Physical Sciences and Mathematics Commons^™

Separation Of The N-Sphere By An (N - 1)-Sphere, James C. Cantrell

Masters Theses

In this thesis we consider certain (n-1)-spheres embedded in S^n (we will frequently use the fact that S^n is topologically equivalent to the one point compactification of E^n). The problem is then to establish the existence or non-existence of certain topological properties of the two domains into which S^n is separated by the given (n-1)-spheres.

Pfaffian Differential Expressions And Equations, K. Raman Unni

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

It is needless to point out the necessity and the importance of the study of Pfaffian differential expressions and equations. While it is interesting to consider from the pure mathematical point of view, their applications in many branches of applied mathematics are well known. To mention a few, one may observe that they arise in connection with line integrals (example, determination of work). They provide a more rational formulation of the foundations of thermodynamics as developed by the Greek mathematician Caratheodory. They also arise in the problem of determining the orthogonal trajectories. In many branches of engineering and other physical …

A Determination Of The Earth's Gravity Field In Spheroidal Coordinates, M. Spencer Hamilton Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The earth's gravity field G * at a point P in the region surrounding the earth's surface is defined as the force acting on a unit mass concentrated at P. This is a force resulting from two components: (1) G₁ due to the gravitational attraction of the earth's mass, and (2) G₂ due to the earth's rotation.

As a result of Newton's law of gravitation, G₁ can be written in integral form as follows:

G₁ = k ( (_V ( rdm/r³

where r = PQ, r = |r|, Q is a point which ranges …

A Generalization Of The Rayleigh Distribution, Ruth H. Lemon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This papers is divided into numbered sections. The equations are numbered anew in each section, and equation numbers are always enclosed in parentheses. Merely the equation number is given when referring to an equation in the same section as the references; otherwise the section number is prefixed. Thus equation (4) refers to the fourth equation of the same section as the reference, and equation (2.2) refers to the second equation of the second section.