A Few Facts about Fakes

A few new (?) facts about infinite elements

We discuss the (conjugated) Bubnov–Galerkin and Petrov–Galerkin infinite element (IE) discretizations to Helmholtz equation including the use of elements of locally variable order, optimal choice of IE shape functions, calculation of Echo Area (EA), and automatic hp-adaptivity. The discussion is illustrated with 2D numerical experiments. 2005 Elsevier B.V. All rights reserved. MSC classificatio...

Spina bifida: a few simple facts about a complex condition.

A Few New Facts about the EKG Sequence

The EKG sequence is defined as follows: a1 = 1, a2 = 2 and an is the smallest natural number satisfying gcd(an−1, an) > 1 not already in the sequence. The sequence was previously investigated by Lagarias, Rains and Sloane. In particular, we know that (an) is a permutation of the natural numbers and that the prime numbers appear in this sequence in an increasing order. Lagarias, Rains and Sloane...

A few facts on integrality

The purpose of this note is to collect some theorems and proofs related to integrality in commutative algebra. The note is subdivided into three parts. Part 1 (Integrality over rings) consists of known facts (Theorems 1, 4, 5) and a generalized exercise from [1] (Corollary 3) with a few minor variations (Theorem 2 and Corollary 6). Part 2 (Integrality over ideal semifiltrations) merges integral...

Non-specific binding of antibodies in immunohistochemistry: Fakes and facts