In the context of constructive locale or frame theory (locale theory over a fixed base locale), we study some aspects of ’frame distributions’, meaning sup preserving maps from a frame to the base frame. We derive a relationship between results of Jibladze-Johnstone and Bunge-Funk, and also descriptions in distribution terms, as well as in double negation terms, of the ’interior of closure’ ope...

It is the purpose of the present paper to outline an introduction in theory of embeddings in the 2-osculator bundle. First, we recall the notion of 2-osculator bundle ([9], [2], [4]) and the notion of submani-folds in the 2-osculator bundle ([9]). A moving frame is constructed. The induced connections and the relative covariant derivation are discussed in the fourth and fifth section ([15], [16...

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

One of the paramount problems manifest in modern cosmological theories is that of the initial singularity. Gasperini and Veneziano have proposed the pre-big-bang (PBB) model [2] based on the assumption that the Universe evolved out of a ten-dimensional Minkowski spacetime which is an exact vacuum of string theory, in hopes of resolving the singularity problem. Recently, Brandenberger, Easther a...

Cognitive perspective-taking has attracted considerable attention in the mainstream developmental literature, and is most commonly studied under the rubric of Theory of Mind. The current article reviews the levels of understanding of informational states that are believed to underlie cognitive perspective-taking from this conceptual framework. An alternative approach to perspective-taking from ...

Preface Application-oriented mathematics develops theoretical results and new mathematical concepts, motivated by application, in contrast to " applied mathematics " focusing just on providing and applying mathematical tools for the applied sciences. The application-oriented approach produces results significant both for mathematics and the applied sciences. In this context we developed new con...