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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Solving Boundary Value Problems On Various Domains, Ibraheem Otuf
Solving Boundary Value Problems On Various Domains, Ibraheem Otuf
MSU Graduate Theses
Domain-sensitivity is a hallmark in the realm of solving boundary value problems in partial differential equations. For example, the method used in solving a boundary value problem on an finite cylindrical domain is very different from one that arises from a rectangular domain. The difference is also reflected in the types of functions employed in the processes of solving these boundary value problems, as are the mathematical tools utilized in deriving an analytic solution. In this thesis, we solve an important class of partial differential equations with boundary conditions coming from various domains, such as the n dimensional cube, circles, …
When There Is A Unique Group Of A Given Order And Related Results, Haya Ibrahim Binjedaen
When There Is A Unique Group Of A Given Order And Related Results, Haya Ibrahim Binjedaen
MSU Graduate Theses
It is well-known that any group whose order is a prime number must be cyclic, that is there is only one group of that order up to isomorphism. This is also the case for some non-prime orders, for example there is only one group of order 15 up to isomorphism. This thesis provides the necessary background material to completely characterize those n for which these is a unique group of order n, namely when n and the Euler phi function of n are relatively prime. We also determine for which n there are exactly two groups of order n up …
A Geometric Approach To Ramanujan's Taxi Cab Problem And Other Diophantine Dilemmas, Zachary Kyle Easley
A Geometric Approach To Ramanujan's Taxi Cab Problem And Other Diophantine Dilemmas, Zachary Kyle Easley
MSU Graduate Theses
In 1917, the British mathematician G.H. Hardy visited the Indian mathematical genius Ramanujan in the hospital. The number of the taxicab Hardy arrived in was 1729. Ramanujan immediately recognized this as the smallest positive integer that can be expressed as the sum of two cubes in two essentially different ways. In this thesis, we use properties of conics and elliptic curves to investigate this problem, its generalization to fourth powers, and a Diophantine equation involving the distance of a point from the vertices of a regular tetrahedron (the latter extends work of Christina Bisges).
On The Number Of Distinct Cyclic Subgroups Of A Given Finite Group, Joseph Dillstrom
On The Number Of Distinct Cyclic Subgroups Of A Given Finite Group, Joseph Dillstrom
MSU Graduate Theses
In the study of finite groups, it is a natural question to consider the number of distinct cyclic subgroups of a given finite group. Following an article by M. Tarnauceanu in the American Mathematical Monthly, we consider arithmetic relations between the order of a finite group and the number of its cyclic subgroups. We classify several infinite families of finite groups in this fashion and expand upon an open problem posed in the article.
A Cycle Generating Function On Finite Local Rings, Tristen Kirk Wentling
A Cycle Generating Function On Finite Local Rings, Tristen Kirk Wentling
MSU Graduate Theses
We say a function generates a cycle if its output returns the initial value for some number of successive applications of . In this thesis, we develop a class of polynomial functions for finite local rings and associated functions . We show that the zeros of one are precisely the fixed points of the other and that every ring element is either one of these fixed points or is in a cycle of fixed length equal to the order of 2 in the associated group of units. Particular emphasis is given to rings of integers modulo the square of a …