John Ralph Wagner

Aroma, Oxygen and Moisture Barrier Behavior of Coated and Vacuum Coated OPP Films for Packaging

Various coated and vacuum coated, biaxially oriented polypropylene film product designs are examined in terms of their moisture, oxygen and aroma barriers. Factors that are thought to control oxygen barrier in these products are discussed and extended to aroma barrier development. The differences between the various vacuum coated and uncoated films with three organic permeants are evaluated and discussed in relationship to the impact on the polymer/coating interface and the development of aroma barrier in coated films. It is demonstrated that the existence of an evaporated barrier layer does not guarantee the existence of a chemical barrier. New combinations of film technology are described that permit the development of excellent aroma, oxygen and moisture barrier films.

Polymer Selection for Coextrusion

To produce an acceptable coextruded structure, proper resin systems have to be used with the correct die and/or feedblock technology. Just having the proper extruder, feedblock, and die design will not guarantee successful coextrusion.

Preface to Second Edition

In the preface to the first edition of this book I remarked on the paucity of introductory texts devoted to the arithmetic of elliptic curves. That unfortunate state of affairs has long since been remedied with the publication of many volumes, among which may be mentioned books by Cassels [43], Cremona [54], Husemöller [118], Knapp [127], McKean et. al [167], Milne [178], and Schmitt et. al [222] that highlight the arithmetic and modular theory, and books by Blake et. al [22], Cohen et. al [51], Hankerson et. al [107], and Washington [304] that concentrate on the use of elliptic curves in cryptography. However, even among this cornucopia of literature, I hope that this updated version of the original text will continue to be useful. The past two decades have witnessed tremendous progress in the study of elliptic curves. Among the many highlights are the proof by Merel [170] of uniform boundedness for torsion points on elliptic curves over number fields, results of Rubin [215] and Kolyvagin [130] on the finiteness of Shafarevich–Tate groups and on the conjecture of Birch and Swinnerton-Dyer, the work of Wiles [311] on the modularity of elliptic curves, and the proof by Elkies [77] that there exist infinitely many supersingular primes. Although this introductory volume is unable to include proofs of these deep results, it will guide the reader along the beginning of the trail that ultimately leads to these summits. My primary goals in preparing this second edition, over and above the pedagogical aims of the first edition, are the following:

32 – Troubleshooting Profile and Pipe

A few potential problems exist in pipe, tube, and profile extrusion. Pipe and tubing involve a symmetrical profile extrusion. For pipe and tubing, the cooling or calibration tank has sizing rings and one or more vacuum chambers to shape the pipe to the desired outside diameter.