Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient condi...Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient conditions for A in the semigroup Gn（C） to be primitive are given. We also show that Gc（Jn） is a subsemigroup of Gn（C）.展开更多
Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In t...Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In this paper, we prove the following two results：（1）Let n≥13,n-3≥k〉Sl,Si＋〉Si,i=1,2…,l-1.if k＋l≤n,then for any m=2^k＋2^S1-l＋…＋2^S1,there exists A∈Bn,such that ｜R（A）｜=m.（2）Let n≥13,n-3≥k〉Sn-k-1〉Sn-k-2〉…S1〉λt〉λt-1〉…〉λ1,2≤t≤n-k.If exist γi（k＋1≤γi≤n-1,i=1,2…,t-1）γi〈γi＋1 and λt-λt-1≤k-Sn-γ1,λt-i-λt-i-1≤Sn-γi-Sn-γii＋1,i=1,2…,t-2,then for any m=2^k＋2^Sn-k-1＋2^Sn-k-1＋2^Sn-k-2＋…＋2^S1＋2^λt＋2^λt-1…＋2^λ1,there exists A∈Bn,as such that ｜R（A）｜=m.展开更多
Boolean control network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean network is used for modeling complex system. In this paper, we have presented a model...Boolean control network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean network is used for modeling complex system. In this paper, we have presented a model of a context-aware system used in smart home based on Boolean control networks. This modeling describes the relationship between the context elements (person, time, location, and activity) and services (Morning Call, Sleeping, Guarding, Entertainment, and normal), which is effective to logical inference. We apply semi tensor matrix product to describe the dynamic of the system. This matrix form of expression is a convenient and reasonable way to design logic control system.展开更多
基金Supported by the National Natural Science Foundation of China(11071272,11101087)the Postdoctoral Science Foundation of China(2013M531785)+1 种基金the Natural Science Foundation of Fujian Province(2013J05006)the Foundation of Fuzhou University(2012-XQ-30)
文摘Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient conditions for A in the semigroup Gn（C） to be primitive are given. We also show that Gc（Jn） is a subsemigroup of Gn（C）.
基金Foundation item： Supported by the Guangdong Provincial Natural Science Foundation of China（06029035）
文摘Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In this paper, we prove the following two results：（1）Let n≥13,n-3≥k〉Sl,Si＋〉Si,i=1,2…,l-1.if k＋l≤n,then for any m=2^k＋2^S1-l＋…＋2^S1,there exists A∈Bn,such that ｜R（A）｜=m.（2）Let n≥13,n-3≥k〉Sn-k-1〉Sn-k-2〉…S1〉λt〉λt-1〉…〉λ1,2≤t≤n-k.If exist γi（k＋1≤γi≤n-1,i=1,2…,t-1）γi〈γi＋1 and λt-λt-1≤k-Sn-γ1,λt-i-λt-i-1≤Sn-γi-Sn-γii＋1,i=1,2…,t-2,then for any m=2^k＋2^Sn-k-1＋2^Sn-k-1＋2^Sn-k-2＋…＋2^S1＋2^λt＋2^λt-1…＋2^λ1,there exists A∈Bn,as such that ｜R（A）｜=m.
文摘Boolean control network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean network is used for modeling complex system. In this paper, we have presented a model of a context-aware system used in smart home based on Boolean control networks. This modeling describes the relationship between the context elements (person, time, location, and activity) and services (Morning Call, Sleeping, Guarding, Entertainment, and normal), which is effective to logical inference. We apply semi tensor matrix product to describe the dynamic of the system. This matrix form of expression is a convenient and reasonable way to design logic control system.
