We prove that Stein surfaces with boundary coincide up to orientation preserving diffeomorphisms with simple branched coverings of B4 whose branch set is a positive braided surface. As a consequence, we have that a smooth oriented 3-manifold is Stein fillable iff it has a positive open-book decomposition.

This paper presents an account of morbidity in a suburban practice in London with special reference to psychiatric disability. Clinical and administrative features of this practice (Chalke and Fisher, 1957) and its social and demographic characteristics (Stein, 1960) have also been described, and an outline of the present investigation has been presented elsewhere (Shepherd, Fisher, Stein, and ...

We consider the estimation of mean a multivariate normal distribution with known variance. Most studies risk competing estimators, that is trace squared error matrix. In contrast we whole matrix, in particular its eigenvalues. prove there are only two distinct eigenvalues and apply our findings to James–Stein Thompson class estimators. It turns out famous Stein paradox no longer when matrix rat...

We apply the methods developed in [Br1] to study holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds. In particular, we extend and strengthen certain results of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds in the case of coverings of Stein manifolds.

An expression in the exterior algebra of a Peano space yielding Pappus' theorem was originally given by Doubilet, Rota, and Stein [Doubilet, P., Rota, G.-C. & Stein, J. (1974) Stud. Appl. Math. 8, 185-216]. Motivated by an identity of Rota, I give an identity in a Grassmann-Cayley algebra of step 3, involving joins and meets alone, which expresses the theorem of Pappus.

We provide sufficient conditions assuring that a suitably decorated 2-polyhedron can be thickened to a compact 4-dimensional Stein domain. We also study a class of flat polyhedra in 4-manifolds and find conditions assuring that they admit Stein, compact neighborhoods. We base our calculations on Turaev’s shadows suitably “smoothed”; the conditions we find are purely algebraic and combinatorial.

We build on the formalism developed in Ernst et al. (First order covariance inequalities via Stein’s method, 2019) to propose new representations of solutions Stein equations. provide uniform and nonuniform bounds these (a.k.a. factors). use obtain for differences between expectations terms apply compute abstract Stein-type Kolmogorov, total variation Wasserstein distances arbitrary distributio...