Chain length of closed circle DNA is equal. The same closed circle DNA＇s position corresponds to different recognition sequence, and the same recognition sequence corresponds to different foreign DNA segment, so clos...Chain length of closed circle DNA is equal. The same closed circle DNA＇s position corresponds to different recognition sequence, and the same recognition sequence corresponds to different foreign DNA segment, so closed circle DNA computing model is generalized. For change positive-weighted Hamilton circuit problem, closed circle DNA algorithm is put forward. First, three groups of DNA encoding are encoded for all arcs, and deck groups are designed for all vertices. All possible solutions are composed. Then, the feasible solutions are filtered out by using group detect experiment, and the optimization solutions are obtained by using group insert experiment and electrophoresis experiment. Finally, all optimization solutions are found by using detect experiment. Complexity of algorithm is concluded and validity of DNA algorithm is explained by an example. Three dominances of the closed circle DNA algorithm are analyzed, and characteristics and dominances of group delete experiment are discussed.展开更多
It has been shown by Sierpinski that a compact, Hausdorff, connected topological space (otherwise known as a continuum) cannot be decomposed into either a finite number of two or more disjoint, nonempty, closed sets o...It has been shown by Sierpinski that a compact, Hausdorff, connected topological space (otherwise known as a continuum) cannot be decomposed into either a finite number of two or more disjoint, nonempty, closed sets or a countably infinite family of such sets. In particular, for a closed interval of the real line endowed with the usual topology, we see that we cannot partition it into a countably infinite number of disjoint, nonempty closed sets. On the positive side, however, one can certainly express such an interval as a union of c disjoint closed sets, where c is the cardinality of the real line. For example, a closed interval is surely the union of its points, each set consisting of a single point being closed. Surprisingly enough, except for a set of Lebesgue measure 0, these closed sets can be chosen to be perfect sets, i.e., closed sets every point of which is an accumulation point. They even turn out to be nowhere dense (containing no intervals). Such nowhere dense, perfect sets are sometimes called Cantor sets.展开更多
基金supported by the National Natural Science Foundation of China(60574041)the Natural ScienceFoundation of Hubei Province(2007ABA407).
文摘Chain length of closed circle DNA is equal. The same closed circle DNA＇s position corresponds to different recognition sequence, and the same recognition sequence corresponds to different foreign DNA segment, so closed circle DNA computing model is generalized. For change positive-weighted Hamilton circuit problem, closed circle DNA algorithm is put forward. First, three groups of DNA encoding are encoded for all arcs, and deck groups are designed for all vertices. All possible solutions are composed. Then, the feasible solutions are filtered out by using group detect experiment, and the optimization solutions are obtained by using group insert experiment and electrophoresis experiment. Finally, all optimization solutions are found by using detect experiment. Complexity of algorithm is concluded and validity of DNA algorithm is explained by an example. Three dominances of the closed circle DNA algorithm are analyzed, and characteristics and dominances of group delete experiment are discussed.
文摘It has been shown by Sierpinski that a compact, Hausdorff, connected topological space (otherwise known as a continuum) cannot be decomposed into either a finite number of two or more disjoint, nonempty, closed sets or a countably infinite family of such sets. In particular, for a closed interval of the real line endowed with the usual topology, we see that we cannot partition it into a countably infinite number of disjoint, nonempty closed sets. On the positive side, however, one can certainly express such an interval as a union of c disjoint closed sets, where c is the cardinality of the real line. For example, a closed interval is surely the union of its points, each set consisting of a single point being closed. Surprisingly enough, except for a set of Lebesgue measure 0, these closed sets can be chosen to be perfect sets, i.e., closed sets every point of which is an accumulation point. They even turn out to be nowhere dense (containing no intervals). Such nowhere dense, perfect sets are sometimes called Cantor sets.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60403002) 浙江省自然科学基金(the NaturalScience Foundation of Zhejiang Province of China under Grant No.ZJNSF- Y105654)。
