- P-ISSN3059-0604
- E-ISSN3059-1309
- KCI
ISSN : 3059-0604
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Vol.32 No.4
Abstract
Analogical reasoning has been utilized in the extension of mathematical thinking and problem solving. In this study, by using conceptual analogy, we conjectured identities in the generalized Pell sequence corresponding to those in Heo([9])’s generalized Fibonacci sequence, and by using methodological analogy, we proved that the conjectured identities hold. Furthermore, we conjectured identities in certain forms of second-order linear recurrence sequences and proved their validity. This study expands identities from generalized Fibonacci sequences to those of certain second-order linear recurrence sequences by employing conceptual and methodological analogy.
Abstract
This work extends the distance–product idea, traditionally assuming all real roots, to real-coefficient polynomials with one real root and one complex–conjugate pair. For cubics, introducing the tangent line to the function at the real root shows a systematic link between the contact point and slope and the real and imaginary parts of the complex roots. The same principle generalizes to quartics and higher degrees via contact polynomials tailored to the degree, preserving a common structure. The framework simplifies definite integrals in the presence of nonreal roots by reducing them to linear combinations of standard polynomial terms.
Abstract
This study proposed a method for applying Deductive Problem Making (DPM) to past College Scholastic Ability Test (CSAT) mathematics questions. Three questions related to function graphs were selected, and new problems were created through DPM. The newly generated problems were compared with the original ones to identify altered and maintained aspects, and their interrelationships were also examined. The findings confirm the possibility of expanding initial problem substructures and indicate that DPM facilitates a deeper understanding of given problems, thereby contributing to the enhancement of problem-solving skills.
Abstract
Hermite-Hadamard type inequalities are among the most well-known integral inequalities in mathematics. In this article, we have established several results concerning fractional Hermite-Hadamard type inequalities for twice differentiable (s,m)-convex functions of both the 1st and 2nd kinds. These findings offer a broader generalization compared to the results presented in [9].
Abstract
F-index of a graph is the sum of the cube of the degrees of the vertices. Thus, for a graph G with vertex set V(G) and edge set E(G), the degree based topological index F-index is defined as $$F(G)=\sum\limits_{v\in V(G)}{{{d}_{G}}{{(v)}^{3}}}=\sum\limits_{uv\in E(G)}{[{{d}_{G}}{{(u)}^{2}}+{{d}_{G}}{{(v)}^{2}}]},$$ where dG(v) denotes the degree of the vertex v. In this paper, we investigate the F-indices of unicyclic graphs by introducing some transformation, and characterize the unicyclic graphs with the first five largest F-indices and the unicyclic graphs with the first two smallest F-indices, respectively.