The Delaunay Refinement Algorithm for quality meshing is extended to three dimensions. The algorithm accepts input with arbitrarily small angles, and outputs a Conforming Delaunay Tetrahedralization where most tetrahedra have radius-to-shortest-edge ratio smaller than some user chosen μ > 2. Those tets with poor quality are in well defined locations: their circumcenters are describably near inp...

Abstract. Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. Xu introduced a large category of contact simple Lie algebras which are related to locally finite derivations and are in general not finitely graded. The isomorphism classes of these Lie algebras were determined in a previous pape...

Here the theory of finite-dimensional supermanifolds is generalized in two directions. First, we introduce infinite-dimensional locally isomorphic to arbitrary Banach (or, more generally, convex) superspaces. This achieved by considering as functors (equipped with some additional structure) from category Grassmann superalgebras into corresponding smooth manifolds (Banach or convex). Selected ex...

A collocation method based on optimal nodal splines is presented for the numerical solution of linear Volterra integral equations of the second kind with weakly singular kernel. Since the considered spline operator is a bounded projector we can prove that, for sequences of locally uniform meshes, the approximate solution error converges to zero at exactly the same optimal rate as the spline app...

A geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g. a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous vector bundle over homogeneous spaces. In this paper, we study the relationship between partial flag and complete flag cases. Our main result is that the locally ...

A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. 23 We prove that finitely generated HNN-free implies virtually polycyclic for a large class of groups. We also consider finitely generated groups with no free subsemigroups of rank 2 25 and show that in many situations such groups are virtually nilpotent. Finally, as an application of our results, we determine...

A new numerical method for computing the divergence-free part of the solution of the time-harmonic Maxwell equations is studied in this paper. It is based on a discretization that uses the locally divergence-free CrouzeixRaviart nonconforming P1 vector fields and includes a consistency term involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an a...

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with a non-zero identity and $M$ be a graded $R$-module. In this article, we introduce the concept of graded almost semiprime submodules. Also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.

The next-generation medical implants require locally customised biomechanical behaviour to echo the properties of hard tissues, making additive manufacturing (AM) an ideal route due its superior flexibility. AM titanium alloys with designed porosity is mainstream for artificial implants, which, however, hardly balance strength-modulus combination. Here a martensitic TiNi biomaterial low modulus...