相关论文: Flipping Cubical Meshes
We discuss a class of regions and conformal mappings which are useful in several problems of approximation theory, harmonic analysis and spectral theory.
In this paper we study polycubes: orthogonal polyhedra with axis-aligned quadrilateral faces. We present a complete characterization of polycubes of any genus based on their dual structure: a collection of oriented loops which run in each…
We develop some theory of double fibration transforms where the cycle space is a smooth manifold and apply it to complex projective space.
We compute a complete set of isomorphism classes of cubic fourfolds over $\mathbb{F}_2$. Using this, we are able to compile statistics about various invariants of cubic fourfolds, including their counts of points, lines, and planes; all…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
As the cover of embryos and adult organisms, epithelial tissues are subjected to substantial mechanical forces in tissue morphogenesis. However, the finite deformation behaviors of epithelial tissues remain largely unexplored. This study…
The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras,…
This paper presents the technique of flex-and-flip manipulation. It is suitable for grasping thin, flexible linear objects lying on a flat surface. During the manipulation process, the object is first flexed by a robotic gripper whose…
We study semistable extremal threefold neighborhoods following earlier work of Mori, Koll\'ar, and Prokhorov. We classify possible flips and extend Mori's algorithm for computing flips of extremal neighborhoods of type k2A to more general…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of pivotally decomposable operations…
We study quasisymmetric maps, which act on the boundary of the hyperbolic plane, by looking at their action on the Farey triangulation. Our main results identify exactly which quasisymmetric maps correspond to pinched lambda lengths in…
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and M\"{o}bius transformations on the extended complex plane.
Fluid-structure interactions are a widespread phenomenon in nature. Although their numerical modeling have come a long way, the application of numerical design tools to these multiphysics problems is still lagging behind. Gradient-based…
We investigate slice-quaternionic Hopf surfaces. In particular, we construct new structures of slice-quaternionic manifold on $\mathbb{S}^1\times\mathbb{S}^7$, we study their group of automorphisms and their deformations.
The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…
We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.
If a finite element mesh contains concave elements, it is said to tangled. Tangled meshes can occur during mesh generation, mesh optimization, and large deformation simulations, and will lead to erroneous results during finite element…