We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive p...We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as homothety, of these operators are discussed the Commuting property with translation and as well.展开更多
A cellular model based on the Incrementally Modular Abstraction Hierarchy （IMAH） is a novel model that can represent the architecture of and changes in cyberworlds, preserving invariants from a general level to a sp...A cellular model based on the Incrementally Modular Abstraction Hierarchy （IMAH） is a novel model that can represent the architecture of and changes in cyberworlds, preserving invariants from a general level to a specific one. We have developed a data processing system called the Cellular Data System （CDS）. In the development of business applications, you can prevent combinatorial explosion in the process of business design and testing by using CDS. In this paper, we have first designed and implemented wide-use algebra on the presentation level. Next, we have developed and verified the effectiveness of two general business applications using CDS： 1） a customer information management system, and 2） an estimate system.展开更多
In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the ...In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.展开更多
基金Supported by the National Natural Science Foundation of China（11671293, 11271282）
文摘We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as homothety, of these operators are discussed the Commuting property with translation and as well.
文摘A cellular model based on the Incrementally Modular Abstraction Hierarchy （IMAH） is a novel model that can represent the architecture of and changes in cyberworlds, preserving invariants from a general level to a specific one. We have developed a data processing system called the Cellular Data System （CDS）. In the development of business applications, you can prevent combinatorial explosion in the process of business design and testing by using CDS. In this paper, we have first designed and implemented wide-use algebra on the presentation level. Next, we have developed and verified the effectiveness of two general business applications using CDS： 1） a customer information management system, and 2） an estimate system.
文摘In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.
