The objective of this paper is to describe the design of a real-time system to control two hydroelectric power plants by a digital
computer. The two controlling relations are stated as the continuity
of water flow and the inequality of power generation requirements.
It contains the logical sequence in finding...
The computation of symmetric functions can be tedious.
For this reason, the object of this paper is to devise a computer
program so that these symmetric functions can be handled automatically.
The contribution of this investigation is a heuristic for
finding the polynomials proved to exist by the Fundamental Theorem...
The system of partial differential equations which governs the
motion of a Newtonian fluid has been known for over a century. Yet,
due to the complexity of the equations, an analytical solution is known
only for a few simple geometries or a few special cases such as very
slow motion....
The study of water movement in unsaturated soils by using appropriate
diffusion equations has attracted considerable attention in
recent years.
In this study, a numerical technique is developed for solving
a generalized, dimensionless diffusion equation by the use of a digital.
computer. Diffusivity and capillary conductivity equations derived
by Brooks...
The purpose of this paper is to show that arithmetic
is consistent if Euclidean geometry is. Specifically, a
model of Peano's axioms [2] is defined in the space of
Euclidean geometry, where Hilberts axioms [3] are taken
to be the axioms of Euclidean geometry.
This paper is a continuation of William Zell's thesis, A Model of Non-Euclidean Geometry in Three Dimensions. The purpose of that thesis was to show that the axioms of non-Euclidèan geometry are consistent if Euclidean geometry an& hence arithrnetic is consistent. Mr. Zell. discussed the axioms of connection and order...
In this paper we present a model of Non-Euclidean geometry
in three dimensions. This will show that the axioms of Non-Euclidean
geometry are consistent if Euclidean geometry and, hence, arithmetic
is consistent. However, the model is incomplete for we have not
included the topic of congruence, the axiom of Archimedes,...
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,...
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...
FORTRAN is readily feasible to translation into ALGOL since
they share many common features. Most of the features that are
unique to FORTRAN can be translated by restricting them somewhat.
The translator will handle explicit declarations of each item
in a block, compensate for the differences in various operators,
compensate...
It is well- known that a real number can be defined as an equivalence
class of fundamental rational sequences. In fact, it is also possible
to define a real number as an equivalence class of sequences of
nested closed rational intervals. This paper is devoted to the latter
case.
In this paper we investigate the Lyapunov mapping
P --> AP + PA *
where A is a positive stable matrix and P is a hermitian
matrix. In particular, for special positive stable A we
characterize the image of the cone of positive definite matrices
under this mapping. In Section...
This paper is a classification of 181 problems, each of which involves the evaluation or application of determinants. The problems are those which have appeared in the "Problems and Solutions" sections of the American Mathematical Monthly, Deutsche Mathematiker-Vereinigung Jahresbricht, Mathematics Magazine, and School Science and Mathematics. The problems are classified,...