Uniform distribution distributions

In the experiments, the probabilities were estimated from the processed signal by means of a histogram. It is well known that the entropy is large for nearly uniform distributions and small for distributions with few peaks. Thus it is an interesting candidate as a performance measure when the goal is to process a signal to become more easily interpreted. 

Fig. 1 shows the two-layered profile on a substrate. The quality of reconstruction of this highly contrasted profile is good. The reconstruction of a more complicated three-layered profile on a substrate is shown in Fig. 2. To estimate the robusmess of the approach, a random signal uniformly distributed over the interval [-0.02 +0.02] was added to the real and...

Fig. 1. Circular aperture array with uniformly distributed transducer elements (No. 1, 2. . N).

Very shortly, the first one is based on the stress measurement performed using a rosetta strain gauge located in an area of sufficiently uniform stress distribution. In this case, the calibration factor Cr can be easily obtained by the following equation ... 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

Fig. 2. Empirical cdf s for many samples of increasing size from a uniform distribution...

The initial velocities may also be chosen from a uniform distribution or from a simp Gaussian distribution. In either case the Maxwell-Boltzmann distribution of velocities usually rapidly achieved. 

It is important to note that simply sampling displacements of the three Euler angles does nc lead to a uniform distribution it is necessary to sample from cos 6 rather than 6 (Figure 8.5... 

Fig. 8.5 To achieve a uniform distribution of points over the surface of a sphere it is necessary to sample from cos 8 rather than 6. If the sampling is uniform in 8 then the number of points per unit area increases with 6, leading to an uneven distribution over the sphere.

The plot of y against I gives a curve of the well known bell-shaped form (Fig. 1.13). The sharpness of the peak is determined by the value of <7 , the peak becoming narrower as the value of o decreases. Curve I of Fig. 1.13, with its sharper peak, corresponds to a more uniform size distribution than does Curve II. 

Fig. 1.13 Gaussian particle size distributions. Curve I represents a more uniform size distribution than does Curve II.

This involves a more uniform distribution of charge because of the identical substituents and thus lacks the stabilizing effect of the polar resonance form. The activation energy for this mode of addition is greater than that for alternation, at least when X and Y are sufficiently different. 

If the poorer solvent is added incrementally to a system which is poly-disperse with respect to molecular weight, the phase separation affects molecules of larger n, while shorter chains are more uniformly distributed. These ideas constitute the basis for one method of polymer fractionation. We shall develop this topic in more detail in the next section. 

Sonochemistry is also proving to have important applications with polymeric materials. Substantial work has been accomplished in the sonochemical initiation of polymerisation and in the modification of polymers after synthesis (3,5). The use of sonolysis to create radicals which function as radical initiators has been well explored. Similarly the use of sonochemicaHy prepared radicals and other reactive species to modify the surface properties of polymers is being developed, particularly by G. Price. Other effects of ultrasound on long chain polymers tend to be mechanical cleavage, which produces relatively uniform size distributions of shorter chain lengths. 

UNIPAJSI. The uniform distribution, Langmuir local isotherm model (9,12) ... 

Fabrication Technology. Stabili2iag additives must be uniformly distributed within the starting powders for 2irconia ceramics. 

If the solute is uniformly distributed through the soHd phase the material near the surface dissolves first to leave a porous stmcture in the soHd residue. In order to reach further solute the solvent has to penetrate this outer porous region the process becomes progressively more difficult and the rate of extraction decreases. If the solute forms a large proportion of the volume of the original particle, its removal can destroy the stmcture of the particle which may cmmble away, and further solute maybe easily accessed by solvent. In such cases the extraction rate does not fall as rapidly. 

Dilution. In many appHcations, dilution of the flocculant solution before it is mixed with the substrate stream can improve performance (12). The mechanism probably involves getting a more uniform distribution of the polymer molecules. Since the dosage needed to form floes is usually well below the adsorption maximum, a high local concentration is effectively removed from the system at that point, leaving no flocculant for the rest of the particles. A portion of the clarified overflow can be used for dilution so no extra water is added to the process. 

The paste-extmsion process includes the incorporation of ca 16—25 wt % of the lubricant (usually a petroleum fraction) the mixture is roUed to obtain uniform lubricant distribution. This wetted powder is shaped into a preform at low pressure (2.0—7.8 MPa or 19—77 atm) which is pushed through a die mounted in the extmder at ambient temperature. The shear stress exerted on the powder during extmsion confers longitudinal strength to the polymer by fibrillation. The lubricant is evaporated and the extmdate is sintered at ca 380°C. 

The pressure of the extmder forces uniform plastic distribution throughout the mold. Cooling the mold solidifies the plastic with slight shrinkage. The mold is maintained closed by mechanical or hydraulic pressure while the thermoplastic is injected and solidified. 

In the cuspation—dilation thermoforming process developed in AustraHa, sheet formation is promoted by expanding blades extending into aU areas and distributing the material uniformly throughout the mold. This process is claimed to deHver uniform distribution of high barrier components of sheet coextmsions and laminations. The process also permits almost vertical side waUs to cups (2). 

In practice a uniform distribution of the working stress cannot be achieved, but it may be approached by various methods of constmction such as compound shrinkage, tape winding, and autofrettage which have their origin in the design of ordnance. 

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