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.

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.

Delamination Buckling of Piezoelectric Laminated Cylindrical Shell under Axial Compression

2013 ◽  
Vol 753-755 ◽  
pp. 1207-1211
Author(s):  
Jin Hua Yang ◽  
De Liang Chen ◽  
Xu Long Peng
Keyword(s):  
Cylindrical Shell ◽  
Constitutive Relations ◽  
Step Function ◽  
Governing Equations ◽  
Heaviside Step Function ◽  
Laminated Shell ◽  
Numerical Examples ◽  
Delamination Buckling ◽  
Laminated Cylindrical Shell ◽  
Delamination Length

The buckling of the piezoelectric laminated cylindrical shell with throughout circumference delamination is analyzed in this paper. By introducing the Heaviside step function into assumed displacement components and using elastic piezoelectric theory, the constitutive relations of the piezoelectric laminated shell with delamination are established. Then the buckling governing equations of the structure are derived through variational principle. In numerical examples, the effects of delamination length, depth, material property and thickness of piezoelectric layer on the buckling load of piezoelectric laminated shell with delamination are investigated.

scholarly journals Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 324
Author(s):  
Maria T. Vasileva
Keyword(s):  
Open Access ◽  
Probability Distribution ◽  
Hausdorff Distance ◽  
Hausdorff Metric ◽  
Software Module ◽  
Numerical Examples ◽  
Horizontal Asymptote ◽  
Dynamic Software ◽  
Distribution Family

In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.

Free Vibration of Piezoelectric Laminated Cylindrical Shell with Delamination

2012 ◽  
Vol 538-541 ◽  
pp. 2576-2581 ◽  
Author(s):  
Jin Hua Yang ◽  
De Liang Chen ◽  
Cheng Jiang
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Constitutive Relations ◽  
Step Function ◽  
Governing Equations ◽  
Heaviside Step Function ◽  
Laminated Shell ◽  
Numerical Examples ◽  
Laminated Cylindrical Shell ◽  
Delamination Length

Abstract. The free vibration of the piezoelectric laminated cylindrical shell with throughout circumference delamination is analyzed in this paper. By introducing the Heaviside step function into assumed displacement components and using elastic piezoelectric theory, the constitutive relations of the piezoelectric laminated shell with delamination are established. Then the dynamic governing equations of the structure are derived through variational principle. In numerical examples, the effects of delamination length, depth, boundary condition, material property and thickness of piezoelectric layer on the first natural frequency of piezoelectric laminated shell with delamination are investigated.

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 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 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.

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