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Showing 1 to 20 of 1589 for “"Quadratic"”.
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Quadratic Spatial Soliton Interactions
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These …
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COUPLING OF QUADRATIC LATTICES
… \vspace{14pt} \noindent TITLE: COUPLING OF QUADRATIC LATTICES % Change title above and put all in CAPS \vspace{14pt} \noindent MAJOR PROFESSOR: Dr. A. Earnest \vspace{14pt}\\ The subject of this dissertation is the representation theory of quadratic lattices over the ring of rational …
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Quadratic and cubic reciprocity
… this thesis, we seek to prove results about quadratic and cubic reciprocity in great detail. Although these results appear in many textbooks, the proofs often contain large gaps that may be difficult for the average reader to follow. To achieve this goal, we have 'built up to reciprocity …
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Quadratic Reciprocity: Proofs and Applications
The law of quadratic reciprocity is an important result in number theory. The purpose of this thesis is to present several proofs as well as applications of the law of quadratic reciprocity. I will present three proofs of the quadratic reciprocity. We begin with a proof that depends on Gauss's …
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Quadratic differentials and Loewner evolutions
… In this thesis, we develop a method using quadratic differentials to study paths on 2-dimensional lattices. We will then use this method to derive properties of the LDE. In particular, we will be able to derive formulae for the driving function of the LDE for paths on certain lattices. We …
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A discussion of homogenous quadratic equations
This thesis will look at Quadratic Diophantine Equations. Some well known proofs, including how to compute all Pythagorean triples and which numbers can be represented by the sum of two and four squares will be presented. Some concepts that follow from these theorems will also be presented. These …
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Quadratic Differential Systems for Mathematical Models
Made available in DSpace on 2014-12-09T22:17:30Z (GMT). No. of bitstreams: 1 6612355.pdf: 3897204 bytes, checksum: 985a1adb7e02bb5e4c0c5f8ebae2e606 (MD5) Previous issue date: 1966
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Comparing Quadratic Voting and Likert Surveys
… decades. In this thesis, we compared it with Quadratic Voting, or QV, a voting mechanism designed to facilitate collective decision making. We compared the two surveying methods under scenarios in which a decision-maker had to choose among K options. First, we created a pretest that …
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Aspects of multivariate complex quadratic forms
… properties of certain multivariate complex quadratic forms and their characteristic roots are investigated. Multivariate complex distribution theory was originally introduced by Wooding (1956), Turin (1960) and Goodman (1963a) when they derived and studied the multivariate complex normal …
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The quadratic Zeeman effect in hydrogen
Thesis (B.S.) Massachusetts Institute of Technology. Dept. of Physics, 1952.
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A Classification of some Quadratic Algebras
In this paper, for a select group of quadratic algebras, we investigate restrictions necessary on the generators of the ideal for the resulting algebra to be Koszul. Techniques include the use of Gröbner bases and development of Koszul resolutions. When the quadratic algebra is Koszul, we provide …
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The Fermat equation over quadratic fields
… Last Theorem over the rational numbers to quadratic fields. In particular, under certain congruence conditions it is shown that the Fermat equation of exponent p has no solution over Q(√m) when p is a m-regular prime. Completely analogous to the work of Kummer, it is shown that m-regular …
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Quadratic minimization and least distance programming
Quadratic minimization problems constitute a significant and important subset of optimization problems. Research has shown that a convex quadratic programming problem can be reduced to a least distance programming problem using a unique and non-singular "linear least distance transformation." A …
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Model Updating Using a Quadratic Form
… ways; two different approaches, denoted as the Quadratic Compression Method (QCM) and the Full Vector Method (FVM), are described in this paper. It is shown that the QCM possesses superior robustness properties with respect to noise in the data. This fact, as well as the simplicity offered by …
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The Pure Virtual Braid Group is Quadratic
… graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this thesis we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra …
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Curves of genus 2 and quadratic forms
… focuses on a special associated integral quadratic form qC, which is intrinsically attached to a curve C of genus 2. This form, known as the refined Humbert invariant, was introduced by Kani (1994). Our first main result is the classification of those imprimitive ternary quadratic forms …
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Relative oriented class groups of quadratic extensions
… relative oriented class groups associated to quadratic extensions of number fields L/K, extending work of Bhargava concerning composition laws for binary quadratic forms over number fields of higher degree. This work generalized the classical correspondence between ideal classes of quadratic …
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Exploring Quadratic Expressions through the 5E Model
… four sequential Algebra I lessons exploring quadratic expressions using the 5E Instructional Model. This model, rooted in constructivist principles, provides a structured framework intended to address the new pedagogical wave. The 5E Model can promote a stronger foundation for student …
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Quadratic Lie algebras. Algorithms and (de)constructions
In this dissertation we are going to study quadratic Lie algebras, with special interest in the ones which are 2-step nilpotent, and to give algorithmic procedures to build a wide range of examples. After an introduction and a overview of the known results in this matter, we start with a …
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