Twice

It is found in lichens and in some algae. It has m.p. 120 C, is very soluble in water and is about twice as sweet as sucrose. It is a reference compound upon which the erythro nomenclature is based. 

An extended reach well is loosely defined as having a horizontal displacement of at least twice the vertical depth. With current technology a ratio of over 4 (horizontal displacement / vertical depth) can be achieved. 

A Monte Carlo simulation is fast to perform on a computer, and the presentation of the results is attractive. However, one cannot guarantee that the outcome of a Monte Carlo simulation run twice with the same input variables will yield exactly the same output, making the result less auditable. The more simulation runs performed, the less of a problem this becomes. The simulation as described does not indicate which of the input variables the result is most sensitive to, but one of the routines in Crystal Ball and Risk does allow a sensitivity analysis to be performed as the simulation is run.This is done by calculating the correlation coefficient of each input variable with the outcome (for example between area and UR). The higher the coefficient, the stronger the dependence between the input variable and the outcome. 

In this case the slot length is about twice the probe diameter. The material chosen has a very low penetration depth of 0.15 mm at the given frequency of 25.1 kHz. The slot depth is 20 times greater than the penetration depth. 

Here fg is the centre frequeney and Af the 6 dB bandwidth. Apart from being simple, this spectmm has Some advantages. With a given bandwidth only a frequency band that is twice the bandwidth need to be computed and this is very important as it leads to a minimal number of... 

In order to verify the repetitiveness of the results, each test will be realized twice. 

Defects intervening in pieces are listed by official norms. For segmentation needs, we have divided the set of defects in two categories, volumetric and linear defects. A defect is considered as linear if its width is twice inferior to the size of the grain, all the rest are considered as volumetric defects. 

As the anodes of the cathode-grounded tubes are cooled through the ceramic insulator, narrower insulators should lead to more heat transferable. For lower voltages, tube designs with twice the actual anode load are feasible. 

Because of the double sound path involved in PE measurements of the back wall echo, we approximate the corresponding attenuation at a certain frequency to be twice as large as the attenuation that would be obtained by an ordinary TT measurement. We propose to use the logarithm of the absolute value of the Fourier transform of the back wall echo as input data, i.e... 

Results can sometimes be unexpected. The first study of this type made use of labeled Aerosol OTN [111], an anionic surfactant, also known as di-n-octylsodium sulfosuccinate. The measured F was twice that in Eq. III-93 and it was realized that hydrolysis had occurred, that is, X + H2O = HX + OH , and that it was the undissociated acid HX that was surface-active. Since pH was essentially constant, the activity of HX was just proportional to C. A similar behavior was found for aqueous sodium stearate [112]. 

Examination of Fig. VII-4 shows that the mutual interaction between a pair of planes occurs once if the planes are a distance a apart, twice for those la apart and so on. If the planes are labeled by the index I, as shown in the figure, the mutual potential energy is... 

In these equations, the sums give twice the desired quantity because each atom is counted twice. In addition, the condition that the atoms be at their equilibrium distances gives, from differentiation of Eq. VII-14,... 

Optical second-harmonic generation (SHG) has recently emerged as a powerful surface probe [95, 96]. Second harmonic generation has long been used to produce frequency doublers from noncentrosymmetric crystals. As a surface probe, SHG can be caused by the break in symmetry at the interface between two centrosymmetric media. A high-powered pulsed laser is focused at an angle of incidence from 30 to 70° onto the sample at a power density of 10 to 10 W/cm. The harmonic is observed in reflection or transmission at twice the incident frequency with a photomultiplier tube. 

Since it is not possible to generate antisynnnetric combinations of products if the same spin orbital appears twice in each tenn, it follows that states which assign the same set of four quantum numbers twice cannot possibly satisfy the requirement P.j i = -ij/, so this statement of the exclusion principle is consistent with the more general symmetry requirement. An even more general statement of the exclusion principle, which can be regarded as an additional postulate of quantum mechanics, is... 

If we apply the operation (12) twice, or the operation (123) three times, we obviously get back to the starting point. We write this as... 

Fluctuations in energy are related to the heat capacity Cy and can be obtained by twice differentiating log Q with respect to p, and using equation (A2.2.69) ... 

Notice that each collision is counted twice, once for the particle with velocity v and once for the particle with velocity v We also note that we have assumed that the distribution fiinctions/do not vary over distances which are the lengths of the collision cylinders, as the interval 6t approaches some small value, but still large compared with the duration of a binary collision. 

To integrate this expression, we note that 0 starts at n when r = co, then it decreases while r decreases to its turning point, then r retraces back to oo while 0 continues to evolve back to n. The total change in 0 is then twice the integral... 

Similar reasoning shows that were one to view along tiieX, Yand Z axes and polarization analyse the signal each time, whether excited by linearly or by naturally polarized light, the total intensity should be given by + 2/. Given eauation (Bl.3.23). if we add its denominator to twice the numerator we find that A... 

When a time window twice the duration of the delay time is used, perfect coincidence is at the centre of the time window and it is possible to make an accurate assessment of the background by considering the region to either side of the perfect coincidence region. An example of a time spectrum is shown m figure Bl.10.8. 

For the confocal arrangement in transmission, the objective and the collector are used for imaging in reflection the objective is used twice. Therefore, the radial mtensity distribution in tlie image is the square of that of the conventional microscope ... 

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are core and valence AOs. The use of more basis functions is motivated by a desire to provide additional variational flexibility so the LCAO-MO process can generate MOs of variable difhiseness as the local electronegativity of the atom varies. 

By carefully adjustmg the variational wavefiinction used, it is possible to circumvent size-extensivity problems for selected species. For example, the Cl calculation on Bc2 using all 2 CSFs fomied by placing the four valence electrons into the 2a, 2a, 30g, 3a, In, and iTt orbitals can yield an energy equal to twice that of the Be atom described by CSFs in which the two valence electrons of the Be atom are placed into the... 

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