-pre-E-convex and geodesic γ-E-convex functions on Riemannian manifolds. The sufficient condition of equivalence class of geodesic γ-pre-E-convexity and geodesic γ-E-convexity for differentiable function on Riemannian manifolds is studied. We discuss the sufficient condition for E-epigraph to be geodesic E-convex set. At the end, we establish some optimality results with the aid of geodesic γ-pre-E-convex and geodesic γ-E-convex functions and discuss the mean value inequality for geodesic γ-pre-E-convex function.
基金Supported by the National Natural Science Foundation of China(Grant No.11471246)the Jiangxi Provincial Science and Technology Project(Grant No.20161BAB211021)
文摘In this paper, we get necessary and sufficient conditions for a Finsler space en- dowed with an （α,β）-metric where its geodesic coefficients G^i （x, y） and the reverse of geodesic coefficients G^i（x,-y） have the same Douglas curvature. They are the conditions such that （α,β）-metrics have reversible geodesics.
文摘It is shown to be a relevant study involving terrestrial methods of measurement, such as： forward and backward intersections, geometric leveling, trigonometric leveling with short distance targeted and spatial positioning GNSS methods, for the definition of field reference points and field-object points located in rough terrain. The geodesic structures were implemented in the Historic Site of Olinda employing GNSS （global navigation satellite system） receivers, total stations and digital level. The historical site of Olinda was recorded by UNESCO as Historical and Cultural Heritage of Humanity. The study area is located in the center of the busiest site with a quite roughly relief. This area has been studied since 2007 involving Research of Scientific Initiation and Pos-Graduation Course. This paper aims to present the realized experiments for the implementation and definition of geodesic structures in environments with very rough relief, including large old houses and historic monuments.
基金supported by the National Natural Science Foundation of China(Grant No.41505066)the Basic Scientific Research and Operation Foundation of Chinese Academy Meteorological Sciences(Grant Nos.2015Z002,2015Y005)the National Research and Development Key Program:Global Change and Mitigation Strategies(No.2016YFA0602101)
文摘An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.
基金the National Natural Science Foundation of China(No.813716234)the National Basic Research Program(973) of China(No.2010CB834302)the Shanghai Jiao Tong University Medical Engineering Cross Research Funds(Nos.YG2013MS30 and YG2011MS51)
文摘Computer-aided detection(CAD) for CT colonography refers to a scheme that automatically detects polyps in CT images of colon. Current CAD schemes already have a relatively high sensitivity and a low false positive rate. However, misdiagnosis and missed diagnosis are still common to happen, mainly due to the existence of haustral folds(HFs). An innovative idea of segmenting semilunar HFs from the smooth colonic wall and then using different methods to detect polyps on HFs and those on the smooth colonic wall is proposed in this paper to reduce the false positives and false negatives caused by HFs. For the polyps on HFs, a novel segmentation method is specially developed based on complementary geodesic distance transformation(CGDT). The proposed method is tested on four different models and real CT data. The property of CGDT is proved and our method turns out to be effective for HF segmentation and polyp segmentation. The encouraging experimental results primarily show the feasibility of the proposed method and its potential to improve the detection performance of CAD schemes.
基金Project supported by the National Natural Science Foundation of China （Grant No 10475036）, the Natural Science Foundation of Liaoning Province, China （Grant No 20032012） and the Scientific Research Foundation of the Higher Education Institute of Liaoning Province, China （Grant No 05L215）.
文摘Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m^＊ = 0 and m^＊ 〈〈 M, respectively.
基金supported by the National Natural Science Foundation of China (Grant No. 10873004)the Program for Excellent Talents in Hunan Normal University (Grant No. ET10803)+3 种基金the State Key Development Program for Basic Research Project of China(Grant No. 2010CB832803)the Key Project of the National Natural Science Foundation of China (Grant No. 10935013)the Constructing Program of the National Key Disciplinethe Program for Changjiang Scholars and Innovative Research Teamin University (Grant No. IRT0964)
文摘Recently Malihe Heydari-Fard obtained a spherically symmetric exterior black hole solution in the brane-world scenario, which can be used to explain the galaxy rotation curves without postulating dark matter. By analysing the particle effective potential, we have investigated the time-like geodesic structure of the spherically symmetric black hole in the brane-world. We mainly take account of how the cosmological constant α and the stellar pressure β affect the time-like geodesic structure of the black hole. We find that the radial particle falls to the singularity from a finite distance or plunges into the singularity, depending on its initial conditions. But the non-radial time-like geodesic structure is more complex than the radial case. We find that the particle moves on the bound orbit or stable （unstable） circle orbit or plunges into the singularity, or reflects to infinity, depending on its energy and initial conditions. By comparing the particle effective potential curves for different values of the stellar pressureβ and the cosmological constant α, we find that the stellar pressure parameter β does not affect the time-like geodesic structure of the black hole, but the cosmological constant a has an impact on its time-like geodesic structure.
基金This work was supported by National Natural Science Foundation of PRC(No.60503058,No.60533080)the Science and Technology Fund of Huawei Technologies Co.,Ltd.
文摘We present a new algorithm to compute a geodesic path over a triangle mesh. Based on Novotni＇s propagating wavefront method which is similar to the well known Dijkstra algorithm, we made some improvements which Novotni had missed and we also gave the method to find out the geodesic path which Novotni had not. It can handle both convex and non-convex surfaces or even with boundaries. Experiment results show that our method works very well both in efficiency and precision.
基金Project(12 High-tech Urban C22)supported by High-tech Urban Development Program,Ministry of Land,Transport and Moritime Affairs of Korea
文摘Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern.This search approach is very simple,and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method.Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information.Additionally,the geodesic cutting pattern saved about 21%of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.
基金supported by National Natural Science Foundation of China(Nos.12075057,11775069,11320101005,51821005 and 11875020)Jiangxi Provincial Natural Science Foundation(No.20202ACBL201002)+1 种基金Doctoral Foundation(Nos.DHBK2017134 and DHBK 2018059)Grant-in-Aid for Scientific Research of JSPS(Nos.15H02155,15H02335,16H02442)。
文摘The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as 10–100 ms-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.
基金the Project of China Scholarship Council(No.201708615011)the Xi’an Science and Technology Plan Project(No.GXYD1.7)。
文摘Convolutional neural networks(CNNs)are prone to mis-segmenting image data of the liver when the background is complicated,which results in low segmentation accuracy and unsuitable results for clinical use.To address this shortcoming,an interactive liver segmentation algorithm based on geodesic distance and V-net is proposed.The three-dimensional segmentation network V-net adequately considers the characteristics of the spatial context information to segment liver medical images and obtain preliminary segmentation results.An artificial algorithm based on geodesic distance is used to form artificial hard constraints to modify the image,and the superpixel piece created by the watershed algorithm is introduced as a sample point for operation,which significantly improves the efficiency of segmentation.Results from simulation of the liver tumor segmentation challenge(LiTS)dataset show that this algorithm can effectively refine the results of automatic liver segmentation,reduce user intervention,and enable a fast,interactive liver image segmentation that is convenient for doctors.
文摘The purpose of this paper is to give a sufficient and necessary condition of totally geodesic on invariant submanifold of contact metric manifold and is to generalize the results in [3] and [4].
基金Partially supported by NSF (10801079)Partially supported by RFDP (20080551002)+1 种基金Partially supported by LPMC of MOE of ChinaPartially supported by the 973 Program of MOST, NNSF, MCME, RFDP, LPMC of MOE of China, S. S. Chern Foundation, and Nankai University
文摘In this paper, the concavity of closed geodesics proposed by M. Morse in 1930s is studied.
文摘The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection of 1-jet bundle. The dynamical flow concerning the non-autonomous case motion of an nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on 1-jet bundle, which is different from the case in an autonomous mechanical system.
文摘This paper aims to determine the geodesic precession in Yu's (Ω, Aab)-field the- ory[1], and to compare the result with that of the Schwarzschild orbit.
文摘Based on the theory of differential geometry, the geodesic equation of surfaces of rotation is derived and the mathematical model for geodesic winding of surfaces of rotation is established. It is the theoretical foundation of combination winding.
