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Mathematics, Volume 9, Issue 23

December-1 2021 - 159 articles

Cover Story: A rectifying curve is a twisted curve with the property that all of its rectifying planes pass through a fixed point. If this point is the origin of the Cartesian coordinate system, then the position vector of the rectifying curve always lies in the rectifying plane. A remarkable property of these curves is that the ratio between torsion and curvature is a nonconstant linear function of the arc-length parameter. In this paper, we give a new characterization of rectifying curves; namely, we prove that a curve is a rectifying curve if and only if it has a spherical involute. Consequently, rectifying curves can be constructed as evolutes of spherical twisted curves. We express the curvature and the torsion of a rectifying spherical curve and give the necessary and sufficient conditions for a curve and its involute to be both rectifying curves. View this paper.
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Articles (159)

  • Article
  • Open Access
11 Citations
4,110 Views
20 Pages

Dynamical Analysis of a Navigation Algorithm

  • Mireya Cabezas-Olivenza,
  • Ekaitz Zulueta,
  • Ander Sánchez-Chica,
  • Adrian Teso-Fz-Betoño and
  • Unai Fernandez-Gamiz

6 December 2021

There is presently a need for more robust navigation algorithms for autonomous industrial vehicles. These have reasonably guaranteed the adequate reliability of the navigation. In the current work, the stability of a modified algorithm for collision-...

  • Article
  • Open Access
15 Citations
2,388 Views
20 Pages

6 December 2021

In this paper, we carry out a demonstration and comparative analysis of known methods of the synthesis of various control laws ensuring the invariance of the output (controlled) variable with respect to external disturbances under various assumptions...

  • Article
  • Open Access
7 Citations
3,737 Views
18 Pages

Application of Machine Learning Model for the Prediction of Settling Velocity of Fine Sediments

  • Wing Son Loh,
  • Ren Jie Chin,
  • Lloyd Ling,
  • Sai Hin Lai and
  • Eugene Zhen Xiang Soo

6 December 2021

Sedimentation management is one of the primary factors in achieving sustainable development of water resources. However, due to difficulties in conducting in-situ tests, and the complex nature of fine sediments, it remains a challenging task when dea...

  • Article
  • Open Access
3 Citations
2,627 Views
15 Pages

6 December 2021

Recently, using interval-valued fuzzy soft sets to rank alternatives has become an important research area in decision-making because it provides decision-makers with the best option in a vague and uncertain environment. The present study aims to giv...

  • Article
  • Open Access
2 Citations
2,943 Views
26 Pages

6 December 2021

A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles. The evolution of the edges and triangles is...

  • Article
  • Open Access
3 Citations
2,963 Views
10 Pages

Attribute Service Performance Index Based on Poisson Process

  • Kuen-Suan Chen,
  • Chang-Hsien Hsu and
  • Ting-Hsin Hsu

6 December 2021

The purpose of a shop enhancing customer satisfaction is to raise its total revenue as the rate of customer purchases in the shop increases. Some studies have pointed out that the amount of customer arrival at a shop is a Poisson process. A simple an...

  • Article
  • Open Access
6 Citations
2,357 Views
13 Pages

6 December 2021

We consider the Benjamin–Bona–Mahony (BBM) equation of the form ut+ux+uux−uxxt=0,(x,t)∈M×R where M=T or R. We establish norm inflation (NI) with infinite loss of regularity at general initial data in Fourier amalgam and W...

  • Article
  • Open Access
9 Citations
3,630 Views
18 Pages

Control Method for Flexible Joints in Manipulator Based on BP Neural Network Tuning PI Controller

  • Hexu Yang,
  • Xiaopeng Li,
  • Jinchi Xu,
  • Dongyang Shang and
  • Xingchao Qu

6 December 2021

With the development of robot technology, integrated joints with small volume and convenient installation have been widely used. Based on the double inertia system, an integrated joint motor servo system model considering gear angle error and frictio...

  • Article
  • Open Access
8 Citations
2,630 Views
13 Pages

On g-Noncommuting Graph of a Finite Group Relative to Its Subgroups

  • Monalisha Sharma,
  • Rajat Kanti Nath and
  • Yilun Shang

6 December 2021

Let H be a subgroup of a finite non-abelian group G and g∈G. Let Z(H,G)={x∈H:xy=yx,∀y∈G}. We introduce the graph ΔH,Gg whose vertex set is G\Z(H,G) and two distinct vertices x and y are adjacent if x∈H or y∈H and...

  • Article
  • Open Access
2,305 Views
12 Pages

6 December 2021

This work is aimed to continue studying the packing sets of digraphs via the perspective of partitioning the vertex set of a digraph into packing sets (which can be interpreted as a type of vertex coloring of digraphs) and focused on finding the mini...

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Mathematics - ISSN 2227-7390