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In spite of their different composition, the CRB Futures and Spot Indexes usually trend in the same direction. To fully understand why they diverge at certain times, it's important to consult the two sub-indexes that comprise the CRB Spot Index the Spot Raw Industrials and the Spot Foodstuffs. Significantly different trend pictures sometimes develop in these two sectors. For example, the Raw Industrial Index bottomed out in the summer of 1986, whereas the Foodstuffs didn't bottom out until the first quarter of 1987. The Foodstuffs, on the other hand, peaked in mid-1988 and dropped sharply for a year. The Raw Industrials continued to advance into the first quarter of 1989. While the Raw Industrials turned up first in mid-1986, the Foodstuffs turned down first in mid-1988. By understanding how industrial and food prices perform relative to one another, the analyst gains a greater understanding into why some of the broader commodity indexes perform so differently at certain times. Some rely more heavily on industrial prices and some, like the CRB Futures Index, are more food-oriented. Many economists believe that industrial prices more truly reflect inflation pressures and strength or weakness in the economy than do food prices, which are more influenced by such things as agricultural subsidies, weather, and political considerations. Still, no one denies that food prices do play a role in the inflation picture. One popular commodity index goes so far as to exclude food prices completely. Since its creation in 1986, the Journal of Commerce (JOC) Index has gained a following among economists and market observers as a reliable indicator of commodity price pressures.

/********************************************************************************** calcVega: computes the pathwise approximation of vega assuming del_lambda del_theta = 1 [in]: M : number of simulations [out]: none /*********************************************************************************/ void VegaApprox::calcVega(long M) { oat nyear=5, delta=.25, epsilon=.25,B=1; int m=1, N=20; oat F0[20],sigma[20]; FILE * le_ptr; int i,j,run,n,t; double F[20],res[20][2],z[1],B0[20],K[20],sumz,dd; double v,w,discount,lam,sen,Del_dft[20],Del[20]; cout.precision(9); try { le_ptr=fopen( F0 , rt ); if( le_ptr==NULL) cout << File not found << endl; for(i=0;i<N;i++) fscanf( le_ptr, %f , &(F0[i])); fclose( le_ptr); le_ptr=fopen( sigma , rt ); if ( le_ptr==NULL) cout << File not found << endl;

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and any matrix commutes with itself, of course. One "unfortunate" property of matrix multiplication is that the equation [-/!][ ] = [A][C] does NOT imply that [B] = [C]. In the same vein, the equation [A](c) = [B](c) does not imply equality of [A] and [B]. If a square matrix is multiplied by itself k times, the resultant matrix is defined as [A]k [A]k=[A][A]...[A]

ative value of content decreases, and billing of content is performed along with the transport service.

Other basis types include Hermite, Legendre, Chebyshev, Jacobi, and Gegenbauer polynomials. Numerical tests also show Fourier or trigonometric series and even simple powers of the state variables yield accurate results.

( i j t )

Sometimes, calculating the difference between two days is more difficult. To demonstrate, consider the common fence-post analogy. If somebody asks you how many units make up a fence, you can respond with either of two answers: the number of fence posts, or the number of gaps between the fence posts. The number of fence posts is always one more than the number of gaps between the posts. To bring this analogy into the realm of dates, suppose you start a sales promotion on February 1, and end the promotion on February 9. How many days was the promotion in effect Subtracting February 1 from February 9 produces an answer of eight days. Actually, the promotion lasted nine days. In this case, the correct answer involves counting the fence posts, not the gaps. The formula to calculate the length of the promotion (assuming you have appropriately named cells) appears like this:

In any ideal lossless transformer, the rotor power would remain unchanged when referred to the stator and, therefore, from equations (10.16) and (10.17),

U0 (v j , Zi, j )) 2

=RIGHT(A1,10)

Juana has provided Nicholas with a copy of her RFI_Tel3 telephone listing file. He wants to compare it with Freston s new RFI_et_al_Tel#s file, the one Freston mentioned to him at lunch. See how the standard error output from Nicholas next command, to cat RFI_Tel3 and /root/RFI_et_al_Tel#s, goes directly to the screen or system console:

in combustion presents a lilac-blue ame and small red stains. It does not leave soot and produces minimal pollution. The caloric power of biogas depends on the amount of methane in its composition, which could reach 5000 to 6000 kcal/m3 . Biogas can be used for stove heating, campaniles, water heaters, torches, motors, and other equipment. 8.4 BIOMASS FOR BIOGAS

This appendix gives a few additional considerations to coding, modulation and multiple access. These considerations apply to systems based on geostationary satellites with transparent transponders.

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