We present the Z-property for rewriting, relate it to the triangle property , show it induces a hyper-cofinal strategy, and present (non-)examples. 1 The Z-property We present the Z-property and one of the various examples of rewrite relations having that property, as can be found in [4]. Definition 1. A map • : A → A has the Z-property for a rewrite relation → on A (see Fig. 1) if for all a, b...

‎‎‎Recently Samet et al. introduced the notion of $alpha$-$psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $alpha$-$(psi,varphi)$-contractive mappings and stablish coincidence and common fixed point theorems for two mapping in complete metric spaces. We present some examples to illustrate our results. As application...

The 3x+ 1 problem concerns iteration of the map T : Z → Z given by

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

We show how to express a conformal map Φ of a general two connected domain in the plane such that neither boundary component is a point to a representative domain of the form Ar = {z : |z + 1/z| < 2r}, where r > 1 is a constant. The domain Ar has the virtue of having an explicit algebraic Bergman kernel function, and we shall explain why it is the best analogue of the unit disc in the two conne...

N be a rational map, where f 0 ,. .. , f N are homogeneous polynomials of degree d with no common factors. Then φ is defined at all points not in the indeterminacy locus Z(φ) = { P ∈ P N : f 0 (P) = · · · = f N (P) = 0 }. The map φ is said to be dominant if the image φ (P N Z(φ)) is Zariski dense, i.e., does not lie in a proper algebraic subset of P N. Alternatively, the map φ is dominant if th...

The 3x+ 1 problem concerns iteration of the map T : Z → Z given by

BACKGROUND Ziziphus Mill. (jujube), the most valued genus of Rhamnaceae, comprises of a number of economically and ecologically important species such as Z. jujuba Mill., Z. acidojujuba Cheng et Liu and Z. mauritiana Lam. Single nucleotide polymorphism (SNP) markers and a high-density genetic map are of great benefit to the improvement of the crop, mapping quantitative trait loci (QTL) and anal...

Atiyah and Hirzebruch gave the first counterexamples to the Hodge conjecture with integer coefficients. In particular, there is a smooth complex projective variety X of dimension 7 and a torsion element of H(X,Z) which is not the class of a codimension-2 algebraic cycle [4]. In this paper, we provide a more systematic explanation for their examples: for every smooth complex algebraic variety X ...