The notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems. Bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics, and, in particular, reachability. In this paper, the framework of bisimilar transition systems is app...

generators. Our goal is to make this description more concrete. Note that G(k, n) = U(n)/(U(k)×U(n− k)) = St(k, n)/U(k) is the quotient by U(k) of the complex Stiefel manifold St(k, n) of partial orthonormal k-frames in C. Thus any finite-dimensional representation ρ : U(k) −→ GL(W ) of U(k) gives rise to the natural vector bundle St(k, n)×ρ W −→ G(k, n), where St(k, n) −→ G(k, n) is viewed as ...

Abstract The purpose of this paper is to introduce ‐maps (), which describe higher homotopy normalities, and study their basic properties examples. An ‐map defined with homotopical conditions. It shown that a homomorphism an if only there exists fiberwise maps between projective spaces some properties. Also, the quotient be ‐space its LS category not greater than . As application, we investigat...

We prove that a discrete group G is amenable iff it is strongly unitarizable in the following sense: every unitarizable representation π on G can be unitarized by an invertible chosen in the von Neumann algebra generated by the range of π. Analogously a C *-algebra A is nuclear iff any bounded homomorphism u : A → B(H) is strongly similar to a *-homomorphism in the sense that there is an invert...

Let S be an unramified regular local ring of mixed characteristic p≥3 and Sp the subring obtained by lifting to image Frobenius map on S/pS. R integral closure in a biradical extension degree p2 its quotient field adjoining p-th roots sufficiently general square free elements f,g∈Sp. We show that admits birational maximal Cohen-Macaulay module. It is noted not automatically Cohen-Macaulay.

A few years ago, the first example of a closed manifold admitting an Anosov diffeomorphism but no expanding map was given. Unfortunately, this is not explicit and high-dimensional, although its exact dimension unknown due to type construction. In paper, we present family concrete 12-dimensional nilmanifolds with map, where nilmanifold defined as quotient 1-connected nilpotent Lie group by cocom...