Cross-protection in plants has been widely used to control losses caused by virus diseases in the world. Here, a non-autonomous plant-virus disease model was developed includ- ing cross-protection. Global dynamics of ...Cross-protection in plants has been widely used to control losses caused by virus diseases in the world. Here, a non-autonomous plant-virus disease model was developed includ- ing cross-protection. Global dynamics of the model was discussed. Under the quite weak assumptions, integral form conditions were resolved for permanence of the system and extinction of diseases. Furthermore, we looked into the sufficient conditions that plants could be protected against the detrimental effects of infection by an infection with the mild virus isolates. Last, we performed numerical simulations. Our investigations sug- gested that cross-protection played an important role in controlling the spread of the challenging virus in plants.展开更多
This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which make...This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which makes use of effective distance between the estimated probabilities and the empirical frequencies. It is shown that the proposed cross-entropy minimization estimator is more efficient than the usual estimator and has some desirable large sample properties. With some necessary modifications, the method can be applied to two-phase sampling for stratification and non-response. A simulation study is presented to assess the finite sample performance of the proposed estimator.展开更多
基金The research has been supported by the National Natural Science Foundation of China （11561004）, the Development for Local Colleges and Universities Foundation of China - the Applied Mathematics Innovative Team Building, and the Bidding Project of Gannan Normal University （16zb02）.
文摘Cross-protection in plants has been widely used to control losses caused by virus diseases in the world. Here, a non-autonomous plant-virus disease model was developed includ- ing cross-protection. Global dynamics of the model was discussed. Under the quite weak assumptions, integral form conditions were resolved for permanence of the system and extinction of diseases. Furthermore, we looked into the sufficient conditions that plants could be protected against the detrimental effects of infection by an infection with the mild virus isolates. Last, we performed numerical simulations. Our investigations sug- gested that cross-protection played an important role in controlling the spread of the challenging virus in plants.
基金supported by the National Natural Science Foundation of China under Grant No.61070236
文摘This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available. The authors employ an informationtheoretic approach which makes use of effective distance between the estimated probabilities and the empirical frequencies. It is shown that the proposed cross-entropy minimization estimator is more efficient than the usual estimator and has some desirable large sample properties. With some necessary modifications, the method can be applied to two-phase sampling for stratification and non-response. A simulation study is presented to assess the finite sample performance of the proposed estimator.
