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Both u-separation and d-separation satisfy the graphoid axioms. For u-separation this is evident from the illustration shown in Figure 4.2 [Pearl 1988] (symmetry is trivial and thus neglected). Therefore the graphoid axioms are sound w.r.t. inferences about u-separation in graphs. However, they are not complete, because they are much weaker than u-separation. To be more precise, the weak union axiom allows us only to extend the separating set Z by specific sets of nodes, namely those for which it is known that they are separated by Z from one of the sets X and Y (which are separated by Z), whereas u-separation is monotonic, that is, any superset of a separating set is also a separating set. That is, u-separation cannot be destroyed by enlarging a separating set by any set of nodes, while the graphoid axioms do not exclude this. A set of axioms for u-separation that has been shown to be sound and complete [Pearl and Paz 1987] are the graphoid axioms with the weak union axiom replaced by the following two axioms: strong union: transitivity: (X Y | Z) (X Y | Z W) (X Y | Z) A V (X Y Z) : ({A} Y | Z) (X {A} | Z)

for t 0 and 1 + 2 = 3 , and for 1 + 2 = 3 it is fT (t) = ( 2 + 1 3 t) exp( 3 t). (5.18)

CSS is one of the most important technologies used with XUL. CSS is used to attach behavioral bindings to XML elements with XBL. Style sheets are also used in conjunction with the skinning of the Mozilla browser. Before XUL, the only control over the browser interface in a standards-based Web browser was in the document display area. XUL and CSS enable you to skin, or change, the whole look and feel of the browser creating a Netscape theme. The menus, windows, and everything viewable to a user are easily modified in a Netscape theme. The potential for this is tremendous. In the future, imagine that a visitor to your music-oriented Web site sees a browser that transforms

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where ^ t is the approximation for v t . The integral (1.8.5) can be evaluated by v using residue calculus and choosing the path of integration along the in nite arc

The effective length for a single-turn air core receiving loop is:

(February 25, 2002), A-3.

Business case Making the business case Provides architectural principles Project proposal Supports impact analysis Anticipatory Defensive

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A matching network for an electrically small antenna or for a superdirective array must cancel the large reactance and must transform the small radiation plus loss resistance to the nominal value, usually 50 ohms. Generally each element of an array will require a different matching network, although symmetric (broadside) arrays need fewer. If the matching network is composed of discrete L and C components, the low-R, high-X requirements will produce very large circulating currents in the overall circuit, consisting of the array element, the matching network, and the generator. These circulating currents will magnify the intrinsic loss to a much larger realized loss. Similarly, a distributed matching network under low-R, high-X conditions will have very large standing waves along the stubs and transformer sections. Again the intrinsic loss is magni ed. In both cases the larger loss is due to power being proportional to voltage (or current) squared; the circulating currents or standing waves are large. A transmission line transformer is typical. Let the matched loss be L and the antenna voltage standing wave ratio be VSWR. Then the actual loss L a is (Moreno, 1948): La = (VSWR + 1)2 L2 (VSWR 1)2 4 L VSWR VSWR ( L2 1) 4L (2.42)

where mA x , the membership function, is de ned as mA : U ! 0; 1 2:2

make Number num 78.90; make Number num 89.01; make Number num 90.12; make Number num 01.23; make Number num 32.10; make Number num 21.09; make Number num 32.10; make Number num 43.21; make Number num 54.32; make Number num 65.43; make Sum total 0; fire block 1 off; message "ready to run SUM.PAR\n"; message "fireable rule stack\:\n"; prstack; message "Ready to execute \ run 1\ \n"; run 1; write "fireable rule stack\:\n"; prstack; write "Ready to execute \ run 1\ \n"; run 1; string = "SUM.PAR finished.\n"; string + "Compare to program SUM.FPS!\n"; message "<string>"; exit; : ***************************************************** * call urc.exe;

The equality involving the function cen is immediate. The last equality can be easily translated into |Q||W| cQ cW |Q| + |W| =

The explanations provided by the earlier sections should make the above code self-explanatory rendering further comment unnecessary. Figure 12.6 shows an example session pricing a Bermudan in an Excel session. Pricer VBA Client Here is the example client code for interfacing to the ppf.pricer COM object. PPF HullWhiteLatticePrice The function for obtaining the price of a trade via the Hull White model on a lattice.

(Estimated) conditional probability of the attribute value ci given that p N attribute A has the value aj , that is, pi|j = pij = Nij . .j .j

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