let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

What happens to the entropy increase principle as the Universe evolve to form the bigcrunch singularity? What happens to the uncertainity relations along the process of gravitational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of ψ is equal to or less than the diameter of the atom? What is the position...

What happens to the entropy increase principle as the Universe evolve to form the bigcrunch singularity? What happens to the uncertainity relations along the process of gravitational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of ψ is equal to or less than the diameter of the atom? What is the position...

What happens to the entropy increase principle as the Universe evolve to form the bigcrunch singularity? What happens to the uncertainity relations along the process of gravitational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of ψ is equal to or less than the diameter of the atom? What is the position...

We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab the 3-d space. show how different terms of energy modified and we derive reduced equations remaining directions. In Thomas–Fermi model, prove that there is perfect screening, provide decay estimates electronic density away from slab. Kohn–Sham models, Paul...

now that rapid changes in deferent aspects of human life have become a reality, innovations in policies and different programs can not be a motto but a necessity. islamic revolution of iran was an innovative phenomenon and iran-iraq war was a space for our inner abilities and creativities to burst out. doubtlessly, in narrating this war to our next generations, we must consider this principle, ...

We prove that a connected, countable dense homogeneous space is n-homogeneous for every n, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers in the negative Problem 136 of Watson in the Open Problems in Topology Book.