Spherical harmonics, one of the most widely used basis functions for shape description, rely heavily on a spherical parameterization given surface. Additionally, harmonics based 3D modeling works well only closed surfaces, while many anatomical structures are hemisphere-like open objects. Therefore, it is more natural to have hemisphere-based approach their description. In this work, we propose...

suppose $f$ is a map from a non-empty finite set $x$ to a finite group $g$. define the map $zeta^f_g: glongrightarrow mathbb{n}cup {0}$ by $gmapsto |f^{-1}(g)|$. in this article, we show that for a suitable choice of $f$, the map $zeta^f_g$ is a character. we use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin g$) is a character, where $w(t_1,t...

Area-preserving maps and flows play an essential role in the study of motions of mechanical systems, especially in celestial mechanics (see [1, 14]). Since one is often interested in the behavior of an area-preserving map around a fixed point and in the number and type of critical points and periodic orbits of an area-preserving flow, the ./i'xed-point index of a map and the index oj" a singula...

This paper investigates a self-organizing map algorithm which is simultaneously given multiple inputs, and introduces a criterion of ordering process as the twist measurement for reference vectors in multidimensional array. The self-organizing algorithm and the criterion are termed the parallel self-organizing algorithm and the index of twist, respectively. The algorithm updates reference vecto...

Digital product passports (DPPs) are an emerging technology and considered as enablers of sustainable circular value chains they support management (SPM) by gathering containing life cycle data. However, some data sensitive stakeholders, resulting in a reluctance to share such This contribution provides concept illustrating how science machine learning approaches enable electric vehicle battery...