Solution of a Mathematical Model Describing the Change of Hormone Level in Thyroid Using the Laplace Transform

2013 ◽  
Vol 2 (1) ◽  
pp. 99-108
Author(s):  
Shama M. Mulla ◽  
Chhaya H. Desai
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Hormone Level ◽  
The Laplace Transform

scholarly journals The Concentration of Digoxin Activity after Intravenous in Three Compartments Mathematical Model

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3653-3657
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Digoxin Concentration ◽  
Compartment Model ◽  
System Of Equations ◽  
Transfer Coefficients ◽  
Linear Ordinary Differential Equations ◽  
Concentration Time ◽  
The Laplace Transform ◽  
Three Compartment Model

Present paper is designed to compare the distribution of digoxin in three compartment model administered through an intravenous (i.v). These models under consideration is denoted by a system of non-linear ordinary differential equations. The Eigenvalue and the Laplace transform methods were used to solve the system of equations. Digoxin was administered to five subjects through Intravenous then, the serum digoxin concentrations were measured respectively over a period of 72 hours. The transfer coefficients were obtained from observed digoxin concentrations using method of residuals and the variation of digoxin concentration – time curves plotted using MATLAB.

scholarly journals The Mathematical Models of Lattice Functions in Modelling of Control System

2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Mathematical Models ◽  
Control Systems ◽  
Time Domain ◽  
Discrete Control ◽  
Automatic Control Systems ◽  
The Laplace Transform ◽  
Lattice Function ◽  
The Time Domain

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

Analytical Forces Parameters Identification of Hybrid Journal Gas Bearing Based on Transfer Function

2011 ◽  
Author(s):  
Guang-hui Zhang ◽  
Zhan-sheng Liu ◽  
Gui-long Wang ◽  
Jia-jia Yan
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Laplace Transform ◽  
Pressure Distribution ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
The Laplace Transform ◽  
Hybrid Bearing ◽  
Gas Bearing ◽  
Gas Journal Bearing

A mathematical model for the flow in the hybrid gas journal bearing is depicted by the transfer function in this paper. The average and modified parameters from the pressure distribution of multi-orifices aerostatic journal bearing are acquired to describe the characteristics accurately. The transient gas film forces of multi-orifices hybrid bearing is derived in the generalized form by analytical means, and then the dynamic characteristics coefficients are got by employing the Laplace transform. It indicates that the obtained forces can calculate the dynamic characteristics coefficients simply, quickly and accurately, which provide an efficient means for designing rotor-bearing systems.

scholarly journals Laplace transform of distribution-valued functions and its applications

2004 ◽  
Vol 129 (29) ◽  
pp. 61-78
Author(s):  
Bogoljub Stankovic
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Existence Of Solutions ◽  
The Laplace Transform

For the distribution-valued functions the Laplace transform, is defined and some properties of it are proved. In order to illustrate the elaborated results, the conditions are proved to have the unicity and existence of solutions to a mathematical model of the vibrating rod with boundary conditions. .

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

scholarly journals Algebraic inversion of the Laplace transform

2005 ◽  
Vol 50 (1-2) ◽  
pp. 179-185 ◽  
Author(s):  
P.G. Massouros ◽  
G.M. Genin
Keyword(s):  
Laplace Transform ◽  
The Laplace Transform

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

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