Fibonacci and Lucas numbers with only one distinct digit.
Domain decomposition algorithms for first-order system least squares methods.
Additive Schwarz methods for the p-version finite element method.
Neumann-Neumann algorithms for spectral elements in three dimensions
Domain decomposition methods and scientific computing applications
This paper reviews the basic mathematical ideas and convergence analysis of domain decomposition methods. These are parallel and scalable iterative methods for the efficient numerical solution of partial differential equations. Two examples are then presented showing the application of domain decomposition methods to large-scale numerical simulations in computational mechanics and electrocardiology.
Infinite families of noncototients
For any positive integer let ϕ(n) be the Euler function of n. A positive integer is called a noncototient if the equation x-ϕ(x)=n has no solution x. In this note, we give a sufficient condition on a positive integer k such that the geometrical progression consists entirely of noncototients. We then use computations to detect seven such positive integers k.
The Distribution of Integers n Divisible by Lomega(n)
On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ
For any positive integer n let ϕ(n) and σ(n) be the Euler function of n and the sum of divisors of n, respectively. In [5], Mąkowski and Schinzel conjectured that the inequality σ(ϕ(n)) ≥ n/2 holds for all positive integers n. We show that the lower density of the set of positive integers satisfying the above inequality is at least 0.74.
Representing integers as linear combinations of S-units
Two Diophantine approaches to the irreducibility of certain trinomials
Minimal Niven numbers
Page 1