Novel Research Aspects in Mathematical and Computer Science Vol. 6

Utility of Exponential Diophantine Equation \(3^x + b^y = c^z\)

S. P. Behera — 2022-07-21

At the current time, we use the Diophantine equation for any polynomial equation with integer coefficients and associated unknowns are taken to be rational integers. This definition is commonly extended to any variety of equations involving integers and where the unknowns are integers. An emblematic example is Fermat's equation xⁿ + bⁿ= cⁿ, where x, b, c and n > 3 are unknown positive integers. We regularly use the terminology “exponential Diophantine equation” when one or more exponents are unknown.
Now consider that for b and c are be a positive integer with fixed coprime here min c} > 1.In this research article, every positive number solution (x, y, z) of the equation \(3^x + b^y = c^z\) is classified in this section.
Further, we have to prove that, if c = b+ 3, In that case, the equation contains only positive integer solutions i.e (x, y, z) = (3, 2, 2), except for (b, x, y, z) = (3, 3, 2, 2) and (3^r -1, r + 3, 3, 3), Here r is a positive integer number of r \( \geq\) 3 by an elementary approach.

Influence of Flexible Alternating Current Transmission System on Transient Stability of Power Systems Using MATLAB CODE and Power World Simulator

Aissa Souli — 2022-07-21

The goal of this work is to investigate how FACTS affects the transient stability of power systems utilising the Power World Simulator software and the MATLAB-created transient stability code, or "TRANS STAB CODE." We made an effort to describe transient stability in the work's introduction, including its definition, criteria, and equations. Next, we provided a general review of FACTS modelling in power systems, including its definition, different types, schemes, and equations. Then, we provided an example using the UPFC (Unified Power Flow Controller) model. Second, we reviewed the MATLAB code called "TRANS STAB CODE" by describing its structure using graphics windows. After that, I described privately the Power World Simulator simulation software. The test electrical network was then shown, together with the results of this network's transient stability as measured by Power World Simulator and the code "TRANS STAB CODE" for both the presence and absence of flexible alternating current transmission systems. We concluded our work by analysing the outcomes of both programmes in both scenarios—with and without Flexible Alternating Current Transmission System.

A Guide on Strategies for Volatility Trading: A Conceptual Overview

Luisa Tibiletti — 2022-07-21

This document addresses volatility trading for investors seeking excess returns by shorting derivatives during periods of stability. Firstly, we introduce the notion of historical and implied volatility. Secondly, we discuss the use of the S&P 500-based CBOE VIX index, the leading benchmark index to measure the market’s expectation of future volatility. CBOE VIX is also known as the "fear gauge index", because it tends to rise in bearish stock market environments and to fall or remain steady during bullish ones. Next, we discuss the most popular trading strategies based on options, variance swaps and futures. Empirical studies complement the conceptual debate.

The Non-parametric Regression Methods in Sequence Data Study

Autcha Araveeporn — 2022-07-21

The regression analysis is the statistical methodology for creating related functions among response variables and explanatory variables for estimating response variables given explanatory variables. However, sometimes two variables may not be the regression analysis's assumption. The non-parametric regression method is proposed to avoid this problem. The estimating parameters construct the smoothing curve with the data or called the smoothing method in the form of non-linear relationship data. This research aims to study and compare the efficiency of six non-parametric regression methods for sequence data: kernel smoothing, smoothing spline, natural cubic spline, B-spline, penalized spline, and trend filtering methods. The efficiency of the non-parametric regression method determines by the lowest average mean squared error. The smoothing parameter is used to control the smoothing performance of the curves by using the cross-validation method and defining the number of knots for fitting the curve on the closet data. The response variable character is simulated in trend, non-linear, and cycle data, where the explanatory variable is defined as the sequence data. The R program sets the sample sizes as 50, 100, 150, and 200 and repeats 500 times in each situation, while the standard deviation of error is 1, 3, and 5. The results were founded that the natural cubic spline method played the lowest average mean squared error in all cases. When the data character was considered, the cycle data had the lowest mean squared error in all sample sizes. It can be concluded that the natural cubic spline method was the performance method for sequence data.

Secured Communication using Distributed Caching Techniques

D. Bhuvana Suganthi — 2022-07-21

In Mobile Communication due to unstable connections, lack of flexibility and failure communication in transmission rate. Initially, the reliable path is calculated based on estimated link quality, energy, and delay towards the destination node. Due to the mobility of nodes present in the mobile ad-hoc network, it becomes mandatory to consider the quality of the link. The Distributed Caching and Fault-tolerant Communication (DCFC) protocol is used to track routing tree failures and launch a failure recovery approach that can increase data transmission rates while minimising failures along the chosen reliable path. To combat packet drops and increased overhead brought on by security flaws, the Trusted Security Policy based Routing Algorithm (TSPRA) is used. This algorithm shows that data is well secured due to precise access control policies and raising the high secured data size. A proposed method conveys a Safe Alert Routing (SAR) protocol for an accident-free road through Hybrid Optimal Trust (HOT) technique. The SAR-HOT algorithm is compared with Privacy Preservation Authentication Secure Geographical Routing Protocol (PPASGR) develops effective results in the simulation part in terms of all parameters such as delay, energy, speed.

Combinatorial Problems on Algebraic Configured Graphs

N. Mohamed Rilwan — 2022-07-21

Zero divisor graph and unitary addition Cayley graph are the targeted algebraic networks. Our first objective is to allocate the frequencies to their every channel (nodes) at the same time reduce the consumption of their spectral domain, in this case upper frequency bound is denoted by \(\lambda\). Next, decycle the aimed networks in order to reconstruct as trees or forest which has the less proximity than others. Let \(\varphi\)(\(\Gamma\)UA(Rn)) denotes the decycling number of \(\Gamma\)UA(Rn) which is the cardinality of the smallest decycling set of the unitary addition Cayley graph \(\Gamma\)UA(Rn) and A(\(\Gamma\)UA(Rn); x) denotes the acyclic polynomial of \(\Gamma\)UA(Rn). In this chapter, we obtained the frequency bound by the distance labeling constraint which is defined based on the diameter of a graph. Here, \(\lambda\) 2;1(\(\Gamma\)Rp ) and \(\lambda\) 3;2;1(\(\Gamma\)Rp ) denotes the least upper frequency bounds of zero divisor graphs. Also we obtained the acyclic number bounds and we derived the acyclic polynomial with their roots.

\(\varrho\)J-Closed Sets in Topological Spaces

K. P. Vethavarna — 2022-07-21

In this chapter, a new class of sets \(\varrho\)J-closed sets is initiated in topological spaces. The properties and relationships with other g-closed sets are analysed. Some important characterizations are obtained.

Estimators for the Product of Two Population Means Using Auxiliary Attribute in the Presence of Non-response

Kamlesh Kumar — 2022-07-21

The problem of non-response generally occurs due to the lack of interest, not at home, refusal etc. Many authors developed estimators for estimation of population mean in the presence of nonresponse. Sometimes estimation of product of two population means in the presence of non-response is also needed. Keeping this fact in the view, some estimators for the product of two population means using auxiliary attribute in the presence of non-response have been suggested. The properties of the suggested estimators are also studied. A comparative study of the suggested estimators with the relevant estimators is given. Using a real data set, a numerical study is also given to check the efficiency of the proposed estimators in comparison to the relevant estimators. From numerical study it has been found that the proposed estimators work better that the other exiting estimators in some given conditions.

Local Dynamics of a Discrete-time Host-Parasitoid Model

Tahmineh Azizi — 2022-07-21

In this chapter,We investigate a non-dimensionalized Nicholson and Bailey discrete-time Host-Parasitoid model. For various parameter ranges, phase portraits are made to show the system's complex dynamics. With regard to intrinsic growth rate r and searching efficiency a, we perform the bifurcation analysis. We see a wide variety of complex dynamics, including chaos and periodic windows. Period- doubling bifurcations are used to build a path to chaotic dynamics. Conditions of occurrence of the period-doubling, Neimark-Sacker and saddle-node bifurcations are analyzed for b \(\neq\) a where a, b are searching efficiency. At this non-dimensionalize system, we investigate stable and unstable manifolds for various equilibrium points as well as the presence of various attractors. The host population behaves according to the Ricker model's dynamics in the absence of the parasitoid. We were able to better comprehend the dynamical behaviour of host-parasitoid interactions with intraspecific knowledge from the current work, which can be employed to enhance the traditional biological management of parasitoids.