minimisation. The technique is applicable to deflection functions with multiple degrees of freedom and seems to have more effective convergence than the Raleigh–Ritz technique [ 14 ]. The work principle is combined with Taylor's series to form the deflection
A methodology is proposed to calculate statistical average and standard deviation of long time water quality parameter series along a river network. The method considers the water network as a graph consisting of straight sessions and junctions. With a Taylor-series approximation, statistical values of an arbitrary point of the network can be calculated from upstream ones without the need to calculate the single downstream values. According to preliminary results of the first calculations on a pilot area, mean value of the downstream biological oxygen demand and the so called ‘transfer coefficient’ can be approximated with a relative accuracy of 10%.
The k0-standardization method of neutron activation analysis (NAA) is very sensitive to the irradiation and counting time during measurement of the induced radionuclide by -spectrometry on the HP Ge detector. If the irradiation and counting time of the sample and co-irradiated standard is relatively short or the decay constant small, the application of the standard equation in the software for the specific count rate may become numerically unstable and the program aborts. In this work, attention is focused on the direct influence of saturation and "measurement" factors on the specific count rate for simple decay and for more complex types calculated directly by exponential functions, and by an alternative form using a truncated Taylor's series expression.
Quantitative determinations of many radioactive analytes in environmental samples are based on a process in which several independent measurements of different properties are taken. The final results that are calculated using the data have to be evaluated for accuracy and precision. The estimate of the standard deviation, s, also called the combined standard uncertainty (CSU) associated with the result of this combined measurement can be used to evaluate the precision of the result. The CSU can be calculated by applying the law of propagation of uncertainty, which is based on the Taylor series expansion of the equation used to calculate the analytical result. The estimate of s can also be obtained from a Monte Carlo simulation. The data used in this simulation includes the values resulting from the individual measurements, the estimate of the variance of each value, including the type of distribution, and the equation used to calculate the analytical result. A comparison is made between these two methods of estimating the uncertainty of the calculated result.
The temperature dependence of the Gibbs free energy difference (ΔG) between the undercooled liquid and the corresponding equilibrium solid has been analysed for metallic glass forming systems
in the frame of the expression obtained by expanding free energies of the undercooled liquid and solid phases in the form
of Taylor's series expansion. The enthalpy difference (ΔH) and the entropy difference (ΔH) between the undercooled liquid and solid phases have also been analysed. The study is made for five different metallic glass
forming materials, Au77Ge13.6Si9.4, Au53.2Pb27.5Sb19.3, Au81.4Si18.6, Mg85.5Cu14.5 and Mg81.6Ga18.4 and a very good agreement is found between calculated and experimental values of ΔG. The ideal glass transition temperature (Tk) and the residual entropy (ΔSR) of these materials have also been studied due to their important role in assigning the glass formation ability of materials.
Authors:V. I. Belevantsev, K. V. Zherikova, N. B. Morozova, V. I. Malkova and I. K. Igumenov
Expanding the term ln( T / T * ) in a Taylorseries, we obtain:
where ξ is the residual. Usually, temperature ranges in tensimetry are such that:
For this reason, it is possible to expect that for most real situations, in
the inverse function for ,
Our goal is to calculate for a given z . The transformation rate can be obtained from the first derivative of Eq. 5 29
If we compare Eq. 28 to Eq. 1 , we obtain:
And from the Taylorseries expansion of
In Coats–Redfern method, the integral of Eq. 4 is taken, and the resulting exponential integral which does not have an exact analytical solution is approximated using a Taylorseries expansion. The obtained equation is simplified by considering 2RT