Let X be a metric space. We say that a continuous surjection f:X→X is a topological Anosov map (abbrev. TA map) if f is expansive and has pseudo orbit tracing property with respect to some compatible me...Let X be a metric space. We say that a continuous surjection f:X→X is a topological Anosov map (abbrev. TA map) if f is expansive and has pseudo orbit tracing property with respect to some compatible metric for X . This paper studies the properties of TA maps of non compact metric spaces and gives some conditions for the map to be topologically mixing.展开更多
Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively ...Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively generalized and strengthened.Moreover,we can describe the complete distributivity of lattices with them as well.In this paper,we give the mutually descrip- tive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices, and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces, weakly induced spaces and induced spaces(they are called S-spaces).Furthermore,we will investi- gate the structure of the co-topology of S-space,solve a series of interesting problems on product, N-compactness and metrization of S-spaces.展开更多
With the rapid increase of the size of applications and the complexity of the supercomputer architecture,topology-aware process mapping becomes increasingly important.High communication cost has become a dominant cons...With the rapid increase of the size of applications and the complexity of the supercomputer architecture,topology-aware process mapping becomes increasingly important.High communication cost has become a dominant constraint of the performance of applications running on the supercomputer.To avoid a bad mapping strategy which can lead to terrible communication performance,we propose an optimized heuristic topology-aware mapping algorithm(OHTMA).The algorithm attempts to minimize the hop-byte metric that we use to measure the mapping results.OHTMA incorporates a new greedy heuristic method and pair-exchange-based optimization.It reduces the number of long-distance communications and effectively enhances the locality of the communication.Experimental results on the Tianhe-3 exascale supercomputer prototype indicate that OHTMA can significantly reduce the communication costs.展开更多
We showed in [G. H], if f is a Cr-topologically mixing map of the circle (r ≥0),then its rotation set will be non-trivial. But this statement is only satisfied for generic(open and dense) subset of all Cr-topological...We showed in [G. H], if f is a Cr-topologically mixing map of the circle (r ≥0),then its rotation set will be non-trivial. But this statement is only satisfied for generic(open and dense) subset of all Cr-topologically mixing maps of the circle (r≥0). Here,we present another proof of the above statement. Moreover, we introduce a topologicallymixing map of the circle with trivial rotation set.展开更多
文摘Let X be a metric space. We say that a continuous surjection f:X→X is a topological Anosov map (abbrev. TA map) if f is expansive and has pseudo orbit tracing property with respect to some compatible metric for X . This paper studies the properties of TA maps of non compact metric spaces and gives some conditions for the map to be topologically mixing.
基金The Project Supported by National Natural Science Foundation of China.
文摘Lattice-valued semicontinuous mappings play a basic and important role in solving the problems of L-fuzzy compactification theory,and make the previous work on weakly induced spaces and induced spaces determinatively generalized and strengthened.Moreover,we can describe the complete distributivity of lattices with them as well.In this paper,we give the mutually descrip- tive relation between lattice-valued semicontinuous mappings and the complete distributivity of lattices, and the construction theorems of open sets and closed sets in lattice-valued fully stratified spaces, weakly induced spaces and induced spaces(they are called S-spaces).Furthermore,we will investi- gate the structure of the co-topology of S-space,solve a series of interesting problems on product, N-compactness and metrization of S-spaces.
基金Project supported by the National Key Research and Development Program of China(No.2017YFB0202104)。
文摘With the rapid increase of the size of applications and the complexity of the supercomputer architecture,topology-aware process mapping becomes increasingly important.High communication cost has become a dominant constraint of the performance of applications running on the supercomputer.To avoid a bad mapping strategy which can lead to terrible communication performance,we propose an optimized heuristic topology-aware mapping algorithm(OHTMA).The algorithm attempts to minimize the hop-byte metric that we use to measure the mapping results.OHTMA incorporates a new greedy heuristic method and pair-exchange-based optimization.It reduces the number of long-distance communications and effectively enhances the locality of the communication.Experimental results on the Tianhe-3 exascale supercomputer prototype indicate that OHTMA can significantly reduce the communication costs.
文摘We showed in [G. H], if f is a Cr-topologically mixing map of the circle (r ≥0),then its rotation set will be non-trivial. But this statement is only satisfied for generic(open and dense) subset of all Cr-topologically mixing maps of the circle (r≥0). Here,we present another proof of the above statement. Moreover, we introduce a topologicallymixing map of the circle with trivial rotation set.
