Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for Lφ affine surface areas are established. 2000 AMS subject classification: Primary 52A20; Secondary 53A15. Finding the right notion of affine surface area was one of the first questions asked within affine differential geometry. At ...

We construct a polyhedron that is topologically convex (i.e., has the graph of a convex polyhedron) yet has no vertex unfolding: no matter how we cut along the edges and keep faces attached at vertices to form a connected (hinged) surface, the surface necessarily unfolds with overlap.

Given a collection of minimal graphs,M1,M2, . . . ,Mn, with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions onM1,M2, . . . ,Mn so that a convex combination of themwill be a minimal graph. We will then provide two examples, taking a convex combination of Scherk’s doubly periodic surface with the catenoid and Enneper’s surface, respecti...

Background. China is the largest producer of rape oilseed in the world; however, the mechanization level of rape harvest is relatively low, because rape materials easily adhere to the cleaning screens of combine harvesters, resulting in significant cleaning losses. Previous studies have shown that bionic nonsmooth surface cleaning screens restrain the adhesion of rape materials, but the underly...

In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-con...

In the present research, free convection heat transfer from isothermal concave and convex body shapes is studied numerically. The body shapes investigated here, are bi-sphere, cylinder, prolate and cylinder with hemispherical ends; besides, they have the same height over width (H/D = 2). A Numerical simulation is implemented to obtain heat transfer and fluid flow from all of the geometries in a...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

We present a method for computing a surface classifier that can be used to detect convex ridges on voxel surfaces extracted from 3D scans. In contrast to classical approaches based on (discrete) curvature computations, which can be sensitive to various types of noise, we propose here a new method that detects convex ridges on such surfaces, based on the computation of the surface’s 3D skeleton....