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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
21 Citations
4,107 Views
29 Pages

Determination of Bounds for the Jensen Gap and Its Applications

  • Hidayat Ullah,
  • Muhammad Adil Khan and
  • Tareq Saeed

5 December 2021

The Jensen inequality has been reported as one of the most consequential inequalities that has a lot of applications in diverse fields of science. For this reason, the Jensen inequality has become one of the most discussed developmental inequalities...

  • Article
  • Open Access
8 Citations
3,965 Views
25 Pages

5 December 2021

The genetic toggle switch is a well known model in synthetic biology that represents the dynamic interactions between two genes that repress each other. The mathematical models for the genetic toggle switch that currently exist have been useful in de...

  • Article
  • Open Access
6 Citations
3,867 Views
13 Pages

5 December 2021

This paper proposes, validates and analyzes the dynamics of the susceptible exposed infectious recovered (SEIR) model for the propagation of COVID-19 in Saudi Arabia, which recorded the largest number of cases in the Arab world. The model incorporate...

  • Article
  • Open Access
32 Citations
5,301 Views
24 Pages

Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods

  • Mehdi Dasineh,
  • Amir Ghaderi,
  • Mohammad Bagherzadeh,
  • Mohammad Ahmadi and
  • Alban Kuriqi

5 December 2021

This study investigates the characteristics of free and submerged hydraulic jumps on the triangular bed roughness in various T/I ratios (i.e., height and distance of roughness) using CFD modeling techniques. The accuracy of numerical modeling outcome...

  • Article
  • Open Access
26 Citations
5,537 Views
20 Pages

5 December 2021

Education has changed dramatically due to the severe global pandemic COVID-19, with the phenomenal growth of e-learning, whereby teaching is undertaken remotely and on digital platforms. E-learning is revolutionizing education systems, as it remains...

  • Article
  • Open Access
112 Citations
10,534 Views
19 Pages

XCM: An Explainable Convolutional Neural Network for Multivariate Time Series Classification

  • Kevin Fauvel,
  • Tao Lin,
  • Véronique Masson,
  • Élisa Fromont and
  • Alexandre Termier

5 December 2021

Multivariate Time Series (MTS) classification has gained importance over the past decade with the increase in the number of temporal datasets in multiple domains. The current state-of-the-art MTS classifier is a heavyweight deep learning approach, wh...

  • Article
  • Open Access
5 Citations
4,075 Views
16 Pages

A New Method for Time Normalization Based on the Continuous Phase: Application to Neck Kinematics

  • Carlos Llopis-Albert,
  • William Ricardo Venegas Toro,
  • Nidal Farhat,
  • Pau Zamora-Ortiz and
  • Álvaro Felipe Page Del Pozo

5 December 2021

There is growing interest in analyzing human movement data for clinical, sport, and ergonomic applications. Functional Data Analysis (FDA) has emerged as an advanced statistical method for overcoming the shortcomings of traditional analytic methods,...

  • Article
  • Open Access
1 Citations
3,943 Views
15 Pages

Modelling of Heat Transfer Processes in Heat Exchangers for Cardiopulmonary Bypass

  • Valentyna Danilova,
  • Vladyslav Shlykov,
  • Vitalii Kotovskyi,
  • Nikolaj Višniakov and
  • Andžela Šešok

4 December 2021

A model of the heat exchange process in the heat exchanger of the cardiopulmonary bypass device is proposed which allows for automation of the process of temperature regulation in the cardiopulmonary bypass with an accuracy of ±1 °C during...

  • Article
  • Open Access
6 Citations
3,354 Views
17 Pages

4 December 2021

The randomness of earthquake excitation has a significant impact on the seismic performance of high earth-rock dams. In this paper, the seismic performance of geosynthetic-reinforced soil structures (GRSS) of high concrete face rockfill dams (CFRDs)...

  • Article
  • Open Access
11 Citations
2,070 Views
16 Pages

Resolutions of the Jerk and Snap Vectors for a Quasi Curve in Euclidean 3-Space

  • Ebrahem Hamouda,
  • Clemente Cesarano,
  • Sameh Askar and
  • Ayman Elsharkawy

4 December 2021

This work aims at studying resolutions of the jerk and snap vectors of a point particle moving along a quasi curve in Euclidean 3-space E3. In particular, we obtain the resolution of the jerk and snap vectors along the quasi vectors and offer an alte...

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Mathematics - ISSN 2227-7390