Gaussian-like

Approximate Methods For certain conditions, symmetrical, Gaussian-like peaks are obtained experimentally. Such peaks may be empirically described by ... 

Linear combinations of primitive gaussians like these are used to form the actual basis functions the latter are called contracted gaussians and have the form ... 

Applying the TABS model to the stress distribution function f(x), the probability of bond scission was calculated as a function of position along the chain, giving a Gaussian-like distribution function with a standard deviation a 6% for a perfectly extended chain. From the parabolic distribution of stress (Eq. 83), it was inferred that fH < fB near the chain extremities, and therefore, the polymer should remain coiled at its ends. When this fact is included into the calculations of f( [/) (Eq. 70), it was found that a is an increasing function of temperature whereas e( increases with chain flexibility [100],... 

If U0 and U1 were the functions of a sufficient number of identically distributed random variables, then AU would be Gaussian distributed, which is a consequence of the central limit theorem. In practice, the probability distribution Pq (AU) deviates somewhat from the ideal Gaussian case, but still has a Gaussian-like shape. The integrand in (2.12), which is obtained by multiplying this probability distribution by the Boltzmann factor exp (-[3AU), is shifted to the left, as shown in Fig. 2.1. This indicates that the value of the integral in (2.12) depends on the low-energy tail of the distribution - see Fig. 2.1. 

In general, this type of extrapolation is not very successful, because its reliability deteriorates, often rapidly, as we move away from the region in which the function is known with a good accuracy. In the particular case of Pq AU), we might, however, be more successful, because this function is smooth and Gaussian-like. We shall exploit these features by considering three different representations of Pq(AU). 

For the OS calculation, (6.58), the same optimal solution is reached by choosing a Gaussian-like hyperbolic secant function for w(Au) ... 

Gaussian-like data with heavier tail (from Chen et al., 1998). 

A surprising aspect of SD is how rapidly C i) in highly polar solvents decays relative to other relaxation processes such as reorientation of solvent dipoles. This very rapid time scale cannot be ascribed to dynamical solvent-solvent correlations, which, as illustrated in Fig. 6, are modest even for the longest ranged A . Thus the key to imderstanding the reasons for the rapid decay of C i) is in examining how solvent-solvent correlations contribute to it and to what extent their contributions can be accounted for in terms of static correlations measured by ((5A ) ), Eq. (32). The initial cmvature of C(t), which characterizes its short-time Gaussian-like behavior is often characterized in terms of the solvation frequency co o/v... 

As manufactured, most resins have a Gaussian-like distribution of particle size. Very few are as small as 0.3 mm or as large as 1.0 mm. Most are between 0.5—0.8 mm. A backwash before using new resin is common practice to assure uniform flow during the adsorption and regeneration steps. The backwash eliminates air pockets that may have formed while filling the column and sorts the beads such that the smaller sizes are at the top of the bed and... 

An infrared C02 laser (1060 nm) was used to cut through a polycarbonate PC (black) (carbon-coated) wafer of 250-pm thickness to create microfluidic channels. The laser-machined black PC wafer was then thermally bonded between two transparent PC wafers at 139°C under two tons of pressure for 45 min [937], A C02 laser was also used to ablate Mylar sheets (with adhesive). Then the machined Mylar sheets were laminated together [1051]. Moreover, a PMMA substrate was machined by a C02 laser [201,202]. However, the microchannel ( 200 pm deep) has a Gaussian-like cross section and a certain degree of surface roughness [201], The C02 laser has also been used to machine PET substrates [203],... 

We examine a solute zone migrating under linear conditions. For the moment we confine our attention to the solute in the mobile phase. If complete equilibrium between phases existed at all points, the mobile-phase solute would form a Gaussian-like concentration profile as indicated by the shaded profile in Figure 10.7. However the actual profile for the mobile phase, shown by the dashed line, is shifted ahead of the shaded (equilibrium) profile due to solute migration. The basis of the profile shift is explained as follows. 

PSD turns out to be a Gaussian-like function of jco foo- The model applies equally well to the isotopically substituted formaldehydes (Fig. 39), for which the observed shift of PSD s to higher jco values is proportional to the square root of the reduced mass of the molecule. Chang et al. studied the decay of formaldehyde using classical trajectories on a semiempirical six-dimensional PES [315] starting the trajectories at the TS. Since the final step of the reaction is very fast, classical dynamics produce PSD s which agree well with the experiment. 

Gaussian-like distribution of energy around the energy average. Other ensembles with non-Boltzmann distributions can enhance the sampling considerably for example, in the multi-canonical approach [97, 98], all the conformations are equiprobable in energy in Tsallis statistics [99], the distribution function includes Boltzmann, Lorentzian, and Levy distributions. 

Gaussian-like peak A bell-shaped curve described by the equation Y = Aexp — (x /B). See Chapter 10 for more details. 

The curve seems to be unique and to have a gaussian-like behaviour The only discrepancies are due to ... 

In this case, the question is whether H+ should be considered a third substrate. It has, in fact, been treated in this manner by researchers, who have shown that if both pymvate and NADH concentrations are maintained at saturating levels, the initial rate of the enzymatic reaction is pH dependent, showing a Gaussian-like curve over the pH range 6-8. Data taken on the alkaline side of this curve may be used to obtain a KmU value, or, alternately, the alkaline pH value at Vm ix/2 value may be read... 

---