Spreading definition

Now let us use the wavepackets just discussed to extract the physically measurable infomration about our problem, namely, the probabilities of reflection and transmission. As long as the wavepackets do not spread much during the collision, these probabilities are given by the general definition ... 

Consider, for example, the data in Table 4.1 for the mass of a penny. Reporting only the mean is insufficient because it fails to indicate the uncertainty in measuring a penny s mass. Including the standard deviation, or other measure of spread, provides the necessary information about the uncertainty in measuring mass. Nevertheless, the central tendency and spread together do not provide a definitive statement about a penny s true mass. If you are not convinced that this is true, ask yourself how obtaining the mass of an additional penny will change the mean and standard deviation. 

Since the development of a method for polymer characterization has been spread over several sections and since the literature contains several variations in the manner data is displayed, a summary of some pertinent definitions and relationships will be helpful at this point ... 

It has been shown (16) that a stable foam possesses both a high surface dilatational viscosity and elasticity. In principle, defoamers should reduce these properties. Ideally a spread duplex film, one thick enough to have two definite surfaces enclosing a bulk phase, should eliminate dilatational effects because the surface tension of an iasoluble, one-component layer does not depend on its thickness. This effect has been verified (17). SiUcone antifoams reduce both the surface dilatational elasticity and viscosity of cmde oils as iUustrated ia Table 2 (17). The PDMS materials are Dow Coming Ltd. polydimethylsiloxane fluids, SK 3556 is a Th. Goldschmidt Ltd. siUcone oil, and FC 740 is a 3M Co. Ltd. fluorocarbon profoaming surfactant. 

The complete mathematical definition of a particle size distribution is often cumbersome and it is more convenient to use one or two single numbers representing say the mean and spread of the distribution. The mean particle size thus enables a distribution to be represented by a single dimension while its standard deviation indicates its spread about the mean. There are two classes of means ... 

This average spread is, by its definition, zero for a classical system and is thus a measure of the pure quantum contribution to the librations or rotations of the individual rotators. 

This energy measure is equal to Brode s definition of the energy, multiplied by a factor 2. The reason for the multiplication is that the Brode definition applies to free-air burst, while Eq. (6.3.15) is for a surface burst. In a fiee-air burst, explosion energy is spread over twice the volume of air. 

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

The terminology is not yet homogeneous. The use of the prefix nano spread out in the 1990s. Until then, the common term used to be mesoscopic structures, which continues to be used. According to a definition by IUPAC of 1985, the following classification applies to porous materials microporous, < 2 nm pore diameter mesoporous, 2-50 nm macroporous, > 50 nm. 

If you mix sulfur and iron filings in a certain proportion and then heat the mixture, you can see a red glow spread through the mixture. After it cools, the black solid lump which has been produced, even if crushed into a powder, does not dissolve in carbon disulfide and is not attracted by a magnet. The material has a new set of properties it is a compound, called iron(II) sulfide. It has a definite composition, and if, for example, you had mixed more iron with the sulfur originally, some iron(II) sulfide and some leftover iron would have resulted. The extra iron would not have become part of the compound. 

Hardness is a somewhat ambiguous property. A dictionary definition is that it is a property of something that is not easily penetrated, spread, or scratched. These behaviors involve very different physical mechanisms. The first relates to elastic stiffness, the second to plastic deformation, and the third to fracturing. But, for many substances, the mechanisms of these are closely related because they all involve the strength of chemical bonding (cohesion). Thus discussion of the mechanism for one case may provide some understanding of all three. 

We conclude that the Li-poor stars definitely have different evolutionary histories to Li-normal plateau stars. A mass-transfer mechanism may explain the origin of these objects, but irrespective of whether this is the correct explanation, the Li-poor objects cannot be included in studies of Li depletion mechanisms that affect normal single stars. Consequently we conclude that the small (zero ) intrinsic spread in plateau Li abundances inferred by [25] is representative of normal halo stars, and thus signifies at most a small depletion in Li, <0.1 dex by the models of [17]. 

The company knows about it and mentions it in the first few pages of the datasheet. This is an instance where the company is quite forthright about the problem, but perhaps not definite enough about its spread or its impact, to guarantee it in the EC table (or unable to test it). Fair enough. You can work with them if you suspect a widening problem. 

---