RELATION BETWEEN UNCERTAINTY EXPONENT AND MEAN LIFETIME OF CHAOTIC TRANSIENT FOR MAP ON ANNULUS

2000 ◽  
Vol 14 (05) ◽  
pp. 167-172 ◽  
Author(s):  
V. PAAR ◽  
N. PAVIN
Keyword(s):  
Lyapunov Exponent ◽  
Series Expansion ◽  
Taylor Series ◽  
Order Term ◽  
Taylor Series Expansion ◽  
Second Order ◽  
Mean Lifetime ◽  
The Mean ◽  
Chaotic Transient

For a map on the annulus, it is tested numerically that, within errors of the calculation of 0.4%, the inverse of the mean lifetime of chaotic transient is equal to the product of the uncertainty exponent and the Lyapunov exponent. The second-order term in the Taylor series expansion for inverse lifetime has no effect within the precision of the calculation.

The second-order theory of conformal solutions

1957 ◽  
Vol 240 (1223) ◽  
pp. 561-580 ◽  
Keyword(s):  
Thermodynamic Properties ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Order Theory ◽  
Second Order ◽  
Intermolecular Potential ◽  
Cell Theory ◽  
Reference Solution ◽  
Random Mixing

This paper describes a theoretical contribution to the statistical thermodynamics of mixtures of spherical molecules. The second-order perturbation free energy of a conformal solution is obtained by a rigorous Taylor-series expansion of the configuration integral in powers of the differences between intermolecular energy and size parameters, about an ideal unperturbed reference solution. Unlike the first-order terms, those of the second order contain statistical functions of the reference solution which cannot, in general, be related to its thermodynamic properties. All but one of these functions are concerned with departures from a random molecular distribution, and have been called molecular fluctuation integrals ; the remaining function can be related exactly to thermodynamic properties for the Lennard-Jones form of the intermolecular potential. The expressions for the molecular fluctuation integrals implied by the full random mixing approximation and by the semi-random mixing approximation of the cell theory, are derived and compared with the correct expressions given by the cell theory. The role of the Taylor series expansion as a critique of solution theories is discussed.

scholarly journals Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowang Li ◽  
Zhongmin Deng
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Time History ◽  
Taylor Series Expansion ◽  
Second Order ◽  
New Method ◽  
Dynamic Loads ◽  
Discrete Equation ◽  
System Response ◽  
Structural Dynamic

A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.

A TAYLOR FORMULA TO PRICE AND HEDGE EUROPEAN CONTINGENT CLAIMS

2001 ◽  
Vol 04 (04) ◽  
pp. 603-620
Author(s):  
MARIA ELVIRA MANCINO
Keyword(s):  
Stochastic Integral ◽  
Order Term ◽  
Approximation Error ◽  
Taylor Series Expansion ◽  
Second Order ◽  
Taylor Formula ◽  
Contingent Claim ◽  
Malliavin Derivative ◽  
No Arbitrage ◽  
The Mean

We present the no-arbitrage price and the hedging strategy of an European contingent claim through a representation formula which is an extension of the Clark-Ocone formula. Our formula can be interpreted as a second order Taylor formula of the no arbitrage price of a contingent claim. The zero order term is given by the mean of the contingent claim payoff, the first order term by the stochastic integral of the mean of its Malliavin derivative and the second order term by the stochastic integral of the conditional expectation of the second Malliavin derivative. A Taylor series expansion is also provided together with a bound to the approximation error obtained by neglecting the second order term in the Taylor formula.

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