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The 11 bit program counter register contains the address of the next ~n~truction be executed After a reset 11in normal mode to the program counter 8 inilialized 10 Ox800 s

(1219)



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and the notation is the same for all tempered distributions T In view of (1218), we can extend (1219) to locally integrable functions f (z, z ) that increase like 2 e |z| p(z, z ) for some < 1 and some polynomial p, and to all distributions that are derivatives (in the distributional sense) of such functions We recall here that partial derivatives of distributions are given by r s T, z r z s = ( 1)r+s T, r s z r z s (1220)

Macromolecules Containing Metal and Metal-Like Elements, Volume 6: Transition Metal-Containing Polymers, edited by Alaa S. Abd-El-Aziz, Charles E. Carraher Jr., Charles U. Pittman Jr., and Martel Zeldin. Copyright 2006 John Wiley & Sons, Inc.

We also recall that the multiplication of distributions T by smooth functions (z, z ) C (R2 ) is understood through S(R2 ) T , = T ,





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Table 31 Energy Consumption, 2006

(1221)

Now, equipped with the above distributional material, we consider as acceptable observables those distributions in D (R2 ) that obey the following condition

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De nition 122 (Coherent state quantizable observable) A distribution T D (R2 ) is a coherent state quantizable classical observable if there exists < 1 such that the 2 product e |z| T S (R2 ), that is, is a tempered distribution

1,721 1,147 518 386 277 248 245 195 171 160 7,912

Of course, all compactly supported distributions such as the Dirac distribution and its derivatives are tempered and so are coherent state quantizable classical observable The Dirac distribution supported by the origin of the complex plane is denoted as usual by (and abusively in the present context by (z, z )): C (R2 ) , = d 2 z (z, z ) (z, z ) = (0, 0)

(1222)

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Let us now coherent state quantize the Dirac distribution using the recipe provided by (123) and (128): 1 (z, z ) |z z| d 2 z =

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1 n!n !

The unit variability caused by elimination by a metal-containing group during polymerization is one of the most important types of structural defects in metallopolymeric chains. Attempts to polymerize many MCMs have failed due to the elimination of a metal hydride and the formation of polymers devoid of the metal (scheme 13).70 As a rule, introduction of a vinyl group into the ligand environment of a metal complex decreases its reactivity, apparently due to conjugation with the metal d-electrons. In the case of MCMs with other types of polymerizable groups (styryl, allyl, methacryate, etc.), the probability of these processes occuring is low.

1 1 = |z = 0 z = 0| = 00 (1223) We thus nd that the ground state (as a projector) is the quantized version of the Dirac distribution supported by the origin of the phase space The obtaining of all possible diagonal projectors nn = |n n| or even all possible operators nn = |n n | is based on the quantization of partial derivatives of the distribution First, let us quantize the various derivatives of the Dirac distribution: U a,b = = b a (z, z ) |z z| d 2 z z b z a ( 1)n+a

b! a! 1 n b,n a nn (b n)! n!n !

Source: US Energy Administration, International Energy Annual, 2007

(1224)

s 10

Once this quantity U a,b is at hand, one can invert the formula to get the operator r+s,r = |r + s r| as

1 U p, p+s , p!(s + p)!(r p)!

0 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030

(1225)

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