We consider topological dynamical systems ( X , T ) where is a compact metrizable space and denotes an action of countable amenable group G on by homeomorphisms. For two such Y S factor map π : → intermediate system Z R for which can be written as composition maps ψ φ . In this paper, we show that any -subshifts the set entropies subshift factors dense in interval [ h ] As corollary, also prove...

In this paper, the concept of cyclic (φ− ψ)-Kannan and cyclic (φ− ψ)-Chatterjea contractions, and fixed point theorems for these types of mappings in the context of complete metric spaces have been introduced. The results proved here extend some fixed point theorems in the literature.

The Banach contraction principle is one of the pivotal results in the metric fixed-point theory. It is a popular tool for the solution of existence problems in various fields of mathematics. There are several generalizations of the Banach contraction principle in the related literature on the metric fixed-point theory. Ran and Reurings [15] extended the Banach contraction principle in partially...

where capG(S, S̄) is the total weight of the edges crossing from S to S̄ = V − S. We show that the minimum generalized eigenvalue λ(LG, LH) of the pair of Laplacians LG and LH satisfies λ(LG, LH) ≥ φ(G,H)φ(G)/8, where φ(G) is the usual conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to λ(LG, LH). The inequality complements a...

The present study was undertaken to investigate the role of cyclic AMP and cyclic GMP in the regulation of the contraction-relaxation cycle in isolated smooth muscle cells from guinea pig taenia caeci. The contraction of isolated smooth muscle cells induced by both caffeine (4 X 10(-3) M) and carbachol (10(-4) M) consisted of an initial activation phase and a following spontaneous relaxation ph...

Agents which elevate cyclic AMP (cAMP) cause teleost retinal rods to contract. We have characterized this cAMP effect and have evaluated the role of the cytoskeleton in cyclic nucleotide-induced contraction, using actin and microtubule inhibitors. The necklike myoid region of the rod contracts in the dark and elongates in the light. If long, light-adapted rods are cultured with cAMP analogs and...

Let C be an additive subgroup of Z n 2k for any k ≥ 1. We define a Gray map Φ : Z n 2k −→ Z kn 2 such that Φ(C) is a binary propelinear code and, hence, a Hamming-compatible group code. Moreover, Φ is the unique Gray map such that Φ(C) is Hamming-compatible group code. Using this Gray map we discuss about the nonexistence of 1-perfect binary mixed group code.

Proof. First note that the map φ is uniquely determined by its components φ11, φ12, φ21, φ22. Indeed, by the universal property of the coproduct M1 ⊕ M2 we see that φ is uniquely determined by the maps φ∗1 := φ◦ι1 and φ∗2 := φ◦ι2. Then from the universal property of the product N1⊕N2 we see that the map φ∗1 is uniquely determined by the maps φ11 = π1 ◦φ∗1 and φ21 = π2 ◦ φ∗1. Similarly, φ∗2 is u...

In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multivalued mappings. © 2012 Elsevier Ltd. All rights reserved.