scholarly journals A Study on the Unit-logistic, Unit-Weibull and Topp-Leone Cumulative Sigmoids

2019 ◽  
Vol 6 (1) ◽  
pp. 1 ◽  
Author(s):  
Anton Iliev Iliev ◽  
Asen Rahnev ◽  
Nikolay Kyurkchiev ◽  
Svetoslav Markov
Keyword(s):  
Step Function ◽  
Heaviside Step Function ◽  
Additional Criterion ◽  
Hausdorff Approximation ◽  
The One

In this paper we study the one--sided Hausdorff approximation of the Heaviside step function by a families of Unit-Logistic (UL), Unit-Weibull (UW) and Topp-Leone (TL) cumulative sigmoids.The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in ''saturation'' study.Numerical examples are presented using CAS MATHEMATICA.

scholarly journals Investigations on the G Family with Baseline Burr XII Cumulative Sigmoid

2019 ◽  
Vol 5 (2) ◽  
pp. 101
Author(s):  
Nikolay Kyurkchiev ◽  
Anton Iliev Iliev ◽  
Asen Rachnev
Keyword(s):  
Oil Palm ◽  
Step Function ◽  
Lifetime Distribution ◽  
Programming Environment ◽  
Heaviside Step Function ◽  
New Model ◽  
Additional Criterion ◽  
Hausdorff Approximation ◽  
The One

In this paper we study the one--sided Hausdorff approximation of the shifted Heaviside step function by a class of the Zubair-G family of cumulative lifetime distribution with baseline Burr XII c.d.f. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in ''saturation'' study.As an illustrative example we consider the fitting the new model against experimental oil palm data.Numerical examples, illustrating our results are presented using programming environment.

scholarly journals An Asymptotic Approach for the Elastodynamic Problem of a Plate under Impact Loading

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Penelope Michalopoulou ◽  
George A. Papadopoulos
Keyword(s):  
Laplace Transform ◽  
Impact Loading ◽  
Step Function ◽  
Infinite Strip ◽  
Asymptotic Approach ◽  
Heaviside Step Function ◽  
Inertia Effects ◽  
Elastodynamic Problem ◽  
Line Force ◽  
The One

An approach is presented for analyzing the transient elastodynamic problem of a plate under an impact loading. The plate is considered to be in the form of a long strip under plane strain conditions. The loading is taken as a concentrated line force applied normal to the plate surface. It is assumed that this line force is suddenly applied and maintained thereafter (i.e., it is a Heaviside step function of time). Inertia effects are taken into consideration and the problem is treated exactly within the framework of elastodynamic theory. The approach is based on multiple Laplace transforms and on certain asymptotic arguments. In particular, the one-sided Laplace transform is applied to suppress time dependence and the two-sided Laplace transform to suppress the dependence upon a spatial variable (along the extent of the infinite strip). Exact inversions are then followed by invoking the asymptotic Tauber theorem and the Cagniard-deHoop technique. Various extensions of this basic analysis are also discussed.

scholarly journals On the Hausdorff distance between the shifted Heaviside step function and the transmuted Stannard growth function

BIOMATH ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 1609041 ◽  
Author(s):  
Anton Iliev Iliev ◽  
Nikolay Kyurkchiev ◽  
Svetoslav Markov
Keyword(s):  
Hausdorff Distance ◽  
Growth Curves ◽  
Growth Function ◽  
Step Function ◽  
Upper And Lower Bounds ◽  
Programming Environment ◽  
Software Module ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
The One

In this paper we study the one-sided Hausdorff distance between the shifted Heaviside step--function and the transmuted Stannard growth function. Precise upper and lower bounds for the Hausdorff distance have been obtained. We present a software module (intellectual property) within the programming environment CAS Mathematica for the analysis of the growth curves. Numerical examples, illustrating our results are given, too.

A family of recurrence generated sigmoidal functions based on the Verhulst logistic function. Some approximation and modelling aspects

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Nikolay V. Kyurkchiev
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation ◽  
Logistic Functions

  In this note we construct a family of recurrence generated sigmoidal logistic functions based on the Verhulst logistic function.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

scholarly journals A family of recurrence generated sigmoidal functions based on the Verhulst logistic function. Some approximation and modelling aspects

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Nikolay Kyurkchiev
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation ◽  
Logistic Functions

In this note we construct a family of recurrence generated sigmoidal logistic functions based on the Verhulst logistic function.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

scholarly journals A family of recurrence generated sigmoidal functions based on the Log-logistic function. Some approximation aspects

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Nikolay Kyurkchiev ◽  
Svetoslav Markov
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Biochemical Reactions ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation

In this note we construct a family of recurrence generated sigmoidal functions based on the Log--logistic function. The study of some biochemical reactions is linked to a precise Log--logistic function analysis.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given. The plots are prepared using CAS Mathematica.

scholarly journals A new transmuted cumulative distribution function based on the Verhulst logistic function with application in population dynamics

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Nikolay Kyurkchiev
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Logistic Function ◽  
Step Function ◽  
Cumulative Distribution ◽  
Heaviside Step Function ◽  
Numerical Examples ◽  
New Class ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation

In this note we find application of a new class cumulative distribution function transformations to construct a family of sigmoidal functions based on the Verhulst logistic function. We prove estimates for the Hausdorff approximation of the shifted Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

scholarly journals The new trasmuted C.D.F. based on Gompertz function

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Nikolay V. Kyurkchiev
Keyword(s):  
Step Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Gompertz Function ◽  
Heaviside Step Function ◽  
Cumulative Distribution Functions ◽  
Sigmoidal Functions ◽  
Hausdorff Approximation

In this paper we find application of some new cumulative distribution functions transformations to construct a family of sigmoidal functions based on the Gompertz logistic function.We prove estimates for the Hausdorff approximation of the shifted Heaviside step function by means of these families.Numerical examples, illustrating our results are given.

A Meshless Local Petrov-Garlerkin Method for Solving the Biharmonic Equation

2014 ◽  
Vol 931-932 ◽  
pp. 1488-1494
Author(s):  
Supanut Kaewumpai ◽  
Suwon Tangmanee ◽  
Anirut Luadsong
Keyword(s):  
Relative Error ◽  
Biharmonic Equation ◽  
Interpolation Method ◽  
Step Function ◽  
Special Treatment ◽  
Maximum Relative Error ◽  
Heaviside Step Function ◽  
Treatment Techniques ◽  
Point Interpolation Method ◽  
Point Interpolation

A meshless local Petrov-Galerkin method (MLPG) using Heaviside step function as a test function for solving the biharmonic equation with subjected to boundary of the second kind is presented in this paper. Nodal shape function is constructed by the radial point interpolation method (RPIM) which holds the Kroneckers delta property. Two-field variables local weak forms are used in order to decompose the biharmonic equation into a couple of Poisson equations as well as impose straightforward boundary of the second kind, and no special treatment techniques are required. Selected engineering numerical examples using conventional nodal arrangement as well as polynomial basis choices are considered to demonstrate the applicability, the easiness, and the accuracy of the proposed method. This robust method gives quite accurate numerical results, implementing by maximum relative error and root mean square relative error.

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