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 $\varepsilon_2$

Normalization conventions for Newton's constant and the Planck scale in arbitrary spacetime dimension

We calculate, in d spacetime dimensions, the relationship between the coefficient 1/K^2 of the Einstein-Hilbert term in the action of general relativity and the coefficient G_N of the force law that results from the Newtonian limit of general relativity. The result is K^2=2[(d-2)/(d-3)]Vol(S^[d-2])G_N, where Vol(S^n) is the volume of the unit n-sphere. While the d=4 case is an elementary calculation in any general relativity text, the arbitrary case presented here is slightly less well known. We discuss the relevance of this result for the definition of the so-called "reduced Planck mass" and comment very briefly on the implications for brane world models. [abstract abridged]Comment: 4 pages, 2 figures, RevTeX

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 $\wp_{\Lambda}$

The Clifford algebra and its antidual

We analyze the purely algebraic antidual $C'(V)$ of the complex Clifford algebra $C(V)$ over a real inner product space $V$. In particular, we introduce a partially defined product in $C'(V)$ and study its properties

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

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