Taylor Series with Limit-Points on a Finite Number of Circles

Lattice Points on Circles

We prove that the lattice points on the circles x2 + y2 = n are well distributed for most circles containing lattice points.

Labeling Points with Circles

Points with Circles ∗

We present a new algorithm for labeling points with circles of equal size. Our algorithm tries to maximize the label size. It improves the approximation factor of the only known algorithm for this problem by more than 50 % to about 1/20. At the same time, our algorithm keeps the O(n log n) time bound of its predecessor. In addition, we show that the decision problem is NP-hard and that it is NP...

Close Lattice Points on Circles

We classify the sets of four lattice points that all lie on a short arc of a circle which has its center at the origin; specifically on arcs of length tR on a circle of radius R, for any given t > 0. In particular we prove that any arc of length ( 40 + 40 3 √ 10 )1/3 R on a circle of radius R, with R > √ 65, contains at most three lattice points, whereas we give an explicit infinite family of 4...

A Taylor-series Analysis of Finite-difference Formulations of Convection-diffusion Equations: Limitation on Grid Peclet Number and Grid Size

A simple Taylor-series analysis is made of the finite-difference formulations of the convection terms of convection-diffusion equations. A limitation is derived on grid Peclet number and grid size for a formulation to produce the expected numerical results. To verify the theory, the systematic numerical computations were carried out of a simple one-dimensional convection-diffusion equation. The...