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Full-Text Articles in Algebra
N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy
N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of type II which is introduced in this book. In case of n-linear algebra of type II, we are in a position to define linear functionals which is one of the marked difference between the n-vector spaces of type I and II. However all the applications mentioned in n-linear algebras of type I can be appropriately extended to …
Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra
Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra
Mathematics Faculty Works
The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.