DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural mod...DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff＇s analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.展开更多
For multi-way tables with ordered categories, the present paper gives a decomposition of the point-symmetry model into the ordinal quasi point-symmetry and equality of point-symmetric marginal moments. The ordinal qua...For multi-way tables with ordered categories, the present paper gives a decomposition of the point-symmetry model into the ordinal quasi point-symmetry and equality of point-symmetric marginal moments. The ordinal quasi point-symmetry model indicates asymmetry for cell probabilities with respect to the center point in the table.展开更多
For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed 3<span style="font-family:""> </span><span style=&qu...For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed 3<span style="font-family:""> </span><span style="font-family:Verdana;">×</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">3 tables with some adjacent categories combined in the original table. This paper con</span><span style="font-family:Verdana;">siders the point-symmetry model (Wall and Lienert, 1976) for collapsed</span><span style="font-family:Verdana;"> tables and proposes a measure to represent the degree of departure from point-symmetry for collapsed tables. Also it gives approximate confidence interval for the proposed measure.</span></span>展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10672143 and 10472067, and the Natural Science Foundation of Henan Province under Grant No 0511022200.
文摘DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff＇s analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.
文摘For multi-way tables with ordered categories, the present paper gives a decomposition of the point-symmetry model into the ordinal quasi point-symmetry and equality of point-symmetric marginal moments. The ordinal quasi point-symmetry model indicates asymmetry for cell probabilities with respect to the center point in the table.
文摘For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed 3<span style="font-family:""> </span><span style="font-family:Verdana;">×</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">3 tables with some adjacent categories combined in the original table. This paper con</span><span style="font-family:Verdana;">siders the point-symmetry model (Wall and Lienert, 1976) for collapsed</span><span style="font-family:Verdana;"> tables and proposes a measure to represent the degree of departure from point-symmetry for collapsed tables. Also it gives approximate confidence interval for the proposed measure.</span></span>
