On Strong Inclusions and Asymmetric Proximities in Frames

Stable Compactifications of Frames

In a classic paper, Smirnov [14] characterized the poset of compactifications of a completely regular space in terms of the proximities on the space. Later, Smyth [15] introduced the notion of a stable compactification of a T0-space and described them in terms of quasi-proximities on the space. Banaschewski [1] formulated Smirnov’s results in the pointfree setting, defining a compactification o...

Uniformities and covering properties for partial frames (II)

This paper is a continuation of [Uniformities and covering properties for partial frames (I)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. After presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

Seismic Behavior of Asymmetric Two-Story X-braced Frames

Concentrically braced frames (CBFs) are one of the efficient lateral load resisting systems in high seismicity regions. One of the common problems with the use of concentrically braced frames is limitation in the architectural application and position of the openings. Two-story X braced frames have more advantages than other configurations of concentrically braced frames, since in many cases th...

Stimulus Bias, Asymmetric Similarity, and Classification

This article proposes that patterns of proximity data that have been characterized in terms of “asymmetric similarity” may be alternatively characterized in terms of differential “bias.” Bias is a characteristic pertaining to an individual object, as opposed to similarity, which is a relation between two objects. It is proposed that biases can be stimulus based as well as response based, and nu...

Visualizing asymmetric proximities with MDS models