Some remarks on a problem of J.H.C. Whitehead

Some Remarks on a Problem of Chowla

Cette conjecture fut par la suite prouvée et généralisée par Baker, Birch et Wirsing. Dans leur article conjoint, Baker, Birch et Wirsing affirment que Chowla a aussi résolu le cas particulier que ce dernier a énoncé, mais ne donnent aucune indication sur le genre de démonstration effectuée. En nous basant sur certains articles préalablement écrits par Chowla, nous essayons de reconstruire ce q...

Some Remarks on Prill’s Problem

If f : X → Y is a non-constant map of smooth curves over C and if there is a degree two map π : X → C where C is a smooth curve with genus less than that of Y , we show that for a general point P ∈ Y , f−1(P ) does not move except possibly in one particular case. In particular, this implies that Prill’s problem has an affirmative answer if X as above is hyperelliptic or if f is Galois. 2000 Mat...

Some remarks on inverse Wiener index problem

The sum of distances between all pairs of vertices W (G) in a connected graph G as a graph invariant was first introduced by Wiener [9] in 1947. He observed a correlation between boiling points of paraffins and this invariant, which has later become known as Wiener index of a graph. Today, the Wiener index is one of the most widely used descriptors in chemical graph theory. Due to its strong co...

Some remarks on a problem of A ardi

SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-kno...