In the new period, the physical education in colleges and universities is of greater and greater significance for the enhancement of students' learning efficiency. In this paper, the current situation of the current ...In the new period, the physical education in colleges and universities is of greater and greater significance for the enhancement of students' learning efficiency. In this paper, the current situation of the current physical education is analyzed, and also related suggestions on the optimization of the P.E. course teaching plan are proposed.展开更多
The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of ...The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of cobordism and the Menger-Urysohn dimensional theory in conjunction with von Neumann-Connes dimensional function of Klein-Penrose modular holographic boundary of the E8E8 exceptional Lie group bulk of our universe. The final result is a lucid sharp mental picture, namely that the quantum wave is an empty set representing the surface, i.e. boundary of the zero set quantum particle and in turn quantum spacetime is simply the boundary or the surface of the quantum wave empty set. The essential difference of the quantum wave and quantum spacetime is that the wave is a simple empty set while spacetime is a multi-fractal type of infinitely many empty sets with increasing degrees of emptiness.展开更多
In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-t...In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.展开更多
In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscali...In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscaling of c namely . Since the maximal height in the one-dimensional universe must be where is the unit interval length and note that the topological mass (m) and topological dimension (D) where m = D = 5 are that of the largest unit sphere volume, we can conclude that the potential energy of classical mechanics translates to . Remembering that the kinetic energy is , then by the same logic we see that when m = 5 is replaced by for reasons which are explained in the main body of the present work. Adding both expressions together, we find Einstein’s maximal energy . As a general conclusion, we note that within high energy cosmology, the sharp distinction between potential energy and kinetic energy of classical mechanics is blurred on the cosmic scale. Apart of being an original contribution, the article presents an almost complete bibliography on the Cantorian-fractal spacetime theory.展开更多
Properties from random matrix theory allow us to uncover naturally embedded signals from different data sets. While there are many parameters that can be changed, including the probability distribution of the entries,...Properties from random matrix theory allow us to uncover naturally embedded signals from different data sets. While there are many parameters that can be changed, including the probability distribution of the entries, the introduction of noise, and the size of the matrix, the resulting eigenvalue and eigenvector distributions remain relatively unchanged. However, when there are certain anomalous eigenvalues and their corresponding eigenvectors that do not follow the predicted distributions, it could indicate that there’s an underlying non-random signal inside the data. As data and matrices become more important in the sciences and computing, so too will the importance of processing them with the principles of random matrix theory.展开更多
文摘In the new period, the physical education in colleges and universities is of greater and greater significance for the enhancement of students' learning efficiency. In this paper, the current situation of the current physical education is analyzed, and also related suggestions on the optimization of the P.E. course teaching plan are proposed.
文摘The paper presents a very simple and straight forward yet pure mathematical derivation of the structure of actual spacetime from quantum set theory. This is achieved by utilizing elements of the topological theory of cobordism and the Menger-Urysohn dimensional theory in conjunction with von Neumann-Connes dimensional function of Klein-Penrose modular holographic boundary of the E8E8 exceptional Lie group bulk of our universe. The final result is a lucid sharp mental picture, namely that the quantum wave is an empty set representing the surface, i.e. boundary of the zero set quantum particle and in turn quantum spacetime is simply the boundary or the surface of the quantum wave empty set. The essential difference of the quantum wave and quantum spacetime is that the wave is a simple empty set while spacetime is a multi-fractal type of infinitely many empty sets with increasing degrees of emptiness.
文摘In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.
文摘In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscaling of c namely . Since the maximal height in the one-dimensional universe must be where is the unit interval length and note that the topological mass (m) and topological dimension (D) where m = D = 5 are that of the largest unit sphere volume, we can conclude that the potential energy of classical mechanics translates to . Remembering that the kinetic energy is , then by the same logic we see that when m = 5 is replaced by for reasons which are explained in the main body of the present work. Adding both expressions together, we find Einstein’s maximal energy . As a general conclusion, we note that within high energy cosmology, the sharp distinction between potential energy and kinetic energy of classical mechanics is blurred on the cosmic scale. Apart of being an original contribution, the article presents an almost complete bibliography on the Cantorian-fractal spacetime theory.
文摘Properties from random matrix theory allow us to uncover naturally embedded signals from different data sets. While there are many parameters that can be changed, including the probability distribution of the entries, the introduction of noise, and the size of the matrix, the resulting eigenvalue and eigenvector distributions remain relatively unchanged. However, when there are certain anomalous eigenvalues and their corresponding eigenvectors that do not follow the predicted distributions, it could indicate that there’s an underlying non-random signal inside the data. As data and matrices become more important in the sciences and computing, so too will the importance of processing them with the principles of random matrix theory.