We derive minimal conditions on a symmetry group of a linearly elastic material that implies its isotropy. A natural setting for the formulation and analysis is provided by the group representation theory where the necessary and sufficient conditions for isotropy are expressed in terms of the irreducibility of certain group representations. We illustrate the abstract results by (re)deriving sev...

In this paperwe give an alternate combinatorial description of the “(l, 0)-Carter partitions” (see [4]). The representation-theoretic significance of these partitions is that they indicate the irreducibility of the corresponding specialized Specht module over the Hecke algebra of the symmetric group (see [7]). Our main theorem is the equivalence of our combinatoric and the one introduced by Jam...

This essay deals with the concept of truth in the context of a version of internal realism. In §1 I define some variants of realism using a set of realistic axioms. In §2 I will argue that for semantical reasons we should be realists of some kind. In §3 I plead for an internalistic setting of realism starting from the thesis that truth is, at least, not a non-epistemic concept. We have to bear ...

The Eisenstein irreducibility critierion is part of the training of every mathematician. I first learned the criterion as an undergraduate and, like many before me, was struck by its power and simplicity. This article will describe the unexpectedly rich history of the discovery of the Eisenstein criterion and in particular the role played by Theodor Schönemann. For a statement of the criterion,...

He noted then that the conjecture is true if n = p 1 2 or if n = p where p is a prime and r a positive integer. Calculations showed the conjecture also held for n 100. Recently, in a study of more general polynomials, the rst author [2] obtained further irreducibility results for f(x); in particular, he established irreducibility in the case that n+ 1 is a squarefree number 3 and in the case th...