JOURNAL OF ADVANCES IN MATHEMATICS

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

Miloš Čojanović — Tue, 04 Feb 2025 00:00:00 +0000

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.

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

Ting Li, Bingjun li — Fri, 28 Mar 2025 00:00:00 +0000

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.

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

Wafaa Hadi Abdul Suhib I — Sat, 14 Jun 2025 00:00:00 +0000

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.