The classical van der Waerden Theorem says that for every every finite set S of natural numbers and every k-coloring of the natural numbers, there is a monochromatic set of the form aS+b for some a > 0 and b ≥ 0. I.e., monochromatism is obtained by a dilation followed by a translation. We investigate the effect of reversing the order of dilation and translation. S has the variant van der Waerde...

We consider F , the class of …nite unary functions, i.e. the class of pairs of the form (A; f) where A is a …nite set and f is an unary function on A. We also consider two subclasses of F : B and Fk for k > 1. B contains structures (A; f) with the property that f is a bijection of the set A, and Fk contains structures (A; f) with the property that inverse image of every point in A under f has c...

Adopting the definition of excedances of type B due to Brenti, we give a type B analogue of the q-derangement polynomials. The connection between q-derangement polynomials and Eulerian polynomials naturally extends to the type B case. Based on this relation, we derive some basic properties of the q-derangement polynomials of type B, including the generating function formula, the Sturm sequence ...

In this paper, we prove coincidence point for two pair of mappings satisfying (CLR)-property in b-metric spaces. Moreover, also attain unique common fixed weakly compatible pairs.

This study aims to show that four maps in a b-metric space satisfy pairwise weak compatibility have common fixed points under certain conditions. In the main results of this paper, (CLR) property is employed, and for weakly compatible mappings are established. All our findings backed up by befitting examples. Our generalize extend previous literature.

We explore the perturbative QCD corrections to the inclusive semileptonic decays of B mesons. In inclusive B decay processes the parton picture works well and the scaling feature manifests because the mass of b quark is larger than the QCD scale. Due to this property, the decay rate may be expressed by a single structure function describing the light–cone distribution of b quark apart from the ...