This thesis contains a collection of properties of the greatest integer part function which were obtained by an extensive literature search. A few original properties are stated and proved and some of the properties which were found unproved in the literature are proved.
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...
This thesis brings together under one cover a survey of the
history of the real number pi along with a study of the present state
of its theory, application, and calculation.
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...
This thesis contains a collection of summation formulas for
the greatest integer part function. Proofs are supplied for original
results and for those formulas which are stated without proof in the
literature. References are given for formulas and proofs which
appear in the literature.
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 Murderers Creek Area, within the Aldrich Mountain province of
northeast Oregon, originated in an arc-trench gap during Permian-early
Triassic time. The area represents a small portion of a forearc
depositional basin and tectonic highland which borders the basin along
its seaward margin. The trench associated with an east dipping...