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

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

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

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

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

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

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

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

Application Of Multipoint Secant-Type Method ForFinding Roots 0f Nonlinear Equations

In this paper, we introduce a family of pk-order iterative schemes for finding the simple root of a nonlinear algebraic equation of the function fx=0 by using the divided difference approximation. The proposed method uses one evaluation of the function per iteration and can achieve convergence order pk. The error equation and asymptotic convergence constant are proved theoretically and numerically. Numerical examples are included to demonstrate the exceptional convergence speed of the proposed method and thus verify the theoretical result

REVIEW OF WπGR CLOSED SETS IN TOPOLOGICAL SPACES

In this paper we introduce a new class of sets called weakly π generalized regular closed (wπgr closed) sets. A subset A of X is called wπgr closed set if cl( int A) ⊆U whenever A⊆U and U is πgr open in X. The complement of wπgr-closed set is called wπgr-open set in X. We denote the family of all wπgr closed sets in X by wπGRC(X)  and wπgr open sets in X by wπGRO(X)

Optimal ordering quantity by retailer from supplier with transportation cost in a supply chain

Successful retailer-supplier collaborative relationship enhance profitability in the delivery of products or services to customers in a supply and can help alleviate pressures along all key points in the supply system. A strong alliance can bring products to market faster; reduce production and logistics costs, drive market shares, and increase sales, while maximizing profit for both partners. The success of fast-moving consumer goods from the suppliers has a direct relationship with the performance of the leading retailers, which are their main channel of distribution. The objective of this study was to establish a profit model between a single supplier and multiple supply chain collaboration that will enhance response to customer requirements. We considered the costs for various parties and use a referenced simplified framework model to obtain joint optimal pair for the outcome of coordination between the retailer and supplier. Our results showed that the value of the annual cost, with the same optimal ordering quantity, is higher when the retailer incurs transportation cost than when the supplier incurs transportation cost. This study revealed that the supplier will minimize cost when incurring transportation charges and maximize profit

Significant Effect Of Amended Soil On Microbial Flora Of Soil And Plant Growth In Comparison With Natural Low Nutritive Soil

Soil chemical properties, such as Carbon and Nitrogen levels, are crucial for fulfilling the basic needs of plants. The presence of secondary and tertiary nutrients plays a vital role in constructing soil structure, influencing the survival of normal microbial flora, seeds, and later plant growth. The use of chemical fertilizers addresses nutritional deficiencies, but reports indicate that only 40% is utilized by plants, leading to soil issues like salinity and drought logging. When soil lacks essential nutrients, external amendments are necessary, impacting plant growth and crop yield by enhancing normal microbial flora i.e. Plant growth-promoting rhizobacteria (PGPRs). Recognizing the significance of both chemical nutrients and physical properties for healthy plant growth, a soil amendment called "Fertisol soil" was developed. This involved adding basic and secondary nutrients to the soil. The amended soil underwent analytical characterization and was compared with natural soil through chemical analysis and microbial growth assessments. Comparative studies using the amended soil showed improved plant growth and flowering capacity compared to control plants in terms of height and flowering. This highlights the positive impact of balanced nutrient amendments on soil health and overall plant performance

Using Activated carbon of Date Seeds for the Removal of Methyl Red from aqueous Solutions

In this study, the activated carbon that was obtained from date seeds, after heating at 500 ºC, was used to remove methyl red dye from its aqueous solutions. Different parameters were applied including (the effect of dose, the effect of adsorption time, and the effect of pH value). The extent of dye removal increased with increasing adsorption time. An acidic pH is optimal for enhancing dye adsorption. The Langmuir isotherm was applied to the data obtained, and its constants were calculated at the optimum conditions. According to Langmuir isotherm, the monolayer saturation capacity (q m ) is 0.9 mg/g. The study concludedthat date seeds activated carbon (DSAC) has demonstrated effective adsorption results in removing methyl red and suggests its potential for use in other adsorption studies

Some new results for αβ-statistical convergence through difference compact operator of fuzzy 2- normed spaces

The research aims to provide advanced compact for order αβ-converge of statistic in the normed spaces of fuzzy-2 and introduce universal the  spaces̕ s