The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent vectors as derivations. Manifolds of mappings and diffeomorphisms are treated. Finally the differential structure on the inductive limits of the groups GL(n), S...

COVID-19 is well known as “Global Pandemic” and it a dreadful disaster on the world. However, other hand, pandemic becomes study issues for many researchers their juniors followers. Moreover, some negative attitudes of Myanmar people to National Soldiers become positive them. has conflicts between who stand with NLD (National League Democracy) Military. On Social Media pages, public have quarre...

We determine the periodic cyclic homology of the Iwahori-Hecke algebras Hq, for q ∈ C∗ not a “proper root of unity.” (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a “weakly spectrum preserving” morphism of finite type algebras induces an isomorphism in periodic cyclic ...

While virtual worlds have evolved to provide a good medium for social communication, they are very primitive in their social and affective communication design. The social communication methods within these worlds have progressed from early text-based social worlds, e.g. MUDS (multi-user dungeons) to 3D graphical interfaces with avatar control, such as Second Life. Current communication methods...

This article contributes to the emerging literature on social and emotional learning (SEL) from a Vygotskian perspective. A critical perspective on SEL in the context of schooling in the United States situates current interest in SEL programs. Vygotsky’s foundational work from the 1920s and 1930s is used to clarify learning as unified, and the concept of feeling is elaborated with literature re...

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