Abstract Given a negatively graded Calabi-Yau algebra, we regard it as DG algebra with vanishing differentials and study its cluster category. We show that this is sign-twisted realise category triangulated hull of an orbit derived the singularity finite-dimensional Iwanaga-Gorenstein algebra. Along way, give two results stand on their own. First, coherent sheaves over has natural tilting subca...

Introduced in [1] by Jason Cantarella, Greg Kuperberg, Robert B. Kusner, and John M. Sullivan, the hull number is a complexity measure for links similar to the bridge number. By definition, it is the maximum integer n such that for any realization of the link there is a point c ∈ R such that any plane through c intersects the curves representing the link at least 2n times. Clearly, the hull num...

A coarse outer hull of a mesh is a good tool used in computer graphics to reduce algorithm complexity, especially, in applications such as collision detection or ray-tracing. It is often required that the hull has some very specific parameters concerning its shape and quality since these influence general flexibility and numerical stability of the algorithms. This paper overviews existing probl...

The range of an AUV is dictated by its finite energy source and minimising the energy consumption is required to maximise its endurance. One option to extend the endurance is by obtaining the optimum hydrodynamic hull shape with balancing the trade-off between computational cost and fluid dynamic fidelity. An AUV hull form has been optimised to obtain low resistance hull. Hydrodynamic optimisat...

Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time. However, it is often the case that a heuristic procedure is applied to reduce the original set of n points to a set of s < n points which contains the hull and so...

The two independent domestication events in the genus Oryza that led to African and Asian rice offer an extremely useful system for studying the genetic basis of parallel evolution. This system is also characterized by parallel de-domestication events, with two genetically distinct weedy rice biotypes in the US derived from the Asian domesticate. One important trait that has been altered by ric...

Given a finite set of points P ⊆ R, we would like to find a small subset S ⊆ P such that the convex hull of S approximately contains P . More formally, every point in P is within distance from the convex hull of S. Such a subset S is called an -hull. Computing an -hull is an important problem in computational geometry, machine learning, and approximation algorithms. In many real world applicati...

Hull form optimization from a hydrodynamic performance point of view is an important aspect of ship design. This study presents a computational method to estimate the ship seakeeping in regular head wave. In the optimization process the Genetic Algorithm (GA) is linked to the computational method to obtain an optimum hull form by taking into account the displacement as design constrain...

The visual hull is a geometric tool which relates the 3D shape of a concave object to its silhouettes or shadows. This paper develops the theory of the visual hull of objects bounded by smooth curved surfaces. From the basic definitions of visual hull we determine the surfaces which bound the visual hull of such objects. We show that these surfaces are patches of some surfaces which partition t...