In this paper, we study the effect the choice of mesh quality metric, preconditioner, and sparse linear solver have on the numerical solution of elliptic partial differential equations (PDEs). We smoothe meshes on several geometric domains using various quality metrics and solve the associated elliptic PDEs using the finite element method. The resulting linear systems are solved using various c...

iv erative methods to solve least squares problems more efficiently. We especially focused on one kind of preconditioners, in which preconditioners are the approximate generalized inverses of the coefficient matrices of the least squares problems. We proposed two different approaches for how to construct the approximate generalized inverses of the coefficient matrices: one is based on the Minim...

This paper develops and investigates iterative tensor methods for solving large-scale systems of nonlinear equations. Direct tensor methods for nonlinear equations have performed especially well on small, dense problems where the Jacobian matrix at the solution is singular or ill-conditioned, which may occur when approaching turning points, for example. This research extends direct tensor metho...

Minimal generating subspaces of “weak PBW-type” for vertex operator algebras are studied and a procedure is developed for finding such subspaces. As applications, some results on generalized modules are obtained for vertex operator algebras that satisfy a certain condition, and a minimal generating space of weak PBW-type is produced for VL with L any positive-definite even lattice.

In this paper we prove that if M ⊂ R, n = 8 or n = 9, is a n− 1 dimensional stable minimal complete cone such that its scalar curvature varies radially, then M must be either a hyperplane or a Clifford minimal cone. By Gauss’ formula, the condition on the scalar curvature is equivalent to the condition that the function κ1(m) 2 + · · ·+ κn−1(m) 2 varies radially. Here the κi are the principal c...

We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the existence of a minimal nonnegative nontrivial stationary solution and study the large-time behavior of the solution of the initial boundary value problem. To the ...

We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G of bounded index and G/G equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth auth...

In this note we consider boundary perturbations in the A-Series unitary minimal models by φr,r+2 fields on superpositions of boundaries. In particular, we consider perturbations by boundary condition changing operators. Within conformal perturbation theory we explicitly map out the space of perturbative renormalisation group flows for the example φ13 and find that this sheds light on more gener...

Let G be a group with the property that there are no infinite descending chains of non-subnormal subgroups of G for which all successive indices are infinite. The main result is that if G is a locally (soluble-by-finite) group with this property then either G has all subgroups subnormal or G is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same autho...

“Minimal group” paradigms investigate social preferences arising from mere group membership. We asked whether demand characteristics contribute to children’s apparent minimal bias in a preregistered experiment (N = 160). In condition, we attempted replicate findings of following assignment groups. A second closely matched no-group condition retained potential while removing assignment. Parallel...