A-lines

A loop is a path which begins and ends at the same point, such as CGDHC in Fig. 7.1a. If two loops have a line in common, they can be linked to form a third loop by deleting the common line. In Fig. 7.1a, for example, BGCEB and CGDHC can be linked to give BGDHCEB. In this case, this last loop is said to be dependent on the other two. 

A line of constant Xp is compared with a line of constant Fp in Fig. 7.9. It can be seen that the line of constant Xp avoids the regions of steep slope. 

The development of a line of lubricant additives is an expensive and slow undertaking the market for these products —on the order of 10 billion dollars in 1992— is very large and is dominated by a few companies. 

Crude oil and gas from offshore platforms are evacuated by pipeline or alternatively, in the case of oil, by tanker. Pipeline transport is the most common means of evacuating hydrocarbons, particularly where large volumes are concerned. Although a pipeline may seem a fairly basic piece of equipment, failure to design a line for the appropriate capacity, or to withstand operating conditions over the field life time, can prove very costly in terms of deferred oil production. 

It is known and widely applied a method, when the spatial model of object is formed by a set of plane sections or tomographic slices. An experienced sample, created in Californian University and reffered to as Dynamic Cardiac 3D densitometer, is constructed by this principle [2]. The serial model of this tomograph of the company Imatron Associates appeared on the market in the end 1983r.[13]. On this basis a line of computer tomographs has been created. 

For each frequency 100 points were taken along a line running from the surface of the conductor into a depth of 30 mm in that region below the coil, where the maximum eddy currents are located (dashed vertical lines in the sketch). These data are fitted by appropriate polynomials to obtain an analytical expression for s (to, z) in the frequency and depth interval mentioned above. 

In Fig. 3a,b are shown respectively the modulus of the measured magnetic induction and the computed one. In Fig. 3c,d we compare the modulus and the Lissajous curves on a line j/ = 0. The results show a good agreement between simulated data and experimental data for the modulus. We can see a difference between the two curves in Fig. 3d this one can issue from the Born approximation. These results would be improved if we take into account the angle of inclination of the sensor. This work, which is one of our future developpements, makes necessary to calculate the radial component of the magnetic field due to the presence of flaw. This implies the calculation of a new Green s function. 

Figures 8a-16a show the stress levels of scan areas on the basis of a linearly subdivided colour map. Figures 8b-16b show the stress level along a line horizontally crossing the area scan graphic.

An average temperature of cells, that have left a zone of stability, is calculated (clinker in these cells is rolling down along a line of the greatest angle). 

This paper deals with the control of weld depth penetration for cylinders in gold-nickel alloy and tantalum. After introducing the experimental set-up and the samples description, the study and the optimization of the testing are presented for single-sided measurements either in a pulse-echo configuration or when the pump and the probe laser beams are shifted (influence of a thermal phenomenon), and for different kind of laser impact (a line or a circular spot). First, the ultrasonic system is used to detect and to size a flat bottom hole in an aluminium plate. Indeed, when the width of the hole is reduced, its shape is nearly similar to the one of a slot. Then, the optimization is accomplished for... 

Most of the situations encountered in capillarity involve figures of revolution, and for these it is possible to write down explicit expressions for and R2 by choosing plane 1 so that it passes through the axis of revolution. As shown in Fig. II-7n, R then swings in the plane of the paper, i.e., it is the curvature of the profile at the point in question. R is therefore given simply by the expression from analytical geometry for the curvature of a line... 

Fig. VII-6. Generation of a line having the fractal dimension 1.26. .. (see text).

If we represent the /bond by a line with two open circles to denote the coordinates of the particle 1 and 2, then the first two virial coefficients can be depicted graphically as... 

In the graphical representation of the integral shown above, a line represents the Mayer function f r.p between two particles and j. The coordinates are represented by open circles that are labelled, unless it is integrated over the volume of the system, when the circle representing it is blackened and the label erased. The black circle in the above graph represents an integration over the coordinates of particle 3, and is not labelled. The coefficient of is the sum of tln-ee tenns represented graphically as... 

An exponent a governs the limiting slope of the molar heat capacity, variously y, ( or along a line tln-ongh the critical point,... 

Mixtures of such polymeric substances with solvents show a line of critical points that in theory end at a tricritical point. (See section A2.5.9 for fiirther discussion of tricritical phenomena.)... 

Figure A2.5.30. Left-hand side Eight hypothetical phase diagrams (A through H) for ternary mixtures of d-and /-enantiomers with an optically inactive third component. Note the syimnetry about a line corresponding to a racemic mixture. Right-hand side Four T, x diagrams ((a) tlirough (d)) for pseudobinary mixtures of a racemic mixture of enantiomers with an optically inactive third component. Reproduced from [37] 1984 Phase Transitions and Critical Phenomena ed C Domb and J Lebowitz, vol 9, eh 2, Knobler C M and Scott R L Multicritical points in fluid mixtures. Experimental studies pp 213-14, (Copyright 1984) by pennission of the publisher Academic Press.

Consider the collision of an atom (denoted A) with a diatomic molecule (denoted BC), with motion of the atoms constrained to occur along a line. In this case there are two important degrees of freedom, the distance R between the atom and the centre of mass of the diatomic, and the diatomic intemuclear distance r. The Flamiltonian in tenns of these coordinates is given by ... 

For a sample at diennal equilibrium there is a distribution of speeds which depends on the mass of the molecules and on the temperature according to the Boltzmaim distribution. This results in a line shape of the form... 

Shearing of the data is perfonned to obtam isotropic spectra in the FI dimension and to facilitate easy extraction of the ID slices for different peaks. Shearing is a projection of points that lie on a line with a slope equal to the anisotropy axis onto a line that is parallel to the F2 axis [24]- Shearing essentially achieves the same as the split-t experiment or delayed acquisition of the echo. Although sheared spectra may look more attractive, they do not add any extra infomiation and they are certainly not necessary for the extraction of QIS and values. 

Eqnation (B3.4.1) is general and applies to both scattering and bonnd state spectroscopy. Scattering will be considered first. For shnplicity, the discnssion rises the collinear model for the A -l- BC AB -l- C reaction (i.e. assuming all particles lie on a line). This model is easy to visualize and embodies most elements of tlnee-dimensional (3D) scattering of larger molecules. 

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