Non sharp

In Figure 9.4, letters within parentheses stand for the components that will be present if nonsharp separation takes place. For example, stream 7 will consist of component B only if the recovery of this component in column I is incomplete (which means that column I is a nonsharp separator. The bottom product of column I (stream 10) can, in principle, contain all four components. If the feed to column I, stream 6, contains all four components, then stream 10 would contain all four components for non-sharp separation and only B, C, and D for sharp separation. Sharp separation is taken to mean recoveries greater than 99%. If stream 6 consists of only A and B, then stream 10 would contain A and B or B only, depending on whether the separation is nonsharp or sharp. The operation of columns II and III can be described in a similar fashion. This shows that the superstructure consists of both options for each column - sharp or nonsharp separation. The main steps in the derivation of the superstructure for a four-component feed stream are as follows ... 

To determine a minimum total annual cost configuration of non-sharp distillation columns out of the many alternatives embedded in the postulated superstructure, we define variables for the... 

The SAXS patterns at higher k-values display asymptotic linear slopes indicating a power law relation. For a sharp interfece with a smooth geometry, the intensity is expected to foUow a k power law in this Porod region. The observed slope varies systematically with pore size, membrane orientation and thickness. In some cases, exponents more negative than 4 are observed. This may arise from either angulosity or a non-sharp interface, and is discussed in more detail elsewhere [15]. 

Chan, W. K and Prince, R. G. H. Heuristic Evolutionary Synthesis with Non-Sharp Separators, in Third International Symposium on Process Systems Engineering, Sydney, 1988, p. 300-312 (1988). 

The alternative Bayesian interpretation of P(SC C)x 1 ) retains the idea of a single, entire universe in which values of initial conditions (S( -C)x) should be regarded as fixed aspects of a unique N, and no maximal invariant proper subset N C N exists. Although theories of initial conditions are by assumption not causal, they are expected to commit to specific forms the same way they currently specify the algorithmic structure of natural laws. A non-sharp P(SC C)x 1 ) is then associated by Bayesians with a range of... 

If sharp separation is feasible, then product points at real separation can be located as much as one wants close to vertexes or sides of concentration triangle. We call such separation quasisharp one. If sharp separation is not feasible (i.e., at supposed sharp separation product point does not get into possible product segment Reg or Reg ), neither is quasisharp separation. In this case, only nonsharp separation is feasible, for that there is some minimum feasible content of admixture component or components. We call the separation at minimum feasible content of admixture component or components f/te best non-sharp one. 

This is the same simultaneous s rstem which always formed the basis of the non-sharp resonances in the ansatze up to now. 

Fig. 2 shows the CFRP-sandwich specimen and the transducer mounted on the scanner. Fig. 23 presents a C-scan of the specimen as first interesting result. Only the defects visible from the outside are indicated. The distance between transducer and specimen was smaller than the focal length, so that the angle of incidence at the edge of the sound beam converts the longitudinal waves to Rayleigh-waves in the specimen. These waves provide a very sharp image of the surface. This method opens the possibility for a non-contact acoustic microscope. 

The key quantity in barrier crossing processes in tiiis respect is the barrier curvature Mg which sets the time window for possible influences of the dynamic solvent response. A sharp barrier entails short barrier passage times during which the memory of the solvent environment may be partially maintained. This non-Markov situation may be expressed by a generalized Langevin equation including a time-dependent friction kernel y(t) [ ]... 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

To obtain a reliable value of from the isotherm it is necessary that the monolayer shall be virtually complete before the build-up of higher layers commences this requirement is met if the BET parameter c is not too low, and will be reflected in a sharp knee of the isotherm and a well defined Point B. For conversion of into A, the ideal adsorptive would be one which is composed of spherically symmetrical molecules and always forms a non-localized film, and therefore gives the same value of on all adsorbents. Non-localization demands a low value of c as c increases the adsorbate molecules move more and more closely into registry with the lattice of the adsorbent, so that becomes increasingly dependent on the lattice dimensions of the adsorbent, and decreasingly dependent on the molecular size of the adsorbate. 

Another recently discovered form of epitaxy is graphoepitaxy (Geis et al. 1979). Here a non-crystalline substrate (often the heat-resistant polymer polyi-mide, with or without a very thin metallic coating) is scored with grooves or pyramidal depressions the crystalline film deposited on such a substrate can have a sharp texture induced by the geometrical patterns. More recently, this has been tried out as an inexpensive way (because there is no need for a monocrystalline substrate) of preparing oriented ZnS films for electroluminescent devices (Kanata et al. 1988). 

Observable Characteristics - Physical State (as shipped) Liquid Color. Colorless Odor. Mild, sharp, non-residual. 

The 8 functions limit the non-vanishing regions of / -space to discrete layer planes perpendicular to k. These layer planes are infinitely sharp, because the helix was assumed to be infinitely long. Limiting the summation to a finite length of the helix would lead to broadening of these layer planes. 

It is not an easy task to develop computer codes which correctly treat the advancement of a folding interface as a boundary condition to a diffusion or flow field. In addition, the interface between a solid and a liquid, for example, is usually is not absolutely sharp on an atomic scale, but varies over a few lattice constants [32,33]. In these cases, it is sometimes convenient to treat the interface as having a finite non-zero thickness. An order parameter is then introduced, which for example varies from the value zero on one side of the interface to the value one on the other, representing a smooth transition from liquid to solid across the interface. This is called the phase-field... 

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