For a family F of n mutually disjoint unit disks in the plane, we show that if any four disks are intersected by a line then there is a line that intersects at least n− 1 disks of F .

We give an easy description of the barycentric extension of a map of the unit circle to the closed unit disk using some ideas from dynamical systems. We then prove that every circle endomorphism of the unit circle of degree db 2 (with a topological expansion condition) has a conformally natural extension to the closed unit disk which is real analytic on the open unit disk. If the endomorphism i...

Abstract The increasing importance of the Common European Framework Reference (CEFR) has led to research on linguistic characteristics its levels, as this would help application CEFR in design teaching materials, courses, and assessments. This study investigated whether levels can be distinguished with reference syntactic complexity (SC). 14- 17-year-old Finnish learners English (N=397) wrote t...

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a num...

There is considerable interest in community interventions for health promotion, where the community is the experimental unit. Because such interventions are expensive, the number of experimental units (communities) is usually small. Because of the small number of communities involved, investigators often match treatment and control communities on demographic variables before randomization to mi...

let denote the unit circle in the complex plane. given a function , one uses t usual (harmonic) poisson kernel for the unit disk to define the poisson integral of , namely . here we consider the biharmonic poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . we then consider the dilations for and . the ...

In the figure above, we see a lattice of black and white atoms. These could be B and N atoms respectively for a BN-sheet. Using one of the equivalent unit cells (hashed area) and combinations of the unit vectors, ~a1 and ~a2, we can generate the entire lattice. A general translational vector in a periodic lattice can be written as the sum of integer multiples of unit vectors, ~ T (~n) = ~ T (n1...

in a field experiment, during three successive years of 2007, 2008 and 2009, the effects of planting pattern and high corm density on agronomic performance of saffron was investigated at the research station of ferdowsi university of mashhad. a complete randomized block design in a factorial arrangement of three replications being employed. treatments consisted of three corm rates of planting (...