This paper presents an exposition of the stochastic models
for the Brownian motion. The results of Einstein and Wiener are
presented, together with the Uhlenbeck-Ornstein process which
gives a more realistic model of the Brownian motion of a particle.
Finally, applying a one-one transformation on the forward
Kolmogorov equation we...
The thesis discusses stability of procedures based on linear
computing formulas for numerical integration of an ordinary first-order
differential equation. The theorems are proved: (1) If the
procedure is asymptotically stable it is stable for small positive step
size if the Lipschitz number is negative; (2) Relative stability always
exists...
In his book on abstract algebra, Nathan Jacobson
poses and solves the problem of finding the number of
ways of inserting parentheses in a string of given length
with binary operators. We continue the work of Jacobson
and go beyond it in that we no longer consider one binary
operator...