UNITS, ADMISSIBLE ORIENTED PARALLELOPIPEDS AND BASES.
Item
-
Title
-
UNITS, ADMISSIBLE ORIENTED PARALLELOPIPEDS AND BASES.
-
Identifier
-
AAI8023663
-
identifier
-
8023663
-
Creator
-
AULICINO, DANIEL JOSEPH.
-
Contributor
-
Harvey Cohn
-
Date
-
1980
-
Language
-
English
-
Publisher
-
City University of New York.
-
Subject
-
Mathematics
-
Abstract
-
(1) The theory of unit calculation as developed by Minkowski and Voronoii is presented in a unified manner. (2) The geometry and neighboring processes of admissible oriented parallelopipeds is developed in origin symmetric discrete arrays, a more general setting than an irreducible lattice. (3) A new type of admissible oriented parallelopiped, the edge-face admissible oriented parallelopiped, is presented. Its geometry and neighboring process is developed. (4) The concept of rank matrix is introduced to aid in the proofs and understanding of the above theory. It is shown that in n-dimensions, there are p(n) types of n-dimensional admissible oriented parallelopipeds, where p(n) is the partition function. (5) Some new proofs are given of Voronoii's theorems. (6) The basis approach to calculating units is described and placed in a general setting. (7) Cohn's basis approach is described. A minor flaw is located: one of his theorems is invalid. Some new proofs of his theorems are given. Also, a clearer connection is established between MAOP and Cohn bases. Finally, a connection is shown between VAOP and Cohn bases. As a result of these connections a new proof that Cohn bases will generate units results. A possible new way of calculating fundamental units by Cohn bases results and also a possible way of calculating units in higher dimensions is suggested.
-
Type
-
dissertation
-
Source
-
PQT Legacy CUNY.xlsx
-
degree
-
Ph.D.
-
Program
-
Mathematics
