Means, best

Means, best The best practical means for preventing the escape of noxions or offensive gases, smoke, grit, and dust from a process into the atmosphere. (U.K. Alkali Regulations.)... 

Notice the difference between the two words princiPAL (meaning best, top or most important ) and prin-ciPLE (meaning idea, thought or concept ). 

In order to establish a correlation with the previous results, a few runs were done with styrene and (1) as initiator. The results are collected in Table 1 and shown in Figure 1. The plot gives c = 1.3 x 10 4 mol dm3 and kp = 212 10 dm moH s"1 compatible with our previous [2] value of 188 9 dm moH s"1, giving a weighted mean best value of 195 15 dm moH-s 1. The agreement of the two values obtained by different workers with different apparatus establishes the continuity of the present results with those obtained... 

And how are these candles made I have told you about dips, and I will shew you how moulds are made. Let us imagine any of these candles to be made of materials which can be cast. Cast you say. Why, a candle is a thing that melts and surely if you can melt it, you can cast it Not so. It is wonderful, in the progress of manufacture, and in the consideration of the means best fitted to produce the required result, how things turn up which one would not expect beforehand. Candles cannot always be cast. A wax candle can... 

Value based Feigenbaum 1983 Quality means best of certain conditions (a) the actual use, and (b) the seUing price. ... 

The activation energy of ignition and ignition temperatures at different inhibitors ratios are shown in Fig. 5. As inhibitors ratio decreases, the ignition activation energy first increase, then reduce. When the ratio of FR-1 is 1 2, all ignition activation energy reaches maximum value, which mean best resistance ratio. 

Number of or values used to determine the mean Best value of (tr for substituent type. 

In co-operation with LM Glasfiber, a complete section of a rotor blade was produced with a number of well defined defects in order to perform an initial sensitivity test by means of ultrasound, vibrations techniques and real-time radiography. Based on the results of this initial test it was found that automated ultrasonic inspection was the best suited teclmique. In co-... 

The use of these equations is perhaps best illustrated by means of a numerical example. In a measurement of the surface tension of benzene, the following data are obtained ... 

To use direct dynamics for the study of non-adiabatic systems it is necessary to be able to efficiently and accurately calculate electronic wave functions for excited states. In recent years, density functional theory (DFT) has been gaining ground over traditional Hartree-Fock based SCF calculations for the treatment of the ground state of large molecules. Recent advances mean that so-called time-dependent DFT methods are now also being applied to excited states. Even so, at present, the best general methods for the treatment of the photochemistry of polyatomic organic molecules are MCSCF methods, of which the CASSCF method is particularly powerful. 

After selection of descriptors/NN training, the best networks were applied to the prediction of 259 chemical shifts from 31 molecules (prediction set), which were not used for training. The mean absolute error obtained for the whole prediction set was 0.25 ppm, and for 90% of the cases the mean absolute error was 0.19 ppm. Some stereochemical effects could be correctly predicted. In terms of speed, the neural network method is very fast - the whole process to predict the NMR shifts of 30 protons in a molecule with 56 atoms, starting from an MDL Molfile, took less than 2 s on a common workstation. 

This algorithm alternates between the electronic structure problem and the nuclear motion It turns out that to generate an accurate nuclear trajectory using this decoupled algoritlun th electrons must be fuUy relaxed to the ground state at each iteration, in contrast to Ihe Car-Pairinello approach, where some error is tolerated. This need for very accurate basis se coefficients means that the minimum in the space of the coefficients must be located ver accurately, which can be computationally very expensive. However, conjugate gradient rninimisation is found to be an effective way to find this minimum, especially if informatioi from previous steps is incorporated [Payne et cd. 1992]. This reduces the number of minimi sation steps required to locate accurately the best set of basis set coefficients. 

The transference of a liquid from one vessel to another is best carried out by means of a dropping pipette A (Fig. 30). For measuring out a definite volume of liquid it is obviously an advantage to have a calibrated pipette B (Fig. 30) of i or 5 ml. total capacity. Alternatively, semi-micro burettes reading to 0 02 ml. are particularly convenient for class work. 

When we report the result of a measurement a , there are two things a person reading the report wants to know the magnitude (size) of the measurement and the reliability of the measurement (its scatter ). If measuring errors are random, as they very frequently are, the magnitude is best expressed as the arithmetic mean p of N repeated tr ials xi... 

In so doing, we obtain the condition of maximum probability (or, more properly, minimum probable prediction error) for the entire distribution of events, that is, the most probable distribution. The minimization condition [condition (3-4)] requires that the sum of squares of the differences between p and all of the values xi be simultaneously as small as possible. We cannot change the xi, which are experimental measurements, so the problem becomes one of selecting the value of p that best satisfies condition (3-4). It is reasonable to suppose that p, subject to the minimization condition, will be the arithmetic mean, x = )/ > provided that... 

This method, because it involves minimizing the sum of squares of the deviations xi — p, is called the method of least squares. We have encountered the principle before in our discussion of the most probable velocity of an individual particle (atom or molecule), given a Gaussian distr ibution of particle velocities. It is ver y powerful, and we shall use it in a number of different settings to obtain the best approximation to a data set of scalars (arithmetic mean), the best approximation to a straight line, and the best approximation to parabolic and higher-order data sets of two or more dimensions. 

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