JOURNAL OF ADVANCES IN MATHEMATICS

Solving cubic and quartic equations by means of Vieta's formulas

Miloš Čojanović — 2025-02-04

In this paper, we will prove that with the use of Vieta's formulas, it is possible to apply a unified method in solving equations of the third and fourth degree.

Exact Solutions and Stability Analysis of Pulse-Front Pairs in Coupled Complex Ginzburg–Landau Equations

Tat Leung YEE — 2025-07-22

This work introduces new exact solutions demonstrating how localized pulses and fronts can coexist in coupled complex
Ginzburg–Landau systems. Using a novel analytical method, we establish conditions for the stability and phase-locking
of these structures, revealing relationships between amplitude, wave-number, and dispersion effects. In practical optical
setups like dual-core fibers, these solutions can produce stable wave patterns that transfer energy efficiently. Our
approach addresses existing difficulties in analyzing complex dissipative systems and enhances understanding of their
wave interactions.

Ordering Unicyclic Graphs with a Fixed Girth by p-Sombor Indices

Ting Li — 2025-03-28

The p-Sombor index of a graphs G is deffned as, SOp(G) = X xy∈E(G) (d p (x) + d p (y)) 1 p , where d(x) represents the degree of vertex x in graph G. Our focus centers on exploring the p-Sombor index of unicyclic graphs, speciffcally addressing graphs with a predetermined girth. We determine the ffrst four smallest p-Sombor index and identifying the corresponding graphs that achieve these extremes.

Application of Metaheuristics for Facility Location Optimization

Albina Basholli — 2025-10-24

Facility location problems are a fundamental component of supply chain optimization, particularly in agriculture, where collection centers must be strategically positioned to minimize transportation costs and improve accessibility for producers. Traditional mathematical programming techniques are suitable for small-scale problems but become computationally expensive as the problem size increases. To overcome these limitations, this study applies metaheuristic approaches, specifically Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), to determine the optimal siting of agricultural collection centers in Elbasan, Albania. The case study considers thirteen administrative areas with annual production volumes used as demand weights, while distances are calculated using geographic coordinates. The proposed algorithms aim to minimize the weighted travel distance between farmers and assigned collection facilities. Results show that both GA and PSO successfully identify near-optimal solutions with significantly reduced total transportation costs compared to single-facility baselines.

Controlling Chaos in the Lozi Map Using Hidden Variables: A Novel Approach for Stability Enhancement

Wafaa Hadi Abdul Suhib I — 2025-06-14

In this paper, we provide a novel 3D system that demonstrates the existence of a hidden attractor. Although equilibrium points are present in the system, this hidden attractor cannot be found by examining equilibrium points or their surroundings, in contrast to self-excited attractors. Differential equation theory explains this behavior by showing that the system has intricate dynamics that are not directly dependent on equilibrium points. We added a hidden variable to the system to make it more complex and improve its stability by adding the following equation to the original system: zn+1=wzn+r3xn, where the hidden variable interacts with the original system through control parameters r1, r2, and r3, increasing chaos or improving the system stability. where it appeared us more complex dynamic behaviors.