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.

this paper has examined the phenomenon of convergence of per capita out put levels across the ic countries for the 1960-1998 periods. three concepts of convergence, i.e., sigma beta and relative beta, have been used. the estimated beta values reveals only a very weak convergence (?=.0014) across ic for 1960-1998 period. but when a more homogeneous group of countries were selected, the results s...

We use techniques in the shuffle algebra to present a formula for partition function of one-dimensional log-gas comprised particles (possibly) different integer charges at certain inverse temperature $\beta$ terms Berezin integral an associated non-homogeneous alternating tensor. This generalizes previously known results by removing restriction on number species odd charge. Our methods provide ...

This paper is concerned with embeddings of homogeneous spaces into Euclidean spaces. We show that any homogeneous metric space can be embedded into a Hilbert space using an almost bi-Lipschitz mapping (biLipschitz to within logarithmic corrections). The image of this set is no longer homogeneous, but ‘almost homogeneous’. We therefore study the problem of embedding an almost homogeneous subset ...

Human Interferon β (INF-β) is a member of cytokines family which different studies have shown its immunomodulatory and antiviral activities. In this study an expression vector was designed and constructed for expression of human INF-β-1b either in shake flasks and bench top bioreactor. The designed vector was constructed based upon pET-25b(+) with T7 promoter. Recombinant human beta interferon ...

The quantum duality principle (QDP) for homogeneous spaces gives four recipes to obtain, from a quantum homogeneous space, a dual one, in the sense of Poisson duality. One of these recipes fails (for lack of the initial ingredient) when the homogeneous space we start from is not a quasi-affine variety. In this work we solve this problem for the quantum Grassmannian, a key example of quantum pro...

Human Interferon β (INF-β) is a member of cytokines family which different studies have shown its immunomodulatory and antiviral activities. In this study an expression vector was designed and constructed for expression of human INF-β-1b either in shake flasks and bench top bioreactor. The designed vector was constructed based upon pET-25b(+) with T7 promoter. Recombinant human beta interferon ...

We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space ΞB contained in the space of bounded Borel measures on T in such a way that the map B → ΞB defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of a...

We prove that for every homogeneous and strongly locally homogeneous Polish space X there is a Polish group admitting a transitive action on X. We also construct an example of a homogeneous Polish space which is not a coset space and on which no separable metrizable topological group acts transitively.