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, Eric Justice Eduboah, Noureddine Ouerfelli — Thu, 25 Jun 2026 00:00:00 +0000

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 — Fri, 26 Jun 2026 00:00:00 +0000

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, Abhishek Kumar Chaurasiya, Praveen Kumar Sherawat — Tue, 30 Jun 2026 00:00:00 +0000

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 — Wed, 01 Jul 2026 00:00:00 +0000

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, Arun Kumar — Wed, 01 Jul 2026 00:00:00 +0000

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.