Some new rational approximations to the error function

1976 ◽  
Vol 10 (2) ◽  
pp. 475-478
Author(s):  
O. Ersoy
Keyword(s):  
Error Function ◽  
Rational Approximations

Ray Sequences of Best Rational Approximants For |x|α

1997 ◽  
Vol 49 (5) ◽  
pp. 1034-1065 ◽  
Author(s):  
E. B. Saff ◽  
H. Stahl
Keyword(s):  
Error Function ◽  
Extreme Points ◽  
Rational Approximations ◽  
Rational Approximants ◽  
Convergence Behavior ◽  
Distribution Of Poles ◽  
Poles And Zeros ◽  
Lower Triangle ◽  
Image Position ◽  
Best Rational Approximants

AbstractThe convergence behavior of best uniform rational approximations with numerator degree m and denominator degree n to the function |x|α, α > 0, on [-1, 1] is investigated. It is assumed that the indices (m, n) progress along a ray sequence in the lower triangle of the Walsh table, i.e. the sequence of indices {(m, n)} satisfiesIn addition to the convergence behavior, the asymptotic distribution of poles and zeros of the approximants and the distribution of the extreme points of the error function on [-1, 1] will be studied. The results will be compared with those for paradiagonal sequences (m = n + 2[α/2]) and for sequences of best polynomial approximants.

The Pricing Error Function

2008 ◽  
Author(s):  
Huntley Schaller ◽  
Lynda Khalaf
Keyword(s):  
Error Function ◽  
Pricing Error

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.

scholarly journals From Stress to Shape: Equilibrium of Cloister and Cross Vaults

2021 ◽  
Vol 11 (9) ◽  
pp. 3846
Author(s):  
Andrea Montanino ◽  
Carlo Olivieri ◽  
Giulio Zuccaro ◽  
Maurizio Angelillo
Keyword(s):  
Error Function ◽  
Membrane Surface ◽  
Equilibrium Analysis ◽  
Test Cases ◽  
Order Partial Differential Equation ◽  
Negative Semidefinite ◽  
Historical Heritage ◽  
Masonry Vaults ◽  
Membrane Shape ◽  
The Given

The assessment of the equilibrium and the safety of masonry vaults is of high relevance for the conservation and restoration of historical heritage. In the literature many approaches have been proposed for this tasks, starting from the 17th century. In this work we focus on the Membrane Equilibrium Analysis, developed under the Heyman’s theory of Limit Analysis. Within this theory, the equilibrium of a vault is assessed if it is possible to find at least one membrane surface, between the volume of the vaults, being in equilibrium under the given loads through a purely compressive stress field. The equilibrium of membranes is described by a second order partial differential equation, which is definitely elliptic only when a negative semidefinite stress is assigned, and the shape is the unknown of the problem. The proposed algorithm aims at finding membrane shapes, entirely comprised between the geometry of the vault, in equilibrium with admissible stress fields, through the minimization of an error function with respect to shape parameters of the stress potential, and then, with respect to the boundary values of the membrane shape. The application to two test cases shows the viability of this tool for the assessment of the equilibrium of existing masonry vaults.

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.

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