This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model...This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model complete, and hence there exist no built-in Skolem function. Moreover, the ultraproduct BCK algebras and the fuzzy ultraproduct of fuzzy subsets of BCK algebras were proposed by using the concept of ultrafilters with corresponding properties of fuzzy ideals discussed.展开更多
Based on the C-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes （splitting...Based on the C-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes （splitting, merging, and intersection） during the evolution of the monopoles.展开更多
Optical vortices as topological objects exist ubiquitously in nature.In this paper,by making use of the Duan's topological current theory,we investigate the topology in the closed and knotted optical vortices.The ...Optical vortices as topological objects exist ubiquitously in nature.In this paper,by making use of the Duan's topological current theory,we investigate the topology in the closed and knotted optical vortices.The topological inner structure of the optical vortices are obtained,and the linking of the knotted optical vortices is also given.展开更多
Thin cuprous oxide films have been prepared by chemical vapor deposition(pulsed spray evaporation-chemical vapor deposition)method without post-treatment.The synthesis of cuprous oxide was produced by applying a water...Thin cuprous oxide films have been prepared by chemical vapor deposition(pulsed spray evaporation-chemical vapor deposition)method without post-treatment.The synthesis of cuprous oxide was produced by applying a water strategy effect.Then,the effect of water on the morphology,topology,structure,optical properties and surface composition of the obtained films has been comprehensively investigated.The results reveal that a pure phase of Cu2O was obtained.The introduction of a small quantity of water in the liquid feedstock lowers the band gap energy from 2.16 eV to 2.04 eV.This finding was mainly related to the decrease of crystallite size due to the effect of water.The topology analyses,by using atomic force microscope,also revealed that surface roughness decreases with water addition,namely more uniform covered surface.Moreover,theoretical calculations based on density functional theory method were performed to understand the adsorption and reaction behaviors of water and ethanol on the Cu2O thin film surface.Formation mechanism of the Cu2O thin film was also suggested and discussed.展开更多
A conformal structure of a prion protein is thought to cause a prion disease by S.B. Prusiner＇s theory. Knot theory in mathematics is useful in studying a topological difference of topological objects. In this articl...A conformal structure of a prion protein is thought to cause a prion disease by S.B. Prusiner＇s theory. Knot theory in mathematics is useful in studying a topological difference of topological objects. In this article, concerning this conjecture, a topological model of prion proteins （PrPc, PrPsc） called a prion-tangle is introduced to discuss a question of whether or not the prion proteins are easily entangled by an approach from the mathematical knot theory. It is noted that any prion-string with trivial loop which is a topological model of a prion protein can not be entangled topologically unless a certain restriction such as ＂Rotaxsane Property＂ is imposed on it. Nevertheless, it is shown that any two split prion-tangles can be changed by a one-crossing change into a non-split prion-tangle with the given prion-tangles contained while some attentions are paid to the loop systems. The proof is made by a mathematical argument on knot theory of spatial graphs. This means that the question above is answered affirmatively in this topological model of prion-tangles. Next, a question of what is the simplest topological situation of the non-split prion-tangles is considered. By a mathematical argument, it is determined for every n 〉 1 that the minimal crossing number of n-string non-split prion-tangles is 2n or 2n-2, respectively, according to whether or not the assumption that the loop system is a trivial link is counted.展开更多
A class of finitely continuous topological spaces(in short,FC-spaces)is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compac...A class of finitely continuous topological spaces(in short,FC-spaces)is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compactly local intersection property are proved in FC- spaces.As applications,some new fixed point theorems are obtained in FC-spaces.These theorems improve and generalize many known results in recent literature.展开更多
文摘This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model complete, and hence there exist no built-in Skolem function. Moreover, the ultraproduct BCK algebras and the fuzzy ultraproduct of fuzzy subsets of BCK algebras were proposed by using the concept of ultrafilters with corresponding properties of fuzzy ideals discussed.
基金The project supported by National Natural Science Foundation of China and under Grant No. 10475034
文摘Based on the C-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes （splitting, merging, and intersection） during the evolution of the monopoles.
基金supported by National Natural Science Foundation of China
文摘Optical vortices as topological objects exist ubiquitously in nature.In this paper,by making use of the Duan's topological current theory,we investigate the topology in the closed and knotted optical vortices.The topological inner structure of the optical vortices are obtained,and the linking of the knotted optical vortices is also given.
基金supported by the Ministry of Science and Technology of China(No.2017YFA0402800)the National Natural Science and Technology of China(No.91541102 and No.51476168)+2 种基金the support by Chinese Academy of Sciences for Senior International Scientists within President’s International Fellowship Initiative(PIFI)programthe financial support during his Ph.D.research stay at Bielefeld UniversityThe Moroccan institute of IRESEN is acknowledged for the financial support(Innowind13 Nanolubricant)
文摘Thin cuprous oxide films have been prepared by chemical vapor deposition(pulsed spray evaporation-chemical vapor deposition)method without post-treatment.The synthesis of cuprous oxide was produced by applying a water strategy effect.Then,the effect of water on the morphology,topology,structure,optical properties and surface composition of the obtained films has been comprehensively investigated.The results reveal that a pure phase of Cu2O was obtained.The introduction of a small quantity of water in the liquid feedstock lowers the band gap energy from 2.16 eV to 2.04 eV.This finding was mainly related to the decrease of crystallite size due to the effect of water.The topology analyses,by using atomic force microscope,also revealed that surface roughness decreases with water addition,namely more uniform covered surface.Moreover,theoretical calculations based on density functional theory method were performed to understand the adsorption and reaction behaviors of water and ethanol on the Cu2O thin film surface.Formation mechanism of the Cu2O thin film was also suggested and discussed.
文摘A conformal structure of a prion protein is thought to cause a prion disease by S.B. Prusiner＇s theory. Knot theory in mathematics is useful in studying a topological difference of topological objects. In this article, concerning this conjecture, a topological model of prion proteins （PrPc, PrPsc） called a prion-tangle is introduced to discuss a question of whether or not the prion proteins are easily entangled by an approach from the mathematical knot theory. It is noted that any prion-string with trivial loop which is a topological model of a prion protein can not be entangled topologically unless a certain restriction such as ＂Rotaxsane Property＂ is imposed on it. Nevertheless, it is shown that any two split prion-tangles can be changed by a one-crossing change into a non-split prion-tangle with the given prion-tangles contained while some attentions are paid to the loop systems. The proof is made by a mathematical argument on knot theory of spatial graphs. This means that the question above is answered affirmatively in this topological model of prion-tangles. Next, a question of what is the simplest topological situation of the non-split prion-tangles is considered. By a mathematical argument, it is determined for every n 〉 1 that the minimal crossing number of n-string non-split prion-tangles is 2n or 2n-2, respectively, according to whether or not the assumption that the loop system is a trivial link is counted.
基金Foundation item： the Natural Science Foundation of Sichuan Provincial Education Department of China （No. 2003A081 SZD0406）.
文摘A class of finitely continuous topological spaces(in short,FC-spaces)is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compactly local intersection property are proved in FC- spaces.As applications,some new fixed point theorems are obtained in FC-spaces.These theorems improve and generalize many known results in recent literature.
