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Full-Text Articles in Number Theory
Existence And Nonexistence Of Positive Solutions For Fractional Boundary Value Problems With Lidstone-Inspired Fractional Conditions, Jeffrey Lyons, Jeffrey T. Neugebauer, Aaron G. Wingo
Existence And Nonexistence Of Positive Solutions For Fractional Boundary Value Problems With Lidstone-Inspired Fractional Conditions, Jeffrey Lyons, Jeffrey T. Neugebauer, Aaron G. Wingo
EKU Faculty and Staff Scholarship
This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order 𝛼 +2𝑛, where 𝛼 ∈(𝑚 −1,𝑚] with 𝑚 ≥3 and 𝑚,𝑛 ∈ℕ. The conjugate fractional boundary conditions are inspired by Lidstone conditions. The nonlinearity depends on a positive parameter on which we identify constraints that determine the existence or nonexistence of positive solutions. Our method involves constructing Green’s function by convolving the Green functions of a lower-order fractional boundary value problem and a conjugate boundary value problem and using properties of this Green function to apply the Guo–Krasnosel’skii …
The Monochromatic Column Problem: The Prime Case, Loran Elizabeth Crowell
The Monochromatic Column Problem: The Prime Case, Loran Elizabeth Crowell
Online Theses and Dissertations
Let p1, p2, . . . , pn be pairwise coprime positive integers and let P = p1p2 · · · pn. Let 0,1,...,m−1 be a sequence of m different colors. Let A be an n×mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color, with colors 0 through m − 1 repeated cyclically. The Monochromatic Column problem is to determine the number of columns of A in which every entry is the same color. A partial solution for the case when m is prime is given.
Gaussian Amicable Pairs, Ranthony Ashley Clark
Gaussian Amicable Pairs, Ranthony Ashley Clark
Online Theses and Dissertations
Amicable pairs are two integers where the sum of the proper divisors of one is the other and vice versa. Since the Gaussian integers have many of the properties of the regular integers, we sought to discover whether there exist any pairs of Gaussian integers with the same property. It turns out that they do exist. In fact, some of the normal amicable pairs carry over as Gaussian amicable pairs. Also discovered are pairs that have a complex part.