The fractal structure shown by the poligonal created by unions of middle points of vertices, nodes or peaks of dendograms terminal classes is presented. Its generating fractal, the details of its construction, and the...The fractal structure shown by the poligonal created by unions of middle points of vertices, nodes or peaks of dendograms terminal classes is presented. Its generating fractal, the details of its construction, and the way to measure its segments are defined; its property of inverted scale, the type of meshing, its property of axial symmetry and a theorem on transformation of linear affinity are considered. This is exemplified by means of one application with real data.展开更多
The stabilization energies of substituted lithium carbene cations were calculated by using ab initio molecular orbital theory,and the relationship between the stabilization energies and molecular orbitals was discusse...The stabilization energies of substituted lithium carbene cations were calculated by using ab initio molecular orbital theory,and the relationship between the stabilization energies and molecular orbitals was discussed.The substituents with pi donor engender strong stabilization to CH2Li+.The calculations show the Y-C*bond lengths of cations become shorter and H-Y bond lengths longer than those of corresponding neutral molecules.展开更多
In non-Hermitian systems,the dynamic encircling of exceptional points(EPs)engenders intriguing chiral phenomena,where the resultant state characteristics are intrinsically dependent upon the encircling handedness.An i...In non-Hermitian systems,the dynamic encircling of exceptional points(EPs)engenders intriguing chiral phenomena,where the resultant state characteristics are intrinsically dependent upon the encircling handedness.An ingenious approach using simple leaky optical elements has been presented to emulate this chiral behavior without physically encircling an EP.This innovative simplification of EP properties enables a more straightforward implementation of asymmetric switching of polarization and path.Given that photons inherently possess multiple physical degrees of freedom,the research focus has shifted from single-dimensional to multidimensional asymmetric switching.Hence,there is a fundamental challenge of how to achieve multidimensional asymmetric switching through a simple and universally applicable architecture.Here,we propose and experimentally demonstrate a novel topology-optimized architecture,termed EP-encirclement emulation tailoring,enabling multidimensional asymmetric switching.Theoretical analysis reveals that our architecture eliminates the 3-dB inherent loss in conventional architecture by replacing couplers with(de)multiplexers.Building upon this architecture,we harness all-fiber devices to implement a high-performance asymmetric switching of polarization,mode,and orbital angular momentum(OAM).To our knowledge,this is the first experimental demonstration of asymmetric OAM switching to date.Our work provides an efficient topology architecture for emulating dynamic EP encirclement,paving the way for universal and flexible asymmetric switching devices.展开更多
To raise traditional medicine to a higher level of scientific research, a mathematical model has been proposed using symbolic notations and operators to describe several disease symptoms generally recognized in tradit...To raise traditional medicine to a higher level of scientific research, a mathematical model has been proposed using symbolic notations and operators to describe several disease symptoms generally recognized in traditional medicine. Even though this model to a certain degree offers a mathematical approach to identify the relationships between yin-yang and the five viscera, it is not an efficient means of explaining the pathology in traditional medicine due to its use of superfluous notations and definitions. In this paper, we introduce two concise operators, a self-development operator and an action operator： the former describes the effect of a viscus in the unbalanced state on other viscera： the latter explains the engendering and restraining relationships between the two viscera. These tools are useful to elucidate the interactions among the states of the five viscera based on yin-yang and the five elements theory. Our mathematical model with these two operators facilitates description for the scheme of deficiency-excess of yin-yang in the five viscera. Accordingly, we have mathematically refined the existing results and shown clinical applications as well.展开更多
文摘The fractal structure shown by the poligonal created by unions of middle points of vertices, nodes or peaks of dendograms terminal classes is presented. Its generating fractal, the details of its construction, and the way to measure its segments are defined; its property of inverted scale, the type of meshing, its property of axial symmetry and a theorem on transformation of linear affinity are considered. This is exemplified by means of one application with real data.
文摘The stabilization energies of substituted lithium carbene cations were calculated by using ab initio molecular orbital theory,and the relationship between the stabilization energies and molecular orbitals was discussed.The substituents with pi donor engender strong stabilization to CH2Li+.The calculations show the Y-C*bond lengths of cations become shorter and H-Y bond lengths longer than those of corresponding neutral molecules.
基金supported by the National Key R&D Program of China(2025YFE0102200)the National Natural Science Foundation of China(NSFC)(62125503,62261160388)+3 种基金the Natural Science Foundation of Hubei Province of China(2023AFA028)the Technology Innovation Program of Hubei Province(Major Science and Technology Project)(2024BAA001,2024BAA005)the Hubei Optical Fundamental Research Center(HBO2025TQ004)the High Quality Development Special Project of the Ministry of Industry and Information Technology,and the China Association for Science and Technology Youth Talent Support Engineering Doctoral Program.
文摘In non-Hermitian systems,the dynamic encircling of exceptional points(EPs)engenders intriguing chiral phenomena,where the resultant state characteristics are intrinsically dependent upon the encircling handedness.An ingenious approach using simple leaky optical elements has been presented to emulate this chiral behavior without physically encircling an EP.This innovative simplification of EP properties enables a more straightforward implementation of asymmetric switching of polarization and path.Given that photons inherently possess multiple physical degrees of freedom,the research focus has shifted from single-dimensional to multidimensional asymmetric switching.Hence,there is a fundamental challenge of how to achieve multidimensional asymmetric switching through a simple and universally applicable architecture.Here,we propose and experimentally demonstrate a novel topology-optimized architecture,termed EP-encirclement emulation tailoring,enabling multidimensional asymmetric switching.Theoretical analysis reveals that our architecture eliminates the 3-dB inherent loss in conventional architecture by replacing couplers with(de)multiplexers.Building upon this architecture,we harness all-fiber devices to implement a high-performance asymmetric switching of polarization,mode,and orbital angular momentum(OAM).To our knowledge,this is the first experimental demonstration of asymmetric OAM switching to date.Our work provides an efficient topology architecture for emulating dynamic EP encirclement,paving the way for universal and flexible asymmetric switching devices.
基金Supported by the Korea Institute of Oriental Medicine Project Grants(No.C11060,C12060 and K13092)
文摘To raise traditional medicine to a higher level of scientific research, a mathematical model has been proposed using symbolic notations and operators to describe several disease symptoms generally recognized in traditional medicine. Even though this model to a certain degree offers a mathematical approach to identify the relationships between yin-yang and the five viscera, it is not an efficient means of explaining the pathology in traditional medicine due to its use of superfluous notations and definitions. In this paper, we introduce two concise operators, a self-development operator and an action operator： the former describes the effect of a viscus in the unbalanced state on other viscera： the latter explains the engendering and restraining relationships between the two viscera. These tools are useful to elucidate the interactions among the states of the five viscera based on yin-yang and the five elements theory. Our mathematical model with these two operators facilitates description for the scheme of deficiency-excess of yin-yang in the five viscera. Accordingly, we have mathematically refined the existing results and shown clinical applications as well.
