Asian Research Journal of Mathematics

Analysis of Errors Related to the Concept of Derivative among 3rd-year Science Students in Goma, DR Congo

Gratien KOPI MBONYE — 2025-10-25

Learning the concept of derivatives often poses difficulties for secondary school students. This study analyzes the errors produced by 3rd year science students (3rd HTS) from a school in Goma (DR Congo) during three assignments on the derivability and calculation of derivatives. 37 copies from two classes (3rd Scientific A: 20; 3rd Scientific B: 17) were analyzed. An a priori analysis of the statements was carried out in order to anticipate potential difficulties. The error analysis is based on Charnay 's typology (1989). Error coding was carried out by two independent raters and inter-rater reliability was assessed by Cohen's kappa coefficient (K = 37). The observed errors are mainly divided into: (i) errors related to the lack of mastery of the formal definition of the derivative, (ii) errors in algebraic calculation (manipulation of radicals and simplifications), (iii) difficulties related to absolute value and left/right differentiability. The analyses show that the statements, although not ambiguous, push some students towards heavy strategies (systematic passage through the definition instead of applying a simpler rule). The results suggest that many of the observed errors are more attributable to pedagogical inadequacies and previous shortcomings than to a lack of student effort. We recommend targeted teacher training actions and didactic sequences focused on mastering algebraic knowledge and common differentiation procedures.

Positive Periodic Solutions to Lie´nard Equation with Indefinite Weights

Ruina Zhao — 2025-10-27

The Liénard equation is not only of significant theoretical interest but also plays a fundamental role in physical modeling. In particular, Liénard equations with indefinite weights introduce additional complexities that render their analysis more challenging. This paper establishes sufficient conditions for the existence of positive periodic solutions to a class of generalized Liénard equations with sign-changing coefficients. Our approach is primarily based on the Krasnoselskii’s-Guo fixed point theorem, combined with the positivity properties of the associated Green function.

Compactness Properties of Pseudo-differential Operators Related with the Coupled Fractional Fourier Transform

Abhisekh Shekhar — 2025-10-31

In this paper, we introduce the characterization of compactness of the coupled fractional Fourier transform (CFrFT). Few results on compactness of pseudo-differential operators (P.D.O) connected with CFrFT are investigated.

Stability of Additive and a Generalized Quadratic Functional Equations in Banach Spaces

Bhavin Mansukhlal Patel — 2025-11-01

In this research article, we investigate the Hyers-Ulam stability of additive and generalized quadratic type

functional equation

f(x + ay) + af(x − y) = f(x − ay) + af(x + y)

for a ∈ Z \ {−1, 0, 1} and x, y ∈ X × X, where f : X × X → Y , (X, ∥·, ·∥) is a 2-normed space and (Y, ∥ · ∥) is a Banach space.