Journal of the Nigerian Society of Physical Sciences
Journal of the Nigerian Society of Physical Sciences is a peer-reviewed journal published quarterly (February, May, August & November) by the Nigerian Society of Physical Sciences. It offers an exciting publication outlet for Physical Science reports.
The group-theoretic origin of spin: the reality locus andcohomology of the spin spectrum
With the sole physical input that quantum symmetries act projectively on states, this work develops a group-theoretic account of spin as the obstruction to lifting a projective unitary representation to an ordinary one, controlled by two invariants: an infinitesimal class in H2(g, bR) and a topological character in Hom(pi1(G), bT). A lifting dichotomy determines, for every connected Lie group, whether and how its projective representations lift; it recovers the double cover from the special unitary group SU(2) to the special orthogonal group SO(3), the half-integer spins, the Frobenius--Schur values nu(rhoj) = (-1)2j, and the trichotomy of the rotation, Poincar'e, and Galilei groups. In the topological regime, the spin sectors form the Pontryagin dual widehat{pi1(G)}, a continuum for the planar rotation group SO(2), where it yields fractional (anyonic) spin. Two further results are established. First, the self-conjugate sectors---a necessary condition for compatibility with an antiunitary time reversal---form the 2-torsion subgroup widehat{pi1 (G)}[2], which remains finite even when the spectrum is a continuum; for the plane, it is {0, tfrac12}, explaining why generic anyons break time reversal. Second, the spectrum and this locus are the cohomology groups H1(G; bT) and H1(G; bZ/2), and the Bockstein sequence of bZ to bR to bT splits spin into a free part carrying the anyons and the torsion of H2 (G; bZ), an integral class whose modulo-2 reduction is, for the rotation group, the Stiefel--Whitney class obstructing spin structures on spacetime.
Mathematical, Computer & Statistical Sciences
Copyright (c) 2026 Mohammad F. Marashdeh (Author) https://creativecommons.org/licenses/by/4.0
Modeling and stability analysis of a fractional-order tuberculosisvmodel with different exposed populations progressing to infection
This study develops a fractional-order mathematical model based on the Atangana--Baleanu--Caputo (ABC) operator to investigate the transmission dynamics of tuberculosis (TB). The framework incorporates memory and nonlocal effects to represent the spread and progression of TB within a population. The first derivative of a Lyapunov function is used to evaluate the infection locally and globally within the fractional-order model. The model satisfies the essential mathematical properties of positivity, boundedness, existence, and uniqueness of solutions, thereby establishing its biological and mathematical well-posedness. Fixed-point theory is used to analyze the model and bound its solution. The analysis establishes local and global stability conditions and identifies the parameters that most strongly affect disease transmission. An advanced numerical method is used to obtain approximate solutions of the fractional-order system and evaluate the effect of the fractional-order parameter. Numerical simulations show that decreasing the fractional-order parameter enhances memory effects and produces smoother convergence toward equilibrium states than the classical integer-order model. The results indicate that the fractional-order framework provides a useful representation of TB dynamics and may support the understanding and control of TB transmission.
Copyright (c) 2026 Muhammad Farman, Kottakkaran Sooppy Nisar (Author) https://creativecommons.org/licenses/by/4.0
New fractional Hermite–Hadamard and Fejér inequalities involving special functions with applications to numerical quadrature rules
The principal objective of this article is to establish new and refined variants of Hermite--Hadamard- and Fej'{e}r-type integral inequalities in the interval-valued setting by exploiting the auxiliary transformed mapping mathcal{G}(s) := mathcal{F}(s^{1/rho}). This transformation preserves convexity and facilitates the systematic application of fractional integral techniques over a suitably rescaled domain through the Katugampola fractional operator. The resulting bounds are expressed explicitly in terms of the Gamma function, which enriches the analytical structure of the inequalities and yields sharper and more precise estimates than existing results. The validity and applicability of the theoretical findings are demonstrated through nontrivial illustrative examples and detailed remarks, and several previously known inequalities are recovered as limiting cases under suitable parameter configurations. As a further application, the derived inequalities are used to construct inclusion-type error estimates for numerical quadrature rules, with particular emphasis on the trapezoidal rule applied to interval-valued functions in the Katugampola fractional framework.
Interval-valued Katugampola fractional integrals
Functional analysis, convex analysis, fractional calculus, numerical analysis, convex functions, integral inequalities, and numerical approximation methods.
Copyright (c) 2026 Haitham Qawaqneh, Waqar Afzal, Mujahid Abbas, Muhammad Tariq, Mehreen Shehzadi Khan, Siegfried Macías, Jorge E. Macías-Díaz, Hijaz Ahmad, Waleed Mohammed Abdelfattah (Author) https://creativecommons.org/licenses/by/4.0
A mathematical model of cybercrime contagion: impact ofemployment on youth offending
The growing incidence of youth cybercrime, driven by unemployment and the precarity of temporary employment, constitutes a major social crisis that has received limited mathematical analysis. This study develops a deterministic four-compartment UCTR model comprising unemployed (U), cybercriminal (C), temporarily employed (T), and regularly employed (R) youth populations to examine interactions among unemployment, temporary employment, stable employment, and illicit digital activity. Using the next-generation matrix, we derive the cybercrime generation number, N0, and establish that the cybercrime-free equilibrium is globally stable when N0 < 1. Global sensitivity analysis based on Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCCs) identifies peer influence and recruitment into cybercrime from temporary employment as the strongest drivers of cybercrime. Conversely, transition to stable employment and legal prosecution are the principal deterrents. Numerical simulations show that high job-loss rates and continued entry into temporary employment sustain the cybercriminal population, whereas consistent transition to permanent employment substantially reduces cybercrime over time. These findings indicate that cybercrime control requires structural policies that strengthen long-term employment security rather than short-term interventions that do not provide sustained socioeconomic stability.
Copyright (c) 2026 Chinwendu Emilian Madubueze, Kazeem A. Tijani, Elijah Iji Ajogi, Madumelu H. C. Madubueze (Author) https://creativecommons.org/licenses/by/4.0
Evaluating lung cancer control through a time-delay mathematical model with detailed sensitivity analysis
Lung cancer (LC) is a leading cause of cancer-related deaths worldwide, posing a significant threat to public health due to its complex development, late diagnosis, and poor response to treatment. Rising rates, particularly among those exposed to tobacco consumption and environmental pollution, highlight the need for a realistic interpretation of disease dynamics through mathematical modeling. In this study, a nonlinear dynamical model of LC with time delay is formulated to represent the lag associated with smoking exposure and the evolution of smoking-related effects. The delay acts specifically through the delayed smoking-exposure interaction terms and does not represent treatment or immune response. The model is analyzed to confirm that solutions remain positive and bounded, ensuring biological feasibility. The basic reproduction number is calculated to describe threshold dynamics, and local stability of both the disease-free and endemic equilibrium is examined. Sensitivity analysis identifies the parameters influencing the model threshold quantity. The displayed analysis shows positive effects of theta, a, b, and e on Re0 and negative effects of d, g, m, and tau. These signs describe the mathematical sensitivity of the threshold quantity and do not establish treatment or recovery effects. Numerical simulations using nonstandard finite difference (NSFD), Euler, and fourth-order Runge--Kutta (RK4) methods validate the analytical results, with NSFD proving to be more stable and dynamically consistent. Findings suggest that government interventions, including tobacco control, education, and early screening awareness, can reduce the disease burden. These results offer insights for policymakers to develop cost-effective strategies.
Copyright (c) 2026 Shah Zeb, Awais Ahmad, Rizwana Kausar, Siti Ainor Mohd Yatim, Nurulhuda Ramli, Muhammad Rafiq (Author) https://creativecommons.org/licenses/by/4.0
Optimal control of fractional-order stochastic systems under uncertainty with Poisson and V-jump perturbations
We address the optimal control problem for a novel class of fractional-order uncertain--stochastic dynamical systems perturbed simultaneously by stochastic and epistemic jump disturbances. The system dynamics are governed by Caputo fractional derivatives and driven by a multi-noise framework comprising Brownian motion, Poisson random measures, canonical Liu processes, and finite-variation uncertain V-jump processes, thereby establishing a hybrid fractional system with double-jump features. The primary novelty is a unified analytical framework that combines memory effects with dual-source jump discontinuities under probabilistic randomness and epistemic uncertainty. We prove the existence, uniqueness, and continuous dependence of mild solutions in a hybrid probability--belief L2 framework under standard Lipschitz and growth conditions. We then define an optimal control problem with a combined probabilistic--uncertain performance criterion, verify the existence of optimal controls, and derive a Pontryagin-type maximum principle using a backward fractional adjoint system. Finally, numerical simulations for a fractional portfolio optimisation problem demonstrate the practical implications of memory, control, and multiple-jump disruptions.
Copyright (c) 2026 Philip Ajibola Bankole, Sunday Emmanuel Fadugba, Mabel Eruore Adeosun, Malesela C. Kekana (Author) https://creativecommons.org/licenses/by/4.0
Transmission dynamics of dengue–Zika co-infection with antibody-dependent enhancement, cross-immunity, and vaccination: backward bifurcation analysis and data calibration
The co-circulation of dengue virus (DENV) and Zika virus (ZIKV) in Aedes aegypti-endemic regions creates a significantly more dangerous epidemiological landscape than either pathogen alone. Yet no existing model simultaneously incorporates antibody-dependent enhancement (ADE), dual Zika transmission routes, synergistic co-infection mortality, dengue vaccination, and calibration against confirmed co-endemic surveillance data. We address this gap by developing a sixteen-compartment deterministic model that captures ADE through susceptibility multipliers epsilon_1 and epsilon_2, partial cross-immunity, imperfect dengue vaccination, and both vector-borne and sexual Zika transmission. We derived the disease-free equilibrium and obtained closed-form expressions for the component reproduction numbers mathcal{R}_{0d} and mathcal{R}_{0z}. The overall reproduction number mathcal{R}_0 = rho(FV^{-1}), computed as the spectral radius of the 8 X 8 next-generation matrix, satisfies mathcal{R}_0 geq max{mathcal{R}_{0d}, mathcal{R}_{0z}}, with equality only when the linear cross-infection parameters beta_{z3}, beta_{vd2}, beta_{vz2} are zero. All co-infection effects, including ADE, are confined to the nonlinear regime. This confirms that single-disease models can systematically underestimate epidemic risk during co-circulation. Local asymptotic stability of the disease-free equilibrium when mathcal{R}_0 < 1, uniform persistence when mathcal{R}_0 > 1, and the existence of at least one endemic equilibrium are established. Centre manifold analysis reveals backward bifurcation in both submodels, implying that reducing \mathcal{R}_0 below unity is necessary but not sufficient for disease elimination. The model was calibrated using 36 weeks of SINAN surveillance data from Esp\'{i}rito Santo state, Brazil (January--September 2021), yielding key fitted parameters: b^* = 1.278~wk^{-1}, beta_d^* = 0.749, beta_{z2}^* = 0.161, beta_{vd1}^* = 0.118, and beta_{vz1}^* = 0.252, with Pearson correlations of r = 0.594 (dengue) and r = 0.739 (Zika). Sensitivity analysis identifies the mosquito biting rate b and vector mortality \mu_v as the dominant intervention targets. Simulations reveal super-linear amplification of co-infections with rising biting rates and a 120-fold suppression of peak dengue incidence when vector mortality doubles. These findings support an integrated control strategy in which sustained vector management is the most cost-effective lever, complemented by improved healthcare access and high-coverage dengue vaccination to mitigate ADE-driven amplification.
Copyright (c) 2026 Thomas U. Onoja, Benson A. E. Afere, Ayodele Gabriel Fasanya, Sunday Yomi, Bolarinwa Bolaji (Author) https://creativecommons.org/licenses/by/4.0
Geometric admissibility of hypergeometric and integral operators for the synthesis of digital filters
In this study, rigorous analytical criteria are developed to determine when the Gaussian hypergeometric function belongs to the Sakaguchi-type class P(delta, sigma,t). A computable sufficient condition is established in Theorem 2.1, and the associated integral operator G( lambda, mu; nu; z) is shown to satisfy the admissibility conditions for membership in P(delta, sigma,t) under the stated parameter assumptions. These theoretical results are interpreted in the context of digital filter synthesis through an admissibility-based design framework. The proposed approach provides a systematic procedure for selecting admissible parameter values that satisfy the required geometric conditions for filter construction. Numerical examples, including admissibility contour maps and frequency-response characteristics, illustrate the proposed framework and demonstrate its potential for digital filter design based on geometric function theory.
Copyright (c) 2026 R. Kamali, S. Prema (Author) https://creativecommons.org/licenses/by/4.0
Modeling traffic-light systems: A neutrosophic graph approach
The coloring of neutrosophic graphs (NGs) is an important concept with extensive real-world applications. This research focuses on chromatic numbers for NGs and their operations. We define the neutrosophic chromatic number based on the alpha-, beta-, and gamma-cuts, as well as the strong alpha-, beta-, and gamma-cuts, of an NG. Furthermore, a comparative analysis of the proposed neutrosophic chromatic number is performed using the neutrosophic independent vertex set, demonstrating the effectiveness of the proposed approach. Several properties related to the union of NGs are also investigated using the proposed neutrosophic chromatic number. Finally, an illustrative traffic-light case study demonstrates the applicability of the proposed graph-coloring framework. The case study shows how the framework can model uncertain traffic conflicts and determine the minimum number of signal phases required for safe traffic operation. In the illustrative example, the obtained neutrosophic chromatic numbers indicate that the traffic network can be managed using five (k=5) signal phases under the proposed model, illustrating the framework's potential for efficient traffic-light scheduling, the reduction of potential traffic conflicts, and support for intelligent traffic-management decisions under uncertainty.
Neutrosophic Graph Coloring, Chromatic Number, Traffic Light Problem
Copyright (c) 2026 K Deva, K Siva, Gamachu Adugna Ganati, Walid Abdelfattah, Fikadu Tesgera Tolasa, Naisr Ali, Aseel Smerat, A. Mehmood (Author) https://creativecommons.org/licenses/by/4.0
Application of the SEE transform with the Adomian decomposition method to a nonlinear tumor growth model
This study examines the combination of the Sadiq-Emad-Eman (SEE) integral transform and the Adomian decomposition method (ADM) for solving a nonlinear tumor growth model. The combined approach provides a direct analytical procedure for obtaining the exact solution of the model. The SEE transform is used because it generalizes several integral transforms and simplifies the required algebraic operations. The ADM is then applied to represent the nonlinear term as a series of Adomian polynomials. The resulting formulation yields the closed-form solution of the tumor growth model and illustrates how the model depends on the initial tumor-cell population, growth rate, and environmental carrying capacity. The results show that the combined SEE--ADM approach offers a simple analytical method for this nonlinear model while preserving its biological interpretation.
Exact Solutions in Differential Equations
Copyright (c) 2026 Ahmed Fadhil Noaman, Zaid Adil Abdalkareem, Bareq Baqi Salman (Author) https://creativecommons.org/licenses/by/4.0
Unsteady MHD Casson nanofluid transport over an inclined permeable cylinder in an anisotropic porous medium: effects of nonlinear radiation and Joule heating
The present study investigates the coupled momentum, thermal, solutal, and magnetic transport characteristics of unsteady induced magnetohydrodynamic (MHD) Casson nanofluid flow over an inclined permeable cylindrical surface embedded in an anisotropic porous medium. The model incorporates several important physical mechanisms, including nonlinear thermal radiation, Joule heating, viscous dissipation, Brownian motion, thermophoresis, and higher-order chemical reaction kinetics. The governing nonlinear partial differential equations describing the conservation of mass, momentum, energy, nanoparticle concentration, and magnetic induction are transformed into a system of nonlinear ordinary differential equations through suitable similarity transformations derived using Lie group analysis. The resulting equations are solved using the semi-analytical homotopy perturbation method (HPM). The influence of key physical parameters on the velocity, temperature, nanoparticle concentration, and magnetic field profiles is analyzed through graphical and tabular results. The results indicate that increasing the magnetic parameter suppresses fluid motion due to the resistive Lorentz force while enhancing the thermal boundary layer thickness. The Casson parameter is found to significantly influence the velocity distribution, reflecting the non-Newtonian characteristics of the fluid. Thermal radiation and viscous dissipation increase the temperature field, whereas Brownian motion and thermophoresis strongly affect nanoparticle concentration profiles. Furthermore, anisotropic porous medium parameters and chemical reaction kinetics play important roles in controlling mass transfer rates. The study provides useful insights into magnetically controlled nanofluid transport in porous cylindrical geometries, which may assist in the design of advanced thermal systems in engineering applications.
Copyright (c) 2026 Bukola Oluwatosin Falomo, Olugbenga John Fenuga, Israel Olutunji Abiala (Author) https://creativecommons.org/licenses/by/4.0
On the effect of fixed-bandwidth kernel density estimation on the exponential distribution
Kernel density estimation (KDE) is widely used as a nonparametric smoothing operator in statistics. In this work, we study fixed-bandwidth KDE as a convolution operator applied to an exponential baseline distribution with rate parameter (beta > 0). We show that, for any compactly supported kernel K on [-1,1] and any fixed bandwidth h > 0, the expected KDE admits an exact factorization in the interior region y ge h: mathbb{E}[widehat f(y)] = beta e^{-beta y} C0, where C0 = (int_{-1}^{1}K(u)e^{beta h u} du) depends only on the kernel and bandwidth. Thus, the exponential density is an eigenfunction of the kernel-smoothing operator in the interior domain: its shape is preserved up to multiplication by the eigenvalue C0. After normalization on (h, infty), the resulting distribution reduces exactly to the shifted exponential density (beta e^{-beta(y-h)}). The result clarifies the role of boundary effects in kernel smoothing and shows that fixed-bandwidth KDE does not generate new parametric families from exponential baselines under tail normalization.
Copyright (c) 2026 Anwar Bataihah (Author) https://creativecommons.org/licenses/by/4.0
A novel parametric intuitionistic fuzzy entropy measure with applications to image edge detection
In digital image processing, edge detection is a fundamental operation used to identify intensity discontinuities in an image. In this paper, we propose a novel one-parameter generalization of an entropy measure for intuitionistic fuzzy sets (IFSs). IFSs provide additional flexibility by incorporating membership, non-membership, and hesitation information. A proof of validity is given for the proposed measure, together with numerical and graphical demonstrations. The entropy measure is applied to generate an edge map in which pixels exhibiting higher uncertainty are marked as image edges. Experimental results for standard benchmark images and real photographic images demonstrate superior edge localization and improved quantitative performance compared with existing fuzzy-entropy-based techniques.
Generalized entropy in intuitionistic fuzzy sets, used it for edge detection of an image
Information theory, Entropy in Fuzzy sets, Intuitionistic fuzzy sets, Image edge detection
Copyright (c) 2026 Vaishali Manish Joshi, Javid Gani Dar (Author) https://creativecommons.org/licenses/by/4.0
Adaptive finite element analysis of thermal and elasticity problems using Zienkiewicz–Zhu recovery-based error estimation
This paper presents a verification-to-adaptivity analysis of a finite element framework for scalar and vector-valued elliptic problems that employs recovery-based a posteriori error estimation. Conforming bilinear quadrilateral (Q4) and linear triangular (T3) finite elements are used to discretise the thermal Poisson equation and the linear elasticity equations. Standard Galerkin methods are combined with uniform and adaptive mesh refinement in this approach. The approach of manufactured solutions under uniform refinement is first used for verification, where both discretizations regain the theoretical H1- and L2-norm convergence rates, proving the accuracy of the scalar and vector formulations. The Zienkiewicz–Zhu (ZZ) recovery approach is then used to incorporate adaptive refinement, using stress recovery for elasticity and gradient recovery for the thermal problems. The adaptive meshes show conservative effectivity behaviour, monotonic estimator–error correlation, and stable localisation. Differences between Q4 and T3 outcomes are consistent with their known approximation features across all test cases. The findings show that for thermal diffusion and linear elasticity issues, ZZ-driven adaptivity offers a dependable extension of a validated finite element framework.
Finite element method, Adaptive mesh refinement, Zienkiewicz–Zhu recovery, Posteriori error estimation
Copyright (c) 2026 J. K. Odeyemi, S. A. Odunlami (Author) https://creativecommons.org/licenses/by/4.0
Mathematical modelling and optimal-control strategies of schistosomiasis–typhoid fever co-infection: using the demographic setting of Makurdi, Benue State, Nigeria
Co-infection of schistosomiasis and typhoid fever presents a significant public-health challenge and complicates clinical management. Both diseases are prevalent and endemic in African regions, particularly Nigeria, but their co-dynamics remain insufficiently studied. This study developed a deterministic mathematical model to examine the co-dynamics of schistosomiasis and typhoid fever in Makurdi, Benue State, Nigeria. The basic reproduction number (R0) for the sub-models and the full co-infection model was calculated to assess the stability of the disease-free equilibrium and to conduct bifurcation analysis. The endemic equilibrium was derived. Global sensitivity analysis was conducted, and an optimal-control model was formulated with five time-dependent controls: prevention of schistosomiasis, prevention of typhoid fever, screening and treatment for schistosomiasis, screening and treatment for typhoid fever, and screening and treatment for co-infections. The model was analysed using the Pontryagin maximum principle and the forward--backward sweep method. Numerical simulations included single, pairwise, and combined interventions. The results indicate that prevention strategies for both diseases are more effective than treatment alone. The study recommends implementing concurrent control interventions for both diseases to achieve optimal co-infection management.
Copyright (c) 2026 Kazeem A. Tijani, Chinwendu E. Madubueze, Reuben I. Gweryina, Terhemen Aboiyar (Author) https://creativecommons.org/licenses/by/4.0
A practical deep learning framework for multi-class skin cancer detection using U-Net segmentation and ResNet50 transfer learning
Existing artificial intelligence (AI)-based diagnostic systems often lack interpretability, clinical decision support, and accessibility for practical deployment, despite the importance of early skin cancer detection in improving patient outcomes. This paper proposes an integrated deep learning framework for multi-class skin cancer detection that combines lesion segmentation using U-Net with transfer-learning classification of seven skin-lesion classes using ResNet50. The framework links classification results with segmented lesion regions to improve interpretability and uses Gradient-weighted Class Activation Mapping (Grad-CAM) to provide visual explanations of model predictions, thereby improving transparency and clinician confidence in the recommendations. It is implemented as a lightweight web-based application for remote, resource-efficient skin-lesion screening without costly local hardware. Experimental results on the HAM10000 dataset indicate that the framework outperforms baseline deep learning models in segmentation and classification while providing interpretable predictions and computationally efficient computer-aided dermoscopic screening. The proposed system offers an explainable decision-support approach for preliminary skin cancer assessment and may support earlier diagnosis in resource-limited clinical settings.
Copyright (c) 2026 Mahesh Kumar Singh, Arun Kumar Singh, Pushpa Choudhary, Akhilesh Kumar Singh, Lalit Kumar Tyagi (Author) https://creativecommons.org/licenses/by/4.0
Optimal control of smoking-induced asthma and cardiovascular disorders with medical and public health interventions
Smoking is a major public health concern because of its harmful effects on several organs and its association with respiratory and cardiovascular complications. Cardiovascular disease is more common among smokers, and awareness of smoking cessation is important for reducing smoking prevalence. In this study, a compartmental model is developed to analyze the effect of awareness on the control of smoking and smoking-induced asthma and cardiovascular disorders. The positively invariant region, boundedness, positivity, and other basic dynamical properties of the model are established. Equilibria are obtained, and local and global stability analyses are performed. The normalized forward sensitivity index is used to assess the influence of key parameters on smoking cessation. Numerical simulations are conducted using a reliable nonstandard finite difference (NSFD) method. The simulation results show that smoking substantially increases the risk of respiratory and cardiovascular illnesses and that intervention strategies can reduce disease severity and prevalence. The model is further extended to an optimal-control framework that emphasizes the importance of treatment implementation and public awareness in reducing smoking-related harm. The results highlight the importance of media-based awareness and the need to inform potential smokers about the dangers of smoking. The proposed mathematical framework can support policymakers and health professionals in designing targeted interventions to reduce tobacco and cigarette use.
Copyright (c) 2026 Muhammad Farman, Noreen Asghar, Muhammad Umer Saleem, Nezihal Gokbulut, Evren Hincal, Aseel Smerat, Mohamed Hafez (Author) https://creativecommons.org/licenses/by/4.0
Adsorption of dithiazolidine compounds on Fe(110) surface and potential for corrosion inhibition: DFT calculations and adsorption locator/Monte Carlo adsorption simulations
Many corrosion inhibitors act through an adsorption mechanism by forming a stable film that protects the surface from an aggressive environment. The adsorption behaviour of two dithiazolidine derivatives, namely, 3,5-diphenyl-imino-1,2,4-dithiazolidine (DPID) and 3-phenyl-imino-5-chlorophenylimino-1,2,4-dithiazolidine (PCID), on the Fe(110) surface was investigated via density functional theory (DFT) calculations and adsorption locator/Monte Carlo adsorption simulations. Quantum study results reveal that PCID exhibits higher HOMO energy, higher tendency to accept electrons, and greater molecular softness than DPID, though with a smaller HOMO--LUMO energy gap (Delta)E = 0.10355 Ha. Fukui function and Mulliken charge analyses led to the identification of sulphur atoms as the most active adsorption centres in both inhibitors. Adsorption locator/Monte Carlo adsorption simulations confirm that both compounds are strongly adsorbed on the Fe(110) surface in a parallel orientation. DPID and PCID afforded adsorption energies of -137.419 kcal mol-1 and -147.611 kcal mol-1, respectively, whereas the rigid adsorption energy of PCID reached -149.555 kcal mol-1, a demonstration of stronger surface binding. These highly negative adsorption energies suggest predominantly very strong inhibitor-surface interactions, and that both compounds have theoretical potential as corrosion inhibitors for Fe-based surfaces. However, the adsorption strength and predicted inhibition potential of PCID would be greater compared with DPID, which provides theoretical guidance for rational design and prioritization of dithiazolidine-based corrosion inhibitors for future experimental evaluation.
Copyright (c) 2026 Ekemini Ituen, Peace Madu, Adewale Olamoyesan, Gospel Asuquo, Chibueze J. Olelewe, Emmanuel E. Etim (Author) https://creativecommons.org/licenses/by/4.0
Weaker and deficiency of even vertex odd edge root square mean labeling graphs
This paper introduces and investigates a relaxed variant of even vertex odd edge root square mean labeling (EVOERSML), called weaker EVOERSML. For a graph G, a weaker EVOERSML is an injective labeling f : V (G) \rightarrow\ {0, 2, 4, . . . , 2(q+k)}, where k \in \mathbb\ Z+, such that all vertex labels are distinct non-negative even integers. The induced edge labels are obtained by applying either the floor or ceiling function to the square root of the average of the squares of the labels of the end vertices. This relaxed labeling framework extends the applicability of root square mean labelings to a broader class of graphs. The minimum labeling bound Kmin(G) is defined as the least integer k for which G admits a weaker EVOERSML, and methods for determining this bound are discussed. The existence of weaker EVOERSML is established for several families of graphs, and their structural properties are analyzed. The deficiency associated with weaker EVOERSML is also examined, with particular emphasis on connected graphs of orders 3, 4, and 5, yielding complete classifications and illustrative examples.
Copyright (c) 2026 K. N. Babu, S. Meenakshi (Author) https://creativecommons.org/licenses/by/4.0
Bipolar soft neighborhoods with application in decision-making
This paper introduces bipolar soft (BS) neighborhood structures within the framework of soft set theory. First, several properties associated with lower and upper approximations based on a binary BS relation are examined, and the proposed approximation operators are shown to satisfy several fundamental properties. Next, an additional structure formulated through BS neighborhoods is explored. The concept of bipolar soft NjBS-neighborhood spaces is investigated, and their main characteristics are analyzed. Two types of topologies, overline{T}_zeta and underline{T}_zeta, induced by bipolar soft reflexive relations are then characterized. These topological structures are used to approximate rough sets, and a direct method is proposed to generate such topologies from the underlying relations. Finally, a numerical example is provided to illustrate the applicability of the proposed approach to decision-making.
Copyright (c) 2026 Saif Z. Hameed, Heba I. Mustafa, Abdelaziz E. Radwan (Author) https://creativecommons.org/licenses/by/4.0
Chemometric authentication of branded and crude spices using integrated GC–MS fingerprints and elemental profiling
Counterfeit and substandard spice products present significant risks to food safety, nutritional quality, and consumer confidence. This study applied an integrated chemometric approach, GC--MS chemical profiling, and elemental analysis to authenticate and discriminate among crude, genuine-branded, and potentially adulterated spice products. Twenty spice samples from curry, ginger, turmeric, nutmeg, and thyme were analysed using gas chromatography--mass spectrometry (GC--MS) for volatile compounds, flame photometry for macroelements, and atomic absorption spectrometry (AAS) for microelements, respectively. Principal component analysis (PCA) and hierarchical cluster analysis (HCA) revealed clear separation between crude and branded spices. An optimized model framework using two principal components explained 70.55% of the total calibration variance (70.29% cross-validated variance). The hierarchical cluster analysis (HCA) dendrograms confirmed distinct clustering, highlighting close substitutability among certain spices based on their nutrient profiles. Elemental analysis indicated significant variation across samples: branded curry 3 and branded ginger 3 were rich in zinc and selenium, while branded nutmeg 1 exhibited exceptionally high iron content. Conversely, some branded products, such as branded curry powder, consistently showed low or absent levels of essential micronutrients. GC--MS profiling identified dominant fatty acids, including Octadec-9-enoic acid and Octadecanoic acid. These compositional differences underpin the discriminatory power of chemometric models, enabling reliable authentication of the crude and branded spices and the detection of potential adulteration. The study demonstrated that integrated chemical fingerprinting with multivariate analysis provides a robust framework for quality assurance and regulatory monitoring of commercial spice products.
Food Science and Technology Applied Chemistry
Copyright (c) 2026 E. Udensi, R. B. Salau, S. O. Salihu, M. M. Ndamitso, M. T. Bisiriyu (Author) https://creativecommons.org/licenses/by/4.0
Even vertex odd edge root square mean labeling of some cycle-related graphs
An injective mapping (f:V(G)\rightarrow \{0,2,4,...,2|E|\}\) is said to satisfy the even vertex odd edge root square mean labeling (EVOERSML) condition when vertices are assigned distinct even values and each edge \(uv\in E(G)\) receives a distinct odd label determined by \( \left\lceil \sqrt{\frac{f(u)2+f(v)2}\{2}} \right\rceil \quad or \quad \left\lfloor \sqrt{\frac{f(u)2+f(v)2}\{2}} \right\rfloor.\) Graphs that admit such assignments are called EVOERSML graphs. The present study examines this labeling scheme on several graph structures closely related to cycles. Constructive methods are provided for families including ladder graphs, tadpole graphs, polygon-chain graphs, dumbbell graphs, and sunlet graphs. The obtained results emphasize how parity restrictions influence labeling existence and uniqueness. This work enriches the theory of root square mean labeling and opens further scope for studying EVOERSML-type labelings in more complex graph families and applied network models.
Graph Theory, Graph Labeling, Even Vertex Odd Edge Root Square Mean Labeling (EVOERSML), Root Square Mean Labeling, Cycle Related Graphs, Ladder Graphs, Tadpole Graphs, Polygon Chain Graphs, Dumbbell Graphs, Sunlet Graphs
Discrete Mathematics or Graph Theory and Combinatorics or Pure Mathematics
Applications of quadrilateral finite element meshes with four-node, eight-node, and twelve-node for efficient microwave energy transfer in curved waveguides
This study proposes a two-dimensional higher-order finite element method for computing eigenvalues in planar and multiply connected curved domains relevant to microwave energy transfer and electromagnetic waveguide problems. A fully automated quadrilateral mesh generator implemented in MAPLE-18 is used to convert triangular finite elements into quadrilateral elements with Four-node, Eight-node, and Twelve-node so that curved boundaries can be represented with improved accuracy. The formulation combines a Galerkin finite element procedure, an automated higher-order meshing strategy, and a Gauss quadrature rule to obtain numerical solutions of Helmholtz-type eigenvalue problems. Five curved waveguide domains are considered: an annular circular domain, a circular domain with a square hole, the union of two circular disks, a circular region with two unequal holes, and an L-shaped domain with a quarter-circular curved boundary. The computed eigenvalues are compared with published numerical and analytical results. The comparisons show that increasing the element order from Four-node, Eight-node, and Twelve-node improves the accuracy of the predicted eigenvalues while reducing the number of elements required to obtain comparable convergence. The proposed method therefore provides a practical and efficient finite element framework for eigenvalue estimation in curved waveguide geometries.
Mathematics, Computational Mathematics, Applied Mathematics, Numerical Fluid Mechanics
Copyright (c) 2026 K. Lekhana, K. T. Shivaram (Author) https://creativecommons.org/licenses/by/4.0
Fuzzy semi-Markovian stochastic model for single-unit system with repairman arrival delay under Lindley lifetime distribution using bell-shaped membership function
The key objective of the present analysis is to analyze the impact of fuzziness and repairman arrival delay on the mean time to system failure (MTSF) and availability of single-unit systems. Using a semi-Markovian approach, two stochastic models were developed, and recursive relations were obtained for the reliability measures. The lifetime, failure time, and repairman arrival time are considered Lindley-distributed random variables, with a parameter represented as a fuzzy number defined by a bell-shaped membership function. The switching devices and repairs are assumed to be as good as new. The numerical results show that increasing the \alpha-cut reduces fuzziness and improves the estimates, while immediate arrival of the repairman increases system availability. The importance of the results is highlighted using a numerical example generated from a Lindley-distributed random sample of size 1000 by considering \varepsilon = 0.1 and dynamic \delta in RStudio.
Copyright (c) 2026 Monika Saini, Ashish Kumar (Author) https://creativecommons.org/licenses/by/4.0
Weibull-based reliability and profitability analysis of an industrial multi-state repairable system
Reliability is a primary concern in industrial manufacturing because operational interruptions can reduce production, cause substantial economic losses, and create workplace-safety risks. This study applies the two-parameter Weibull distribution and the regenerative point technique (RPT) to a repairable system comprising two non-identical units: a primary unit operating in parallel with a secondary unit arranged in cold standby. The model incorporates inspection, repair, and replacement activities and is used to derive transition probabilities, mean sojourn times, mean time to system failure (MTSF), steady-state availability, maintenance busy periods, and a profit function. Numerical results show that system profitability decreases as the failure rate and Weibull shape parameter increase, whereas a higher repair rate improves profitability. For the reported parameter set, profit increases from 7325.258 to 8726.043 when the repair rate rises from 0.1 to 1.0 at a=0.01, and from 4879.802 to 6970.602 at a=0.05. The analysis also identifies reported zero-profit thresholds near a=1.45, 1.38, and 1.21 for k=0.8, 1.0, and 2.0, respectively. The framework supports maintenance planning and economic assessment of multi-state repairable systems.
Copyright (c) 2026 Priya Dahiya, Jasdev Bhatti, Pankaj Thakur (Author) https://creativecommons.org/licenses/by/4.0
Complex triple-valued neutrosophic soft sets and their topological framework with AI-driven signal-template analysis
This research proposes basic operations on complex triple-valued neutrosophic soft sets (CTVNSs) and defines complex triple-valued neutrosophic soft topological spaces (CTVNSTSs) with interior and closure operators. The study also presents an application to signal-template matching using cotangent similarity. Visual comparisons of four signals (S1--S4) and four templates (T1--T4) show that T4 is the most similar template, T2 is the least similar, and T1 and T3 are moderately similar. Normalization affects dominance and makes T1 relevant in some comparisons. Correlation analysis and clustering using principal component analysis and K-means (K=2) identify one cluster (S1, S2 , and S3) and one outlier (S4). These results indicate that cotangent similarity, together with data visualization and normalization, can effectively support the analysis of complex data.
Complex triple-valued neutrosophic soft sets
Complex triple-valued neutrosophic soft topology
Complex Triple-Valued Neutrosophic Soft Sets, Complex Triple-Valued Neutrosophic Soft Topology, Cotangent Similarity Measures, Data Visualization Techniques.
Copyright (c) 2026 Raed Hatamleh, Diana Amin Mohammad Mahmoud, Haitham Qawaqneh, Hind Y. Saleh, Alaa M. Abd El-latif, Eman Almuhur, Aqeedat Hussain, Arif Mehmood, Cris L. Armada (Author) https://creativecommons.org/licenses/by/4.0
The Editor and Publisher of the Journal of the Nigerian Society of Physical Sciences hereby issue this formal retraction notice for the article titled “Fractional-order modeling of visceral leishmaniasis disease transmission dynamics: strategies in eastern Sudan” by Ghada A. Ahmed, published in Journal of the Nigerian Society of Physical Sciences, Volume 5, 2023, Article ID 1693, DOI: https://doi.org/10.46481/jnsps.2023.1693. The article has been retracted due to errors in the calculations reported in the manuscript. Since the calculations form the basis of the fractional-order mathematical modelling, disease transmission analysis, and resulting conclusions, the identified errors affect the reliability of the findings presented in the article. The retraction decision had previously been reflected on the article page; however, a separate formal retraction notice was not published at that time. This notice is therefore being published now to correct that omission, improve transparency, and ensure that the retraction is properly visible to readers, indexing services, and metadata platforms. The original article should be regarded as retracted and should not be cited as reliable scientific evidence except in discussions relating to the retraction itself. Retracted article: Ghada A. Ahmed, “Fractional-order modeling of visceral leishmaniasis disease transmission dynamics: strategies in eastern Sudan,” Journal of the Nigerian Society of Physical Sciences 5 (2023) 1693. https://doi.org/10.46481/jnsps.2023.1693 Retraction decision date: 06-12-2023 Retraction notice publication date: 26-04-2026
Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
The Editor and Publisher of the Journal of the Nigerian Society of Physical Sciences hereby issue this formal retraction notice for the article titled “Preparation and Characterization of High Performance Dye Sensitized Solar Cells with Silver Nanoparticles in nanocomposite Photoanode” by Eli Danladi, Jamila Tasiu, and Lucky Endas, published in Journal of the Nigerian Society of Physical Sciences, Volume 2, Issue 1, February 2020, pages 7–11, DOI: 10.46481/jnsps.2020.24 [1]. The article was retracted after the authors notified the journal of an incorrect report of the X-ray diffraction analysis. Since the X-ray diffraction result formed part of the material characterization presented in the article, the reported error affected the reliability of the relevant findings and conclusions. Following the authors’ notification and editorial assessment, the article was retracted to maintain the accuracy and integrity of the scholarly record. The retraction decision had previously been reflected on the article page; however, a separate formal retraction notice was not published at the time. This notice is therefore being published now to correct that omission, improve transparency, and ensure that the retraction is properly visible to readers, indexing services, and metadata platforms. The original article should be regarded as retracted and should not be cited as reliable scientific evidence except in discussions relating to the retraction itself. Retraction notice publication date: 26-04-2026
Modeling the dynamics of type 2 diabetes with modifiable lifestyle influence
Type 2 diabetes mellitus (T2DM) is a multifactorial metabolic disorder driven by the interaction of insulin resistance, $\beta$-cell dysfunction, and modifiable lifestyle and environmental factors. Despite substantial advances in treatment, the global burden of T2DM continues to increase, highlighting the need for integrative frameworks that capture both biological and behavioral drivers of disease progression. In this study, we develop and analyze a deterministic compartmental model that incorporates genetic susceptibility, environmental exposure, diagnosis, treatment, and a modifiable lifestyle pressure variable representing socioeconomic and behavioral influences. The model is formulated as a system of nonlinear ordinary differential equations and analyzed using standard qualitative techniques, including positivity, boundedness, and stability analysis. We establish key dynamical properties and show that a disease-free equilibrium exists only under restrictive conditions, whereas an endemic equilibrium persists when environmental pressure and disease conversion are active. A semi-analytical solution obtained via the differential transformation method (DTM) is used to explore system dynamics and intervention scenarios. The results indicate that reducing lifestyle pressure, improving awareness, and increasing treatment initiation significantly reduce disease prevalence. Specifically, lowering lifestyle pressure or enhancing its dissipation reduces the equilibrium burden, while increasing awareness limits transitions into disease states and reduces overall disease spread.
Type 2 diabetes mellitus, population modeling, compartmental models, stability analysis, environmental pressure
Copyright (c) 2026 Opeyemi Odetunde, Tunde Alesinloye, Omoniyi Francis (Author) https://creativecommons.org/licenses/by/4.0
SAE-IF: A hybrid sparse autoencoder–isolation forest framework for real-time credit-card fraud detection and sustainable digital-economy protection
The rapid expansion of online payments and e-commerce has increased exposure to credit-card fraud and related financial crimes, threatening the security and stability of digital economies. Conventional supervised detectors require labelled fraud data, which are scarce and highly imbalanced. This study presents SAE-IF, a hybrid semi-supervised framework that combines a sparse autoencoder (SAE) with an isolation forest (IF) for anomaly detection in credit-card transactions. The SAE learns latent representations from transaction features without using class labels in its reconstruction objective, while labels are used for resampling, validation, fusion-weight optimisation, and threshold selection. A leakage-aware protocol employs stratified data splitting, robust feature scaling, and Bayesian hyperparameter optimisation with Optuna. The framework is evaluated on the ULB/Kaggle credit-card dataset, the IEEE-CIS Fraud Detection dataset, and the PaySim mobile-money dataset. SAE-IF achieved precision--recall area under the curve (PR-AUC) values of 0.832, 0.801, and 0.845, respectively, while maintaining precision above 0.90 and low false-positive counts. On a standard central processing unit, mean offline inference latency was 1.41 ± 0.23 ms per transaction. These results indicate that combining representation learning with anomaly detection can provide accurate and computationally feasible fraud screening in label-scarce financial environments, subject to validation on production infrastructure.
Copyright (c) 2026 Ogochukwu C. Okeke, Ike J. Mgbeafulike, Anthony I. Adigwe, Chidiogo C. Nwokedi, Nwadiogo E. G. Mmaduakonam, Calista U. Okpala, Chinonso J. Okonkwo, Nnamdi C. Ezenwegbu (Author) https://creativecommons.org/licenses/by/4.0