A Survey on Fixed Divisors

In this article, we compile the work done by various mathematicians on the topic of the fixed divisor of a polynomial. This article explains most of the results concisely and is intended to be an exhaustive survey. We present the results on fixed divisors in various algebraic settings as well as the applications of fixed divisors to various algebraic and number theoretic problems. The work is presented in an orderly fashion so as to start from the simplest case of $\Z,$ progressively leading up to the case of Dedekind domains. We also ask a few open questions according to their context, which may give impetus to the reader to work further in this direction. We describe various bounds for fixed divisors as well as the connection of fixed divisors with different notions in the ring of integer-valued polynomials. Finally, we suggest how the generalization of the ring of integer-valued polynomials in the case of the ring of $n \times n$ matrices over $\Z$ (or Dedekind domain) could lead to the generalization of fixed divisors in that setting.Comment: Accepted for publication in Confluentes Mathematic

Fire and heat resistant laminating resins based on maleimido substituted aromatic cyclotriphosphazene polymer

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Aromatic cyclotriphosphazenes

Four-Aminophenoxy cyclotriphosphazenes are reacted with maleic anhydride to produce maleamic acids which are converted to the maleimides. The maleimides are polymerized. By selection of starting materials (e.g., hexakis amino or trisaminophenoxy trisphenoxy cyclotrisphosphazenes), selection of molar porportions of reactants, use of mixtures of anhydrides and use of dianhydrides as bridging groups a variety of maleimides and polymers are produced. The polymers have high limiting oxygen indices, high char yields and other useful heat and fire resistant properties making them useful as, for example, impregnants of fabrics

Aminophenoxycyclotriphosphazene cured epoxy resins and the composites, laminates, adhesives and structures thereof

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