Let A and B be two subsets of the set of all non-negative
integers with 0 ε A and O ε B. The sum of the sets A and B is
the set C = A + B = {a + b: a ε A, b ε B). For n...
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...
In this thesis, we study conditions not involving density which
guarantee that a given positive integer is contained in a sum of sets
of nonnegative integers. We survey the literature, give more detailed
proofs of some known theorems, develop some new theorems,
and make some conjectures.
The Rainbow hydrothermal plume was
discovered during a recent geophysical survey along
200km of the Mid-Atlantic Ridge (MAR), SW of the
Azores Triple Junction, in which at least seven new sites
of hydrothermal activity were identified. Here, we present
the first hydrographic study of the Rainbow plume, 36°
15'N, the...
A study of the running time of several known algorithms and several new algorithms to compute the n[superscript th] element of the Fibonacci sequence is presented. Since the size of the n[superscript th] Fibonacci number grows exponentially with n, the number of bit operations, instead of the number of integer...
This study was concerned with the flow of a magnetic self-propelled
ferrohydrodynamic fluid in a horizontal circular tube subjected
to axially varying temperature and magnetic field. The first
phase of the study involved the analytical solution to the governing
equations for the velocity and temperature profiles within the fully
developed...