In this paper we describe various applications of the RiemannHilbert method to the theory of orthogonal polynomials on the line and on the circle.

The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...

Integration of rolling circle amplification and sensitive bioluminescent detection of pyrophosphate, a homogeneous and label-free method has been developed for detecting single nucleotide polymorphism.

We use the Circle Method to derive asymptotics for functions related to the number of parts of partitions in particular residue classes.

By using integration method, we give a directly proof that the Cauchy process on a circle satisfies the Chapman-Kolmogorov equation.

A new, quick and inexpensive method of precision varnishing of metal microelectrodes is proposed. The circle surface pellicle of dried lacquer produced around the tip promotes microelectrode preparation.

In this paper, a novel geometric calibration method for C-arm cone-beam scanners is presented which allows the calibration of the circle-plus-arc trajectory. The main idea is the separation of the trajectory into two circular segments (circle segment and arc segment) which are calibrated independently. This separation makes it possible to reuse a calibration phantom which has been successfully ...