Volume 32

Volume 32 (2022)

Published in 2022

Issues in this Volume

Issue 2 (December)

Issue 1 (June)

Articles in this Volume

43 articles
1
Research Article DOI: 10.67897/njma.2022.4y6be108

Optimization of two-step method with Bhaskara points for solving non-linear dynamical problems

Umaru Mohammed*, Oyewole Abiodun Oyelami, Jamiu Garba, Abdullahi Aliyu Alhaji, Mikhail Semenov

We derive a two-step method for solving non-linear dynamical problems employing Bhaskara points as off grid points. Deterministic in nature, non-linear dynamical systems display a periodic behavior that is highly dependent on the beginning circumstances, making long-term predictions impossible. Four Bhaskara points are generated as hybrid points to optimized the system. The method is use to solve ...

Dec, 2022 pp. 151-168
2
Research Article DOI: 10.67897/njma.2022.f5p86yl7

Design and Implementation of a Mobile Voice Assistant System for the Visually Impaired

Babatunde Abdulrauph Olarewaju*, Olatinwo Suhurat Ikeola, G. B. Balogun, Mohammed Ahmed Adeola

Voice assistant systems are now becoming the newest technology in human computer interaction. However, the use of voice assistant systems has not been fully explored to help visually impaired individuals get the best out of their mobile devices as there have been challenges revolving around privacy and ease of use. The system was implemented using Kotlin for Android apps to work offline facilitati...

Dec, 2022 pp. 324-333
3
Research Article DOI: 10.67897/njma.2022.iyt0uecc

Gronwall-Bellman-Bihari Type Integral Inequalities of a Certain Class of Nonlinear Second Order Differential Equations

I. Fakunle*, P. O. Arawomo, B. D. Ogunbona

In this paper, we obtain nonlinear integral inequalities similar to Gronwall-Bellman-Bihari type. These inequalities are used to establish the boundedness and asymptotic behaviour of solutions of certain class of nonlinear second order differential equations. An example where f is a singular function is presented to show the application of our main results. 

Dec, 2022 pp. 315-323
4
Research Article DOI: 10.67897/njma.2022.t5rh6g8f

MHD Free Convection Flow of Viscoelastic Fluid Through a Vertical Porous Plate with Thermal Conductivity under Soret-Dufour Influence

A. S. Idowu*, Abdulwaheed Jimoh, Ahmed Lukman Olalekan

A study of MHD heat and mass transfer of viscoelastic fluid past a porous plate with thermal conductivity under soret-dufour effect is investigated. The governing boundary-layer equations are formulated with appropriate boundary conditions. The Roseland diffusion approximation is used to analyze the radiative heat flux and it is appropriate for non-Scattering media. The governing boundary layer eq...

Dec, 2022 pp. 293-314
5
Research Article DOI: 10.67897/njma.2022.z69ctdch

Fixed Point Theorems with Rational Expressions over a Closed Subset of Hilbert Spaces

S. A. Aniki*, E. E. Aribike, M. Raji, F. Adegboye, K. Rauf

In this paper, we prove the existence and uniqueness of a fixed point for a continuous self- mapping over a closed subset of Hilbert spaces satisfying nonlinear rational contractive-type condition. This result is extended and generalized for some positive integer powers of continuous self-mappings in Hilbert spaces.

Dec, 2022 pp. 286-292
6
Research Article DOI: 10.67897/njma.2022.xjkc6uoa

Thermal Diffusion and Diffusion-Thermo Effects on Ohmic Heating with Mhd Free Convective Flow Past a Vertical Porous Plate in the Presence of Viscous Dissipation

H. Usman*, I. J. Uwanta, Z. Sanusi

The MHD laminar boundary layer ow with heat and mass transfer of an electrically conducting viscous uid in a porous medium with ohmic heating and viscous dissipation e ects is studied numerically. The governing systems of nonlinear partial di erential equations of the ow, heat and mass transfer processes are solved using implicit nite di erence scheme of Crank-Nicolson type. The numerical solution...

Dec, 2022 pp. 259-285
7
Research Article DOI: 10.67897/njma.2022.zy2hfpli

A Mathematical Model on Marburg Virus Disease

Ayinla Ally Yeketi*, Ayinla Abdulquadri Yeketi

This research discusses the management of Marburg virus disease (MVD) using a mathematical model. The formulated model consists of five (5) mutually exclusive compartments. The local and global stability of the DFE of the formulated model is established. Subsequently, it is shown that the e ective management of the disease depends greatly on the incubation period and exposure to the infection. The...

Dec, 2022 pp. 241-258
8
Research Article DOI: 10.67897/njma.2022.r0bh89rm

An Orthogonal-Based Block Hybrid Method for the Solution of Third Order Ordinary Differential Equations

F. L. Joseph*

An orthogonal polynomial of the weight function w(x) = x 2+x+1 in the interval [-1, 1] was created as the basis function in block methods using the collocation and interpolation methodology. For third-order problems, an efficient class of continuous and discrete numerical integration techniques of implicit hybrid form were devised and effectively implemented. These schemes were used to address thr...

Dec, 2022 pp. 211-240
9
Research Article DOI: 10.67897/njma.2022.4m322u8w

Assessing the impact of isolation on the transmission dynamics of Lassa Fever

Abubakar Tijjani*, Salisu Usaini, Muhammad Auwal Lawan

A non-linear deterministic mathematical model of Lassa fever with isolation of infected individuals is formulated and analysed. The model is shown to be well posed mathematically and epidemiologically. We obtained an important threshold parameter called the basic reproduction number R0. The presented model is shown to exhibits three equilibrium points each of which is proved to be globally asympto...

Dec, 2022 pp. 182-199
10
Research Article DOI: 10.67897/njma.2022.o067wfzr

The Stability of Solution of a Multifactor Capital Asset Management Model

T. Latunde*, R. O. Folaranmi, A. A. Ayoade

This work focuses on the presentation of a multifactor asset management model based on the uncertainty theory, and the stability of the multifactor model solution to the formulated state design of a real-life situation of management of capital assets. The model is designed as an optimization problem based on the assumption of the Hyperbolic Absolute Risk Aversion utility function. The formulated m...

Dec, 2022 pp. 169-181
11
Research Article DOI: 10.67897/njma.2022.271vn145

Selecting Best Arima Model for Poison Data at Different Parameter Values

I. Akeyede*

A problem occurs when poison data have to be modeled. The number of counts in a certain period can only be an integer that is why the commonly used Autoregressive Moving Average (ARMA) model in time series, which assumes stationarity, seems not very useful anymore, simply because there are some associated problems like outlier and over dispersion that can be encountered in the poison data. For thi...

Dec, 2022 pp. 138-150
12
Research Article DOI: 10.67897/njma.2022.h3cc9y1b

Tripled Fixed Point Theorems in Partially Ordered G-Metric Space

S. A. Aniki*, M. Raji, F. Adegboye, E. E. Aribike, K. Rauf

Tripled fixed point theorem is an improvement to coupled fixed point. In this manuscript, we prove the existence and uniqueness of tripled fixed point for mixed monotone mapping satisfying nonlinear contractions in the framework of partially ordered G-metric space. Our results generalize and improve some results in the literature. 

Dec, 2022 pp. 129-137
13
Research Article DOI: 10.67897/njma.2022.ik5tsfsb

A Zero-Stable Numerical Model as First, Second, and Third-Order Initial Value Problems Solver

Emmanuel Oluseye Adeyefa*, Oladapo Olakunle Kazeem

This paper addresses solutions of multi-order ordinary differential equations (ODEs) using a single formulated scheme. The use of a block method to solve initial value problem of a specific order has attracted a lot of attention in the literature. The discrete method is formulated from continuous schemes obtained via collocation and interpolation techniques and applied in a block-by-block manner a...

Dec, 2022 pp. 120-128
14
Research Article DOI: 10.67897/njma.2022.acp7p281

Diagonally Implicit 2-Point Block Backward Differentiation Formula With Two Off-Step Points For Solving Stiff Initial Value Problems

Hamisu Musa*, Alhassan Buhari, Naghmeh Abasi

A diagonally implicit form of the 2-point block backward differentiation formula (BDF) with two off-step points is developed for solving stiff initial value problems. The method is derived by introducing a lower triangular matrix in the coefficient matrix of the existing 2-point block BDF method with off-step points for solving stiff ordinary differential equations. The method approximates two sol...

Dec, 2022 pp. 108-119
15
Research Article DOI: 10.67897/njma.2022.6w09nbd1

Radiative Effects on Heat and Mass Transfer of Magnetohydrodynamics Fluid Flow in Porous Media

S. A. Amoo*

Magnetohydrodynamics (MHD) flow involving heat and mass transfer under the influence of radiation, heat source, and chemical reaction effects is of great concern in physical sciences and engineering. The gap in earlier studies showed that few parameters emanating from studies like this, due to difficulty usually encountered in reaching quick convergences when solving such problems. The study there...

Dec, 2022 pp. 94-107
16
Research Article DOI: 10.67897/njma.2022.698ddx0p

Result on Partially Ordered Compact Spaces

T. M. Asiru*, R. A. Ibitowa

Partially ordered compact spaces were considered in the paper. E denote a compact Harsdorff space, C(E) denote the set of all continuous real valued functions on the compact Harsdorff space E, C+(E) is the set {f ∈ C(E) : f (t) ≥ 0, ∀t ∈ E} . ≤ denotes a relation of partial order given in E. That is, a binary relation that is reflexive (x ≤ x∀x ∈ E) antisymmetric x ≤ y and y ≤ ximpliesx = y, ∀x, y...

Dec, 2022 pp. 89-93
17
Research Article DOI: 10.67897/njma.2022.9ihmvpoj

An Extended 2-point Super Class of Block Backward Differentiation Formula with off-step Points for Solving Stiff Initial Value Problems

Hamisu Musa*, Ahmad Abubakar Umar

In this paper, we considered an extended 2-point Super class of block backward differentiation formula for solving stiff initial value problems (IVPs) and introduced two off-step points in it. The method produces two solution values together with two off-step points simultaneously at each iteration. The varying free parameter ρ is chosen in the interval (−1, 1) which leads to different forms of th...

Dec, 2022 pp. 76-88
18
Research Article DOI: 10.67897/njma.2022.oj5zh04r

Motion of Casson-Williamson with MHD Chemically Reacting Nanofluids under the Influence of Nonlinear Buoyancy Force and Theories of Cattaneo-Christov

A. S. Idowu*, B. O. Falodun, C. Onwubuoya, F. O. Aiyegbusi

The focus of this research is to examine the Cattaneo-Christov heat and mass transfer processes on Casson-Williamson fluids with nonlinear buoyancy force and thermal radiation. The flow analysis was described by partial differential equations (PDEs). The resulting PDEs were simplified by utilizing suitable variables to derive coupled nonlinear total differential equations. Spectral homotopy analys...

Dec, 2022 pp. 56-75
19
Research Article DOI: 10.67897/njma.2022.tkhiwpg5

Second Derivatives Single Step Block Hybrid Method for Non-Linear Dynamical System

Umaru Mohammed*, Jamiu Garba, Abdullahi Aliyu Alhaji, A. I. Ma’ali, Mikhail Semenov

In this paper, a modified single-step method is proposed to integrate nonlinear dynamical systems resulting to ordinary differential equations. In order to obtain higher order A-stable method, we have used second derivative of the solutions and imposed some special sets of off-grid points in the formulation process of the algorithms. The consistency, convergence and order of accuracy of the algori...

Dec, 2022 pp. 42-55
20
Research Article DOI: 10.67897/njma.2022.iashjcmh

Dynamics of Non-Newtonian Nano fluid Flow Past a Semi-Infinite Vertical Porous Plate Under the Influence of Lorentz Force and Soret-Dufour Mechanism

Ahmed Lukman Olalekan*

This paper considered the boundary layer behavior, and e ects of magnetohydrodynamic (MHD) and viscous dissipation on the simultaneous ow of Casson and Walter-B viscoelastic nano uid past a vertical penetrable plate in the presence of heat generation, radiation, chemical reaction, Soret, and Dufour mechanism. The nature of Casson uids examined in the study are blood and uid juice. These two non-Ne...

Dec, 2022 pp. 14-41
21
Research Article DOI: 10.67897/njma.2022.x7af8ch8

Remarks on L p -CKN Interpolation Inequalities of Hardy and Rellich Types on the Sphere

A. Abolarinwa*, Kamilu RAUF, S. Yin

We prove a new family of L p -Caffarelli-Kohn-Nirenberg (CKN) interpolation inequalities with sharp constants on the unit sphere of dimension greater than or equal to two. Consequently, several sharp Hardy type inequalities are obtained as special cases. Moreover, the same method is adopted to establish a new class of Hardy-Rellich type inequalities on the sphere, though, uncertain whelther or not...

Dec, 2022 pp. 1-13
22
Research Article DOI: 10.67897/njma.2022.w50onxdb

Development of an Order (k+3) Block-Hybrid Linear Multistep Method for the Direct Solution of General Second Order Initial Value Problems

A. A. Oyedeji*

Block hybrid linear multistep method was proposed to overcome the Dahlquist order barrier for linear multistep methods. We are interested in answering questions relating to the convergence, accuracy and effectiveness of block hybrid method when utilized to solve Initial Value Problems. In this research work, we presented an order (k+3) block hybrid method for the direct solution of initial value p...

Dec, 2022 pp. 200-210
23
Research Article DOI: 10.67897/njma.2022.s8bdqmf7

On the Stability Analysis of a Sixth-Stage Fifth- Order Runge-Kutta Method for Solving Initial Value Problems in Ordinary Differential Equations

G. U. Agbeboh, B. C. Ononogbo*, M. E. Ehiemua

This article investigates the stability of a sixth-stage, fifthorder Runge-kutta method which had already been derived in our previous results. The method is subjected to the test equation given as y 0 = λy, where a complex constant is λ, and the resulting expansion and algebraic manipulations were done with the help of Maple-18 and Matlab package, to ease the simplification of the computation. Th...

Jun, 2022 pp. 273-286
24
Research Article DOI: 10.67897/njma.2022.xqua586y

New Approximate Method for Systems of Non-linear Volterra Integro-Differential Equations

M. D. Aloko*, D. A. Johnson, J. A. Osilagun

In this paper, we present a new iterative scheme for approximating nonlinear systems of Volterra-integro-differential equations. The algorithm relies on the principles of the Variational Iteration Method (VIM). The modified method provides successive approximations by variational theory, decomposition techniques, and correction functional on Lagrange’s multiplier. In comparing with numerous result...

Jun, 2022 pp. 250-272
25
Research Article DOI: 10.67897/njma.2022.mbbgqq1o

Incorporating Prior Beliefs into the Construction of Prior Distribution of the Parameters: A: A Survival Analysis Approach

Juliana I. Consul*

Bayesian inference requires the combination of prior experience and the observed data (in the form of the likelihood). There is the need to discuss the specification of prior information about the model parameters. This research has built a structure for the joint prior distribution depending on the type of covariate in the context of a general linear model. Some issues associated with prior elici...

Jun, 2022 pp. 234-249
26
Research Article DOI: 10.67897/njma.2022.9t4m6gdx

Collocation Approach for the Solution of Fredhlom Integro-Differential Equation of Fractional Order

Ajileye Ganiyu, James A. Adewale*, Ayinde M. Abdullahi

In this work, the collocation method is developed to solve the fractional integro-differential equations using the Caputo sense. The integral form of the problem is obtained and transformed into a system of linear algebraic equations. Computed results are solved using Maple 18 in order to show the efficiency and accuracy of the method.

Jun, 2022 pp. 216-233
27
Research Article DOI: 10.67897/njma.2022.u5vfaaj5

Numerical Solution of a Generalized Fractional Burgers Diffusion Equation with Mamadu-Njoseh Polynomials

Emmanuel O. Oduselu-Hassan*, Ignatius N. Njoseh

In this paper, we consider the numerical solution of a generalized fractional Burgers diffusion equation (GFBE). A fractional variational iteration scheme coupled with Mamadu-Njoseh polynomials was developed to effectively solve the GFBE. MAPLE 18 software was used to carry out numerical simulations and approximations. Resulting numerical evidences show that the procedures converges rapidly to the...

Jun, 2022 pp. 202-215
29
Research Article DOI: 10.67897/njma.2022.0d1trgpa

A Class of Two-Step Obrechkoff-Type of Hybrid Block Method for Solving Initial Value Problems in Ordinary Differential Equations

L. A. Ukpebor*, L. O. Adoghe, I. E. Airemen

In this paper, we derived A Class of Two-Step Obrechkoff-Type of Hybrid Block Method for Solving Initial Value Problem (IVP) in Ordinary differential equations (ODEs) by collocation and interpolation techniques. The analysis of the proposed scheme shows that it is zero stable, convergent and consistent. Numerical examples are also presented to show that the method compared favorably with results o...

Jun, 2022 pp. 174-188
30
Research Article DOI: 10.67897/njma.2022.ccbh8a6f

Estimates for some Classes of Analytic Functions Associated with Pascal Distribution Series, Error Function, Bell numbers and q-Differential Operator

E. A. Oyekan*, A. O. Lasode

In this paper, we considered two classes of analytic functions. The classes are associated with Pascal distribution series, error function, Bell numbers and q-derivative operator. Some early coefficient estimates for the classes were established and some interesting nexus between our estimates and that of some earlier known classes were presented. 

Jun, 2022 pp. 163-173
31
Research Article DOI: 10.67897/njma.2022.j4wnhump

Development of an improved numerical integration scheme, its algorithm and application in the least square approximation

A. Y. Issah, K. Issa*, A. S. Olorunnisola

In this paper, we derived an improved numerical integration for finding the approximation of functions. An algorithm was written for the implementation in the least square approximation via shifted Gegenbauer polynomials and subsequently, the accuracy was tested on some selected examples to show the suitability of the scheme. All the computations were done using Matlab.

Jun, 2022 pp. 152-162
32
Research Article DOI: 10.67897/njma.2022.gc4d3wil

Systolic Array Residue Number System Based Smith-Waterman Algorithm

Hassan Kehinde Bello*

Smith-waterman algorithm (SWA) is widely used in computational biology. It is regarded as the most accurate sequence alignment algorithm on state-of-the-art (SOA). However, the algorithm is devoid of highspeed in term of performance. Evidence showed that various platforms have been used to implement the algorithm in order to improve the poor speed of operation, such as systolic array (SA) implemen...

Jun, 2022 pp. 136-151
33
Research Article DOI: 10.67897/njma.2022.1infh7eq

The Stability of Order m = 4 Rational Integrator for the Solution of Ordinary Differential Equation

F. Ebhohimen*, O. Anetor

In this article, investigation is carried out on a rational interpolation scheme of order m = 4, through two major processes of converting the resulting rational function to a complex outlook, and then, transforming the complex function to a polar form, from which the stability region of the method is constructed in the form of Jordan Curve. The regions of stability and instability as well as the ...

Jun, 2022 pp. 47-55
34
Research Article DOI: 10.67897/njma.2022.yw3rpfga

Application of Laplace Beltrami Equation to Solve Vortex Flow in a Closed Cylinder with Dirichlet Boundary Condition

S. O. Momoh*, S. A. Aniki, U. F. Amoo

The guiding equation here happens to be the Laplacian for Cylinder, the equation was obtained by using the known definition of differential operator for Cylindrical coordinates (rho, theta, z), it was then decomposed into three Partial Differential Equation (PDE) by variable separable methods and solved independently to obtain the general solution. Finally, contour plots of the solution describing...

Jun, 2022 pp. 104-116
35
Research Article DOI: 10.67897/njma.2022.bzn36s9k

Modelling Thermo-physical Effects of Heat and Mass Transfer in Unsteady MHD Viscoelastic Fluid Flow in inclined Porous Media

S. A. Amoo*, I. M. Daniel, A. O. Amoo

This research presents the modelling thermo physical effects of heat and mass transfer in unsteady Magnetohydrodynamics MHDviscoelastic fluid flow in inclined porous media. The resulting governing boundary layer equations were non-linear and coupled form of partial differential equations, and they were solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method....

Jun, 2022 pp. 90-103
36
Research Article DOI: 10.67897/njma.2022.hfxgvhz7

Stability of Solutions for a Class of Second Order Nonlinear Integro-Differential Equations with Delay

Daniel Oluwasegun Adams*, Rasheed A ADETONA, Musiliu Tayo Raji, Samson Abidemi Oni, Akinwale Lewis Olutimo

In this paper, we investigate the stability of solutions for a class of second order nonlinear delay integro-differential equations by using a suitable Lyapunov-Krasovskiˇi functional with sufficient conditions to establish some new results. An example is given to show the validity of the results obtained.

Jun, 2022 pp. 80-89
37
Research Article DOI: 10.67897/njma.2022.4rcm0i4v

Malicious PDF Detection Using Support Vector Machine

G. B. Balogun*, P. F. Adinoyi, J. B. Awotunde, M. Abdulraheem, I. D. Oladipo

The aim of this study is to develop a system that can detect and classify the Portable Document Format (PDF) as malware or benign document based on its features, using the Support Vector Machine (SVM) as an underlying model. Based on feature extraction and the Support Vector Machine technique, a method is proposed for efficiently detecting PDFs with harmful payloads. It was proved in this study th...

Jun, 2022 pp. 117-135
38
Research Article DOI: 10.67897/njma.2022.ebv3gty7

Some Properties of a Certain Class of Analytic Functions Defined by a Convolution Operator

Aminat O. Ajiboye*, K. O. Babalola

In this work, we study some properties of subclass B α n+1(β) of the class of analytic functions defined by a convolution operator. In fact, this class generalizes the class of Yamaguchi functions. Thereafter, some geometric properties such as inclusion, Fekete-Szeg¨o functional and upper bounds for some Hankel determinants are presented. Indeed, results from some of our corollaries and remarks sh...

Jun, 2022 pp. 68-79
39
Research Article DOI: 10.67897/njma.2022.jireubgc

Some Combinatorial Results on Star-Like Transformation Semigroup T αω∗ n

Garba Risqot Ibrahim*, Olasunkanmi Jafar Lawal, Sulaiman A. Akinwunmi, G. N. Bakare, Adeshola A. Dauda

Let Xn be a finite set and star-like full transformation semigroup T αω∗ n be a semigroup of Full Transformation semigroup Tn of Xn. Let Height of α ∗ be H+(α ∗ ) = | Imα∗ |, Fixed point of α ∗ be F(α ∗ ) = | {x ∈ X : xα∗ = x} |, Idempotent of α ∗ be | F(α ∗ ) |=| Imα∗ | , Collapse of (α ∗ ) be | ∪{tα−1 : t ∈ T αω∗} | and Relapse of (α ∗ ) be | n − C +((α ∗ )) | and also, Green’s relation of semig...

Jun, 2022 pp. 56-67
40
Research Article DOI: 10.67897/njma.2022.9b6frnnz

An Optimization of Inventory in Retrospect of the Directorate of Physical Planning in Ambrose Alli University Ekpoma, Edo State

E. Egbon*, F. M. Okoro, J. O. Braimah

This study proposes a mathematical model for the Directorate of Physical Planning’s inventory materials at Ambrose Alli University in Ekpoma, Edo State. To minimize the total cost for the year 2015, the study uses the linear programming solver (MATLAB’s linprog solver). To give the most efficient inventory among the products purchased, as well as the ideal minimum cost for the inventory, program c...

Jun, 2022 pp. 31-46
41
Research Article DOI: 10.67897/njma.2022.tl3im48l

Some Generalizations of Opial-type Inequalities on Time Scales

E. E. Aribike*, O. Anthonio, S. A. Aniki, Kamilu RAUF

Opial-type inequalities has grown into a substantial field with many applications in proving the existence and uniqueness of solutions of initial and boundary value problems for differential equations. We shall obtain Hua’s inequality on time scales The methodology employed in this paper is the H¨older’s inequality for convex functions.

Jun, 2022 pp. 22-30
42
Research Article DOI: 10.67897/njma.2022.5aq7r7yb

A Three-Step Algorithm for Solving Second Order Ordinary Differential Equations

L. A. Ukpebor*

A linear Multistep Method (LMM) of step length of three with six integrators and uniform order four through interpolation and collocation procedures were developed. The integrators are implemented on a Vanderpol’s oscillator Problem, stiff problem and, exponential problems. The results acquired compares satisfactorily with the existing method in the literatures. The properties of the integrators a...

Jun, 2022 pp. 14-21
43
Research Article DOI: 10.67897/njma.2022.e25u3qnn

Multifunctional Opial-type Integral Inequalities

Kamilu RAUF*, O. Anthonio, A. Abolarinwa, E. E. Aribike

Some new estimates on integral inequalities of Opial-type for multifunctions are established through some analytic methods. In special cases, the results derived in this paper yield some recently obtained results on Opial’s inequality. Moreover, more results of Opial-type inequality which extend some known results in the literature are also derived.

Jun, 2022 pp. 1-13
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