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.

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 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.

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.

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.

Dynamics of a Tubular Cantilever Simultaneously Subjected to Internal and Partially-Confined External Axial Flows

2018 ◽  
Author(s):  
Ahmed R. Abdelbaki ◽  
Arun K. Misra ◽  
Michael P. Païdoussis
Keyword(s):  
Logistic Function ◽  
Step Function ◽  
Dynamical Behaviour ◽  
External Flow ◽  
Annular Region ◽  
Heaviside Step Function ◽  
Cantilever Length ◽  
Theoretical Predictions ◽  
External Flows ◽  
The Stability

In this paper the dynamics of a tubular cantilever, simultaneously subjected to internal and external axial flows, is examined theoretically. The tube is discharging fluid downwards which then flows upwards through an annular region surrounding the tube. Thus, the internal and external flows are interdependent and in opposite directions. Also, the external flow is confined over a certain range of the cantilever length and unconfined over the rest. The Heaviside step function has been used in the literature, for such a system, to model the discontinuity in the external flow velocity occurring when the flow enters the annular region. A more accurate way to model this discontinuity is introduced in this study, in which the logistic function is used instead of the Heaviside step function. The stability of the system is investigated by analysis of the system eigenfrequencies, and the effects of varying the length of the confined region are theoretically studied. The obtained results are compared to theoretical predictions and experimental data from the literature having the same system parameters. The proposed theory captures the same dynamical behaviour as observed experimentally, and has a better estimation for the onset of instability and the frequency of oscillations compared to the theory in the literature.

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.

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