SELECTION OF THE MATHEMATICAL MODEL FOR THE USE OF ENROFLOXACIN IN CATS

2019 ◽  
pp. 104-109 ◽  
Author(s):  
Galya Shivacheva ◽  
Miroslav Vasilev
Keyword(s):  
Differential Equation ◽  
Akaike Information Criterion ◽  
Order Differential Equation ◽  
Information Criterion ◽  
Research Process ◽  
Second Order ◽  
First Order ◽  
Second Order Differential Equation ◽  
The Mathematical Model ◽  
Selection Of

The process of changing the concentration of enrofloxacin in blood plasma in cats after single intravenous injection was identified by three mathematical models - algebraic and two models represented respectively by a first order differential equation and a second order differential equation. In order to select the best model of the three, the Akaike information criterion corrected is used. With the most identification parameters differs the model based on a second-order differential equation. The lowest value of the Akaike information criterion corrected was also obtained with it. This fact gives reason to choose it for the best model for describing the research process.

scholarly journals SELECTION OF THE MATHEMATICAL MODEL FOR THE USE OF ENROFLOXACIN IN CATS

2019 ◽  
Vol 7 (4) ◽  
pp. 294-299
Author(s):  
Galya Shivacheva ◽  
Miroslav Vasilev
Keyword(s):  
Differential Equation ◽  
Akaike Information Criterion ◽  
Order Differential Equation ◽  
Information Criterion ◽  
Research Process ◽  
Second Order ◽  
First Order ◽  
Second Order Differential Equation ◽  
The Mathematical Model ◽  
Selection Of

The process of changing the concentration of enrofloxacin in blood plasma in cats after single intravenous injection was identified by three mathematical models - algebraic and two models represented respectively by a first order differential equation and a second order differential equation. In order to select the best model of the three, the Akaike information criterion corrected is used. With the most identification parameters differs the model based on a second-order differential equation. The lowest value of the Akaike information criterion corrected was also obtained with it. This fact gives reason to choose it for the best model for describing the research process.

scholarly journals COMPARISON OF MATHEMATICAL MODELS FOR THE USE OF ENROFLOXACIN IN DOGS

2019 ◽  
Vol 7 (2) ◽  
pp. 97-102 ◽  
Author(s):  
Miroslav Vasilev ◽  
Galya Shivacheva
Keyword(s):  
Differential Equation ◽  
Mathematical Models ◽  
Blood Plasma ◽  
Akaike Information Criterion ◽  
Order Differential Equation ◽  
Information Criterion ◽  
Second Order ◽  
Differential Model ◽  
Single Intravenous Injection ◽  
Future Developments

This article analyzes the process of changing the concentration of enrofloxacin in blood plasma in dogs after a single intravenous injection of the substance. Three mathematical models are proposed - algebraic and two models, based on a differential equation of first and second order. Identification of their parameters has been performed. Based on Akaike information criterion corrected as the best model was chosen the represented by a second-order differential equation. Three equations are identified and the exact numerical values of their parameters are obtained. For the evaluation and comparison of the three models, Akaike information criterion was used. The best results showed the second-order differential model. It will be used in future developments.

scholarly journals Weierstrass elliptic difference equations

1987 ◽  
Vol 35 (1) ◽  
pp. 43-48 ◽  
Author(s):  
Renfrey B. Potts
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Elliptic Function ◽  
Order Differential Equation ◽  
Second Order ◽  
Elliptic Difference ◽  
First Order ◽  
Second Order Differential Equation ◽  
Weierstrass Elliptic Function

The Weierstrass elliptic function satisfies a nonlinear first order and a nonlinear second order differential equation. It is shown that these differential equations can be discretized in such a way that the solutions of the resulting difference equations exactly coincide with the corresponding values of the elliptic function.

scholarly journals ON THE QUANTIZATION OF DAMPED SYSTEMS

1993 ◽  
Vol 08 (21) ◽  
pp. 2037-2043 ◽  
Author(s):  
CHIHONG CHOU
Keyword(s):  
Differential Equation ◽  
Harmonic Oscillator ◽  
Time Evolution ◽  
Order Differential Equation ◽  
Second Order ◽  
First Order ◽  
Damped Harmonic Oscillator ◽  
Simple Observation ◽  
Second Order Differential Equation ◽  
Damped Systems

Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the system of a linear damped harmonic oscillator and demonstrate that the time evolution of the Schrödinger equation is unambiguously determined.

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

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