Taylor Standard Series

Gertler, M. (1954). A reanalysis of the original test data for the Taylor Standard Series. Report 806. David Taylor Model Basin Washington DC. 

American naval architect David Watson Taylor was a rear admiral in the U.S. Navy. He was meticulous in his work and developed procedures still in use in model basins. The Taylor Standard Series was a series of trials run with specific models. The results could be used to estimate the resistance of a ship effectively before it was buUt. 

Taylor designed and constructed in 1898 the first experimental tank for models of war vessels in the USA. The probably greatest achievement of his career was the T lor Standard Series including 80 models by systematically varying vessel proportions and prismatic coefficients. The results of this series are still currently used for a preliminary determination of ship resistance for twin screw, moderate- to high-speed naval boats. The book was revised in 1933 with the addition of data on 40 new models. The series data were reanalysed using more recent methods in 1954. Both books Speed and power, and the mentioned Reanalysis were pubhshed in 1998 by SNAME, the centennial of the Experimental Model Basin. 

This section discusses a class of methods known as the first-order reliability methods to compute the probability of failure of structural systems. These methods are based on the first-order Taylor s series expansion of the performance function G(X). The first-method, known as the first-order second-moment (FOSM) method, focuses on approximating the mean and standard deviation of G and uses this information to compute Pf. Then, the FOSM method is extended to the advanced FOSM method in two steps first, the methodology is developed for the case where all the variables in X are Gaussian (normal) and, second, the methodology is extended to the general case of non-normal variables. 

A Maclaunn series is a specific form of the Taylor series for which Xq = 0. Some standard expansions in Taylor series form are ... 

Interestingly, if one Taylor series expands Eq. (36) and equates the terms of the same order in kj with Eq. (37) one can derive the standard Lagrangian FD approximations (i.e., require the coefficient of kj to be —1, and require the coefficient of all other orders in kj up to the desired order of approximation to be 0.) A more global approach is to attempt to fit Eq. (36) to Eq. (37) over some range of Kj = kjA values that leads to a maximum absolute error between Eq. (36) and Eq. (37) less than or equal to some prespecrfied value, E. This is the essential idea of the dispersion-fitted finite difference method [25]. 

More specifically, the reduced variable Kj = kjA is defined on [0, ti]. Generally, the error in an FD approximation (or rather its dispersion relation, Eq. (36)) increases with Kj. The Taylor series approach outlined above, which leads to the standard Lagrangian FD approximations, is essentially perfect for very small Kj but quickly deviates from the correct, quadratic dependence, Eq. (37). The generic behavior is that the error increases monotonically with Kj. Instead of requiring that the fit be perfect in the limit of very small Kj, we require that the error be no greater than s from Kj = 0 up to some... 

At that time I started to work with Dr. Clive R. Taylor, Professor and Chairman of Pathology at the University of Southern California, Keck School of Medicine. Clive is a world renowned pioneer in archival IHC used for pathology since the early 1970s. With his kind help and support, I have been conducting a series of research projects on basic principles, further development, standardization and mechanisms of the AR technique. This work has yielded more than 40 peer reviewed articles and a book. Our AR research has been funded by NIH grant since 2001. 

Source C. E. Moore, National Standard Reference Data Series 34, U.S. Government Printing Office, Washington, D.C., 1970 W. C. Martin, Zalubas, R., and Hagan, L.,J. Phys. Chem. Reference Data, 3 771 (1974) and National Standard Reference Data Series, National Bureau of Standards (U S ), No. 60 (1978) for die Rare Earth Elements and Cohen, E. R. and Taylor, B. 

The most prominent of these methods is probably the second order Newton-Raphson approach, where the energy is expanded as a Taylor series in the variational parameters. The expansion is truncated at second order, and updated values of the parameters are obtained by solving the Newton-Raphson linear equation system. This is the standard optimization method and most other methods can be treated as modifications of it. We shall therefore discuss the Newton-Raphson approach in more detail than the alternative methods. 

Blair, R., Daghir, N.J., Peter, V. and Taylor, T.G. (1983) International nutrition standards for poultry. Nutrition Abstracts and Reviews -Series B 53, 669-713. 

The plot in Fig. 3.2 of the acid dissociation constant for acetic acid was calculated using equation 3.2-21 and the values of standard thermodynamic properties tabulated by Edsall and Wyman (1958). When equation 3.2-21 is not satisfactory, empirical functions representing ArC[ as a function of temperature can be used. Clark and Glew (1966) used Taylor series expansions of the enthalpy and the heat capacity to show the form that extensions of equation 3.2-21 should take up to terms in d3ArCp/dT3. 

Knowing which factors contribute to the overall variability it should be possible to improve the analytical methodology. The whole error (first condition) is composed of the systematic error (or bias), unspecified random errors, and a series of errors produced during chemical or physical analyses. Uncertainty, also expressed as standard deviation (type A uncertainty), is a concept for measuring the quality of the analytical procedures (Taylor and Kuyaat, 1994). 

The main problem now is to calculate the action of the Green s function onto the initial state xo- The standard strategy is to expand G in a power series of H. For vanishing A, a highly efficient expansion exists [215,235] in terms of Chebyshev polynomials, Tn H), which is similar to the one used in short-time wave packet propagations [166,171]. For finite A, this expansion has to be modified to account for the absorbing potential. As was shown by Mandelshtam and Taylor [221], the analytically continued Chebyshev polynomials, can be used for this purpose. If the initial... 

Show that for the same compression ratio the thermal efficiency of the air-standard Otto engine is greater than the themial efficiency of the air-standard Diesel cycle. Hint Show that the fraction which multiplies (l/r) in the above equation for is greater than unity by expanding rc in a Taylor series with the remainder taken to the first derivative. 

The convention used by Levine and Bethea to define the response functions omits the Taylor series factors in the series for the induced dipoles but includes a factor of (3/2) implicitly in the definition of the macroscopic quantity. Their ft is equivalent to jl,. Hence to relate their results to the more usual conventions, the /i-value must be multiplied by 4 x (3/2) x (3/5) = 18/5 and the y value by 4 x (3/2) = 6. Finally a factor (0.30/0.335) must be applied to allow for the change in the quartz standard. Carrying out these operations and converting to atomic units gives the values in Table 10. 

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