The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential ga...The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.展开更多
Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric di...Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.展开更多
Realizing the valley Hall effect by breaking the spatial inversion symmetry of photonic systems has become a cutting-edge field of micro-nano-optics,since the valley degree of freedom was introduced into photonic syst...Realizing the valley Hall effect by breaking the spatial inversion symmetry of photonic systems has become a cutting-edge field of micro-nano-optics,since the valley degree of freedom was introduced into photonic system.Various novel devices based on the domain walls of the valley photonic crystals have also been demonstrated.In this article,we investigate the variation of edge states by the modulation of refractive index within the domain walls,and the geometric difference between the dielectric columns of the sublattices.Straight photonic crystal waveguides with three types of domain walls(bearded,zigzag,armchair)are constructed.Simulation results show that the creation of a double-edge state in the band diagram results in two windows of stable transmission in tunable bands.Our findings might have significant implications in the field of novel optical devices.展开更多
文摘The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.
文摘Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.
基金supported by the Self-Deployment Project Research Program of the Haixi Institutes,Chinese Academy of Sciences(No.CXZX-2022-GH09)the National Natural Science Foundation of China(No.11774103)the Fujian Science&Technology Innovation Laboratory for Optoelectronic Information of China(No.2021ZR114)。
文摘Realizing the valley Hall effect by breaking the spatial inversion symmetry of photonic systems has become a cutting-edge field of micro-nano-optics,since the valley degree of freedom was introduced into photonic system.Various novel devices based on the domain walls of the valley photonic crystals have also been demonstrated.In this article,we investigate the variation of edge states by the modulation of refractive index within the domain walls,and the geometric difference between the dielectric columns of the sublattices.Straight photonic crystal waveguides with three types of domain walls(bearded,zigzag,armchair)are constructed.Simulation results show that the creation of a double-edge state in the band diagram results in two windows of stable transmission in tunable bands.Our findings might have significant implications in the field of novel optical devices.
