scholarly journals Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Saleh Alshammari ◽  
Mohammed Al-Smadi ◽  
Mohammad Al Shammari ◽  
Ishak Hashim ◽  
Mohd Almie Alias
Keyword(s):  
Error Function ◽  
High Accuracy ◽  
Residual Error ◽  
Numerical Comparison ◽  
Analytical Treatment ◽  
Suggested Approach ◽  
Error Functions ◽  
Logistic Equations ◽  
Computational Effect ◽  
Solution Methodology

In this article, an analytical reliable treatment based on the concept of residual error functions is employed to address the series solution of the differential logistic system in the fractional sense. The proposed technique is a combination of the generalized Taylor series and minimizing the residual error function. The solution methodology depends on the generation of a fractional expansion in an effective convergence formula, as well as on the optimization of truncated errors, Resqjt, through the use of repeated Caputo derivatives without any restrictive assumptions of system nature. To achieve this, some logistic patterns are tested to demonstrate the reliability and applicability of the suggested approach. Numerical comparison depicts that the proposed technique has high accuracy and less computational effect and is more efficient.

scholarly journals Searching for optimum adsorption curve for metal sorption on soils: comparison of various isotherm models fitted by different error functions

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Péter Sipos
Keyword(s):  
Experimental Data ◽  
Error Function ◽  
Isotherm Models ◽  
Metal Sorption ◽  
Error Functions ◽  
Sorption System ◽  
Geochemical Properties ◽  
Function Combination ◽  
Soil Metal ◽  
Sorption Curve

AbstractStudies comparing numerous sorption curve models and different error functions are lacking completely for soil-metal adsorption systems. We aimed to fill this gap by studying several isotherm models and error functions on soil-metal systems with different sorption curve types. The combination of fifteen sorption curve models and seven error functions were studied for Cd, Cu, Pb, and Zn in competitive systems in four soils with different geochemical properties. Statistical calculations were carried out to compare the results of the minimizing procedures and the fit of the sorption curve models. Although different sorption models and error functions may provide some variation in fitting the models to the experimental data, these differences are mostly not significant statistically. Several sorption models showed very good performances (Brouers-Sotolongo, Sips, Hill, Langmuir-Freundlich) for varying sorption curve types in the studied soil-metal systems, and further models can be suggested for certain sorption curve types. The ERRSQ error function exhibited the lowest error distribution between the experimental data and predicted sorption curves for almost each studied cases. Consequently, their combined use could be suggested for the study of metal sorption in the studied soils. Besides testing more than one sorption isotherm model and error function combination, evaluating the shape of the sorption curve and excluding non-adsorption processes could be advised for reliable data evaluation in soil-metal sorption system.

An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

2020 ◽  
Vol 70 (3) ◽  
pp. 599-604
Author(s):  
Şahsene Altinkaya
Keyword(s):  
Error Function ◽  
Trigonometric Polynomials ◽  
Error Functions ◽  
The Family ◽  
Coefficient Inequalities

AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined by$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

scholarly journals Some Discussions about the Error Functions on SO(3) and SE(3) for the Guidance of a UAV Using the Screw Algebra Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Error Function ◽  
Elliptic Cylinder ◽  
General Situation ◽  
3 Dimensional ◽  
Error Functions ◽  
Aerial Vehicle ◽  
Algebra Theory ◽  
In The Beginning

In this paper a new error function designed on 3-dimensional special Euclidean group SE(3) is proposed for the guidance of a UAV (Unmanned Aerial Vehicle). In the beginning, a detailed 6-DOF (Degree of Freedom) aircraft model is formulated including 12 nonlinear differential equations. Secondly the definitions of the adjoint representations are presented to establish the relationships of the Lie groups SO(3) and SE(3) and their Lie algebras so(3) and se(3). After that the general situation of the differential equations with matrices belonging to SO(3) and SE(3) is presented. According to these equations the features of the error function on SO(3) are discussed. Then an error function on SE(3) is devised which creates a new way of error functions constructing. In the simulation a trajectory tracking example is given with a target trajectory being a curve of elliptic cylinder helix. The result shows that a better tracking performance is obtained with the new devised error function.

scholarly journals CVaR Regression Based on the Relation between CVaR and Mixed-Quantile Quadrangles

2019 ◽  
Vol 12 (3) ◽  
pp. 107 ◽  
Author(s):  
Golodnikov ◽  
Kuzmenko ◽  
Uryasev
Keyword(s):  
Linear Regression ◽  
Value At Risk ◽  
Risk Measure ◽  
Error Function ◽  
Decomposition Theorem ◽  
Discrete Distributions ◽  
Conditional Value At Risk ◽  
Suggested Approach ◽  
Risk Functions

A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications. The research presented involved developing algorithms for the implementation of linear regression for estimating CVaR as a function of some factors. Such regression is called CVaR (superquantile) regression. The main statement of this paper is: CVaR linear regression can be reduced to minimizing the Rockafellar error function with linear programming. The theoretical basis for the analysis is established with the quadrangle theory of risk functions. We derived relationships between elements of CVaR quadrangle and mixed-quantile quadrangle for discrete distributions with equally probable atoms. The deviation in the CVaR quadrangle is an integral. We present two equivalent variants of discretization of this integral, which resulted in two sets of parameters for the mixed-quantile quadrangle. For the first set of parameters, the minimization of error from the CVaR quadrangle is equivalent to the minimization of the Rockafellar error from the mixed-quantile quadrangle. Alternatively, a two-stage procedure based on the decomposition theorem can be used for CVaR linear regression with both sets of parameters. This procedure is valid because the deviation in the mixed-quantile quadrangle (called mixed CVaR deviation) coincides with the deviation in the CVaR quadrangle for both sets of parameters. We illustrated theoretical results with a case study demonstrating the numerical efficiency of the suggested approach. The case study codes, data, and results are posted on the website. The case study was done with the Portfolio Safeguard (PSG) optimization package, which has precoded risk, deviation, and error functions for the considered quadrangles.

Fekete Szegö theorem for a close-to-convex error function

2019 ◽  
Vol 69 (2) ◽  
pp. 391-398
Author(s):  
C. Ramachandran ◽  
D. Kavitha ◽  
Wasim Ul-Haq
Keyword(s):  
Error Function ◽  
Error Functions ◽  
Sharp Estimates

Abstract By motivating the result of Ramachandran et al. [Certain results on q-starlike and q-convex error functions, Math. Slovaca, 68(2) (2018), 361–368], in this present investigation we derive the classical Fekete Szegö theorem for a close-to-convex error function of order β and the sharp estimates also obtained for real μ.

"An Overview of Using Error function in Adsorption Isotherm Modeling "

2020 ◽  
Vol 8 (1) ◽  
pp. 22-30
Author(s):  
Hawraa K. Hami ◽  
Ruba F. Abbas ◽  
Amel S. Mahdi ◽  
Asma A. Maryoosh
Keyword(s):  
Adsorption Equilibrium ◽  
Error Function ◽  
Common Error ◽  
Analysis And Design ◽  
Error Functions ◽  
The Past ◽  
Adsorption Data ◽  
Best Fitting ◽  
Definition Of ◽  
The Right

"Over the past years, a large number of statistical expressions used as a measure of accuracy, collectively referred to as error functions. These functions use to determine the best fitting data. Since accurate adsorption equilibrium information are necessary for the analysis and design of adsorption, error functions are used to valuation the validity of the adsorption mathematical models with experimental results by finding the most appropriate isotherm. Therefore, this overall review provides a definition of a number of common error function and explains the use of these functions in determine optimal adsorption data and chose the right isotherm.

scholarly journals New handy and accurate approximation for the Gaussian integrals with applications to science and engineering

2019 ◽  
Vol 17 (1) ◽  
pp. 1774-1793 ◽  
Author(s):  
Mario A. Sandoval-Hernandez ◽  
Hector Vazquez-Leal ◽  
Uriel Filobello-Nino ◽  
Luis Hernandez-Martinez
Keyword(s):  
Distribution Function ◽  
Power Series ◽  
Cumulative Distribution Function ◽  
Error Function ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Cumulative Distribution ◽  
Accurate Approximation ◽  
Science And Engineering ◽  
Gaussian Integral

Abstract In this work, we propose to approximate the Gaussian integral, the error function and the cumulative distribution function by using the power series extender method (PSEM). The approximations proposed in this paper present a high accuracy for the complete domain [–∞,∞]. Furthermore, the approximations are handy and easy computable, avoiding the application of special numerical algorithms. In order to show its high accuracy, three case studies are presented with applications to science and engineering.

The Dynamically Loaded Circular Beam on an Elastic Foundation

1980 ◽  
Vol 47 (1) ◽  
pp. 139-144 ◽  
Author(s):  
D. E. Panayotounakos ◽  
P. S. Theocaris
Keyword(s):  
Elastic Foundation ◽  
Discrete System ◽  
Natural Frequencies ◽  
Continuous System ◽  
Rotatory Inertia ◽  
Analytical Treatment ◽  
Linear Partial Differential Equations ◽  
Circular Beam ◽  
Solution Methodology

In this investigation an analytical treatment for the determination of the natural frequencies of a circular uniform beam on an elastic foundation, subjected to harmonic loads, is presented. This problem in the most general case of response is reduced to a system of six-coupled linear partial differential equations. The effects of rotatory inertia and transverse shear deformation are also included in the analysis. The problem is treated by considering the beam as a continuous system, as well as a discrete system. The aforementioned solution methodology is successfully demonstrated through several numerical examples.

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