in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}r...

for all x, y ∈ C and each n ≥ 1. The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] as an important generalization of nonexpansive mappings. It was proved in [1] that if C is a nonempty bounded closed convex subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self mapping on C, then F (T ) is nonempty closed convex subset o...

In this paper, we introduce a class of totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping to modify the Halpern-Mann-type iteration algorithm for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping, which has the strong convergence under a limit condition only in the framework of Banach spaces. Our results are applied to study the approximation probl...

In this paper, we propose two new estimators of the multivariate rank correlation coefficient Spearman's footrule which are based on general for Average Orthant Dependence measures. We compare proposals with a previous estimator existing in literature and show that three asymptotically equivalent, but, small samples, one proposed outperforms others. also analyse Pitman efficiency these indices ...

In a previous paper we showed that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6-regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random d-regular graph for other d between 5 and 10 inclusive is a.a.s. restricted to a range of two integer values...

This paper is concerned with the development of a fast spectral method for solving boundary integral equations in three-dimensional potential theory. Upon discretizing the underlying boundary integrals via a Galerkin approximation, the proposed method overlays the problem domain with a regular Cartesian grid that serves as an auxiliary platform for computation. With the aid of the Fast Fourier ...

This work assesses one specific aspect of the relationship between auditory rhythm cognition and language skill: regularity perception. In a group of 26 adult participants, native speakers of 11 different native languages, we demonstrate a strong and significant correlation between the ability to detect a "roughly" regular beat and rapid automatized naming (RAN) as a measure of language skill (...

We present a Weierstrass-type representation formula which locally represents every regular two-dimensional lightlike surface in Lorentz-Minkowski 4-Space $\mathbb{M}^4$ by three dual functions $(\rho,f,g)$ and generalizes the for surfaces $\mathbb{M}^3$. give necessary sufficient conditions on $\rho$, $f$, $g$ to be minimal, ruled or $l$-minimal. For surfaces, we itself ruled. Furthermore, res...

We have analyzed the initiation and termination sites of transcription in vivo of the colicin E1 gene in Escherichia coli cells by S1-mapping assay and RNA blot hybridization. According to the S1-mapping assay, the transcription was initiated at about 75 base pairs upstream from the NH2-terminal codon of the gene. The initiation site corresponded with one of the two promoters which were previou...

We study the space complexity of querying languages over data streams in the sliding window model. The algorithm has to answer at any point of time whether the content of the sliding window belongs to a fixed regular language. For regular languages, a trichotomy is shown: For every regular language the optimal space requirement is asymptotically either constant, logarithmic, or linear in the si...