907 research outputs found
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 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 matrices over (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
4-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 cyclotriphosphazenes), selection of molar proportions 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
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
Aminophenoxy cyclotriphosphazenes such as hexakis (4-aminophenoxy) cyclotriphosphazene and tris (4-aminophenoxy)-tris phenoxy cyclotriphosphazene are used as curing agents for epoxy resins. These 1,2-epoxy resins are selected from di- or polyepoxide containing organic moieties of the formula (CH2-CHO-CH2) m-W-R-W- (CH2CH-CH2O)m where R is diphenyl dimethylmethane, diphenylmethane; W is a nitrogen or oxygen atom; and m is 1 when W is oxygen and 2 when W is nitrogen. The resins are cured thermally in stages at between about 110 to 135 C for between about 1 and 10 min, then at between about 175 to 185 C for between 0.5 to 10 hr and post cured at between about 215 and 235 C for between 0.1 and 2 hr. These resins are useful for making fire resistant elevated temperature stable composites, laminates, molded parts, and adhesives and structures, usually for aircraft secondary structures and for spacecraft construction
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