Journal•ISSN: 1944-4184
Involve, A Journal of Mathematics
About: Involve, A Journal of Mathematics is an academic journal. The journal publishes majorly in the area(s): Prime (order theory) & Vertex (geometry). Over the lifetime, 690 publications have been published receiving 1644 citations.
Topics: Prime (order theory), Vertex (geometry), Group (mathematics), Fibonacci number, Series (mathematics)
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TL;DR: In this article, the authors apply discrete time optimal control theory to the mathematical modeling of pest control, where the goal is to maximize the "valuable" population, minimize the pest population and the cost to apply the control strategies.
Abstract: We apply discrete time optimal control theory to the mathematical modeling of pest control. Two scenarios: biological control and the combination of pesticide and biological control are considered. The goal is maximizing the “valuable” population, minimizing the pest population and the cost to apply the control strategies. Using the extension of Pontryagin’s maximum principle to discrete system, the adjoint systems and the characterization of the optimal pest controls are derived. Numerical simulations of various cases are provided to show the effectiveness of our methods.
33 citations
TL;DR: In this paper, the determinant and rank for adjacency matrices of zero-divisor graphs of Ωn for various n were studied, and a method for finding nonzero eigenvalues was developed.
Abstract: We study adjacency matrices of zero-divisor graphs of ℤn for various n. We find their determinant and rank for all n, develop a method for finding nonzero eigenvalues, and use it to find all eigenvalues for the case n = p3, where p is a prime number. We also find upper and lower bounds for the largest eigenvalue for all n.
32 citations
TL;DR: A variant of Borůvka’s algorithm that developed during the graph theory course work of undergraduate students is presented, the proof of the algorithm is discussed, it is compared to existing algorithms, and an implementation of the procedure in Maple is presented.
Abstract: The minimum spanning tree problem originated in the 1920s when O. Borůvka identified and solved the problem during the electrification of Moravia. This graph theory problem and its numerous applications have inspired many others to look for alternate ways of finding a spanning tree of minimum weight in a weighted, connected graph since Borůvka’s time. This note presents a variant of Borůvka’s algorithm that developed during the graph theory course work of undergraduate students. We discuss the proof of the algorithm, compare it to existing algorithms, and present an implementation of the procedure in Maple.
31 citations
TL;DR: In this paper, the estimation of parameters of a zero-inflated Poisson (ZIP) distribution as well as using it to model some natural calamities' data is dealt with.
Abstract: This work deals with estimation of parameters of a zero-inflated Poisson (ZIP) distribution as well as using it to model some natural calamities’ data First, we compare the maximum likelihood estimators (MLEs) and the method of moments estimators (MMEs) in terms of standardized bias (SBias) and standardized mean squared error (SMSE) We then proceed to show how datasets from some recent natural disasters can be modeled by the ZIP distribution
30 citations
TL;DR: A survey of the results in this area can be found in this paper, where a characterization of the coefficients of the reciprocal of the Ihara zeta function of a finite graph is given.
Abstract: 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.
30 citations