An operator scheme for composition of Turing machines is
developed and applied to the computation of the recursive functions
over an arbitrary alphabet.
The relative accuracy of solutions to chaotic systems was examined using the Lorenz
system as a case study. The classical fourth order Runge-Kutta method was employed to
generate solutions using various step sizes, and the resultant solutions were compared. A
second set of solutions was then computed using one of...
Under certain conditions, a neural network may be trained to perform a
specific task by altering the weights of only a portion of the synapses.
Specifically, it has been noted that certain three layer feed-forward networks may
be trained to certain tasks by adjusting only the synapses to the output...
In 1932 A. Ya. Khinchin gave the first partial solution of the celebrated 1931 αβ Conjecture of L.G. Schnirelmann and E. Landau of the density of sums of sets on integers, which was completely proved in 1942 by H.B. Mann.
Khinchin's theorem is proved along with theorems of P. Scherk...
There has been a lot of work done in recent decades in the field of symbolic dynamics.
Much attention has been paid to the so-called "complexity" function, which gives a sense
of the rate at which the number of words in the system grow. In this paper, we explore this...