Three Schiff base ligands derived from condensation of ethylenediamine with benzaldehyde, salicylaldehyde, and vanillin, namely (1E,1'E)-N,N'-(ethane-1,2-diyl)bis(1-phenylmethanimine) (BBE), 4,4'-((1E,1'E)-(ethane-1,2-diylbis(azaneylylidene))bis(methaneylylidene))bis(2-methoxyphenol) (BHE), and 2,2'-((1E,1'E)-(ethane-1,2-diylbis(azaneylylidene))bis(methaneylylidene))diphenol (BME), were synthesized and complexed with Co(II), Cu(II), Ni(II), and Cd(II) ions. To the best of our knowledge, these specific metal complexes have not been reported previously, and their biological activities have not been evaluated. The ligands and complexes were characterized by melting point determination, solubility tests, molar conductivity, UV--visible and FTIR spectroscopy, magnetic susceptibility, X-ray fluorescence, powder X-ray diffraction (XRD), and thermogravimetric/differential thermal analyses (TGA/DTA). Low molar conductivity values (10.5--12.0 Omega-1 cm2 mol-1) indicate non-electrolytic behavior, while FTIR and X-ray fluorescence studies indicate coordination through azomethine nitrogen and oxygen donor atoms. XRD patterns show crystalline structures with sharp diffraction peaks, and thermal analyses indicate multistep decomposition and good thermal stability. Biological analysis indicates increased antifungal activity of the metal complexes over the free ligands, with lower minimum inhibitory concentrations; some complexes also showed improved 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activity (IC50 = 0.68101 mg/mL). The first-row transition metals are biologically relevant, while Cd(II) was included only for comparative structure--activity evaluation despite its known toxicity. This study provides insight into Ni(II) and Cd(II) complexes through integrated structural, thermal, and biological characterization.
A fresh class of hybrid special polynomials, termed the Bell-enriched Appell-lambda-polynomials, is constructed through the discrete convolution of Bell-based lambda-polynomials with the Appell sequence. A generating function for this class is established, from which closed-form expansions, convolution identities, and Stirling-number factorizations follow. The multiplicative and derivative operators that give this family its quasi-monomial character are identified, and the associated differential equation is recorded as an immediate corollary. A determinant representation `a la Wang is also obtained. To illustrate the scope of the general theory, three subfamilies are investigated: the Bell-enriched Bernoulli-lambda and Euler-lambda polynomials, which are admissible Appell specializations (mathcal{A}(0) neq 0), and the Bell-enriched Genocchi-lambda polynomials, which belong to the associated-Appell class (mathcal{A}(0)=0) and are treated separately. For the first two subfamilies, operational, quasi-monomial, and determinantal properties are fully established; for the Genocchi subfamily, generating-function and operational results are obtained within the associated-Appell framework. A numerical exploration of polynomial values, zero distributions, and graphical profiles supplements the algebraic development.
This paper proposes a new ranked set sampling (RSS) design, termed modified neoteric RSS (MNRSS), for efficient estimation of the population mean and variance. The proposed method extends the neoteric RSS (NRSS) framework by selecting sampled units in a more dispersed manner while avoiding extreme ranks, thereby improving population representation and estimation accuracy, particularly for the population variance. The theoretical properties of the proposed mean estimator are examined. Under perfect ranking, the estimator is shown to be unbiased when the underlying distribution is symmetric; for asymmetric distributions, it exhibits only a small bias. The performance of MNRSS was evaluated through an extensive simulation study involving several symmetric and asymmetric distributions. The proposed design was compared with simple random sampling (SRS), RSS, median RSS (MRSS), extreme RSS (ERSS), NRSS, systematic RSS (SRSS), and centralized RSS (CRSS). Performance was assessed using bias and mean square error (MSE). The results show that MNRSS generally outperforms the competing methods, particularly for estimating population variance and under asymmetric distributions. An application to Scots pine tree measurements further supports the practical usefulness of the proposed sampling design.
Conversational agents for low-resource languages (LRLs), such as Igbo, face major challenges, including limited annotated data, code-switching, and weak contextual coherence in multi-turn dialogue. This study proposes a multilevel-attention and hybrid-embedding framework that integrates FastText subword representations with multilingual BERT (mBERT) to improve semantic understanding and context retention. The architecture applies hierarchical attention at the word, utterance, and dialogue levels, enabling effective modeling of conversational dependencies and reducing context drift. The model was evaluated on a curated Igbo--English conversational dataset and benchmarked against long short-term memory (LSTM), Transformer, FastText, mBERT, and XLM-R baselines. For response generation, the proposed framework achieved a bilingual evaluation understudy (BLEU) score of 44.1%, a longest-common-subsequence recall-oriented understudy for gisting evaluation (ROUGE-L) score of 60.3%, and a context-retention accuracy (CRA) of 81.5%. For intent classification, it attained an F1-score of 87.3% and an area under the receiver operating characteristic curve (ROC-AUC) of 0.91; for context-dependency detection, it achieved an F1-score of 84.3%. The framework also reduced inference latency and was robust to code-switching and noisy conversational input. Human evaluation confirmed improvements in response clarity, cultural relevance, and multi-turn coherence. The findings show that hybrid embeddings combined with multilevel attention provide an effective and scalable approach to conversational AI for LRLs, with potential applicability to other African languages.
The principal objective of this article is to establish new and refined variants of Hermite--Hadamard- and Fejér-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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
