L1\mathbf L^1 completeness for Fourier series

We note that the Fubini theorem may be used to prove that an $L^1$ function is determined by its Fourier coefficients

Remarks on trigonometric functions after Eisenstein

We modify the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, basing these functions independently on the Eisenstein function $\varepsilon_2$

The bosonic Fock representation and a generalized Shale theorem

We detail a new approach to the bosonic Fock representation of a complex Hilbert space V: our account places the bosonic Fock space S[V] between the symmetric algebra SV and its full antidual SV'; in addition to providing a context in which arbitrary (not necessarily restricted) real symplectic automorphisms of V are implemented, it offers simplified proofs of many standard results of the theory.Comment: LaTeX, 24 pages, no figure

Cubic Hamiltonians

We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.Comment: 8 page

The Peirce axiom scheme and suprema

We present equivalents to the Peirce axiom scheme and highlight its relevance for pairwise suprema

Classical theorems in the Implicational Propositional Calculus

For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC

A tangential approach to trigonometry

We construct the complex tangent as a meromorphic function in the plane, using an approach developed by Weierstrass in his characterization of analytic functions that satisfy algebraic addition theorems

'Twisted duality' for Clifford Algebras

Viewing the complex Clifford algebra $C(V)$ of a real inner product space $V$ as a superalgebra, we offer several proofs of the fact that if $W$ is a subspace of the complexification of $V$ then the supercommutant of the Clifford algebra $C(W)$ is precisely the Clifford algebra $C(W^{\perp})$.Comment: 8 page

Index theory for partial-bijections

We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.Comment: 5 page

Neville's primitive elliptic functions: the case g3=0{\bf g_3 = 0}

The vanishing of the invariant $g_3$ attached to a lattice $\Lambda$ singles out a midpoint lattice and yields a square-root of the associated Weierstrass function $\wp_{\Lambda}$