We prove that any local automaton is contained in a complete one. The proof uses Nasu’s masking lemma. We use the same technique to give a new proof that any weakly deterministic irreducible automaton is contained in a complete one.

There proved that every prime invariant with respect to quantum adjoint action ideal I is completely prime and Fract(R/I) is isomorphic to the skew field of fractions of an algebra of twisted polynomials. We study correspondence between symplectic leaves and irreducible representations. The Conjecture of De Concini-KacProcesi on dimension of irreducible representations is proved for sufficientl...

Masur and Smillie, 1993, proved precisely which singularity index lists arise from pseudo-Anosov mapping classes. In search of an analogous theorem for outer automorphisms of free groups, Handel and Mosher, 2011, ask: Is each connected, simplicial, (2r − 1)-vertex graph the ideal Whitehead graph of a fully irreducible φ ∈ Out(Fr)? We answer this question in the negative by exhibiting, for each ...

We propose a correction of the standard Big Bang nucleosynthesis (BBN) scenario to resolve primordial lithium problem by considering possibility that plasma can deviate from ideal state. In BBN, is assumed be ideal, with particles and photons satisfying Maxwell-Boltzmann Planck distribution, respectively. suggest this assumption being might oversimplify early Universe cause problem. find deviat...

An interesting result proved by Halmos in Hal (Michigan Mathematical Journal, 15, 215–223 (1968) is that the set of irreducible operators dense $${\mathcal {B}}({\mathcal {H}})$$ sense Hilbert-Schmidt approximation. In a von Neumann algebra {M}}$$ with separable predual, an operator $$a\in {\mathcal said to be if $$W^*(a)$$ subfactor , i.e., $$W^*(a)'\cap {M}}={{\mathbb {C}}} \cdot I$$ . Let $$...

0-efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation orM can be shown to be one of the manifolds S3,RP3 or L(3, 1). Similarly, any triangulation of a compact, orientable, irreducible, ∂-irreducible 3-manifold can be modified to a 0-efficient triangula...

In 1907, Oskar Perron showed that a positive square matrix has a unique largest positive eigenvalue with a positive eigenvector. This result was extended to irreducible nonnegative matrices by Geog Frobenius in 1912, and to irreducible nonnegative tensors and weakly irreducible nonnegative tensors recently. This result is a fundamental result in matrix theory and has found wide applications in ...

Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle S1. A simple and useful necessary and sufficient condition is given for a map of a continuum, X, onto S1 to be hereditarily weakly confluent (HWC). It is shown that when X is arcwise connected, an HWC map of X onto S1 is monotone with arcwise connected fibers. A number of...

We prove that the associated variety of a Poisson prime ideal of the centre of a symplectic reflection algebra at parameter t = 0 is irreducible.