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It is highly regrettable that some of the highest qualities of the human mind, such as intuition and direct apprehension, have been banned from our schools and have been overwhelmed by abstract and impersonal mathematical formulas. We cannot forget that in the distant past intuition allowed the execution of works which cannot be analyzed today by the most modern theoretical methods, and before which we must bow in reverent and humble admiration. We cannot deny that the potentialities of mathematical methods are soon exhausted, even when their application is dif cult and complex. Special, skinresistant, and highly indeterminate structures cannot be analyzed by mathematical theories, although they are extremely ef cient from a technical, economical, and architectural viewpoint. Moreover, the most advanced chapters of theory of structures, which deal with the solution of statically indeterminate systems, can be used only to check the stability of a structure. They can be used only to analyze numerically a structure already designed, not only in its general outline, but in all its dimensional relations. The formative stage of a design, during which its main characteristics are de ned and its quality and faults are determined once and for all (just as the characteristics of an organism are clearly de ned in the embryo), cannot make use of structural theory and must resort to intuition and schematic simpli cations.5



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(5.5.50)

411,0

Z2//J,;

FIGURE 11.26 This seven-fold rise in CHTR was preceded by an important double bottom price pattern.

(5.5.51)

dr'El(!r-r'l)e T'!JI, (5.5.52)

The ladder bistatic scattering coefficient is obtained by using (5.5.51) m (5.5.36).

dr' eT'IJL, ls(r')

(5.5.53) Equation (5.5.52) is of the form of the Schwarzschild-Milne problem [Chandrasekhar, 1960]. Its equivalence to radiative transfer equations can be demonstrated as follows. Define upward-going higher-order diffuse specific intensity as





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The essential part of the design of a building consists in conceiving and proportioning its structural system; in evaluating intuitively any dangerous thermal conditions and support settlements, in choosing materials and construction methods best adapted to the nal purpose of the work and to its environment; and, nally, in seeking economy. When all these essential problems have been solved and the structure is thus completely de ned, then and only then can we and should we apply the formulas of the mathematical theory of elasticity to specify with greater accuracy its resisting elements.

(5.5.54)

(5.5.55)

(5.5.56b)

, 1 _eIT-TIJL dlt ,

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strong support zone. Any stock which has been suffering a decline needs to show this line in the sand so that people aren t convinced the security is simply going to $0. A different company (Charles & Colvard) with a nearly identical ticker symbol (CTHR) illustrates this point vividly. The stock certainly had suffered a harrowing loss, falling from $15 to about 50 cents. But on ve different occasions, highlighted in Figure 11.27, the stock refused to go beneath a certain level. As is often the case, the stock was swinging wildly up and down during this time period, as buyers and sellers struggled with establishing leadership. Keep in mind also that, after such a serious decline, there would be a tremendous amount of suspicion with respect to the stock s ability to hold onto any price gains. The time the stock spent in 2001 pushing its way between 50 cents and $1.50 was time well spent, as evidenced in Figure 11.28. The very strong multiple bottom, highlighted with an oval in this chart, gave buyers the con dence to begin reentering the stock in force, and that eventually pushed the stock toward a huge multi-thousand percentage point gain from 2002 through 2005. Incidentally, you can also see another nice bottoming pattern from 2002 through 2004 as the stock rmed up new sup-

(5.5.57)

dlt (I(r,lt)

+ I(r, -It)) =

-- - -

Js(r)

The analysis of existing structures, such as in the eld of historic preservation, requires that we have an appreciation for traditional methods of construction that may have been based on simpli ed engineering. It is only through testing, observation, and measurement that we can gather enough information to build an accurate model of the structure.

dr'E 1 (lr - r l)e T Ill; (5.5.60)

(;;21

dT'E 1 (IT-T'I)e T 'lf l ;

FIGURE 11.28 The support level in 2001 was hit many times before the stock nally started heading upward to a gigantic percentage gain.

(5.5.61a)

dIt (I( T, JL ) + I( T, -JL ))

+ -(;;2

10 dT' El (IT - T'l)e ,1/1;

(5.5.61b)

Most historic structures are constructed of timber and masonry. Simpli ed engineering is justi ed in dealing with these materials when accurate design values cannot be ascertained. The absence of construction documentation and quality control in the manufacture and construction of the component elements requires that analysis be based, at least in part, on judgment. Of course this being the case, one s analysis can only be as good as one s judgment, as well as the initial assumptions that are made. A thorough testing program can narrow the range of applicable design values, but engineering judgment must still be applied. Many historic structures will often times not stand close engineering scrutiny, yet they survive, providing adequate service for many years.

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