A set of axioms of incidence and order for geometry was formulated
by David Hilbert in 1898. In this paper these axioms are reformulated
and particular care is taken with the two relations of order
and incidence. Such phrases as " point P lies on line [cursive small letter L]"...
We discuss a mathematical model arising from the following
physical situation. We consider a gas-filled cylinder with a piston
at one end whose motion is determined by the pressure of the gas
within the cylinder and by external forces. Zero mass flux is
assumed at the piston while the mass...
Our purpose is twofold, to derive a 2-dimensional model of streambed erosion and to develop a solution procedure to solve the equations of our model. The flow domain, which varies in time, is bounded above by a free surface and is bounded below by an erodable streambed. An initial flow...
A mathematical model simulating mass transport of chemicals
in saturated porous medium is given in four parts. Included in the
development is the physical phenomenon of adsorption of molecules
of chemicals on the surrounding walls of the porous medium. The
four main areas of study are:
(1) Simple one dimensional...
In this paper, the general mathematical theory of linear
passive one-ports and the class of positive real functions are briefly
reviewed as background material. Then a time domain method for
synthesis of a finite lumped RC system is given, which involves
breaking down the given system into n subsystems. Finally,...
Quantum field theory has enjoyed much success, indeed for ordinary flat spacetime applications it has been experimentally verified to a great deal of accuracy. However on general cursed spacetime backgrounds there is no canonical method for constructing a quantum field theory. In 1975, Abhay Ashtekar and Anne Magnon made progress...
We discuss a mathematical model arising in the filtration of a
fluid through a porous medium. The model leads to a free boundary
value problem whose governing equation depends on the retention
function. A numerical approximation by means of finite elements
is used to present an existence and uniqueness theorem...
A nonlinear wave equation is developed, modeling the evolution in time of shallow water waves over a variable topography. As the usual assumptions of a perfect fluid and an irrotational flow are not made, the resulting model equation is dissipative due to the presence of a viscous boundary layer at...
A construct is developed which is useful in the
investigation of the global convergence properties of
Newton's method.
This construct is used to study the application of
Newton's method to polynomials. A proof that Newton's
method converges almost globally for polynomials with
only real zeroes is extended to a larger...
Quantization is a non-linear operation of converting a continuous
signal into a discrete one, assuming a finite number of levels N. A
study is made of the quantization procedure, starting from the year
1898 to the present time. Conditions for minimum error are derived
with consideration of quantization in magnitude...
Topological results are applied to boundary value problems modeling nonlinear
beams and dry friction. A classical continuation theorem is used to prove
existence results for nonlinear beams. Unified proofs, where possible, are given for
all the physically relevant boundary conditions. Integration techniques and various
integral inequalities are used to prove...
The classical dimension theories of Menger-Urysohn and Lebesgue are equivalent on metric spaces. However, their infinite-dimensional analogues may differ, even on compact metric spaces. The three such infinite-dimensional dimension theories considered in this thesis are known as countable-dimensionality, property C, and weak infinite-dimensionality. The open questions regarding the relationships between...