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Fig. 7.7.1 the results of the brightness temperatures at 18 GHz between the two approaches are compared for a given set of physical parameters that are characteristic of snow . For the sake of illustration, we have assumed only one species of particles in Fig. 7.7.1. The presence of scattering prevents the thermal emission from reaching the radiometer giving rise to lower brightness temperatures. In this chapter, we only treat non-sticky particles. Since conventional transfer equations predict a much larger albedo, the calculated brightness temperatures are much lower than those of the dense media radiative transfer equations. In Fig. 7.7.2 the theoretical results of the dense media transfer equations for one particle species are compared with experimental data of brightness temperature measurements over snOw. Only the input physical parameters are specified to match the experimental data. A physical fractional volume of 30% is used in calculating the theoretical result. The permittivity of particles E = (3.2 + iO.016)E o represents typical permittivity of ice in snOW and the s calculated mixing formula effective permittivity E~;) according to (7.7.1)(7.7.2) is (1.49 + iO.0029)E o and represents typical permittivity of the overall snOw medium. In the studies of remote sensing of geophysical terrain, very often the ground truth data are given in terms of a histogram of particle size distribution. We next use the modified gamma distribution



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(7.7.8)

In 1985, at my direction, six oor joists from the 1903 Montague Building in Raleigh, North Carolina, were tested to destruction. Of the ve joists tested (of six joists selected; one was found not suitable for testing), the average bending stress at rupture was in excess of 5,000 psi. The average modulus of elasticity was 1,295,000 psi. These measures of strength and stiffness were used to evaluate the capacity of the oor structure. To meet tenant loads for possible retail occupancy in this speculative of ce building, I recommended that all of the existing oor joists be reinforced. (The Montague Building is also discussed in 6).





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where a is the size of particle and n(a)da gives the number of particles per unit volume having sizes between a and a + da. The total fractional volume ftot is obtained by multiplying n(a) by 47ra 3/3 and integrating over the entire range of size from 0 to infinity

lfI 4(47r)2

FIGURE 13.30 Combining Fibonacci studies can yield greater insight. Here the fans and retracements are being used as a combination.

~='" - ,r~-lI:' 1'1 1'2

(5.5.29)

Next define the two-dimensional Fourier transform by making use of the translational invariance property in the horizontal direction:

F(1'l' 1'2) =

The bistatic scattering coefficient for ladder intensity is defined as 41Tr 2 (5.5.31) 'YL(JL s , Pi) = A () h(1') cos i where A is the area of the target under observation. From (5.5.26) we have

dkJ.. eikl- (ra -raj F(kJ..; Zl, Z2)

(5.5.30)

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At Moor elds, a 1792 house in Hillsborough, North Carolina, the excessive de ection of a summer beam was evaluated by measuring offsets in the oor surface above the beam. Based on eld measurements and computer analysis, I was convinced that the summer beam had failed. Indeed, when exposed to view during construction by removing the ceiling plaster, the summer beam contained a severe fracture consistent with a typical bending failure. The only replacement beam available of suf cient stiffness and strength that would t between in the space between the oor sheathing and the ceiling was a steel tube section approximately equal to the original timber beam in size.

(5.5.33)

(5.5.34)

by the retracement lines. The rightmost three rectangles have the bene t of being af rmed by both the fans and the lines. Any time you are approaching an area where two studies agree, you should consider that an especially potent price level. There is no reason to limit yourself to Fibonacci studies when analyzing a graph, of course. Although you do not want to apply so many drawn objects that the chart becomes too noisy with information, the judicious application of well-drawn studies can improve your predictive powers over a stock, index, or any other nancial instrument. In Figure 13.31, a variety of trendlines, channels, Fibonacci retracements, and Fibonacci fan lines have been applied against the S&P 500 index. Working together, these studies are helpful in monitoring and predicting the price behavior on both a large time scale and, as seen on the right side of the chart, a shorter-term time scale as well.

Fo(z', z") = F(kJ.. = 0; z', z")

(5.5.35)

'YL(JL s , JLi) = -

(1 -

e-Td(1/iLs+1!lLi))

(5.5.36) JLi -d -d where Td = "'ed is the optical thickness of the slab. Thus the bistatic scattering coefficient depends only on F(kJ..; z', z") at kJ.. = O. Next, we make

Bridges are built using simpli ed engineering when components such as prestressed, precast concrete are selected from tables for short standard spans.

+ ~ jO dz'jO dz" Fo(z', z") e~,,(ZlliL.+ZII liL;)

use of the plane wave representation of Green's function to calculate the absolute value of the Green's function squared. This will be in terms of a double integral of f dku f dk2J... We then make the transformations of kA.1 = (k a + k2J..)/2 and kD.1 = ku - k2J... Hence

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