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 Laplace transform as an alternative general method for solving linear ordinary differential equations

2021 ◽  
Vol 1 (4) ◽  
pp. 309
Author(s):  
William Guo
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Laplace Transform ◽  
Ordinary Differential Equations ◽  
Case Studies ◽  
Initial Conditions ◽  
Linear Ordinary Differential Equations ◽  
The Laplace Transform ◽  
Linear Odes ◽  
General Method

<p style='text-indent:20px;'>The Laplace transform is a popular approach in solving ordinary differential equations (ODEs), particularly solving initial value problems (IVPs) of ODEs. Such stereotype may confuse students when they face a task of solving ODEs without explicit initial condition(s). In this paper, four case studies of solving ODEs by the Laplace transform are used to demonstrate that, firstly, how much influence of the stereotype of the Laplace transform was on student's perception of utilizing this method to solve ODEs under different initial conditions; secondly, how the generalization of the Laplace transform for solving linear ODEs with generic initial conditions can not only break down the stereotype but also broaden the applicability of the Laplace transform for solving constant-coefficient linear ODEs. These case studies also show that the Laplace transform is even more robust for obtaining the specific solutions directly from the general solution once the initial values are assigned later. This implies that the generic initial conditions in the general solution obtained by the Laplace transform could be used as a point of control for some dynamic systems.</p>

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 Evaluation of Dose-Fractionated Polymyxin B on Acute Kidney Injury Using a Translational In Vivo Rat Model

2020 ◽  
Vol 64 (5) ◽  
Author(s):  
Jiajun Liu ◽  
Gwendolyn M. Pais ◽  
Sean N. Avedissian ◽  
Annette Gilchrist ◽  
Andrew Lee ◽  
...  
Keyword(s):  
Acute Kidney Injury ◽  
Rat Model ◽  
Kidney Injury ◽  
Compartment Model ◽  
Polymyxin B ◽  
Time Curve ◽  
Daily Group ◽  
Concentration Time ◽  
Three Compartment Model

ABSTRACT We investigated dose-fractionated polymyxin B (PB) on acute kidney injury (AKI). PB at 12 mg of drug/kg of body weight per day (once, twice, and thrice daily) was administered in rats over 72 h. The thrice-daily group demonstrated the highest KIM-1 increase (P = 0.018) versus that of the controls (P = 0.99) and histopathological damage (P = 0.013). A three-compartment model best described the data (bias, 0.129 mg/liter; imprecision, 0.729 mg2/liter2; R2, 0.652,). Area under the concentration-time curve at 24 h (AUC24) values were similar (P = 0.87). The thrice-daily dosing scheme resulted in the most PB-associated AKI in a rat model.

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&gt; 0 for eachj&gt; 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.

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