Registered users receive a variety of benefits including the ability to customize email alerts, create favorite journals list, and save searches.
Please note that a Project Euclid web account does not automatically grant access to full-text content. An institutional or society member subscription is required to view non-Open Access content.
Contact email@example.com with any questions.
In this paper we address two-point boundary value problems of the form
where the function resembles for some constants , , . We prove the existence of positive solutions for the semipositone case where , and further prove multiplicity under certain conditions. In particular we extend theorems from Henderson and Thompson to the semipositone case.
For a group with generating set , the -graph of , denoted , is the graph whose vertices are distinct cosets of in . Two distinct vertices are joined by an edge when the set intersection of the cosets is nonempty. In this paper, we study the existence of Hamiltonian and Eulerian paths and circuits in .
We call a graph intrinsically linkable if there is a way to assign over/under information to any planar immersion of such that the associated spatial embedding contains a pair of nonsplittably linked cycles. We define intrinsically knottable graphs analogously. We show there exist intrinsically linkable graphs that are not intrinsically linked. (Recall a graph is intrinsically linked if it contains a pair of nonsplittably linked cycles in every spatial embedding.) We also show there are intrinsically knottable graphs that are not intrinsically knotted. In addition, we demonstrate that the property of being intrinsically linkable (knottable) is not preserved by vertex expansion.
A connection is developed between polynomials invariant under abelian permutation of their variables and minimal zero sequences in a finite abelian group. This connection is exploited to count the number of minimal invariant polynomials for various abelian groups.
The gap functions for generalized vector quasivariational inequalities in Hausdorff topological vector spaces are introduced, then using Fan–Knaster–Kuratowski–Mazurkiewicz (FKKM) theorem, some existence theorems for a class of generalized vector quasivariational inequalities under suitable assumptions are established. The obtained results extend and unify corresponding results in the literature.
The Fibonacci numbers appear in many surprising situations. We show that Fibonacci-type sequences arise naturally in the geometry of , the space of all nonempty compact subsets of under the Hausdorff metric, as the number of elements at each location between finite sets. The results provide an interesting interplay between number theory, geometry, and topology.
In her Ph.D. Thesis, Czarneski began a preliminary study of the coefficients of the reciprocal of the Ihara zeta function of a finite graph. We give a survey of the results in this area and then give a complete characterization of the coefficients. As an application, we give a (very poor) bound on the number of Eulerian circuits in a graph. We also use these ideas to compute the zeta function of graphs which are cycles with a single chord. We conclude by posing several questions for future work.