“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that ...“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that balance global integration with local needs.This also includes management of global business operations across diverse cultures in a multipolar international landscape.The paper briefs the developed and already tested in numerous applications high-level Spatial Grasp Model and Technology(SGT),which can help investigate and manage complex systems with a holistic spatial approach effectively covering various physical and virtual dimensions,their interrelations,and integration as a whole.Different areas will be investigated with examples of practical solutions in them and their combinations in a high-level Spatial Grasp Language(SGL),the key element of SGT.This allows for the creation and distributed management of very large spatial networks with different orientation which can be self-spreading,self-analyzing,self-modifying,and self-recovering in complex terrestrial and celestial environments,and also organize dynamic multi-networking solutions supporting global evolution and integrity.展开更多
We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the...We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.展开更多
The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQ...The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.展开更多
文摘“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that balance global integration with local needs.This also includes management of global business operations across diverse cultures in a multipolar international landscape.The paper briefs the developed and already tested in numerous applications high-level Spatial Grasp Model and Technology(SGT),which can help investigate and manage complex systems with a holistic spatial approach effectively covering various physical and virtual dimensions,their interrelations,and integration as a whole.Different areas will be investigated with examples of practical solutions in them and their combinations in a high-level Spatial Grasp Language(SGL),the key element of SGT.This allows for the creation and distributed management of very large spatial networks with different orientation which can be self-spreading,self-analyzing,self-modifying,and self-recovering in complex terrestrial and celestial environments,and also organize dynamic multi-networking solutions supporting global evolution and integrity.
基金supported by National Natural Science Foundation of China (Grant No. 10871187)supported by the Science Research Program from the Education Department of Heilongjiang Province (Grant No. 11551137)
文摘We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.
基金Supported by the Tsinghua U niversity Science Fund
文摘The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.
