The author first introduces the notion of affine structures on a ringed space and then obtains several related properties.Affine structures on a ringed space,arising from complex analytical spaces of algebraic schemes...The author first introduces the notion of affine structures on a ringed space and then obtains several related properties.Affine structures on a ringed space,arising from complex analytical spaces of algebraic schemes,behave like differential structures on a smooth manifold.As one does for differential manifolds,pseudogroups of affine transformations are used to define affine atlases on a ringed space.An atlas on a space is said to be an affine structure if it is maximal.An affine structure is said to be admissible if there is a sheaf on the underlying space such that they are coincide on all affine charts,which are in deed affine open sets of a scheme.In a rigour manner,a scheme is defined to be a ringed space with a specified affine structure if the affine structures make a contribution to the cases such as analytical spaces of algebraic schemes.Particularly,by the whole of affine structures on a space,two necessary and sufficient conditions,that two spaces are homeomorphic and that two schemes are isomorphic,coming from the main theorems of the paper,are obtained respectively.A conclusion is drawn that the whole of affine structures on a space and a scheme,as local data,encode and reflect the global properties of the space and the scheme,respectively.展开更多
Holding a promise of achieving high power and energy densities,Li-ion hybrid electrochemical capacitors present a crucial future direction for energy storage devices.However,technical challenges remain to appropriatel...Holding a promise of achieving high power and energy densities,Li-ion hybrid electrochemical capacitors present a crucial future direction for energy storage devices.However,technical challenges remain to appropriately couple both high-power capacitor-type and high-energy battery-type electrode materials within a same device.In addition,the current electrode materials in the device are usually prepared separately,which leads to lengthy preparation,time-consuming and high-cost.In this work,we report a simple method to prepare porous carbon materials(PC) with and without MnO nanoparticle cores,which function as very unique anode/cathode pairs for very high-performance Li ion hybrid supercapacitor.Taking the respective merits of high Li storage capacity from the MnO@C anode and high-rate performance from the PC cathode,the resulted device exhibits a remarkable energy density of 89 Wh·kg^(-1)(at 48 W·kg^(-1)) and can reach a battery-inaccessible power density of 18 kW·kg^(-1)(at 45Wh·kg^(-1)).展开更多
In meridian theory of traditional Chinese medicine (TCM), the geometrical descriptions can be traced back to the remote ancient times in China, mainly in The Yellow Emperor’s Internal Classic (The Internal Classic in...In meridian theory of traditional Chinese medicine (TCM), the geometrical descriptions can be traced back to the remote ancient times in China, mainly in The Yellow Emperor’s Internal Classic (The Internal Classic in short). Euclid’s geometry, topology and other classic mathematics are all at their wit’s end to explain the high complexity and non clinear phenomenon of the meridian. In recent over 2000 years, the meridian phenomenon has been being the challenge to fundamental mathematics. Fractral geometry, founded by Mandelbrot (1975), is a branch of learning for investigating irregular geometrical curves. It has successfully solved some qualitative and quantitative problems about the topographical structure of molecular Brown’s movement curve and other irregular complicated curves and geometrical characters. The characteristics of geometrical topographical structure of meridian and its phenomenon belong to the research category of Fractal Geometry. The author of this paper believes that Fractal Geometry may provide a useful mathematical tool and a possible way for revealing the enigma of acup moxibustion meridian theory. The human body is of basic characters of Fractal Geometry in structure, while meridian is the expression form of Fractal structure of the human body. The basic Fractal geometrical characters of meridian are: self similarity, self affinity, symmetry, minute structure and self avoidance, which has been applied for thousands of years in clinic, such as “taking the acupoints on the right side of the body in cases of disorders appearing on the left side and vice versa". The basic characters of meridians are 1) symmetry of the 12 regular meridians on the bilateral sides of the body (symmetry); 2) similarity in characters and actions of acupoints of the same one meridian (self similarity); 3) taking acupoints on the lower part of the body when disorders occurring on the upper part of the body; and taking acupoints on the upper part of the body if disorders appearing on the lower part (self affinity); 4) micro acupuncture system including hand acupuncture, foot acupuncture, scalp acupuncture, auricular acupuncture and eye acupuncture (minute structure); and 5) systematical running of needling sensation (self avoidance).展开更多
Recently, we proved the Griffiths conjecture on the boundedness of the period maps, and then used it to prove global Torelli theorem on the Torelli space under certain natural conditions. This paper serves as a review...Recently, we proved the Griffiths conjecture on the boundedness of the period maps, and then used it to prove global Torelli theorem on the Torelli space under certain natural conditions. This paper serves as a review of these results and an introduction to the main ideas behind the proofs.展开更多
文摘The author first introduces the notion of affine structures on a ringed space and then obtains several related properties.Affine structures on a ringed space,arising from complex analytical spaces of algebraic schemes,behave like differential structures on a smooth manifold.As one does for differential manifolds,pseudogroups of affine transformations are used to define affine atlases on a ringed space.An atlas on a space is said to be an affine structure if it is maximal.An affine structure is said to be admissible if there is a sheaf on the underlying space such that they are coincide on all affine charts,which are in deed affine open sets of a scheme.In a rigour manner,a scheme is defined to be a ringed space with a specified affine structure if the affine structures make a contribution to the cases such as analytical spaces of algebraic schemes.Particularly,by the whole of affine structures on a space,two necessary and sufficient conditions,that two spaces are homeomorphic and that two schemes are isomorphic,coming from the main theorems of the paper,are obtained respectively.A conclusion is drawn that the whole of affine structures on a space and a scheme,as local data,encode and reflect the global properties of the space and the scheme,respectively.
基金financially supported by the National Natural Science Foundation of China (Nos.11632004, 52005151 and U1864208)the Research Program of Local Science and Technology Development under the Guidance of Central (No. 216Z4402G)+6 种基金the National Science and Technology Major Project (No.2017-Ⅶ-0011-0106)the Science and Technology Planning Project of Tianjin (No.20ZYJDJC00030)the Key Program of Research and Development of Hebei Province (No. 202030507040009)the Fund for Innovative Research Groups of Natural Science Foundation of Hebei Province (No.A2020202002)the Key Project of Natural Science Foundation of Tianjin (No. S20ZDF077)support from the Open Project Found of Chongqing Key Laboratory of Green(No.GATRI2021F01005B)support from "Yuanguang" Scholar Program of Hebei University of Technology。
文摘Holding a promise of achieving high power and energy densities,Li-ion hybrid electrochemical capacitors present a crucial future direction for energy storage devices.However,technical challenges remain to appropriately couple both high-power capacitor-type and high-energy battery-type electrode materials within a same device.In addition,the current electrode materials in the device are usually prepared separately,which leads to lengthy preparation,time-consuming and high-cost.In this work,we report a simple method to prepare porous carbon materials(PC) with and without MnO nanoparticle cores,which function as very unique anode/cathode pairs for very high-performance Li ion hybrid supercapacitor.Taking the respective merits of high Li storage capacity from the MnO@C anode and high-rate performance from the PC cathode,the resulted device exhibits a remarkable energy density of 89 Wh·kg^(-1)(at 48 W·kg^(-1)) and can reach a battery-inaccessible power density of 18 kW·kg^(-1)(at 45Wh·kg^(-1)).
文摘In meridian theory of traditional Chinese medicine (TCM), the geometrical descriptions can be traced back to the remote ancient times in China, mainly in The Yellow Emperor’s Internal Classic (The Internal Classic in short). Euclid’s geometry, topology and other classic mathematics are all at their wit’s end to explain the high complexity and non clinear phenomenon of the meridian. In recent over 2000 years, the meridian phenomenon has been being the challenge to fundamental mathematics. Fractral geometry, founded by Mandelbrot (1975), is a branch of learning for investigating irregular geometrical curves. It has successfully solved some qualitative and quantitative problems about the topographical structure of molecular Brown’s movement curve and other irregular complicated curves and geometrical characters. The characteristics of geometrical topographical structure of meridian and its phenomenon belong to the research category of Fractal Geometry. The author of this paper believes that Fractal Geometry may provide a useful mathematical tool and a possible way for revealing the enigma of acup moxibustion meridian theory. The human body is of basic characters of Fractal Geometry in structure, while meridian is the expression form of Fractal structure of the human body. The basic Fractal geometrical characters of meridian are: self similarity, self affinity, symmetry, minute structure and self avoidance, which has been applied for thousands of years in clinic, such as “taking the acupoints on the right side of the body in cases of disorders appearing on the left side and vice versa". The basic characters of meridians are 1) symmetry of the 12 regular meridians on the bilateral sides of the body (symmetry); 2) similarity in characters and actions of acupoints of the same one meridian (self similarity); 3) taking acupoints on the lower part of the body when disorders occurring on the upper part of the body; and taking acupoints on the upper part of the body if disorders appearing on the lower part (self affinity); 4) micro acupuncture system including hand acupuncture, foot acupuncture, scalp acupuncture, auricular acupuncture and eye acupuncture (minute structure); and 5) systematical running of needling sensation (self avoidance).
文摘Recently, we proved the Griffiths conjecture on the boundedness of the period maps, and then used it to prove global Torelli theorem on the Torelli space under certain natural conditions. This paper serves as a review of these results and an introduction to the main ideas behind the proofs.
