First, we may assume, without loss of generality, that the points of the sets ƒ > > are located on the unit circle, by projecting these points on the circumference of the circle. Second, by Carathéodory Theorem (see [3]), we may assume, without loss of generality, that the cardinality of each set + is at most ? , for 4„5X2= >8 @? . In fact, we can further assume that * + *…5†? , for 4„5X2' 98( ...

In this paper we seek for inner product dependent strictly positive definite kernels on subsets of C. We present separated necessary and sufficient conditions in order that a positive definite kernel on C be strictly positive definite. One emphasis is on strictly positive definite kernels on the unit circle. Since positive definite kernels on the circle were already characterized in [1], the st...

The numbers on the inner circle are those that exist in the modular arithmetic. If we continue beyond 7, as shown in the outer ring, the numbers wrap around the wheel. Numbers on the same spoke are equivalent. For example, 0 and 8 are equivalent, 1 and 9 are equivalent, 2 and 10 are equivalent, and so on. Another way to look at it is that when 9 is introduced into modular arithmetic with 8 shaf...

2 Representing a Circle 3 2.1 Quarter of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Degree 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Degree 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Half a Circle . . . . . . . . . . . . . . . . ....

The English literature component has been around in the Malaysian Education system since 2000. However, literature as a subject has always been learned more for transactional purposes rather than for its aesthetic value. Basically, a regurgitation of knowledge from years of learning, poured out in one major examination. In this research, the researcher applies a teaching method, called the lite...

permeability can be directly measured using cores taken from the reservoir in the laboratory. due to high cost associated with coring, cores are available in a limited number of wells in a field. many empirical models, statistical methods, and intelligent techniques were suggested to predict permeability in un-cored wells from easy-to-obtain and frequent data such as wireline logs. the main obj...

According to the randomized circle detection (RCD) algorithm, the probability that four randomly sampled points belong to the same circle is relatively low. A fast algorithm for circle detection in this paper is proposed. Three points will be randomly sampled in the edge image and the fourth point is then sampled within the margin of vertical circumscribed and inscribed squares of the circle de...

A circle graph is the intersection graph of a set of chords on a circle. A graph is Helly circle if there is a model of chords satisfying the Helly property. In 2003 it was conjectured that Helly circle graphs are exactly diamond-free circle graphs. In this work, we propose a method to compress any Helly circle representation of a graph and give some ideas to advance in an inductive proof of th...

Abstract: The intersection graph of a set of chords on a circle is called a circle graph. This class of graphs admits some interesting subclasses, such as: Helly circle graphs, clique-Helly circle graphs, unit circle graphs and proper circular-arc graphs. In this paper, we prove some inclusion relations among these subclasses. A necessary condition for a graph being a Helly circle graph is show...

Polygon-circle graphs are intersection graphs of polygons inscribed in a circle. This class of graphs includes circle graphs (intersection graphs of chords of a circle), circular arc graphs (intersection graphs of arcs on a circle), chordal graphs and outerplanar graphs. We investigate binding functions for chromatic number and clique covering number of polygon-circle graphs in terms of their c...