A function is Perron integrable if it has locally small Riemann sums

How hard is it to determine if a graph has a 2-role assignment?

Role assignments, introduced by Everett and Borgatti [2], who called them role colorings, formalize the idea, arising in the theory of social networks, that individuals of the same social role will relate in the same way to the individuals playing counterpart roles. If G is a graph, a k-role assignment is a function r mapping the vertex set onto the set of integers {1, 2, . . . , k} so that if ...

Zeros of Partial Sums of the Riemann Zeta-function

We write ρX = βX + iγX for a typical zero of FX(s). The number of these up to height T we denote by NX(T ), and the number of these with βX ≥ σ by NX(σ, T ). We follow the convention that if T is the ordinate of a zero, then NX(T ), say, is defined as limǫ→0+ NX(T + ǫ). There are two natural ways to pose questions about NX(T ), NX(σ, T ), and the distribution of the zeros generally. We can fix ...

It Is Not worth Learning If It Is Not Remembered:

The collation, storage and retrieval of information are essential components of successful learning. Whether information is retained depends on a variety of factors, including how the information fits with an individual’s existing knowledge, the way in which information is presented, and its complexity. Some of these factors are under the direct control of the e-learning designers and developer...

If it is to be, it is up to me.

Algebras of Riemann Integrable Functions

In the present paper we shall consider from two different standpoints the real Riemann integrable functions on a bounded closed interval / contained in En. Our results will be extendable to the complex case by standard arguments. (1) In §1 we designate the real valued Riemann integrable functions by R(I). If R(I) is normed by ||/|| =supx6j |/(x)| then it is known that R(I) is a Banach algebra. ...