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New families of sharp inequalities between elementary symmetric polynomials are proven.. We estimate σ n−k above and below by the elementary symmetric polynomials σ
It is suggested by our method that most of the quadratic algebras for all St¨ ackel equivalence classes of 3D second order quantum superintegrable systems on conformally flat
(at least a proof can be reconstructed from it, after correcting a number of misprinted formulae). Other authors have subsequently given different proofs, see for instance [Kn1,
Compared to working adults, junior high school students, and high school students who have a
The study of the eigenvalue problem when the nonlinear term is placed in the equation, that is when one considers a quasilinear problem of the form −∆ p u = λ|u| p−2 u with
Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A
To derive a weak formulation of (1.1)–(1.8), we first assume that the functions v, p, θ and c are a classical solution of our problem. 33]) and substitute the Neumann boundary
The proof uses a set up of Seiberg Witten theory that replaces generic metrics by the construction of a localised Euler class of an infinite dimensional bundle with a Fredholm