Let Kn be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on Rd. We establish variance asymptotics for the re-scaled volume and k-face functional of Kn, k ∈ {0, 1, ..., d − 1}, resolving an open problem. Asymptotic variances and the scaling limit of the boundary of Kn are given in terms of functionals of germ-grain models having parabolic gra...

We describe a new implementation of the quasiparticle random-phase approximation (QRPA) in axially symmetric deformed nuclei with Skyrme and volume-pairing energy-density functionals. After using a variety of tests to demonstrate the accuracy of the code in 24,26Mg and 16O, we report the first fully self-consistent application of the Skyrme QRPA to a heavy deformed nucleus, calculating strength...

We study the qualitative properties of functions belonging to corresponding De Giorgi classes ?Br(1??)(x0)?(x,|?(u?k)±|)dx???Br(x0)?(x,(u?k)±?r)dx,where ?, r?(0,1), k?R and function ? satisfies non-logarithmic condition (r?n?Br(x0)[?(x,vr)]sdx)1s(r?n?Br(x0)[?(x,vr)]?tdx)1t?c(K)?(x0,r),r?v?K?(r), under some assumptions on ?(r) ?(x0,r) numbers s, t>1. These conditions generalize known logarithmic...

The Sylvester (d + 2)-points problem deals with the probability S(K) that d + 2 random points taken from a convex compact subset K of Rd are not the vertices of any convex polytope and asks for which sets S(K) is minimal or maximal. While it is known that ellipsoids are the only minimizers of S(K), the problem of the maximum is still open, unless d = 2. In this paper we study generalizations of...

We present the results of calculations on bulk transition metals Rh, Pd, and Pt using the screened hybrid functional YS-PBE0 [F. Tran and P. Blaha, Phys. Rev. B 83, 235118 (2011)]. The results for the equilibrium geometry are compared with those obtained from (semi)local functionals, namely, the local density approximation and the generalized gradient approximation PBE of Perdew et al. [J. P. P...

We consider tessellations of the Euclidean (d− 1)-sphere by (d− 2)-dimensional great subspheres or, equivalently, tessellations of Euclidean d-space by hyperplanes through the origin; these we call conical tessellations. For random polyhedral cones defined as typical cones in a conical tessellation by random hyperplanes, and for their dual cones, we study expectations of certain geometric funct...

We study the problem of finding an optimal kernel from a prescribed convex set of kernels K for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although K may be an uncountable set, the ...

In the space of C piecewise expanding unimodal maps, k ≥ 2, we characterize the C smooth families of maps where the topological dynamics does not change (the “smooth deformations”) as the families tangent to a continuous distribution of codimension-one subspaces (the “horizontal” directions) in that space. Furthermore such codimension-one subspaces are defined as the kernels of an explicit clas...

Let £ be a partially ordered linear normed space over the field of real numbers whose positive cone K has nonempty interior K0.1 A functional / in E*, the conjugate space of E, is called positive if f(K)^0 and/5^0. A semi-group V of linear operators on E is called positive if r(A7) QK. It will be assumed that T contains the identity operator. This note is concerned with the properties of positi...

A survey of the theory of k-hyponormal operators starts with the construction of a polynomially hyponormal operator which is not subnormal. This is achieved via a natural dictionary between positive functionals on specific convex cones of polynomials and linear bounded operators acting on a Hilbert space, with a distinguished cyclic vector. The class of unilateral weighted shifts provides an op...