This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.
In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to...In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.展开更多
An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a...An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.展开更多
Fusion reactions can be achieved by using deuterium from sea water as the fuel.The amount of deuterium in one gallon of sea water contains energy equivalent to three hundred gallons of gasoline.Satisfactory conditions...Fusion reactions can be achieved by using deuterium from sea water as the fuel.The amount of deuterium in one gallon of sea water contains energy equivalent to three hundred gallons of gasoline.Satisfactory conditions of plasma temperature and density necessary to initiate fusion have been achieved in various research facilities.However,the confinement time is not sufficient for ignition due to plasma instabilities.Here we show that fatal plasma instabilities could be suppressed by the ingenious arrangement of multi-pinched plasma beams converging symmetrically in space based on the minimization principle of plasma potential energy.Confirmation tests are proposed using tiny wires containing deuterium.If successful,the results could lead to a feasible approach to obtaining commercial fusion power from sea water,hence without the need to use expensive and radioactive tritium as the fuel.展开更多
We establish a nice orthonormal frame field on a closed surface minimally immersed in a unit sphere Sn, under which the shape operators take very simple forms. Using this frame field, we obtain an interesting property...We establish a nice orthonormal frame field on a closed surface minimally immersed in a unit sphere Sn, under which the shape operators take very simple forms. Using this frame field, we obtain an interesting property K + K^N= 1 for the Gauss curvature K and the normal curvature K^N if the Gauss curvature is positive. Moreover, using this property we obtain the pinching on the intrinsic curvature and normal curvature, the pinching on the normal curvature, respectively.展开更多
Land use/cover change(LUCC)constitutes the spatial and temporal patterns of ecological security,and the construction of ecological networks is an effective way to ensure ecological security.Exploring the spatial and t...Land use/cover change(LUCC)constitutes the spatial and temporal patterns of ecological security,and the construction of ecological networks is an effective way to ensure ecological security.Exploring the spatial and temporal change characteristics of ecological network and analyzing the integrated relationship between LUCC and ecological security are crucial for ensuring regional ecological security.Gansu is one of the provinces with fragile ecological environment in China,and rapid changes in land use patterns in recent decades have threatened ecological security.Therefore,taking Gansu Province as the study area,this study simulated its land use pattern in 2050 using patch-generating land use simulation(PLUS)model based on the LUCC trend from 2000 to 2020 and integrated the LUCC into morphological spatial pattern analysis(MSPA)to identify ecological sources and extract the ecological corridors to construct ecological network using circuit theory.The results revealed that,according to the prediction results in 2050,the areas of cultivated land,forest land,grassland,water body,construction land,and unused land would be 63,447.52,39,510.80,148,115.18,4605.21,8368.89,and 161,752.40 km^(2),respectively.The number of ecological sources in Gansu Province would increase to 80,with a total area of 99,927.18 km^(2).The number of ecological corridors would increase to 191,with an estimated total length of 6120.66 km.Both ecological sources and ecological corridors showed a sparse distribution in the northwest and dense distribution in the southeast of the province at the spatial scale.The number of ecological pinch points would reach 312 and the total area would expect to increase to 842.84 km^(2),with the most pronounced increase in the Longdong region.Compared with 2020,the number and area of ecological barriers in 2050 would decrease significantly by 63 and 370.71 km^(2),respectively.In general,based on the prediction results,the connectivity of ecological network of Gansu Province would increase in 2050.To achieve the predicted ecological network in 2050,emphasis should be placed on the protection of cultivated land and ecological land,the establishment of ecological sources in desert areas,the reinforcement of the protection for existing ecological sources,and the construction of ecological corridors to enhance the stability of ecological network.This study provides valuable theoretical support and references for the future construction of ecological networks and regional land resource management decision-making.展开更多
We present a study of magnetic transport and radiation properties during compression of a magnetized laboratory plasma.A theta pinch is used to produce a magnetized plasma column undergoing radial implosion,with plasm...We present a study of magnetic transport and radiation properties during compression of a magnetized laboratory plasma.A theta pinch is used to produce a magnetized plasma column undergoing radial implosion,with plasma parameters comprehensively measured through diverse diagnostic techniques.High-resolution observations show the implosion progressing through three stages:compression,expansion,and recompression.An anomalous demagnetization phenomenon is observed during the first compression stage,wherein the magnetic field at the plasma center is depleted as the density increases.We reveal the demagnetization mechanism and formulate a straightforward criterion for determining its occurrence,through analysis based on extended-magnetohydrodynamics theory and a generalized Ohm’s law.Additionally,we quantitatively evaluate the radiation losses and magnetic field variations during the two compression stages,providing experimental evidence that magnetic transport can influence the radiation properties by altering the plasma hydrodynamics.Furthermore,extrapolated results using our findings reveal direct relevance to magnetized inertial confinement fusion,space,and astrophysical plasma scenarios.展开更多
基金Supported by the NNSF of China(10231010)the Trans-Century Training Programme Foundation for Talents by the Ministry of Education of China+1 种基金the Natural Science Foundation of Zhejiang Province(101037) Fudan Postgraduate Students Innovation Project(CQH5928002)
文摘This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.
文摘In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.
文摘An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.
基金supported by the Fund for the Construction of Graduate Degree,China(No.2014XWD-S0805)
文摘Fusion reactions can be achieved by using deuterium from sea water as the fuel.The amount of deuterium in one gallon of sea water contains energy equivalent to three hundred gallons of gasoline.Satisfactory conditions of plasma temperature and density necessary to initiate fusion have been achieved in various research facilities.However,the confinement time is not sufficient for ignition due to plasma instabilities.Here we show that fatal plasma instabilities could be suppressed by the ingenious arrangement of multi-pinched plasma beams converging symmetrically in space based on the minimization principle of plasma potential energy.Confirmation tests are proposed using tiny wires containing deuterium.If successful,the results could lead to a feasible approach to obtaining commercial fusion power from sea water,hence without the need to use expensive and radioactive tritium as the fuel.
基金supported in part by Young Faculty Career Start Program (34000-3171917)NSFC (10901165)+1 种基金NSFGD (9451027501002600)China Postdoc-toral Science Foundation (20090460066)
文摘In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.
文摘We establish a nice orthonormal frame field on a closed surface minimally immersed in a unit sphere Sn, under which the shape operators take very simple forms. Using this frame field, we obtain an interesting property K + K^N= 1 for the Gauss curvature K and the normal curvature K^N if the Gauss curvature is positive. Moreover, using this property we obtain the pinching on the intrinsic curvature and normal curvature, the pinching on the normal curvature, respectively.
基金supported by the Science Fund for the Gansu Provincial Natural Science Foundation Project(22JR5RA339).
文摘Land use/cover change(LUCC)constitutes the spatial and temporal patterns of ecological security,and the construction of ecological networks is an effective way to ensure ecological security.Exploring the spatial and temporal change characteristics of ecological network and analyzing the integrated relationship between LUCC and ecological security are crucial for ensuring regional ecological security.Gansu is one of the provinces with fragile ecological environment in China,and rapid changes in land use patterns in recent decades have threatened ecological security.Therefore,taking Gansu Province as the study area,this study simulated its land use pattern in 2050 using patch-generating land use simulation(PLUS)model based on the LUCC trend from 2000 to 2020 and integrated the LUCC into morphological spatial pattern analysis(MSPA)to identify ecological sources and extract the ecological corridors to construct ecological network using circuit theory.The results revealed that,according to the prediction results in 2050,the areas of cultivated land,forest land,grassland,water body,construction land,and unused land would be 63,447.52,39,510.80,148,115.18,4605.21,8368.89,and 161,752.40 km^(2),respectively.The number of ecological sources in Gansu Province would increase to 80,with a total area of 99,927.18 km^(2).The number of ecological corridors would increase to 191,with an estimated total length of 6120.66 km.Both ecological sources and ecological corridors showed a sparse distribution in the northwest and dense distribution in the southeast of the province at the spatial scale.The number of ecological pinch points would reach 312 and the total area would expect to increase to 842.84 km^(2),with the most pronounced increase in the Longdong region.Compared with 2020,the number and area of ecological barriers in 2050 would decrease significantly by 63 and 370.71 km^(2),respectively.In general,based on the prediction results,the connectivity of ecological network of Gansu Province would increase in 2050.To achieve the predicted ecological network in 2050,emphasis should be placed on the protection of cultivated land and ecological land,the establishment of ecological sources in desert areas,the reinforcement of the protection for existing ecological sources,and the construction of ecological corridors to enhance the stability of ecological network.This study provides valuable theoretical support and references for the future construction of ecological networks and regional land resource management decision-making.
基金the State Key Development Program for Basic Research of China(Grant No.2022YFA1602503)the National Natural Science Foundation of China(Grant Nos.12120101005 and 12205247)
文摘We present a study of magnetic transport and radiation properties during compression of a magnetized laboratory plasma.A theta pinch is used to produce a magnetized plasma column undergoing radial implosion,with plasma parameters comprehensively measured through diverse diagnostic techniques.High-resolution observations show the implosion progressing through three stages:compression,expansion,and recompression.An anomalous demagnetization phenomenon is observed during the first compression stage,wherein the magnetic field at the plasma center is depleted as the density increases.We reveal the demagnetization mechanism and formulate a straightforward criterion for determining its occurrence,through analysis based on extended-magnetohydrodynamics theory and a generalized Ohm’s law.Additionally,we quantitatively evaluate the radiation losses and magnetic field variations during the two compression stages,providing experimental evidence that magnetic transport can influence the radiation properties by altering the plasma hydrodynamics.Furthermore,extrapolated results using our findings reveal direct relevance to magnetized inertial confinement fusion,space,and astrophysical plasma scenarios.
