Two-Party Zero-Error Function Computation with Asymmetric Priors

The focus of this research is to apply the selected error function equation to establish the equilibrium isotherm model that best describes the adsorption of Pb2+ and Mn2+ onto acid-activated shale. Data collected from the batch experiment were analyzed using selected isotherm models (Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Sips and Redlich-Peterson). To compute the isotherm parameters used in choosing the best-fit isotherm model, selected non-linear error functions, namely, error sum of the square, normalized standard deviation, hybrid error function, root mean square error and Marquardt’s percent standard deviation were employed. From the scanning electron microscope results, it was observed that the surface characteristics of the shale change considerably with calcination and acid treatment but the acid-treated shale shows better uneven porous surface characteristics. Error function computation shows that the Dubinin-Radushkevich isotherm model had the least sum of normalized error of 0.3623 for Pb2+ adsorption and 0.5465 for Mn2+ adsorption; hence, it was selected as the best isotherm model for explaining the sorption of Pb(II) and Mn(II) ions unto acid-activated shale.

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ERROR FUNCTION

A-to-Z Guide to Thermodynamics Heat and Mass Transfer and Fluids Engineering ◽

10.1615/atoz.e.errfun ◽

2006 ◽

Vol e ◽

Author(s):

H.G Khajah

Keyword(s):

Error Function

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The Pricing Error Function

SSRN Electronic Journal ◽

10.2139/ssrn.1108465 ◽

2008 ◽

Author(s):

Huntley Schaller ◽

Lynda Khalaf

Keyword(s):

Error Function ◽

Pricing Error

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Fast timer-based maximum function computation over noisy multiple access channels

2016 13th IEEE Annual Consumer Communications & Networking Conference (CCNC) ◽

10.1109/ccnc.2016.7444752 ◽

2016 ◽

Author(s):

Jiajia Huang ◽

Boon-Hee Soong

Keyword(s):

Multiple Access ◽

Maximum Function ◽

Function Computation ◽

Multiple Access Channels

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

SN Applied Sciences ◽

10.1007/s42452-021-04383-0 ◽

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.

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Algorithm 181: complementary error function—large X

Communications of the ACM ◽

10.1145/366604.366638 ◽

1963 ◽

Vol 6 (6) ◽

pp. 315

Author(s):

Henry C. Thacher

Keyword(s):

Error Function ◽

Complementary Error Function

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From Stress to Shape: Equilibrium of Cloister and Cross Vaults

Applied Sciences ◽

10.3390/app11093846 ◽

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.

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