The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

In line with the current research on the ultimate strength assessment of ship hull girders, careful understanding of the collapse behaviour of unstiffened plate elements within the ship hull girders is an important and necessary task. In this paper, the collapse behaviour of unstiffened plates under longitudinal and transverse thrust is studied by elastoplastic large deflection FEM and the char...

Figure 1: Size of hull vs. size of set 1 has a very small number of points on its convex hull in relation to the size of the whole set. In set P2, all points in the set are on the convex hull. Is there an algorithm which is output sensitive in relation to the number of points on the convex hull? It turns out there is such an algorithm KirkpatrickSeidel Marriage Before Conquest. Its complexity, ...

A fast SVM learning algorithm is proposed according to incremental learning and center convex hull operator. It is established on analyzing the relevance of support vector and convex hull from the angle of calculation geometry. The convex hull of current training samples is solved in the first place. Further, Euclidean distance elimination is applied to convex hull. Meanwhile, every time when t...

Hydrodynamic performance of a marine vessel mainly depends on the frictional and pressure resistance. Pressure drag reduction could be achieved by improving the shape of the vessels with implementation of modern hull forms. Hull forms optimization techniques could also be used for this purpose. Other techniques are needed to deal with the viscous portion of the total resistance, which is mainly...

We developed an inverse design framework, constrained crystal deep convolutional generative adversarial networks (CCDCGAN), enabling automated generation of stable multicomponent structures. Their formation energy can be optimized in the latent space based on reversible images with continuous representation. After training by 52,615 structures from Materials Project, CCDCGAN model is able to ge...

A linear-time algorithm that computes the envelope of the offset of a monotone chain is presented. The scallop hull, an extended notion of the convex hull, of the monotone chain is first computed by using an approach similar to that of the convexhull construction algorithm. The offset of the scallop hull, which yields the desired envelope, can then be computed in linear time from the scallop hu...

Selecting a small informative subset from a given dataset, also called column sampling, has drawn much attention in machine learning. For incorporating structured data information into column sampling, research efforts were devoted to the cases where data points are fitted with clusters, simplices, or general convex hulls. This paper aims to study nonconvex hull learning which has rarely been i...

If X is a vector space and E is a subset of X, the convex hull of E is defined to be the intersection of all convex sets containing E, and is denoted by co(E). One checks that the convex hull of E is equal to the set of all finite convex combinations of elements of E. If X is a topological vector space, the closed convex hull of E is the intersection of all closed convex sets containing E, and ...