A note concerning $A\sp{\ast} =L\sb{1}\,(\mu )$

A note concerning Primary Source Knowledge

We add a small increment to understanding the notion of ‘Primary Source Knowledge’ (PSK). PSK is knowledge that the non-expert and the citizen can acquire by assiduously reading the primary scientific journal literature without being embedded in the cultural life of the corresponding technical specialty (Collins and Evans 2007). This comes from exposing four papers to the automated computer fil...

A Note concerning Completely Regular Gyspaces1

A Note on a Conjecture Concerning Symmetric Resilient Functions

In 1985, Chor et al 2] conjectured that the only 1-resilient symmetric functions are the exclusive-or of all n variables and its negation. In this note the existence of symmetric resilient functions is shown to be equivalent to the existence of a solution to a simultaneous subset sum problem. Then, using arithmetic properties of certain binomial coeecients, an innnite class of counterexamples t...

A Note on Deaconescu’s Result concerning Lehmer’s Problem

Let φ(n) be the Euler function of n. We prove that there are at most finitely many composite integers n such that φ(n) | n − 1 and P (φ(n)) ≡ 0 (mod n), where P (X) ∈ Z[X] is any monic non-constant polynomial.

A Note concerning Veblen ' S Axioms for Geometry

Veblen has given a set of axioms for geometry.!. The first eight of these are as follows : % Axiom I. There exist at least two distinct points. Axiom II. If points A, B, C are in the order ABC, they are in the order CBA. Axiom III. If points A, B, C are in the order ABC, they are not in the order BCA. Axiom IV. If points A, B, C are in the order ABC, then A is distinct from C. Axiom V. If A and...