In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div（A∨u） - Vu =0, and the three-ball inequalities on the characteristic plane and the three-cyli...In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div（A∨u） - Vu =0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation Эtu-div（A∨u） ＋ Vu = 0, where the singular potential V belonging to the Kato-Fefferman- Phong＇s class. Some applications are also discussed.展开更多
In a three-sphere system, the middle sphere is acted upon by two opposite depletion forces from the other two spheres. It is found that, in this system, the two depletion forces are coupled with each other and result ...In a three-sphere system, the middle sphere is acted upon by two opposite depletion forces from the other two spheres. It is found that, in this system, the two depletion forces are coupled with each other and result in a strengthened depletion force. So the difference of the depletion forces of the three-sphere system and its corresponding two two-sphere systems is introduced to describe the coupling effect of the depletion interactions. The numerical results obtained by Monte- Carlo simulations show that this coupling effect is affected by both the concentration of small spheres and the geometrical confinement. Meanwhile, it is also found that the mechanisms of the coupling effect and the effect on the depletion force from the ~eometry factor are the same.展开更多
The coupling effects of depletion interactions in three-sphere systems with different size ratio of large- to small-sphere are studied by Monte Carlosimulations in this paper. The numerical results show that this coup...The coupling effects of depletion interactions in three-sphere systems with different size ratio of large- to small-sphere are studied by Monte Carlosimulations in this paper. The numerical results show that this coupling effect is affected by the size ratio of large- to small-sphere: the larger the size ratio is, the larger the coupling effect will be.展开更多
The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers ...The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.展开更多
The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a ...The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In conventional approach it is implemented through tensor product of qubits. In the geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on three-dimensional sphere.展开更多
在分析当前数字海洋三维可视化关键技术及发展的基础上,深入研究Open Scene Graph(OSG)三维可视化引擎的仿真平台构建及渲染机制,建立合理、高效的海洋环境虚拟仿真和可视化模型,建立基于OSG的三维球体可视化框架体系,并初步设计和实现...在分析当前数字海洋三维可视化关键技术及发展的基础上,深入研究Open Scene Graph(OSG)三维可视化引擎的仿真平台构建及渲染机制,建立合理、高效的海洋环境虚拟仿真和可视化模型,建立基于OSG的三维球体可视化框架体系,并初步设计和实现了一个海洋环境虚拟仿真平台。展开更多
基金supported in part by the NNSF of China (10471069, 10771110)by NSF of Ningbo City (2009A610084)
文摘In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div（A∨u） - Vu =0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation Эtu-div（A∨u） ＋ Vu = 0, where the singular potential V belonging to the Kato-Fefferman- Phong＇s class. Some applications are also discussed.
基金Project supported by the Scientific Research Fund of Hunan Provincial Education Department, China (Grant Nos. 08B028 and 10A075)the Natural Science Foundation of Hunan Province, China (Grant No. 08jj6043)
文摘In a three-sphere system, the middle sphere is acted upon by two opposite depletion forces from the other two spheres. It is found that, in this system, the two depletion forces are coupled with each other and result in a strengthened depletion force. So the difference of the depletion forces of the three-sphere system and its corresponding two two-sphere systems is introduced to describe the coupling effect of the depletion interactions. The numerical results obtained by Monte- Carlo simulations show that this coupling effect is affected by both the concentration of small spheres and the geometrical confinement. Meanwhile, it is also found that the mechanisms of the coupling effect and the effect on the depletion force from the ~eometry factor are the same.
文摘The coupling effects of depletion interactions in three-sphere systems with different size ratio of large- to small-sphere are studied by Monte Carlosimulations in this paper. The numerical results show that this coupling effect is affected by the size ratio of large- to small-sphere: the larger the size ratio is, the larger the coupling effect will be.
文摘The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.
文摘The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In conventional approach it is implemented through tensor product of qubits. In the geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on three-dimensional sphere.
