66,028 research outputs found
'Twisted duality' for Clifford Algebras
Viewing the complex Clifford algebra of a real inner product space
as a superalgebra, we offer several proofs of the fact that if is a
subspace of the complexification of then the supercommutant of the Clifford
algebra is precisely the Clifford algebra .Comment: 8 page
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
The triple-zero Painlev\'e I transcendent
We offer elementary proofs for fundamental properties of the unique
triple-zero solution to the first Painlev\'e equation
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
completeness for Fourier series
We note that the Fubini theorem may be used to prove that an function
is determined by its Fourier coefficients
Implicational Completeness
We present a proof of completeness for the implicational propositional
calculus, based on a variant of the Lindenbaum procedure
Conservative inclusion of N\"orlund methods
We offer practical necessary and sufficient conditions in order that every
sequence convergent relative to the N\"orlund summation method be
convergent relative to the N\"orlund summation method without the
requirement that limits be preserved
Automorphisms of Quadratic Liouville Structures
We examine the diffeomorphisms of a symplectic vector space that preserve a
chosen symplectic potential. Our examination yields an explicit description of
these diffeomorphisms when the chosen potential differs from the canonical
potential by the differential of a homogeneous quadratic in one of three broad
classes.Comment: 8 page
Automorphisms of Liouville Structures
By a Liouville structure on a symplectic manifold we mean a
choice of symplectic potential: that is, a choice of one-form on
such that . We determine precisely all the
automorphisms of a Liouville structure in case is a symplectic
vector space and differs from its canonical symplectic potential by
the differential of a homogeneous monomial.Comment: 7 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
- …