The numerical evaluation of Jeffrey fluid and heat source impacts on unsteady magnetized natural
oscillatory flow along a permeable plate immersed in porous medium is analyzed in the optically thin
thermal radiation regime. The exact solutions of the dimensionless equations have been determined. In
view of the assumed oscillatory pressure gradient, the resultant linear partial differential equations
were
reduced to a boundary-valued problem where the unsteady flow is superimposed on the mean steady
flow. The influence of controlling parameters dictating the flow behavior have been demonstrated
graphically and explained thoroughly. It is concluded from the computational results that the action of
Jeffrey fluid and heat source parameters are observed to enhance the fluid velocity. Also, the skin
friction is heightened at the both walls as the suction/injection parameter is raised. Finally, the
results
obtained for limiting case in this work is in good agreement with previous literature, thereby
confirming
the precision and validity of the current investigation.
keywords: Jeffrey fluid parameter, heat source, oscillatory flow, Darcy porous
medium, Slip
parameter
In this paper, a hybrid method combining the Kharrat-Toma transform and the Variational Iteration Method
(VIM) is presented. This approach enables the determination of both exact and approximate solutions for
linear and nonlinear higher-order initial value problems represented by ordinary differential equations
commonly encountered in various applied sciences. Several numerical examples are provided,
demonstrating that the proposed hybrid scheme is both effective and highly accurate.
keywords: Variational Iteration method, Kharrat-Toma Transform, Higher-order
initial value problem,
Ordinary differential equation, Exact and approximate solution.
This paper introduces an efficient integral transform, the "Kharrat-Toma Transform," designed to address
various types of partial differential equations encountered in physical applications. Several examples
are
provided to demonstrate the power and efficiency of this transform. The results obtained highlight the
effectiveness and applicability of the new transform. keywords: Kharrat-Toma Transform, partial differential equation, exact solution.
This paper explores the complex and growing issue of internet addiction, a phenomenon increasingly
affecting individuals across diverse demographics. In the present study, 25 articles published from 2010
to 2024 were reviewed to analyze the occurrence, risk factors, consequences, and preventive measures for
internet addiction. The research demonstrates that problematic uses of the internet are positively
correlated with anxiety, depression, loneliness, sleep disturbances, and musculoskeletal disorders. In
addition, internet addiction has adverse effects on students and workers' productivity, and therefore
their
performance declines. Psychological characteristics, loneliness, and non-limited screen time are also
among the main beaconing causes. The factors determined also include another demographic
characteristic – age, and occupation, which also affects the severity of Internet addiction. The methods
aimed at solving this problem include increasing awareness, aiming at achieving the correct proportion
of
time spent online and offline, offering psychological help, and setting high standards at the workplace
and
for parents. The present paper emphasizes the importance of further research to enhance the
understanding of the nature of IA and to identify interventions and policies appropriate for the
prevention
and treatment of IA in different populations.
keywords: Internet Addiction, screen time, mental health, insomnia, depression,
anxiety, self-esteem,
awareness.
This study examines the Two-Sample Multivariate Behrens-Fisher Problem in high-dimensional data
using simulation in R via the SHT package. The study evaluates the performance of four hypothesis
testing methods. Lopes and Wainwright (LW), Hyodo and Nishiyama (HN), Bai and Saranadasa (BS),
and Srivastava (S), across different sample size scenarios. The methods are assessed based on their
ability to control Type I error rates and maintain statistical power. Results indicate that all four
methods effectively control Type I error, with observed rates closely aligning with the nominal
significance level (α = 0.05). However, HN and BS demonstrate superior power, particularly in larger
sample sizes, making them more effective in detecting true effects. In contrast, LW and S are more
conservative in power estimation, which may be beneficial in scenarios requiring stricter Type I error
control. Based on these findings, researchers should select methods based on their study objectives,
balancing error control and power. The study contributes to knowledge by providing a comparative
evaluation of hypothesis testing methods, offering practical guidance for statistical decision-making in
high-dimensional data analysis. Further research could explore methodological advancements,
robustness testing, Bayesian approaches, and real-world applications to refine statistical inference
techniques.
keywords: High-dimensional data, Hypothesis testing, Type I error, Statistical
power, Sample size,
Srivastava, Wainwright, Bai and Saranadasa, Hyodo and Nishiyama
This study examines rice price volatility in Kebbi State, Nigeria, focusing on WACOT, LABANA,
and RAYHAN using data from January 2010 to February 2024. Statistical and econometric methods,
including descriptive analysis, unit root tests, and GARCH-type models, are employed to assess
volatility dynamics. Descriptive statistics show WACOT has the highest mean price (19,961.8) and
standard deviation (12,653.8), indicating the greatest volatility. LABANA follows with a mean of
19,229.9 and standard deviation of 12,199.0, while RAYHAN exhibits the lowest mean (3,733.3) and
standard deviation (12,002.7). Skewness and kurtosis suggest WACOT and LABANA have a higher
likelihood of extreme price fluctuations. Graphical analysis highlights volatility spikes from late
2023
to early 2024. Correlograms and unit root tests confirm non-stationarity, necessitating first
differencing. Post-differencing analysis establishes stationarity with stable mean and variance.
GARCH-type models identify FIGARCH (1,d,1) as optimal for WACOT and LABANA, while
ARFIMA (1,1,1) is best for RAYHAN. The FIGARCH model for WACOT shows the highest
volatility persistence (α + β = 0.996) and moderate negative asymmetry (ϒ = -0.252). LABANA’s
FIGARCH model exhibits strong asymmetry (ϒ = -0.607) and persistent volatility (α + β = 0.951).
RAYHAN’s ARFIMA model reveals long memory effects (α + β = 0.917) and moderate asymmetry
(ϒ = -0.324). WACOT has the highest volatility, while LABANA shows the strongest asymmetry.
The findings emphasize the need for effective risk management strategies in Kebbi State’s rice
market. This study provides critical insights for policymakers and stakeholders seeking to mitigate
price volatility risks.
keywords: : Volatility dynamics, Stationarity, Rice prices, Unit root tests,
FIGARCH and ARFIMA
models
Mathematical modeling plays a crucial role in understanding and addressing complex real-world issues,
particularly in the analysis of infectious disease dynamics. This study focuses on the mathematical
modeling
of COVID-19 transmission in Nigeria, incorporating treatment as a control strategies to mitigate the
impact
of the pandemic. The model classifies the population into six compartments: susceptible, exposed,
infected,
quarantined, recovered and treated individuals. Through the formulation of differential equations and
assumptions about disease transmission and recovery rates, the study explores the effects of
interventions
such as physical distancing, face mask usage, and treatment. The research emphasizes the importance of
these models in guiding public health responses and forecasting future outbreaks. Key aspects of the
model,
such as positivity, boundedness, and the identification of equilibrium points, are analyzed. The basic
reproduction number, which determines whether the disease will spread or die out, is also computed. The
study highlights the effectiveness of control measures in reducing transmission and underscores the
necessity of ongoing intervention strategies to combat COVID-19.
keywords: Mathematical modeling, COVID-19 transmission, Public health
interventions, Disease
dynamics, Basic reproduction number, Disease forecasting.
1Muhammed Murtala Hamza, 2*Abubakar Muhammad Tsafe, 3Samaila
Kenga-kwai
Ahmad and 4Muhammad Bello Abdullahi
1,2,3Department of Mathematics, Faculty of Physical and Computing Sciences, Usmanu
Danfodiyo
University, P. M. B. 2346 Sokoto State, Nigeria. 4Department of Physics, Faculty of Physical and Computing Sciences, Usmanu Danfodiyo
University, P.
M. B. 2346 Sokoto State, Nigeria.
This study examines the influence of magnetic fields and fluid motion with exponential heat emission
within a porous superhydrophobic (SHO) microchannel. We analyse the natural convective flow of an
electrically conductive fluid through an upstanding parallel plate microchannel exposed to a
perpendicular
magnetic field. One of the parallel plates has a superhydrophobic surface (SHS), while the other plate
has
a no-slip surface. An exact solution was obtained using the theory of simultaneous differential
equations
for case I, depicting the physical scenario of a heated SHS. At the same time, a no-slip surface
remained
unheated, and case II depicts the physical scenario where a no-slip surface is heated while an SHS
remains
unheated. The effects of various flow parameters, such as Darcy number (Da), exponential heat generation
parameter (Qg), and MHD, on velocity, temperature, volume flow rate, skin friction, and Nusselt number
are graphically illustrated. It is observed that temperature profiles rise in both cases, considering
the impact
of the exponential heat generation parameter (Qg). The velocity component and volume flow rate
substantially increased with the influence of Darcy number (Da) and exponential heat source parameter
(Qg), but decreased with the effect of magnetic parameter (M). This work will contribute to the
advancement of knowledge in fluid dynamics and heat transfer with potential applications in various
industries, such as heat transfer advancement, micro-electronic cooling, biomedical devices, and
lab-on-a
chip devices.
keywords: Natural convection, Exponential heat source, Magnetohydrodynamics (MHD),
Porous material, Superhydrophobic surface (SHS), Microchannel,
In the era of big data, the sheer volume of information generated daily makes it challenging to
examine each data point due to constraints like time, labor, and cost. Sampling theory addresses this
by using auxiliary information to develop more efficient estimators for population parameters. This
study proposes an optimal estimation method for population mean in simple random sampling by
incorporating auxiliary attributes, specifically focusing on factor-type estimators for finite
populations. The study refines a generalized class of factor-type estimators, deriving their properties,
including bias and Mean Square Error (MSE) up to the first order of approximation. The minimum
MSE was also computed, followed by a theoretical comparison with existing estimators. Results show
that the modified class of factor-type estimators consistently achieves the lowest MSE, indicating
superior efficiency. Empirical evaluation with real-world data further supports these findings,
showing that the modified estimators outperform commonly used methods. The study recommends
the use of these modified estimators in fields such as education, agriculture, fisheries, and health
sciences and provides a framework for developing improved estimators, offering valuable insights for
further research in this area.
keywords: Factor-type estimator, Auxiliary attributes, Population mean estimation,
Mean square
error (MSE), Percent relative efficiency (PRE), Survey sampling
The invasion of Ukraine by Russia, known to be the third-largest producer of petroleum and liquid
fuels globally,
contributed to the increase in crude oil prices. This study on the computational modelling of
Nigeria’s crude oil prices
during the Russia–Ukraine war was conducted to determine and select an appropriate model that best
describes the
functional behaviour of crude oil prices in Nigeria during this period. The research data were the
daily crude oil prices
collected from the Central Bank of Nigeria website, and the time under review spanned the period
from February 24,
2022, to June 13, 2023. The total observations summed up to three hundred and eighteen (318) days. A
total of six
different regression models were estimated for the study. They include linear, quadratic, cubic,
log-linear, linear-log,
and log-log models, and their results were compared based on some model selection criteria. The
Log-linear model
with the values S = 0.045, R² = 67.6%, F = 660.29, and p = 0.000—alongside the smallest accuracy
measures (MAE
= 0.030; MSE = 0.002; MAPE = 0.034), is adjudged the best-fit model among the six regression models
developed.
This indicates that the estimated Log-linear model best described the impact of the war on Nigeria’s
crude oil prices
during the period under review, corresponding with the Russia–Ukraine war. Consequently, the study
recommends
adopting the Log-linear model for forecasting crude oil prices.
keywords: : Russia-Ukraine war, Crude oil price, least squares, regression,
linear, non-linear,
This paper presents a focused examination of the Euclidean algorithm as an effective method for solving
Diophantine equations equations that seek integer solutions. Emphasis is placed on the extended
Euclidean algorithm, highlighting its capability to identify integer solutions by determining the
greatest
common divisor of coefficients. The study outlines a systematic approach to simplifying and solving both
homogeneous and non-homogeneous linear Diophantine equations. Key theoretical insights and
algorithmic procedures are presented, along with the general solution framework. The findings
demonstrate the Euclidean algorithm’s continued relevance and efficiency in addressing number-theoretic
problems in mathematical research.
This paper demonstrates the effect of nonlinear density variation with temperature (NDT) on a
magnetized mixed flow affected by Arrhenius kinetics in a slit microchannel. One of the parallel plates
is intentionally modified to have superhydrophobic surface (SHS) characteristics, while the other plate
has a no-slip surface (NSS). The ordinary differential equations are treated with a semi-analytical
(regular perturbation) method. The actions of key parameters controlling the flow behavior in terms of
momentum and energy distributions are illustrated graphically. The present study is valid for the
limiting case because it is based on a comparison with earlier studies that backed it up. It was
revealed
that fluid flow is higher in favor of NDT than in linear density variation with temperature.
Additionally,
the action of mixed convection parameter is seen to escalate the fluid velocity. This research will have
applications relevant to cracking in petrochemical engineering, geothermal systems, chemical synthesis,
etc.
keywords: Nonlinear density variation with temperature (NDT), Mixed (Combined)
convection,
Arrhenius kinetics, Magnetohydrodynamics (MHD), Slit Microchannel.
The modified Caesar cipher mixes regular letters with special characters to make the code both stronger
and more
complex. It is designed so that the right people can easily decrypt the message, while it remains
difficult for others
to break. The use of special characters adds another level of challenge, making the cipher tougher to
crack and more
versatile, while still being user-friendly and modulo34 will be implemented to add a security later on
the classical
Ceaser algorithm.
keywords: cryptography, cipher, encryption, decryption, Caesar cipher
The problem is to want a pair of functions h(t) and w(x,t) that satisfy the equation
wt(x,t) − h(t)wxx(x,t) = f(x,t)
under Cauchy boundary conditions. An approximate solution can be found for both functions using the
techniques of generalized inverse problem of moments and can also be found dimensions for the error of
the estimated solution.
keywords: generalized moment problem; integral equations; parabolic equation,
Cauchy conditions.
This work presents a modified ROT13 cipher that incorporates a stack data structure and a dynamic shift
value. The
shift value is determined by the number of letters in the message to be encrypted, taken modulo 26. A
Python
algorithm is designed to automate the encryption and decryption processes, eliminating the need for
manual
computation. The stack-based implementation enables efficient character manipulation, while the dynamic
shift
value enhances security. The proposed cipher offers improved security features compared to the
traditional ROT13
cipher. The Python code provides a user-friendly interface for encrypting and decrypting messages,
making it
suitable for practical applications. This work demonstrates the potential of combining cryptographic
techniques
with programming to create secure and efficient encryption systems.
keywords: Rot13, Ceaser cipher, encryption, decryption, algorithm, cryptography
The integration of artificial intelligence (AI) and machine learning technologies into mathematics
education has sparked significant interest and debate, raising ethical considerations that warrant
careful
examination. This study provides an overview of the ethical dimensions surrounding the use of AI
generated content in mathematics education through a systematic Literature Review. It explores key
ethical concerns, including bias, fairness, transparency, privacy, and intellectual property rights, and
discusses theoretical frameworks that inform ethical decision-making in educational contexts. Drawing
on Ethical Decision-Making Theory, Critical Theory, and Social Learning Theory, this highlights the
importance of navigating ethical dilemmas responsibly to ensure equitable access, promote inclusive
practices, and foster ethical AI integration in mathematics education. The study identified common
themes and trends in ethical consideration in AI-generated content in Mathematics Education. Through
critical reflection, collaboration, and informed decision-making, educators, developers, and
policymakers can work toward creating learning environments that prioritize the well-being and rights
of students while harnessing the transformative potential of AI technologies in mathematics education.
keywords: Ethical Considerations, AI-generated content, Mathematics Education
This study aimed to evaluate and compare the performance of three non-linear growth models—
Mitscherlich, Gompertz, and Power Growth Models—using data from two flour mills. The analysis
involved estimating the initial and final parameters of each model, assessing their performance using
information criteria, and identifying the model that best fits the observed data. Nonlinear least
squares
estimation was employed, utilizing a modified Levenberg-Marquardt algorithm implemented through
Gretl statistical software and the R programming language. The results indicated that the Power Growth
Model provided the best fit, accounting for 97.24% of the variation between total flour cost (in
millions of
Naira) and production volume (in tens of tonnes). Additionally, both the Power and Mitscherlich models
were found to more accurately describe the cost-production relationship than the Gompertz model. While
the Power model emerged as the most efficient overall, the study recommends both the Power and
Mitscherlich models for analyzing non-linear growth data sets.
keywords: Growth models, Non-Linear, Information Criterion; Regression, Forecast
evaluation
statistics and Modified Version of the Levenberg Marquardt.
