We show that any separated essentially finite-type map f of noetherian schemes globally factors as f = hi where i is an injective localization map and h a separated finite-type map. In particular, via Nagata’s compactification theorem, h can be chosen to be proper. We apply these results to Grothendieck duality. We also obtain other factorization results and provide essentialized versions of ma...

We define and study the properties of Darboux-type transformations between Sturm–Liouville problems with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these problems in a unified manner, such as asymptotics of e...

Let S be a finite set of positive integers. A “coprime base for S” means a set P of positive integers such that (1) each element of P is coprime to every other element of P and (2) each element of S is a product of powers of elements of P. There is a natural coprime base for S. This paper introduces an algorithm that computes the natural coprime base for S in essentially linear time. The best p...

We study numerically essentially unsteady evaporation and heat transfer of a rarefied gas using the S-model kinetic equation. Three particular cases are considered: one-dimensional flow from a flat surface and purely radial flows from the surface of a cylinder or a sphere. We present numerical results for different values of the evaporation coefficient and saturatedvapor density which demonstra...

We characterize when a Hankel operator and a Toeplitz operator have a compact commutator. Let dσ(w) be the normalized Lebesgue measure on the unit circle ∂D. The Hardy space H is the subspace of L(∂D, dσ), denoted by L, which is spanned by the space of analytic polynomials. So there is an orthogonal projection P from L onto the Hardy space H, the so-called Hardy projection. Let f be in L∞. The ...

W B Gallie's notion of essentially contested concepts remains of philosophical interest. I argue that medicine is one such concept and look at the consequences of this as regards the inappropriateness of looking for definitions and necessary and sufficient conditions to settle debates about what medicine is and is not.