Asian Research Journal of Mathematics

A Power-Law Framework for Characterizing Global Cancer Burden: Incidence–Mortality Scaling, Severity Ranking, and Cumulative Risk Patterns Using GLOBOCAN 2020

Senyefia Bosson-Amedenu — 2026-06-25

Background: Global cancer burden is unevenly distributed across cancer sites, and several malignancies show mortality levels that are disproportionate to incidence. Quantifying the scaling relationship between incidence and mortality may clarify comparative severity, identify outlying cancer sites, and support population-level prioritisation.

Methods: This study used GLOBOCAN 2020 data for 36 major cancer sites worldwide. The association between incidence (Nc) and mortality (Nd) was assessed using linear, log-log power-law, and quadratic models. Model performance was evaluated using R², adjusted R², RMSE, MAE, AIC, BIC, residual diagnostics, ten-fold cross-validation, outlier exclusion, and subset restriction to the top 20 cancers. A rank-based severity index (σ) was examined against fatality ratio, age-standardised rates, and cumulative death risk.

Results: The log-log power-law model provided the strongest overall representation of the incidence-mortality relationship across all cancer sites (R² = 0.853; adjusted R² = 0.848), with substantially lower AIC (63.67) and BIC (68.33) than the competing models. The estimated scaling exponent was α = 1.031 (95% CI: 0.879-1.182), indicating near-proportional mortality scaling with incidence. Cross-validation supported predictive stability, and the Breusch-Pagan test indicated reduced heteroscedasticity after logarithmic transformation (p = 0.452). The proposed severity index showed positive associations with fatality ratio, ASMR/ASRI, ASMR, and cumulative death risk. Prediction-interval analysis identified lung, liver, stomach, oesophageal, and pancreatic cancers as having higher mortality than expected from incidence alone, whereas breast, thyroid, prostate, testicular, and melanoma cancers showed lower-than-expected mortality.

Conclusions: The findings support a power-law framework for describing global incidence-mortality scaling and suggest that rank-based severity may provide a complementary comparative indicator of cancer burden.

A Study of Factors Affecting Mathematics Learning among Higher Secondary Students in Rural and Urban Areas of Nashik District, Maharashtra, India

Neha Pravin Patil — 2026-06-26

Mathematics is an important subject that helps students develop logical reasoning, analytical thinking and problem-solving skills. However, many students at the higher secondary level experience difficulties in learning mathematics, which adversely affects their academic achievement and confidence. The present study was conducted to analyse the factors affecting mathematics learning among higher secondary students in rural and urban junior colleges of Nashik District. A descriptive survey research design was adopted. Primary data were collected from 120 students belonging to the science stream using structured questionnaires. Statistical tools such as percentage, mean and the chi-square test were used for data analysis and interpretation. The findings reveal that mathematics anxiety is a major problem among students, as 58% of the respondents agreed that they experience fear and stress while learning mathematics. Nearly 46% of students reported weak understanding of basic mathematical concepts, while 45% expressed dissatisfaction with existing teaching methods. The study also found that only 29% of students practise mathematics regularly, whereas 33% rarely practise the subject. In terms of socio-economic support, 33% of students reported low academic and financial support for mathematics learning. The chi-square analysis further confirmed a significant relationship between mathematics anxiety and academic performance (χ² = 9.21), as well as between teaching methods and conceptual understanding (χ² = 8.45). The study concludes that mathematics learning difficulties are influenced by multiple educational, psychological and socio-economic factors. Therefore, activity-based teaching methods, regular practice sessions, counselling support and improved educational resources are suggested to enhance mathematics learning outcomes among higher secondary students.

Fractional Operators Associated with the Generalized Mittag-leffler Function in the Kernel

Chander Prakash Samar — 2026-06-30

This work is devoted to investigating fractional calculus involving integral and differential operators associated with the generalized Mittag-Leffler function in the kernel.

The results include differentiation and fractional calculus operators associated with the generalized Mittag-Leffler function. These outcomes are used to establish analogous properties and derive selected special cases. The relationship between the obtained results and earlier work is also explained.

Tauberian Theorem for Mellin Transform of Hyperfunctions Having Bounded Exponential Growth

A. N. Deepthi — 2026-07-01

Hyperfunctions provide a complex analytic framework for representing singular objects that cannot always be treated adequately by ordinary functions or distributions. The Mellin transform is a central tool for analysing scaling behaviour and asymptotic properties, while Tauberian theorems give conditions under which information about a transform determines corresponding properties of the original object. This paper establishes a Tauberian theorem for the Mellin transform of measurable hyperfunctions having bounded exponential growth and support contained in [1,∞). After recalling the necessary notions concerning hyperfunctions, support, singular support, bounded exponential growth, Mellin transforms, and Dirichlet integrals, the study relates the Mellin transform of a hyperfunction on the positive real axis to the Laplace transform under the substitution y = e^−s. The main result assumes a measurable hyperfunction g(y) with |g(y)| ≤ $\frac{N}{y}$ for y > 0 and a Mellin transform that extends holomorphically to an open set containing the half-plane Re t < 1. Under these hypotheses, the integral $\int ^∞_0$ g(y)dy is shown to converge, and its value is identified with the holomorphic continuation at t = 1, namely ˆg(1). The result adapts a Tauberian theorem for Dirichlet integrals to the setting of hyperfunctions and clarifies the link between Mellin-transform behaviour and convergence of the original hyperfunction integral.

Dominant Hazard Quantification in Dengue Diagnosis via Nano-Topological Attribute Reduction and Bayesian Confidence-Degradation Regression

Manish Gurjar — 2026-07-01

In this paper, we develop an analytical framework to identify the most significant core factor among a set of core factors by quantifying how severely the removal of each factor degrades probabilistic diagnostic performance. Although Jeevitha et al. identified the core factor set {F,L} for dengue diagnosis using attribute reduction through Nano-topology, their approach did not quantify the relative impact of each factor. Over a 15-patient dengue dataset, a Nano-topological space is constructed via Pawlak rough approximations; attribute reduction identifies Core = {F,L}; a classification tensor expressed in terms of topological approximations yields the F1 score as a Jaccard-like overlap and step-function AUC by the trapezoidal rule. Subsequently, we establish a Dirichlet–Beta conjugacy, through which the Bayesian posterior distribution is derived, enabling corrected uncertainty quantification for small-sample bias. Two ordinary least-squares (OLS) regression models—the penalty regression model and the confidence-degradation regression model—are then introduced to quantify the linear relationship between false-positive boundary contamination and diagnostic degradation. Removing LLBP inflates false positives from 1 to 3 at the optimal threshold α^∗ = 0.5, reducing Bayesian diagnostic confidence from 95.3% to 75.9%. The confidence-degradation regression C = 1.0553 − 0.0970 · FP achieves R2 = 0.991, and every comparative metric confirms LLBP to be approximately 2.20 times more hazardous than Fever. The proposed Nano-Topological–Bayesian framework provides a statistically credible and clinically interpretable tool for identifying the dominant core hazard factor in small-sample medical datasets, with LLBP confirmed as the critical hazardous attribute for dengue diagnosis.

An SEIDR Model with Saturated Behavioral-Feedback Incidence and Capacity-Constrained Optimal Control for Workplace Burnout Dynamics

David Olutunde Daniel — 2026-07-11

Aims: To build a population-level model of workplace burnout that captures how workers and workplaces respond to visible distress, to identify which prevention capacity is the binding bottleneck under realistic budget limits, and to express the answer in dollar terms that can guide prevention investment.

Study Design: A compartmental model with capacity-constrained optimal control, supported by a global sensitivity analysis and a study of a re-infection variant of the same model.

Place and Duration of Study: Department of Mathematical Sciences, University of Texas at Dallas, in collaboration with the University of Alabama at Birmingham, 2024 to 2026.

Methodology: A five-compartment model is constructed with susceptible, exposed, infected, distressed, and recovered groups, governed by ordinary differential equations. The exposure rate uses a Capasso-Serio form with two saturation terms, one on visible acute distress and one on visible chronic strain. The basic reproduction number is obtained by the next-generation method. A three-channel optimal-control problem (primary, secondary, and tertiary prevention) is then posed, with a pointwise cap and a total-spending cap on each channel. Existence follows from Cesari’s theorem and short-horizon uniqueness from a Lipschitz-Gronwall argument, with the optimal controls characterized by Pontryagin’s Minimum Principle.

Results: At the illustrative baseline, R₀ = 1.9743. The capacity-constrained run returns an ROI of 12.02, against 19.94 with no budget caps. For this baseline, the shadow prices rank secondary prevention as the binding capacity at $130,769 per unit of budget, above tertiary ($26,978) and primary ($1,328). A re-infection variant shows a saddle-node bifurcation at R₀ ≈ 0.76 and a bistable region below threshold.

Conclusion: The framework offers a model-based, regime-dependent way to identify which prevention capacity binds in a given workforce state. The saddle-node hysteresis explains, in formal terms, why a workforce already in chronic burnout does not recover once pressure is eased.

On Zeros of Bicomplex Meromorphic Functions

Narinder Sharma — 2026-07-11

This paper presents a systematic study of the zeros of bicomplex meromorphic functions on the bicomplex plane T. Via the idempotent decomposition, every bicomplex meromorphic function f corresponds to a pair of complex meromorphic functions (f₁, f₂). We introduce the notions of strong zeros, at which both component functions vanish to positive order, and weak zeros, at which exactly one component vanishes. The set of strong zeros of f is characterized precisely as the collection of points w = αe₁ + βe₂ for which both f₁(α) = 0 and f₂(β) = 0. For strong zeros we establish a local factorization theorem in which the multiplicity, termed the bidegree, is defined as the minimum of the vanishing orders of the two components. Building on this foundation, we derive bicomplex analogues of several classical results: an Enestr¨om–Kakeya-type theorem that confines the zeros to a componentwise exterior region E(1; 1, 1), a Gauss–Lucas-type theorem asserting that the zeros of the derivative lie in the idempotent convex hull of the zeros of f, and a Rouch´e-type theorem for counting zeros in product domains. We further show that the zero-counting function in a bicomplex disk factors as the product of the counting functions of the two complex components, and that the exponent of convergence of the zeros of a bicomplex entire function of finite order equals the maximum of the corresponding component exponents.

Sharp Multidimensional Hardy-type Inequalities with Singular Kernels: Theory, Approximation Methods and Applications

O. A. Olaiju — 2026-07-13

This study examines multidimensional Hardy-type integral inequalities associated with weighted integral operators and singular kernels. Measurable functions on multidimensional domains are considered under convexity, weighted Lebesgue-space, and kernel-integrability assumptions. A class of generalised Hardy operators is formulated, and sufficient boundedness conditions are established using Jensen’s inequality, Hölder’s inequality, Minkowski’s integral inequality, and Fubini’s theorem. Particular attention is given to singular power-law kernels and their relationship with fractional-type integral operators. A finite-grid quadrature framework is also developed to approximate multidimensional Hardy operators. The singularity near the diagonal is treated through kernel regularisation to support stable computation. Numerical tests with exponential, Gaussian, and regularised power-law kernels compare the computed left- and right-hand sides of the proposed inequality and show that the reported test cases satisfy the inequality. Grid-refinement results further show decreasing approximation errors as the resolution increases. The framework is discussed in relation to elliptic partial differential equations, fractional integral operators, Sobolev-type estimates, harmonic analysis, operator theory, and computational methods for partial differential equations. Overall, the paper combines analytical estimates with numerical approximation to provide a structured treatment of Hardy-type inequalities with singular kernels in multidimensional settings, while recognising that sharp constants for the general case and broader high-dimensional validation remain unresolved.

A Mathematical Framework for Ebola Virus Disease Preparedness in Kenya: Modeling Waning Immunity, Vaccination, and Re-infection Dynamics

George M. Mocheche — 2026-07-14

Recurrent infectious disease outbreaks continue to challenge public health systems despite advances in surveillance and vaccination. Motivated by recurrent Ebola virus disease outbreaks in the Democratic Republic of the Congo and the potential risk of importation into Kenya, this study develops a deterministic Susceptible–Exposed–Infectious–Vaccinated–Recovered–Waned Immunity (SEIVRW) model for preparedness and intervention assessment. The framework incorporates vaccination, temporary immunity, disease progression, recovery, disease-induced mortality, waning immunity, and reinfection. The model is formulated as a theoretical decision-support framework because Kenya has not reported confirmed local Ebola transmission and Kenya-specific outbreak data are therefore unavailable for calibration. Its mathematical properties are examined through analyses of positivity, boundedness, disease-free and endemic equilibria, the control reproduction number, and local and global stability. A forward bifurcation framework is also used to characterise the threshold behaviour of the system. The analysis indicates that vaccination and the persistence of acquired immunity are central determinants of the model’s transmission threshold. The disease-free equilibrium is stable when the control reproduction number remains below unity, whereas an endemic equilibrium may exist when the threshold exceeds unity. The model is not intended to provide numerical forecasts; rather, it establishes an analytical basis for future parameter estimation, outbreak assessment, and evaluation of surveillance, vaccination, isolation, contact tracing, and border-health measures when relevant epidemiological data become available.

Monotonic Properties of Nonoscillatory Solutions of Second-Order Linear Delay Difference Equations with Variable Coefficients

V. Karthick — 2026-07-18

This study examines the monotonic properties of nonoscillatory solutions of a second-order linear delay difference equation with positive variable coefficients and a fixed even delay. The analysis focuses on eventually positive solutions of degree zero, also referred to as Kneser-type solutions. By introducing suitable auxiliary sequences and applying repeated summation arguments, decreasing behaviour is established for a weighted transformation of the solution. This property yields estimates for delayed solution terms and leads to sufficient conditions under which degree-zero nonoscillatory solutions cannot exist. A further family of auxiliary sequences is then constructed to obtain a complementary monotonicity property for another weighted transformation. Combining the decreasing and increasing transformations produces an additional nonexistence criterion for Kneser-type solutions. Corollaries are derived from the principal estimates, including conditions expressed through bounds on the auxiliary sequences. Two examples involving constant coefficients are presented to demonstrate how the criteria can be evaluated for specific delay equations and to identify parameter ranges that exclude degree-zero nonoscillatory solutions. The results extend the qualitative analysis of second-order delay difference equations by providing refined monotonic estimates and related oscillation conditions within the stated assumptions. The approach is analytical and preserves the variable-coefficient framework while relying on positivity, convergence, and boundedness requirements imposed on the constructed sequences.

Analyzing Key Maternal Health Risk Indicators using a Multivariate Multiple Regression

Nku George Ekong — 2026-07-18

Assessment of maternal health risks is critical for detecting pregnancy-related complications and supporting timely clinical interventions. Maternal age and blood pressure are important risk factors that are frequently measured because of their association with adverse outcomes for mothers and infants. However, limited research has examined the effects of these risk factors on multiple maternal physiological parameters using a multivariate analytical approach. This study investigated the independent and combined influence of maternal age, systolic blood pressure and diastolic blood pressure on maternal heart rate and body temperature using multivariate multiple regression analysis. Data were obtained from a cross-sectional secondary dataset comprising 500 pregnant women who attended antenatal clinics at the University of Calabar Teaching Hospital, Nigeria, from 2020 to 2025. The independent variables were maternal age, systolic blood pressure and diastolic blood pressure, while heart rate and body temperature were the dependent variables. Before model estimation, the assumptions of linearity, multivariate normality and homoscedasticity were assessed. Statistical significance was tested at the 5% level. Maternal age and systolic blood pressure had significant effects on maternal heart rate, whereas diastolic blood pressure had no significant effect. No predictor had a significant effect on maternal body temperature. The multivariate analysis further indicated significant main and two-way interaction effects on the combined maternal physiological variables, but no significant three-way interaction effect. These findings support the application of multivariate multiple regression for the simultaneous analysis of maternal physiological outcomes and highlight the importance of jointly evaluating maternal age and blood pressure during antenatal assessment.

Research-Based AI Supports for Calculus Instruction: Bridging Teacher Preparation and Student Outcomes in U.S. STEM Pipelines

Emmanuel Nsadha — 2026-07-11

This narrative review synthesises 20 studies on artificial intelligence (AI)-supported calculus instruction, focusing on the relationship between teacher preparation and student outcomes within U.S. STEM pipelines. The evidence suggests that AI tools, including intelligent tutoring systems, generative chatbots, and adaptive platforms, may support student engagement and, under guided instructional conditions, conceptual understanding and problem-solving. However, the findings indicate that these benefits are conditional on teacher guidance, pedagogical alignment, and active student use. The literature remains fragmented: studies of AI tools rarely examine teacher preparation, while studies of teacher readiness seldom measure student calculus outcomes. This review integrates these strands and proposes a cross-level framework linking AI design, teacher preparation, instructional implementation, and student achievement. It also identifies major gaps, including the predominance of small-scale studies, limited longitudinal evidence, limited attention to equity, and the absence of direct research on U.S. STEM pipeline outcomes. The proposed framework offers practical guidance for teacher preparation programmes and institutional policies. It suggests that professional development should focus on helping teachers interpret AI-generated feedback, design effective prompts, and align AI tools with conceptual learning goals. These findings imply that AI-supported calculus instruction should be treated as a coordinated instructional system rather than a technology add-on if it is to contribute meaningfully to the U.S. STEM pipeline.