Uniform space

The clad plate is x-rayed perpendicular from the steel side and the film contacts the aluminum. Radiography reveals the wavy interface of explosion-welded, aluminum-clad steel as uniformly spaced, light and dark lines with a frequency of one to three lines per centimeter. The waves characterize a strong and ductile transition joint and represent the acceptable condition. The clad is interpreted to be nonbonded when the x-ray shows complete loss of the wavy interface (see X-ray technology). 

Color Difference Evaluation. Shade evaluation is comparable in importance to relative strength evaluation for dyes. This is of interest to both dye manufacturer and dye user for purposes of quaUty control. Objective evaluation of color differences is desirable because of the well-known variabihty of observers. A considerable number of color difference formulas that intend to transform the visually nonuniform International Commission on Illumination (CIE) tristimulus color space into a visually uniform space have been proposed over the years. Although many of them have proven to be of considerable practical value (Hunter Lab formula, Friele-MacAdam-Chickering (FMC) formula, Adams-Nickerson formula, etc), none has been found to be satisfactorily accurate for small color difference evaluation. Correlation coefficients for the correlation between average visually determined color difference values and those based on measurement and calculation with a formula are typically of a magnitude of approximately 0.7 or below. In the interest of uniformity of international usage, the CIE has proposed two color difference formulas (CIELAB and CIELUV) one of which (CIELAB) is particularly suitable for appHcation on textiles (see Color). 

Rubber media appear as porous, flexible rubber sheets and microporous hard rubber sheets. Commercial rubber media have 1100-6400 holes/in. with pore diameters of 0.012-0.004 in. They are manufactured out of soft rubber, hard rubber, flexible hard rubber and soft neoprene. The medium is prepared on a master form, consisting of a heavy fabric belt, surfaced on one side with a layer of rubber filled with small round pits uniformly spaced. These pits are 0.020 in. deep, and the number per unit area and their surface diameter determine the porosity of the sheet. A thin layer of latex is fed to the moving belt by a spreader bar so that... 

Table 1 lists typical filtering applications and operating ranges. The simplest and oldest types of designs include a series of thin metal disks that are 3-10 inches in diameter and set in a vertical stack with very narrow uniform spaces between them. The disks are supported on a vertical hollow shaft and fit into a closed cylindrical... 

Figure 11.2-1 shows the layout of a CANDU. The uranium fuel is supported horizontally by uniformly spaced tubes in the calandria (5) which... 

The vessel is a 15 ft high cylinder with a diameter of 16.25 ft constructed of half-in thick, type 304 stainless steel plate. Six outlet nozzles are uniformly spaced around the circumterence at the bottom, and six tapered inlet nozzles are uniformly spaced around the circumference of the water plenum at the top of the vessel. The primary water system PWS contains 40,000 gal of DjO 24,000 gal in the re tank and 16,000 gal in the piping system. Each of the six primary loi ted... 

In buildings away from outside perimeter walls, air and surface temperatures are usually approximately equal. The heat losses from a person by radiation (q ) and convection (q ) are then flowing to the same temperature level. In such uniform spaces, the radiant and convective losses are about equal and together account for about 80-90% of the total heat loss of a sedentary comfortable individual. In the presence of hot or cold surfaces, as may occur in perimeter or other locations in a building, the average surface temperature of the surroundings (called mean radiant temperature) as seen by the person s body may be substantially different from air temperature. If the mean radiant temperature (MRT) is greater or less than air temperature (T,) the person will feel warmer or colder than in a thermally uniform space where MRT =. ... 

Heaviside made a significant contribution to electrical communications when he advocated the introduction of additional inductance in long-distance telephony cables although there was then no practical means to add it. His idea was eventually patented in 1904 by Michael Campbell of AT T after Heaviside and George Pupin of Columbia University had shown it was possible to apply inductance in the form of uniformly spaced loading coils. By 1920 engineers had installed such loading on thousands of miles of cable, particularly in the United States. 

Also known as riser tube distributors (RTD) [131], these consist of a flat tray with orifices uniformly spaced to allow liquid to flow onto the packing below. This tray has vapor risers, uniformly spaced, but not interfering with... 

Each new layer is populated by adding the particles in rows that are uniformly spaced along the y axis that is, by changing the density of misfit dislocations. The grouping of atoms into 2D clusters is an important effect that is excluded by this approach. However, the effects of this type of clustering can be inferred from these results. Since the chemical potential of the film material is fx=dE/dN, the tangent to this curve is ... 

Modem signal processing in analytical chemistry is usually performed by computer. Therefore, signals are digitized by taking uniformly spaced samples from the continuous signal, which is measured over a finite time. 

Here the B-spline Bim(zf, Xj) is the ith B-spline basis function on the extended partition Xj (which contains locations of the knots in the Zj direction), and is a coefficient. We use cubic splines and sufficient numbers of uniformly spaced knots so that the estimation problem is not affected by the partition. The estimation problem now involves determining the set of B-spline coefficients that minimizes Eq. (4.1.26), subject to the state equations [Eqs. (4.1.24 and 4.1.25)], for a suitable value of the regularization parameter. At this point, the minimization problem corresponds to a nonlinear programming problem. 

The nature of the relationships and constraints in most design problems is such that the use of analytical methods is not feasible. In these circumstances search methods, that require only that the objective function can be computed from arbitrary values of the independent variables, are used. For single variable problems, where the objective function is unimodal, the simplest approach is to calculate the value of the objective function at uniformly spaced values of the variable until a maximum (or minimum) value is obtained. Though this method is not the most efficient, it will not require excessive computing time for simple problems. Several more efficient search techniques have been developed, such as the method of the golden section see Boas (1963b) and Edgar and Himmelblau (2001). 

This method for optimizing a process parallels the method given in the mapping example. First, some limit must be placed on all variables. Otherwise it would be impossible to cover the entire surface. In the mapping example it was the continental boundaries. Second, for each independent variable a number of specific points that are uniformly spaced and cover its whole range are chosen. The objective... 

It is estimated that between 1000 and 2500 m3 ha-1 of water are required to produce a rice crop in the southern US and generally less than one third of that requirement is met by rainfall [35]. Levees, which separate fields into bays, or paddies, and control flood depth (i.e., by use of gates or spills), are commonly constructed on contours that were surveyed on 3 to 6 cm vertical intervals. This creates winding, contour-shaped levees in fields that are not precision-leveled, whereas precision leveling to a uniform grade of 0.2% or less allows the construction of uniformly spaced, straight levees and may reduce the number of levees required [34]. 

The DDF was more open in comparison with the DEF and had uniformly spaced trees. The upper story, 11-35 m above ground, was formed by canopies of Shorea obtusa, Pentamo suavis, Dipterocarpus intricatus, Gardenia spp. and others. In the DDF, 875 trees (DBH>5 cm) ha-1 were enumerated, and the total basal area at 1.3 m height was 15 m2ha-1 and the above ground biomass was 73 tons ha-1 (Sahunalu and Dhanmanonda... 

The statistical analysis of these traces revealed all-data-point and plateau-counting histograms with a series of uniformly spaced current peaks (Fig. 28b). The first peak of each sequence could be identified as the single-junction conductance current. The data set of T-PBI plotted in Fig. 28b leads to 21.7 3.8 nS at Es = —0.820 V. 

Holes should be uniformly spaced in the distributor pipe—adjacent holes should be spaced at least 2 to 3 hole diameters apart, center to center. 

In the idealized mode, liquid jet breakup and droplet formation are fairly regular. The liquid jet running downwards collapses, forming droplets of uniform size at uniform spacing. After breakup, the liquid jet of length 4.51 d0 converts into a spherical droplet so that ... 

Two features of the trapezoidal method are that we use a uniform spacing between the positions where we evaluate fix) and that every evaluation of fix) (except the end points) is given equal weight. Neither of these conditions is necessary or even desirable. An elegant class of integration methods called Gaussian quadrature defines methods that have the form... 

Numerical Integration. Using Simpson s rule, applicable to an even number of uniformly spaced intervals on the axis, we find for the data of Table E5.4,... 

As a theoretical check of these ideas, Bartelteta/. (1994a) created in an SOS model a step bunch of 5 steps by initially confining them to half the lattice [in the k direction], then watching them evolve to nearly uniform spacing. There was no energetic interaction between... 

To proceed, we must describe the effective driving force and the effective interactions between steps on this mesoscopic scale. We focus here on two cases of recent experimental and theoretical interest current-induced step bunching on Si( 111) surfaces - " and reconstruction-induced faceting as seen a number of systems including the O/Ag(110) and Si(lll) surfaces" In both cases interesting 2D step patterns can arise from the competition between a driving force that promotes step bunching, and the effects of step repulsions, which tend to keep steps uniformly spaced. 

We can determine the interaction term V in Eq. (2) through the requirement that H reproduce the macroscopic free energy in Eq. (1) in the limit of straight steps with uniform spacing w. Thus if Ly is the length of the system in the y-direction we require... 

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