Concentric circles

For other quantification, specialized graticules are available, including point counting, grids, concentric circles, and special scales. The latest methods of quantification involve automatic image analysis. 

Van Wingerden (1989a) Two plates vertical cylinders in concentric circles (2 x 4 m) C2H4 685 10.0... 

To factor location into the rankings, multiply the total distances by the average population density in the area surrounding the facility. Where population varies with distance, you may need to vaiy the density by distance. One effective approach is to consider population density in concentric circles of 1 km, 2 km, 5 km, and 10 km radius. 

For graphic purposes, the polar plane is usually drawn as a series of concentric circles with the center at the origin and radii 1, 2, 3.Rays from... 

Cationic quaternary ammonium compounds such as distearyldimethylammonium-chloride (DSDMAC) used as a softener and as an antistatic, form hydrated particles in a dispersed phase having a similar structure to that of the multilayered liposomes or vesicles of phospholipids 77,79). This liposome-like structure could be made visible by electron microscopy using the freeze-fracture replica technique as shown by Okumura et al. 79). The concentric circles observed should be bimolecular lamellar layers with the sandwiched parts being the entrapped water. In addition, the longest spacings of the small angle X-ray diffraction pattern can be attributed to the inter-lamellar distances. These liposome structures are formed by the hydrated detergent not only in the gel state but also at relatively low concentrations. 

Fig. 2.52 Kinematic viscosity of solution vs. temperature at various Habon G concentrations. Circles (O) indicate water Habon G, boxes ( ) represent 130ppm, crosses (x) represent 260ppm, empty triangles (A) represent 530 ppm, triangles (A) represent 1,060 ppm. Reprinted from Hetsroni et al. (2001b) with permission...

Analytical solutions for the closure problem in particular unit cells made of two concentric circles have been developed by Chang [68,69] and extended by Hadden et al. [145], In order to use the solution of the potential equation in the determination of the effective transport parameters for the species continuity equation, the deviations of the potential in the unit cell, defined by... 

At the proper magnification and with a special eye piece, one can directly measure particle diameters. The eye-piece must have internally-mcurked concentric circles so that a given particle wlU fall within one or more of the circles. The diameter then can then be read and/or estimated directly as shown in the following ... 

Another example is dendritic crystal growth under diffusion-limited conditions accompanied by potential or current oscillations. Wang et al. reported that electrodeposition of Cu and Zn in ultra-thin electrolyte showed electrochemical oscillation, giving beautiful nanostmctured filaments of the deposits [27,28]. Saliba et al. found a potential oscillation in the electrodeposition of Au at a liquid/air interface, in which the Au electrodeposition proceeds specifically along the liquid/air interface, producing thin films with concentric-circle patterns at the interface [29, 30]. Although only two-dimensional ordered structures are formed in these examples because of the quasi-two-dimensional field for electrodeposition, very recently, we found that... 

The equipment should be drawn approximately to scale. Again, some licence is allowed for the sake of clarity, but the principal equipment items should be drawn roughly in the correct proportion. Ancillary items can be drawn out of proportion. For a complex process, with many process units, several sheets may be needed, and the continuation of the process streams from one sheet to another must be clearly shown. One method of indicating a line continuation is shown in Figure 4.2 those lines which are continued over to another are indicated by a double concentric circle round the line number and the continuation sheet number written below. 

Fig. 13 Plot of plasma concentrations (circles) versus time with the curve divided into vertical segments. (Data shown in Table 7.)...

Fig. 16 Plot of kanamycin plasma concentrations (circles) versus time following multiple IM injections, calculated using Eq. (56).

Figure 4. A set of pole figures for three reflections of a highly oriented linear polyethylene specimen. The concentric circles are parallels of latitude, which represent constant values of x from 0 deg (outermost circle) to 90 deg (north pole) in 15 deg steps. The straight lines are meridians of longitude, which represent constant values of < > from 180 degrees to +180 degrees.

A bar code is a computer or machine-readable representation of information. It is usually made of dark ink on a light background to create high and low reflectance which is converted to Is and Os, when read by the computer program. A similar result may be achieved by patterns of dots, concentric circles, or text codes hidden within images. A bar code containing stored data in the widths and spacings of printed parallel lines or other patterns as... 

This problem is shown in Figure 4.5. The feasible region is defined by linear constraints with a finite number of comer points. The objective function, being nonlinear, has contours (the concentric circles, level sets) of constant value that are not parallel lines, as would occur if it were linear. The minimum value of/corresponds to the contour of lowest value having at least one point in common with the feasible region, that is, at xx = 2, x2 = 3. This is not an extreme point of the feasible set, although it is a boundary point. For linear programs the minimum is always at an extreme point, as shown in Chapter 7. 

Figure 4.12 corresponds to objective functions in well-posed optimization problems. In Table 4.2, cases 1 and 2 correspond to contours of /(x) that are concentric circles, but such functions rarely occur in practice. Elliptical contours such as correspond to cases 3 and 4 are most likely for well-behaved functions. Cases 5 to 10 correspond to degenerate problems, those in which no finite maximum or minimum or perhaps nonunique optima appear. 

First, let us consider the perfectly scaled quadratic objective function /(x) = x + x, whose contours are concentric circles as shown in Figure 6.6. Suppose we calculate the gradient at the point xT = [2 2]... 

Figure 7. A projection of the Fermi surfaces on a plane parallel to the axis of the symmetry breaking. The concentric circles correspond to the two populations of spin/isospin-up and down fermions in spherically symmetric state (Se = 0), while the deformed figures correspond to the state with relative deformation Se = 0.64. The density asymmetry is a = 0.35.

The high spatial resolution of the technique enables identification of a source of contamination by the characteristic fingerprint left on the wafer. This is illustrated in Fig. 10.5, which shows lifetime maps of wafers contaminated in different ways. The concentric circles shown in Fig. 10.5 a are caused by oxygen precipitates. The... 

Symptoms A very common fungal problem that produces soft, brown patches on fruit Concentric circles of white fluffy growth also develop on these areas while fruit is on the tree or in storage. Fruit may turn black. Some fruit on the tree will shrivel, become mummified, and remain attached throughout the winter. 

Figure 55. Presence of fluoroalkyls enhancing the anion stability against moisture. Consumption of H2O and the generation of HF in 1.0 M salt solutions of EC/DMC with added H2O at 500 ppm (for LiPFe) and 1000 ppm (for LiFAP), respectively triangle, Fl20 concentration circle, HF concentration. (Reproduced with permission from ref 498 (Figure 2). Copyright 2001 Elsevier.)...

The lower left panel in Figure 13.2 shows the central composite design in the two factors X, and X2. The factor domain extends from -5 to +5 in each factor dimension. The coordinate axes in this panel are rotated 45° to correspond to the orientation of the axes in the panel above. Each black dot represents a distinctly different factor combination, or design point. The pattern of dots shows a central composite design centered at (Xj = 0, Xj = 0). The factorial points are located 2 units from the center. The star points are located 4 units from the center. The three concentric circles indicate that the center point has been replicated a total of four times. The experimental design matrix is... 

Note 2 The smectic layers within a focal-conic domain adopt the arrangement of Dupin cyclides, since as in these figures there appear concentric circles resulting from the intersection of ellipses and hyperbolae. They also have the distinctive property of preserving an equal distance between them. 

FIGURE 6.5 The measured power of the third harmonic power generated in the bulk of solution containing 0.5- xm-diameter fused silica microspheres as a function of microspheres concentration. Circles are experimentally measured data points the dashed line is a linear fit. 

Apparatus Designed by Henry Cavendish and Used by Charles Hatchett for Determining the Comparative Wear of Gold When Alloyed by Varions Metals. Two frames, one above the other, each carrying twenty-eight coins, rubbed the upper coins backward and forward over the ones below. Each of the smaller concentric circles represents a coin. To avoid the formation of furrows, the direction in which the coins rubbed against each other was made to vary continually. 

Electron microscopy has been performed using a sample synthesised at w = 10, [Cd2+]/[S2 ] = 2, and characterized by 430-nm absorption onset, which corresponds to a CdS diameter equal to 25 A. The microanalysis study shows the characteristic lines of sulfide and cadmium ions, indicating that the observed particles are CdS semiconductor crystallites. The electron diffractogram shows concentric circles, which are compared to a simulated diffractogram of bulk CdS. A good agreement between the two spectra is obtained, indicating the particles keep zinc-blend crystalline structure (fee) with a lattice constant equal to 5.83 A. 

When a crystalline material is placed in a monochromatic X-ray beam, the resulting diffraction or scattering pattern depends on the sample shape or form. Simplistically, if the sample is a powder, then the scattering pattern appears as sharp concentric circles. If the sample is a fiber, then the scattering pattern appears as sharp arcs falling on layered lines. Each maximum arises from the constructive interference between the X-rays scattered by a set of parallel planes within the crystal [3]. Rewriting Bragg s law yields... 

Other travelling waveforms include target patterns, fronts, or pulses as expanding and concentric circles and which may be broken to form spirals (which may also arise apparently spontaneously under some conditions) as shown in Fig. 1.17. 

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