6 papers
The Octonionic Rational Wave Numbers: Non-Associative Sequence Algebras, Moufang Loops, and Exceptional Symmetries
Terence R. Smith
We generalize discrete rational wave numbers (arXiv:2609.23233) to the octonionic rational wave numbers over Cayley's octonions . Rather than as…
Wave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry
Terence R. Smith
We establish a comprehensive algebraic, geometric, and physical classification of the wave closure space generated from primitive plane wave sequences on the discrete spatial latti…
Algebraic Structure and Orthogonality Properties of Rational Polynomial Phase Rings on Discrete Lattices
Terence R. Smith
We formalize the algebraic structure of rational polynomial phase sequences (discrete chirps) over the integer lattice . By constructing a convolution algebra generated…
Sums of Exponential Terms, Conserved Quantities, and the Real Wave Numbers
Terence R. Smith
There is consensus that sums of complex exponential terms, despite their mathematical significance, only possess closed-form representations f…
Rational Wave Numbers and the Algebraic Structure of the Cyclic Groups of the Roots of Unity
Terence R. Smith
Rational wave numbers are periodic sequences in which amplitude a product of powers of trigonometric sequences and ${\bf w}(f,g)=\exp({\…
Natural Wave Numbers, Natural Wave Co-numbers, and the Computation of the Primes
Terence R. Smith
The paper exploits an isomorphism between the natural numbers N and a space U of periodic sequences of the roots of unity in constructing a recursive procedure for representing and…