Journal of Mathematics Research, Issue: Vol.17, No.5

On the Cordial of Weak Labeling of an l-fold Cycle Graph, T_l(C_n)

Wed, 17 Dec 2025 13:59:20 +0000

We investigate a number-theoretic graph labeling known as k-prime cordial labeling, where each vertex of a graph G is assigned a label from the set {1,2, ... , k}, and each edge receives a label equal to the greatest common divisor of its endpoint labels. A weak labeling is k-prime cordial if the number of vertices labeled with each integer differs by at most two, and the number of edges labeled 1 differs from those not labeled 1 by at most two. In this paper, we introduce the concept of the $\ell$-fold of a graph, denoted T_l(G), constructed by joining corresponding vertices across l copies of a base graph G. We focus on the case where G is a cycle graph C_n and show that T_l(C_n) admits a 4-prime cordial weak labeling for all l≥2. This result extends previous work on trigraphs and contributes to the broader understanding of cordial labeling in replicated graph structures.

A B-spline Finite Element Method for Structural Damping Beam Vibration Problem

Tue, 30 Dec 2025 16:46:25 +0000

Beam structures are widely applied in civil engineering, mechanical engineering, and architectural design. The beam vibration equation with damping terms can better describe the specific properties of beams. In this paper, the cubic B-spline finite element method is used to solve the vibration problems of damping beams with a firmly supported edge at both ends, a simply supported edge at both ends, and a firmly supported edge at the left end and a simply supported edge at the right end. Moreover, the treatment methods of B-spline basis functions in the finite element space when solving problems under different boundary conditions are presented. By discretizing both the first and second time derivatives via the central difference scheme, the fully discrete scheme is derived, and a detailed analysis of the error estimation is conducted. Finally, the effectiveness of this method is verified through numerical examples, and the theoretical results are tested.

Running Without Progress: How Game Theory Explains China’s GAOKAO Treadmill

Tue, 30 Dec 2025 16:28:41 +0000

The intense competition in Chinese education has led to several problems in both family and society. To understand the process of how the intense competition appears, past researchers are showcasing the long history of Chinese Keju or using qualitative analysis to present the diverse influence of high involution. Here, I apply the quantitative analysis: Game Theory Model to give a novel lens to explain the situation. Particularly, I use signaling games for a macro perspective and prisoners' dilemma as the micro angle. To conclude, I find ways to break the intense competition by the analysis using Game theory. Overall, I suggest that the government should raise cost for extra studying to weaken the short-run incentive to betray; increase the discounted factor and reduce short term benefit differential to emphasize trust in cooperation; introduce holistic evaluation to deflate the signal so no students gains from overly investment and input.

Existence of Solutions of a Periodic Problem With a Function Φ Continuous on Dom(φ) ⊂ R

Tue, 30 Dec 2025 16:45:10 +0000

We study the existence of solutions of equation \[(\phi(w'(\tau)))'= f(\tau,w(\tau),w'(\tau)),\quad \tau\in [0,\ell]\] submitted to periodic boundary conditions on $[0,\ell]$. Where $f:[0,\ell]\time \mathbb{R}^{2}\rightarrow \mathbb{R}$ is a continuous function and $\phi:Dom(\phi)\subset\mathbb{R}\rightarrow \mathbb{R}$ is considered as a continuous function on $Dom(\phi)\subse \mathbb{R}$ and strictly increasing on $[a,b]\subset Dom(\phi)$ with $0\in[a,b]$ and $a

A Model of Phenotypes of Ontogenetic Growth in Animals and Its Translation into Modelling Growth of Humans

Tue, 30 Dec 2025 16:45:59 +0000

The problem that this study deals with is ontogenetic growth of humans and animals. The novelty of this research is an approach to the problem how to recognise growth phenotypes in animals. The aim of this research was to analyse an analytical model of ontogenetic growth of animals with intention to recognise growth phenotypes. In this study we discuss possibility to extend results to the modelling of growth phenotypes in humans. In this study we not only analysed the model of animal growth but also offer an insight into the option to apply some methods known in mathematical physics and applied mathematics. In this research we concentrate on the modelling of growth of pigs. Pigs are known as a good model animal of humans in many aspects, including growth, obesity, digestion, and some others. In this model two aspects of ontogenetic growth were considered; the intention was to advance the biological understanding of the growth process.

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 17, No. 5

Tue, 30 Dec 2025 16:48:08 +0000

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 17, No. 5