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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio
Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio
Faculty and Research Publications
A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n x n boards that form the cube. The other is to tour within the n stacked copies of the n x n board that form the cube. This paper is concerned with the latter. In this paper …
Estimates Of Positive Solutions To A Boundary Value Problem For The Beam Equation, Bo Yang
Estimates Of Positive Solutions To A Boundary Value Problem For The Beam Equation, Bo Yang
Faculty and Research Publications
We consider a two-point boundary value problem for the fourth order beam equation. New upper and lower estimates of positive solutions of the problem are obtained.
Positive Solutions Of A Nonlinear Higher Order Boundary-Value Problem, John R. Graef, Johnny Henderson, Bo Yang
Positive Solutions Of A Nonlinear Higher Order Boundary-Value Problem, John R. Graef, Johnny Henderson, Bo Yang
Faculty and Research Publications
The authors consider the higher order boundary-value problem u (n)(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i-1)(0) = u (n-2)(p) = u(n-1)(1) = 0, 1 ≤ i ≤ n -2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.