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Full-Text Articles in Mathematics
On The Existence Of Finite Type Link Homotopy Invariants, Blake Mellor, Dylan Thurston
On The Existence Of Finite Type Link Homotopy Invariants, Blake Mellor, Dylan Thurston
Mathematics Faculty Works
We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are not products of the linking numbers. This corrects previous errors of the first author.
The Hadamard Core Of The Totally Nonnegative Matrices, Alissa Crans
The Hadamard Core Of The Totally Nonnegative Matrices, Alissa Crans
Mathematics Faculty Works
An m-by- n matrix A is called totally nonnegative if every minor of A is nonnegative. The Hadamard product of two matrices is simply their entry-wise product. This paper introduces the subclass of totally nonnegative matrices whose Hadamard product with any totally nonnegative matrix is again totally nonnegative. Many properties concerning this class are discussed including: a complete characterization for min{m,n}<4 >; a characterization of the zero–nonzero patterns for which all totally nonnegative matrices lie in this class; and connections to Oppenheim's inequality.
What To Do On Your Summer Vacation, Alissa Crans
What To Do On Your Summer Vacation, Alissa Crans
Mathematics Faculty Works
Summer vacation brings back fond memories: playing frisbee in the park, bike-riding till dusk, sipping lemonade on the porch with Grandpa, collecting shells at the beach, solving that difficult math problem you've been working on for the past several weeks. Wait a minute, you say? Many mathematics majors don't realize that numerous summer opportunities exist (many of them paid, so you don't need to get that job bagging groceries, too). A math program provides intellectual stimulation during those hot summer months, bringing your level of concentration up from swatting flies and applying sunscreen. The following descriptions are from actual participants …