Maplesoft is a technical computation forms which is a heart of problem solving in mathematics especially in graph theory. Maplesoft has established itself as the computer algebra system for researchers. Maplesoft has more mathematical algorithms which is covering a wide range of applications. A new family ( ) of 6-bridge graph still not completely solved for chromatic number, chromatic polynomial and chromaticity. In this paper we apply maplesoft on a kind of 6-bridge graph ( ) to obtain chromatic number, chromatic polynomial and chromaticity. The computations are shown that graph contents 3 different colours for all vertices, 112410 different ways to colour a graph such that any two adjacent vertices have different colour by using 3 dif

Adsorption and ion exchange are examples of fixed-bed sorption processes that show transient behavior. This means that differential equations are needed to design them. As a result, numerical methods are commonly utilized to solve these equations. The solution frequently used in analytical methods is called the Thomas solution. Thomas gave a complete solution that adds a nonlinear equilibrium relationship that depends on second-order reaction kinetics. A computational approach was devised to solve the Thomas model. The Thomas model's validity was established by conducting three distinct sets of experiments. The first entails the adsorption of acetic acid from the air through the utilization of activated carbon. Following

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.

In this paper, we will show that the Modified SP iteration can be used to approximate fixed point of contraction mappings under certain condition. Also, we show that this iteration method is faster than Mann, Ishikawa, Noor, SP, CR, Karahan iteration methods. Furthermore, by using the same condition, we shown that the Picard S- iteration method converges faster than Modified SP iteration and hence also faster than all Mann, Ishikawa, Noor, SP, CR, Karahan iteration methods. Finally, a data dependence result is proven for fixed point of contraction mappings with the help of the Modified SP iteration process.

The paper aims at initiating and exploring the concept of extended metric known as the Strong Altering JS-metric, a stronger version of the Altering JS-metric. The interrelation of Strong Altering JS-metric with the b-metric and dislocated metric has been analyzed and some examples have been provided. Certain theorems on fixed points for expansive self-mappings in the setting of complete Strong Altering JS-metric space have also been discussed.

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.

The control of an aerial flexible joint robot (FJR) manipulator system with underactuation is a difficult task due to unavoidable factors, including, coupling, underactuation, nonlinearities, unmodeled uncertainties, and unpredictable external disturbances. To mitigate those issues, a new robust fixed-time sliding mode control (FxTSMC) is proposed by using a fixed-time sliding mode observer (FxTSMO) for the trajectory tracking problem of the FJR attached to the drones system. First, the underactuated FJR is comprehensively modeled and converted to a canonical model by employing two state transformations for ease of the control design. Then, based on the availability of the measured states, a cascaded FxTSMO (CFxTSMO) is constructed to estim

The demand for electronic -passport photo ( frontal facial) images has grown rapidly. It now extends to Electronic Government (E-Gov) applications such as social benefits driver's license, e-passport, and e-visa . With the COVID 19 (coronavirus disease ), facial (formal) images are becoming more widely used and spreading quickly, and are being used to verify an individual's identity, but unfortunately that comes with insignificant details of constant background which leads to huge byte consumption that affects storage space and transmission, where the optimal solution that aims to curtail data size using compression techniques that based on exploiting image redundancy(s) efficiently.