Index determination and calculationof consistent initial values for DAEs

ABSTRACT The effect of ethyl alcohol on the circulating eosinophil cells has been studied in female albino rats. An intoxicating dose of alcohol caused a marked depletion of circulating eosinophils which was most clearly evident four hours after the administration of the alcohol. The initial values were not reached before 24 hours had elapsed. Intraperitoneal injection of vitamin C 12 hours prior to the alcohol administration very effectively prevented this eosinopenic reaction. The mechanism of regulation of the eosinophil cells in the circulation has been discussed in the light of previous results and of those obtained in this study.

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The Role Of The Pilates Method In The Formation And Development Of The Body Balance

SPORT AND SOCIETY ◽

10.36836/uaic/fefs/10.45 ◽

2019 ◽

pp. 78-83

Author(s):

Irene-Teodora Nica

Keyword(s):

The Body ◽

Target Group ◽

Body Balance ◽

Initial Values ◽

Pilates Method

The study is aimed at training and developing balance through Pilates programs. In order to improve the initial values, we have developed a set of corresponding exercises. The test was applied on a target group, the initial and final results being presented. The conclusion presents the interpretation of the results.

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Projected explicit and implicit Taylor series methods for DAEs

Numerical Algorithms ◽

10.1007/s11075-020-01051-z ◽

2021 ◽

Author(s):

Diana Estévez Schwarz ◽

René Lamour

Keyword(s):

Taylor Series ◽

Multibody Systems ◽

Optimization Problem ◽

Automatic Differentiation ◽

Taylor Coefficients ◽

Integration Schemes ◽

Consistent Initial Values ◽

Taylor Series Methods ◽

Systems Simulation ◽

Derivative Array

AbstractThe recently developed new algorithm for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization opens new possibilities to apply Taylor series integration methods. In this paper, we show how corresponding projected explicit and implicit Taylor series methods can be adapted to DAEs of arbitrary index. Owing to our formulation as a projected optimization problem constrained by the derivative array, no explicit description of the inherent dynamics is necessary, and various Taylor integration schemes can be defined in a general framework. In particular, we address higher-order Padé methods that stand out due to their stability. We further discuss several aspects of our prototype implemented in Python using Automatic Differentiation. The methods have been successfully tested on examples arising from multibody systems simulation and a higher-index DAE benchmark arising from servo-constraint problems.

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On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers

Mathematica Slovaca ◽

10.1515/ms-2017-0378 ◽

2020 ◽

Vol 70 (3) ◽

pp. 641-656

Author(s):

Amira Khelifa ◽

Yacine Halim ◽

Abderrahmane Bouchair ◽

Massaoud Berkal

Keyword(s):

General Solution ◽

Closed Form ◽

Difference Equations ◽

Fibonacci Numbers ◽

Higher Order ◽

Real Numbers ◽

Lucas Numbers ◽

Rational Difference Equations ◽

Initial Values ◽

Fibonacci And Lucas Numbers

AbstractIn this paper we give some theoretical explanations related to the representation for the general solution of the system of the higher-order rational difference equations$$\begin{array}{} \displaystyle x_{n+1} = \dfrac{1+2y_{n-k}}{3+y_{n-k}},\qquad y_{n+1} = \dfrac{1+2z_{n-k}}{3+z_{n-k}},\qquad z_{n+1} = \dfrac{1+2x_{n-k}}{3+x_{n-k}}, \end{array}$$where n, k∈ ℕ0, the initial values x−k, x−k+1, …, x0, y−k, y−k+1, …, y0, z−k, z−k+1, …, z1 and z0 are arbitrary real numbers do not equal −3. This system can be solved in a closed-form and we will see that the solutions are expressed using the famous Fibonacci and Lucas numbers.

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