We will prove two conditions for a tangential quadrilateral to be cyclic. According to one of these, a tangential quadrilateral is cyclic if and only if its Newton line is perpendicular to the Newton line of its contact quadrilateral.

Interpenetrated networks of nanoscaled materials provide the opportunity to construct efficient solar cells from low purity materials and versatile fabrication processes. Instead on relying on long diffusion length in high purity crystals, the nanocomposite solar cells base their ability to convert photon energy to electricity on fast conversion of the photoexcitation to energetic carriers spat...

This paper deals with the numerical approximation of the bending of a plate modeled by Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mix...

The paper presents a locking-free four-node element for laminated composite and sandwich plates based on Refined Zigzag Theory (RZT). Initially, two RZT-based plate elements are derived using eight-node configurations, achieved by way of standard C0 isoparametric shape functions. In addition, with view improving the modelling extremely thin plates, an anisoparametric is developed in which trans...

Abstract. In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of th...

A geometric graph is a graph G = (V;E) drawn in the plane so that the vertex set V consists of points in general position and the edge set E consists of straight line segments between points of V . Two edges of a geometric graph are said to be parallel , if they are opposite sides of a convex quadrilateral. In this paper we show that, for any xed k 3, any geometric graph on n vertices with no k...