An approach to the theory of geometrization of the Universe is proposed. The wave function of the Universe is represented by the Clifford number with the transfer rules that have the structure of the Dirac equation fo...An approach to the theory of geometrization of the Universe is proposed. The wave function of the Universe is represented by the Clifford number with the transfer rules that have the structure of the Dirac equation for any manifold. Solutions of this equation may be obtained in terms of the geometric interpretation. A new model is proposed that can explain the manifestation of the dark energy and dark matter in the Universe as a geometrical entity with a mechanism involving the spontaneous symmetry breaking.展开更多
The discrete fracture system of a rock mass plays a crucial role in controlling the stability of rock slopes.To fully account for the geometric shape and distribution characteristics of jointed rock masses,terrestrial...The discrete fracture system of a rock mass plays a crucial role in controlling the stability of rock slopes.To fully account for the geometric shape and distribution characteristics of jointed rock masses,terrestrial laser scanning(TLS)was employed to acquire high-resolution point-cloud data,and a developed automatic discontinuity-identification technology was coupled to automatically interpret and characterize geometric information such as orientation,trace length,spacing,and set number of the discontinuities.The discrete element method(DEM)was applied to study the influence of the geometric morphology and distribution characteristics of discontinuities on slope stability by generating a discrete fracture network(DFN)with the same statistical characteristics as the actual discontinuities.Based on slope data from the Yebatan Hydropower Station,a simulation was conducted to verify the applicability of the automatic discontinuity identification technology and the discrete fracture network-discrete element method(DFN-DEM).Various geological parameters,including trace length,persistence,and density,were examined to investigate the morphological evolution and response characteristics of rock slope excavation under different joint combination conditions through simulation.The simulation results indicate that joint parameters affect slope stability,with density having the most significant impact.The impact of joint parameters on stability is relatively small within a reasonable range but becomes significant beyond a certain threshold,further validating that the accuracy of field geological surveys is critical for simulation.This study provides a scientific basis for the construction of complex rock slope models,engineering assessments,and disaster prevention and mitigation,which is of great value in both theory and engineering applications.展开更多
Interpretation of wave function for free particle is suggested as a description of microscopic distortion of the space-time geometry, namely, as some closed topological 4-manifold. Such geometrical object looks in thr...Interpretation of wave function for free particle is suggested as a description of microscopic distortion of the space-time geometry, namely, as some closed topological 4-manifold. Such geometrical object looks in three-dimensional Euclidean space as its topological defect having stochastic and wave-corpuscular properties of quantum particle. All possible deformations (homeomorphisms) of closed topological manifold play the role of “hidden variables”, responsible for statistical character of the theory.展开更多
The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to t...The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.展开更多
PL homotopy metheds are effective methods to locate zerces(or fixed points) of highly nonlinearmappirgs. Due to the Jexicographical system, the methods are feasible without exceptions Thispaper presents a geemetrical ...PL homotopy metheds are effective methods to locate zerces(or fixed points) of highly nonlinearmappirgs. Due to the Jexicographical system, the methods are feasible without exceptions Thispaper presents a geemetrical interpretation of the without-exception feasibility.展开更多
文摘An approach to the theory of geometrization of the Universe is proposed. The wave function of the Universe is represented by the Clifford number with the transfer rules that have the structure of the Dirac equation for any manifold. Solutions of this equation may be obtained in terms of the geometric interpretation. A new model is proposed that can explain the manifestation of the dark energy and dark matter in the Universe as a geometrical entity with a mechanism involving the spontaneous symmetry breaking.
基金We acknowledge the funding support from the National Key R&D Program of China(Grant No.2022YFC3080100)the National Natural Science Foundation of China(Grant No.42102316)the opening fund of State Key Laboratory of Hydraulics and Mountain River Engineering,Sichuan University(Grant No.SKHL2306).
文摘The discrete fracture system of a rock mass plays a crucial role in controlling the stability of rock slopes.To fully account for the geometric shape and distribution characteristics of jointed rock masses,terrestrial laser scanning(TLS)was employed to acquire high-resolution point-cloud data,and a developed automatic discontinuity-identification technology was coupled to automatically interpret and characterize geometric information such as orientation,trace length,spacing,and set number of the discontinuities.The discrete element method(DEM)was applied to study the influence of the geometric morphology and distribution characteristics of discontinuities on slope stability by generating a discrete fracture network(DFN)with the same statistical characteristics as the actual discontinuities.Based on slope data from the Yebatan Hydropower Station,a simulation was conducted to verify the applicability of the automatic discontinuity identification technology and the discrete fracture network-discrete element method(DFN-DEM).Various geological parameters,including trace length,persistence,and density,were examined to investigate the morphological evolution and response characteristics of rock slope excavation under different joint combination conditions through simulation.The simulation results indicate that joint parameters affect slope stability,with density having the most significant impact.The impact of joint parameters on stability is relatively small within a reasonable range but becomes significant beyond a certain threshold,further validating that the accuracy of field geological surveys is critical for simulation.This study provides a scientific basis for the construction of complex rock slope models,engineering assessments,and disaster prevention and mitigation,which is of great value in both theory and engineering applications.
文摘Interpretation of wave function for free particle is suggested as a description of microscopic distortion of the space-time geometry, namely, as some closed topological 4-manifold. Such geometrical object looks in three-dimensional Euclidean space as its topological defect having stochastic and wave-corpuscular properties of quantum particle. All possible deformations (homeomorphisms) of closed topological manifold play the role of “hidden variables”, responsible for statistical character of the theory.
基金supported by the National Natural Science Foundation of China(61373174)
文摘The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.
基金The work is supported in part by the Foundation of Zhongshan University, Advanced Research Centre and in part by the National Natural Science Foundation of China
文摘PL homotopy metheds are effective methods to locate zerces(or fixed points) of highly nonlinearmappirgs. Due to the Jexicographical system, the methods are feasible without exceptions Thispaper presents a geemetrical interpretation of the without-exception feasibility.
