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Cross-connection theory developed by Nambooripad is the construction of a regular semigroup from its principal left (right) ideals using categories. We use the cross-connection theory to study the structure of the semigroup $$\textit{Sing}(V)$$ Sing(V) of singular linear transformations on an arbitrary vector space V over a field K. There is an inbuilt notion of duality in the cross-connection theory,...
Transparent and conductive Al doped ZnO thin films were synthesized at room temperature by sol gel technique both pure ZnO and Aldoped( 1,3,and5%) thin films were deposited on a glass substrate. The sols were prepared using zinc acetate dehydrate and aluminum chloride provides Al ions, played an important role in improvement of the c – axis, the structural characteristics have been studied by X-ray...
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