Some new inequalities of Ostowski-type for the Čebyšev functional and applications for Taylor’s expansion and generalised trapezoid formula are pointed out. Mathematics subject classification (2010): Primary 26D15; Secondary 41A55.

The present report describes a case of osteoid osteoma of the trapezoid. It'is an unusual localisation. Synovitis was the first clinical symptom. Tomograms allowed diagnosis and guided the treatment. Radical excision prevented recurrence.

A companion for the Ostrowski and the generalised trapezoid inequalites for various classes of functions, including functions of bounded variation, Lipschitzian, convex and absolutely continuous functions is established. Applications for weighted means are also given.

We develop Trapezoid, Midpoint, and Simpson’s rules for the Riemann-Stieltjes integral, the latter two being new. These rules are completely natural when the notion of relative convexity is used. Mathematics subject classification (2010): 65D30.

We review eight and prove an additional 13 necessary and sufficient conditions for a convex quadrilateral to be a trapezoid. One aim for this paper is to show that many of the known properties of trapezoids are in fact characterizations.

We report an unusual case of carpal coalition between trapezium and trapezoid in a 54-year-old man who was diagnosed after a pain in left wrist following a night's sleep. The patient was otherwise asymptomatic.

In this paper, we give a unified approach to establish midpoint, trapezoid, and Simpson’s inequalities for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real numbers are also given.

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

Coherent light-matter interaction in ultrathin metamaterials has been demonstrated to dynamically modulate intensity, polarization and propagation direction of light. The gradient metasurface with a transverse phase variation usually exhibits an anomalous refracted beam of light dictated by so-called generalized Snell's law. However, less attention has been paid to coherent control of the metas...