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(R2074) A Comparative Study of Two Novel Analytical Methods for Solving Time-Fractional Coupled Boussinesq-Burger Equation
Full text linkIn this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. Furthermore, the VITM’s capacity to surmount challenges arising from the identification of the overarching Lagrange multiplier stands as an augmenting facet, amplifying its advantage over the NTDM technique
Fuzzy Software Reliability and Optimal Release Policy with Log-Logistic Testing Effort: An Analysis
Full text linkWe will discuss a Software Reliability Growth Model (SRGM) using fuzzy and imperfect debugging environments; we integrate Log-Logistic (LL) Testing Effort Function (TEF) into fuzzy SRGMs. Estimation methods, such as Least Square and Maximum Likelihood, are used to obtain the value of Testing-Effort and SRGMs parameters. It is not always possible and is constantly required to quantify the exact value of parameters. Due to human conduct, the value of Testing-Effort and SRGM parameters cannot be exactly quantified. In this scenario, parameters are supposed to be vague or fuzzy. To make the software consistent, the developer needs to propose some quantity of vagueness. Therefore, we propose a reliability growth model together with suspicions involved in parameters of SRGM under imperfect debugging using fuzzy theory. We calculate the entire cost of software development and reliability of proposed model using Triangular Fuzzy Number (TFN) for real data sets. Results obtained are compared with previous works from literature. It is shown the proposed SRGM with LL TEF give realistic extrapolation ability of software reliability and optimized entire software cost under fuzzy environment
Construction of Normal Polynomials using Composition of Polynomials over Finite Fields of Odd Characteristic
Full text linkA monic irreducible polynomial is known as a normal polynomial if its roots are linearly independent over Galois field. Normal polynomials over finite fields and their significance have been studied quite well. Normal polynomials have applications in different fields such as computer science, number theory, finite geometry, cryptography and coding theory. Several authors have given different algorithms for the construction of normal polynomials. In the present paper, we discuss the construction of the normal polynomials over finite fields of prime characteristic by using the method of composition of polynomials
(R2075) Truncated Saddlepoint Approximation for Testing Means of Right-Skewed Populations
Full text linkIn the examination of the mean parameter of the skewed distributions, testing methods often rely on the central limit theorem and data transformation. Notably, Johnson’s and Chen’s modified ttests offer reliable alternatives by incorporating additional sample moments. This work directs its attention towards the truncated saddlepoint (TS) approximation method, which effectively estimates the right-tail probability of right-skewed continuous distributions using a limited number of sample moments. The TS approximation is employed to derive the p-value in one-sample mean testing. To evaluate its performance, a Monte Carlo simulation study is conducted, comparing the TS approximation at four distinct truncation levels with the traditional t-test and its alternatives. The findings indicate that the fifth-order truncation and Chen’s method exhibit better performance for highly skewed distributions, particularly when the sample size is small. Furthermore, a numerical example is provided to illustrate the practical application of the TS approximation and its competitors
(R2083) A Multiobjective Optimization Model for Selecting Portfolios in Emerging Financial Markets under Uncertainty
Full text linkIn the issue of financial portfolio selection, especially in emerging financial markets, the investor usually intends to make the best possible choice based on several conflicting objectives, such as return, risk, and liquidity. To obtain a suitable portfolio using ideal values and the maximum possible deviations, we suggest fuzzy goal programming and its combination with satisfaction functions and expert opinions. The model can determine the best portfolio based on the opinions of financial market experts, taking into account uncertainties. This model formulates a multiobjective financial portfolio selection approach by considering fuzzy parameters obtained from emerging financial markets. In addition, the experiences of market experts are directly included in the model to obtain the satisfaction functions. Finally, the proposed model for portfolio selection in emerging financial markets is applied to the cryptocurrency market, and the final portfolio is selected with 86.95% satisfaction from all the objectives (return, risk and liquidity). Finally, the proposed model was compared with the basic model, and its better performance is clearly noticeable
(R2099) Boundedness and Square Integrability in Neutral Differential Equations with Delay and Exponential Stability in Nonlinear Differential Equations of Third-order
Full text linkThe Lyapunov second method is an eigenvalue-based technique which consist of finding a Lyapunov function candidate for studying the stability of dynamical systems which is hard to deal with especially in most of nonlinear cases. Studying the stability and some of other qualitative behaviors based on the Lyapunov second method is research topic of actuality because of the wide range of applications of the differential equations. Many authors in the literature have used the second method of Lyapunov in the study of some qualitative behaviors from which the stability, the boundedness and the square integrability of solutions for various kinds of differential equations that are different in terms of the order, the linearity, the autonomy, the delay or the neutral case. The present paper contains two main results. The first part is dedicated to establish sufficient conditions that guarantee the boundedness and the square integrability of solutions for a given third order neutral differential equation with delay. The second part of this work is devoted to the purpose of breaking the barrier of reaching exponential stability for some cases of the previous third order differential equation using the direct method of Lyapunov. In the end of the paper, a concrete example is given to illustrate the obtained results
(R2109) Characterizations of Tzitzeica Curves Using Conformable Frenet Frame
Full text linkThe aim of this study, the conditions for a conformable curve and its spherical indicator curves to be a Tzitzeica curve, will be examined. Thus, by understanding the behavior of the Tzitzeica curve, researchers can gain insight into complex systems and make more accurate predictions about their behavior
(R2096) PBIB-Designs Associated with Products of Graphs
Full text linkIn this paper we introduce a design, called “geodetic-design arising from geodetic sets in a graph. A geodetic-design, over a regular graph is an ordered pair D = (V, B), where V = V (G) and B, the set of all geodetic sets, called blocks, containing vertices belonging to geodetic sets, such that every pair of non-adjacent vertices appears in exactly µ blocks. We first find governing results of a geodetic-design, if it exists, and then get such PBIB-designs for different products of graphs. It is common to have geodetic sets of graphs to be independent sets, hence we extend the designs obtained from maximum independent sets of graphs to geodetic-designs for products of graphs