The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller ...The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.展开更多
We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negative...We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.展开更多
We have pointed out that on the principles of special relativity and of propagation of light going along the null geodesic the special relativity of Einstein can be extented to the 3-dimensional Beltrami space-time D_...We have pointed out that on the principles of special relativity and of propagation of light going along the null geodesic the special relativity of Einstein can be extented to the 3-dimensional Beltrami space-time D_λ with constant curvaturesλ<0, λ= 0 and λ>0. The inertial coordinate systems for each of them are so-called Beltrami coordinates and their metrics are also Beltrami展开更多
The metrization of a probabilistic metric space (for short, PM-space )usually implies the metrization of its (ε,λ)-topological structure. Therefore, if a PM-space is metrizable, it only implies that its topological ...The metrization of a probabilistic metric space (for short, PM-space )usually implies the metrization of its (ε,λ)-topological structure. Therefore, if a PM-space is metrizable, it only implies that its topological properties do not have an essential distinction with metric space. However, PM-spaces also have abundant and unique probabilistic metric properties.展开更多
In this paper an evaluation of the influence of luminance L* at the L*a*b* color space during color segmentation is presented. A comparative study is made between the behavior of segmentation in color images using onl...In this paper an evaluation of the influence of luminance L* at the L*a*b* color space during color segmentation is presented. A comparative study is made between the behavior of segmentation in color images using only the Euclidean metric of a* and b* and an adaptive color similarity function defined as a product of Gaussian functions in a modified HSI color space. For the evaluation synthetic images were particularly designed to accurately assess the performance of the color segmentation. The testing system can be used either to explore the behavior of a similarity function (or metric) in different color spaces or to explore different metrics (or similarity functions) in the same color space. From the results is obtained that the color parameters a* and b* are not independent of the luminance parameter L* as one might initially assume.展开更多
The resemblance between the equation for a characteristic hypersurface through which wavefronts of light rays pass and optical metrics of general relativity has long been known. Discontinuities in the hypersurface are...The resemblance between the equation for a characteristic hypersurface through which wavefronts of light rays pass and optical metrics of general relativity has long been known. Discontinuities in the hypersurface are due to refraction involving Snell’s law, as opposed to discontinuities in time that would involve the Doppler effect. The presence of a static gravitational potential in the metric coefficients is accounted by an index of refraction that is entirely dependent on the space coordinates. The two-time Einstein metric must be reinterpreted as a two-space scale metric because of the two different speeds of light. It is shown that the Schwarzschild metric is incompatible with the laws of classical physics. Gravitational waves are identified with the transverse-trans-verse plane wave solutions to Einstein’s equations in vacuum, which propagate at the speed of light. Yet, when energy loss is evaluated, his equations acquire, surprisingly, a source term. Poynting’s vector, which is not a true vector, is defined in terms of the pseudo-gravitational tensor, and hence energy is neither localizable nor conserved. The solutions to the equations of motion are geodesics and, by definition, do not radiate. A finite speed of propagation implies that gravitational waves should aberrate, like their electromagnetic wave counterparts, and if they do not aberrate they cannot radiate.展开更多
With the rapid urbanization in Beijing, the vegetated surfaces have been increasingly replaced by impervious built surfaces. A clear recognition on the changes in green spaces pattern is vital for urban administrators...With the rapid urbanization in Beijing, the vegetated surfaces have been increasingly replaced by impervious built surfaces. A clear recognition on the changes in green spaces pattern is vital for urban administrators and planners to optimize the urban development areas and define the ecological protection red lines. Based on the SPOT images and field investigation data of urban green spaces within the sixth ring road of Beijing in 2000, 2005 and 2010, the study investigated the dynamic changes of urban green spaces in this area, by means of GIS techniques and landscape ecology methods. The results indicated that green spaces in Beijing have decreased by 207 km2 from 2000 to 2010 at the expense of agricultural lands and waters. Although there has been some increases in urban forests and grasslands, it cannot compensate the rapid decrease of urban green spaces. The land cover types conversion occurred mainly in the areas between the fifth and sixth ring roads while the zones encircled by the fourth ring road had a little change. In addition, landscape metrics such as number of patches(NP) and shape index(SHAPE) increased, but the mean nearest-neighbor distance(MNN), aggregation index(AI) and patch cohesion index(COHESION) decreased during the period of 2000-2010. Also green landscapes became considerably isolated and fragmented. The study disclosed the obvious changes of green space size, composition and layout in urban districts of Beijing City from 2000 to 2010, and highlighted that construction of urban green space should consider not only the geometric or aesthetic effect, but also the increase of vertical green volume and optimization of spatial layout to fully develop the ecological service functions of green spaces.展开更多
We see the whole universe as a collection of very simple binary physical systems. With this assumption, we put forward a detailed model of discrete spaces. Our own universe with its four dimensions, shared between one...We see the whole universe as a collection of very simple binary physical systems. With this assumption, we put forward a detailed model of discrete spaces. Our own universe with its four dimensions, shared between one time-like dimension and three space-like dimensions, as well as the Minkowski metrics, are emerging properties of the model.展开更多
文摘The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.
文摘We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.
文摘We have pointed out that on the principles of special relativity and of propagation of light going along the null geodesic the special relativity of Einstein can be extented to the 3-dimensional Beltrami space-time D_λ with constant curvaturesλ<0, λ= 0 and λ>0. The inertial coordinate systems for each of them are so-called Beltrami coordinates and their metrics are also Beltrami
文摘The metrization of a probabilistic metric space (for short, PM-space )usually implies the metrization of its (ε,λ)-topological structure. Therefore, if a PM-space is metrizable, it only implies that its topological properties do not have an essential distinction with metric space. However, PM-spaces also have abundant and unique probabilistic metric properties.
文摘In this paper an evaluation of the influence of luminance L* at the L*a*b* color space during color segmentation is presented. A comparative study is made between the behavior of segmentation in color images using only the Euclidean metric of a* and b* and an adaptive color similarity function defined as a product of Gaussian functions in a modified HSI color space. For the evaluation synthetic images were particularly designed to accurately assess the performance of the color segmentation. The testing system can be used either to explore the behavior of a similarity function (or metric) in different color spaces or to explore different metrics (or similarity functions) in the same color space. From the results is obtained that the color parameters a* and b* are not independent of the luminance parameter L* as one might initially assume.
文摘The resemblance between the equation for a characteristic hypersurface through which wavefronts of light rays pass and optical metrics of general relativity has long been known. Discontinuities in the hypersurface are due to refraction involving Snell’s law, as opposed to discontinuities in time that would involve the Doppler effect. The presence of a static gravitational potential in the metric coefficients is accounted by an index of refraction that is entirely dependent on the space coordinates. The two-time Einstein metric must be reinterpreted as a two-space scale metric because of the two different speeds of light. It is shown that the Schwarzschild metric is incompatible with the laws of classical physics. Gravitational waves are identified with the transverse-trans-verse plane wave solutions to Einstein’s equations in vacuum, which propagate at the speed of light. Yet, when energy loss is evaluated, his equations acquire, surprisingly, a source term. Poynting’s vector, which is not a true vector, is defined in terms of the pseudo-gravitational tensor, and hence energy is neither localizable nor conserved. The solutions to the equations of motion are geodesics and, by definition, do not radiate. A finite speed of propagation implies that gravitational waves should aberrate, like their electromagnetic wave counterparts, and if they do not aberrate they cannot radiate.
基金Sponsored by Study on Space-time Rules of Beijing Urban Green Space Ecosystem Regulating Rainwater Runoff and Control Countermeasures(31200531)
文摘With the rapid urbanization in Beijing, the vegetated surfaces have been increasingly replaced by impervious built surfaces. A clear recognition on the changes in green spaces pattern is vital for urban administrators and planners to optimize the urban development areas and define the ecological protection red lines. Based on the SPOT images and field investigation data of urban green spaces within the sixth ring road of Beijing in 2000, 2005 and 2010, the study investigated the dynamic changes of urban green spaces in this area, by means of GIS techniques and landscape ecology methods. The results indicated that green spaces in Beijing have decreased by 207 km2 from 2000 to 2010 at the expense of agricultural lands and waters. Although there has been some increases in urban forests and grasslands, it cannot compensate the rapid decrease of urban green spaces. The land cover types conversion occurred mainly in the areas between the fifth and sixth ring roads while the zones encircled by the fourth ring road had a little change. In addition, landscape metrics such as number of patches(NP) and shape index(SHAPE) increased, but the mean nearest-neighbor distance(MNN), aggregation index(AI) and patch cohesion index(COHESION) decreased during the period of 2000-2010. Also green landscapes became considerably isolated and fragmented. The study disclosed the obvious changes of green space size, composition and layout in urban districts of Beijing City from 2000 to 2010, and highlighted that construction of urban green space should consider not only the geometric or aesthetic effect, but also the increase of vertical green volume and optimization of spatial layout to fully develop the ecological service functions of green spaces.
文摘We see the whole universe as a collection of very simple binary physical systems. With this assumption, we put forward a detailed model of discrete spaces. Our own universe with its four dimensions, shared between one time-like dimension and three space-like dimensions, as well as the Minkowski metrics, are emerging properties of the model.
