A gap theorem on complete noncompact n-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is proved.If there holds the following condition：integral（sk（x0,s）ds= o...A gap theorem on complete noncompact n-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is proved.If there holds the following condition：integral（sk（x0,s）ds= o（log r）） from n=0 to r then the manifold is flat.展开更多
Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the uni...Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the universe. Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals is identical to the previously measured and theoretically concluded ordinary energy density of the universe, namely a mere 4.5 percent of Einstein’s energy density, i.e. E(O) = mc2/22 where E is the energy, m is the mass and c is the speed of light. Consequently we conclude that the missing dark energy density must be E(D) = 1 - E(O) = mc2(21/22) in agreement with all known cosmological measurements and observations. This result could also be interpreted as a strong evidence for the self similarity of the geometry of spacetime, which is an expression of its basic fractal nature.展开更多
Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigi...Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.展开更多
Consider a supercritical superprocess X = {Xt, t 〉~ O} on a locally compact separable metric space （E, m）. Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching...Consider a supercritical superprocess X = {Xt, t 〉~ O} on a locally compact separable metric space （E, m）. Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching mechanism is of the form展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.70631003)the Natural Science Foundation of Anhui Education Department (Grant No.KJ2011A061)+1 种基金the Natural Science Foundation of Anhui Science and Technology Department (Grant No.1104606M01)the Doctor of Philosophy Foundation of Anhui University of Architecture (Grant No.2007-6-3)
文摘A gap theorem on complete noncompact n-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is proved.If there holds the following condition：integral（sk（x0,s）ds= o（log r）） from n=0 to r then the manifold is flat.
文摘Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the universe. Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals is identical to the previously measured and theoretically concluded ordinary energy density of the universe, namely a mere 4.5 percent of Einstein’s energy density, i.e. E(O) = mc2/22 where E is the energy, m is the mass and c is the speed of light. Consequently we conclude that the missing dark energy density must be E(D) = 1 - E(O) = mc2(21/22) in agreement with all known cosmological measurements and observations. This result could also be interpreted as a strong evidence for the self similarity of the geometry of spacetime, which is an expression of its basic fractal nature.
基金supported by the National Natural Science Foundation of China(No.12271069)the Natural Science Foundation of Chongqing(No.cstc2021jcyj-msxm X0443)+1 种基金the Chongqing“Zhitongche”foundation for doctors(No.CSTB2022BSXM-JCX0101)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJQN202201138)。
文摘Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.
文摘Consider a supercritical superprocess X = {Xt, t 〉~ O} on a locally compact separable metric space （E, m）. Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching mechanism is of the form
