Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with different...Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.展开更多
We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein ...We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.展开更多
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. The...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockw...The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockwise and counterclockwise given. The symmetry of the diffusion process is shown to be equivalent to that for any closed smooth curve. the long time average winding numbers of the projection process in two different directions are equal.展开更多
Over the past 50 years,crown asymmetry of forest trees has been evaluated through several indices constructed from the perspective of projected crown shape or displacement but often on an ad hoc basis to address speci...Over the past 50 years,crown asymmetry of forest trees has been evaluated through several indices constructed from the perspective of projected crown shape or displacement but often on an ad hoc basis to address specifi c objectives related to tree growth and competition,stand dynamics,stem form,crown structure and treefall risks.Although sharing some similarities,these indices are largely incoherent and non-comparable as they diff er not only in the scale but also in the direction of their values in indicating the degree of crown asymmetry.As the fi rst attempt at devising normative measures of crown asymmetry,we adopted a relative scale between 0 for perfect symmetry and 1 for extreme asymmetry.Five existing crown asymmetry indices(CAIs)were brought onto this relative scale after necessary modifi cations.Eight new CAIs were adapted from measures of circularity for digital images in computer graphics,indices of income inequality in economics,and a bilateral symmetry indicator in plant leaf morphology.The performances of the 13 CAIs were compared over diff erent numbers of measured crown radii for 30 projected crowns of mature Eucalyptus pilularis trees through benchmarking statistics and rank order correlation analysis.For each CAI,the index value based on the full measurement of 36 evenly spaced radii of a projected crown was taken as the true value in the benchmarking process.The index(CAI 13)adapted from the simple bilateral symmetry measure proved to be the least biased and most precise.Its performance was closely followed by that of three other CAIs.The minimum number of crown radii that is needed to provide at least an indicative measure of crown asymmetry is four.For more accurate and consistent measures,at least 6 or 8 crown radii are needed.The range of variability in crown morphology of the trees under investigation also needs to be taken into consideration.Although the CAIs are from projected crown radii,they can be readily extended to individual tree crown metrics that are now commonly extracted from展开更多
In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 syst...In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 systems, 32 point groups and 47 single forms belong to crystals. In this paper, the point groups and single forms of quasicrystals are deduced and drawn as stereographic projections by the rules of crystallographic point groups. These stereographic projections integrate the crystal and quasicrystal symmetry theories.展开更多
针对摄像机内部参数的不确定性和投影平面选择难的问题,提出一种新的投影深度算法用于视角不变的动作识别,该算法采用对称镜面平面提取(plane extraction from mirror symmetry,PEMS)策略,有效解决了投影平面选择难的问题。首先通过摄...针对摄像机内部参数的不确定性和投影平面选择难的问题,提出一种新的投影深度算法用于视角不变的动作识别,该算法采用对称镜面平面提取(plane extraction from mirror symmetry,PEMS)策略,有效解决了投影平面选择难的问题。首先通过摄像机组观察获得3D动作姿势,然后运用PEMS策略从场景中提取平面,相对于提取平面估计身体点的投影深度,最后使用这个信息进行动作识别。该算法的核心是投影平面的提取和投影深度组成向量的求解。利用该算法在CMU Mo Cap数据集、TUM数据集和多视图IXMAS数据集上进行测试,精度可分别高达94%、91%和90%,且在较少动作实例情况下,仍然能够准确定义新动作。比较表明,该算法的人体动作识别性能明显优于其他几种较新的算法。展开更多
文摘Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.
基金supported by National Natural Science Foundation of China(Grant Nos.12061060 and 11801141)Scientific and Technological Planning Project of Yunnan Province(Grant No.202305AC160005)Scientific and Technological Innovation Team of Yunnan Province(Grant No.2020CXTD25)。
文摘We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.
基金supported by the Natural Science Foundation China(11126343)Guangxi Natural Science Foundation(2013GXNSFBA019010)+1 种基金supported by Natural Science Foundation China(11071152)Natural Science Foundation of Guangdong Province(10151503101000025,S2011010004511)
文摘This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.
文摘The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockwise and counterclockwise given. The symmetry of the diffusion process is shown to be equivalent to that for any closed smooth curve. the long time average winding numbers of the projection process in two different directions are equal.
基金the Heilongjiang Touyan Innovation Team 747 Program(Technology Development Team for High-effi cient Silviculture of Forest Resources).
文摘Over the past 50 years,crown asymmetry of forest trees has been evaluated through several indices constructed from the perspective of projected crown shape or displacement but often on an ad hoc basis to address specifi c objectives related to tree growth and competition,stand dynamics,stem form,crown structure and treefall risks.Although sharing some similarities,these indices are largely incoherent and non-comparable as they diff er not only in the scale but also in the direction of their values in indicating the degree of crown asymmetry.As the fi rst attempt at devising normative measures of crown asymmetry,we adopted a relative scale between 0 for perfect symmetry and 1 for extreme asymmetry.Five existing crown asymmetry indices(CAIs)were brought onto this relative scale after necessary modifi cations.Eight new CAIs were adapted from measures of circularity for digital images in computer graphics,indices of income inequality in economics,and a bilateral symmetry indicator in plant leaf morphology.The performances of the 13 CAIs were compared over diff erent numbers of measured crown radii for 30 projected crowns of mature Eucalyptus pilularis trees through benchmarking statistics and rank order correlation analysis.For each CAI,the index value based on the full measurement of 36 evenly spaced radii of a projected crown was taken as the true value in the benchmarking process.The index(CAI 13)adapted from the simple bilateral symmetry measure proved to be the least biased and most precise.Its performance was closely followed by that of three other CAIs.The minimum number of crown radii that is needed to provide at least an indicative measure of crown asymmetry is four.For more accurate and consistent measures,at least 6 or 8 crown radii are needed.The range of variability in crown morphology of the trees under investigation also needs to be taken into consideration.Although the CAIs are from projected crown radii,they can be readily extended to individual tree crown metrics that are now commonly extracted from
文摘In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 systems, 32 point groups and 47 single forms belong to crystals. In this paper, the point groups and single forms of quasicrystals are deduced and drawn as stereographic projections by the rules of crystallographic point groups. These stereographic projections integrate the crystal and quasicrystal symmetry theories.
文摘针对摄像机内部参数的不确定性和投影平面选择难的问题,提出一种新的投影深度算法用于视角不变的动作识别,该算法采用对称镜面平面提取(plane extraction from mirror symmetry,PEMS)策略,有效解决了投影平面选择难的问题。首先通过摄像机组观察获得3D动作姿势,然后运用PEMS策略从场景中提取平面,相对于提取平面估计身体点的投影深度,最后使用这个信息进行动作识别。该算法的核心是投影平面的提取和投影深度组成向量的求解。利用该算法在CMU Mo Cap数据集、TUM数据集和多视图IXMAS数据集上进行测试,精度可分别高达94%、91%和90%,且在较少动作实例情况下,仍然能够准确定义新动作。比较表明,该算法的人体动作识别性能明显优于其他几种较新的算法。
