Physical Sciences and Mathematics | Open Access Articles

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

The Numerical Solution Of The Exterior Impedance (Robin) Problem For The Helmholtz’S Equation Via Modified Galerkin Method: Superllipsoid, Hy Dinh

Mathematics Theses

This thesis focuses on finding the solution for the exterior Robin Problem for the Helmholtz Equation and therefore, determines how a convergent smooth surface depending on its outer shape, in this case the superellipsoid, responds to different outer waves. The primary purpose is to calculate the possibility of a certain object, acquiring sufficient conditions, to either submerge under respectively high water pressure or maintain in outer space; if applicable, this approach can be used for a new efficient design of a portion of a submarine or part of a space craft, the second of more interest to NASA, one of …

Go to article

Integral Generalized Binomial Coefficients Of Multiplicative Functions, Imanuel Chen

Summer Research

The binomial coefficients are interestingly always integral. However, when you generalize the binomial coefficients to any class of function, this is not always the case. Multiplicative functions satisfy the properties: f(ab) = f(a)f(b) when a and b are relatively prime, and f(1) = 1. Tom Edgar of Pacific Lutheran University and Michael Spivey of the University of Puget Sound developed a Corollary that determines which values of n and m will always have integral generalized binomial coefficients for all multiplicative functions. The purpose of this research was to determine as many patterns within this corollary as possible as well as …