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, only the diagonal, superdiagonal, and subdiagonal entries are nonzero), we do not have to store all the zeros, but just the nonzero elements The inverse of M, M 1, is not tridiagonal and requires a lot more storage than M We can rewrite the system of equations in (513) as: 1 0 0 K 0 0 0 * p M, d 1 0 K K K K 0 1 K 0 K K where p *M, d = and u * 1, M = i+ ui +1, M , pm u * 1, j +1 = i+ i+ ui +1, j +1 puu * 1, j ,d pm pu pj* j = M + 1, , M 1 (518) pd , pm + p j*1, d = pd ,d pm pu pj* j = M + 1, .

Equation A.6.1 arises when the Maxwell-Stefan equations are solved for the case of steady-state, one-dimensional mass transfer, as discussed in 8. The matrices [k] and [<l>] are as defined in 8, ct is the molar density of the mixture and a scalar, and (Ax) is a column matrix of mole fraction differences. All matrices in Eq. A.6.1 are of order n 1 where n is the number of components in the mixture. For the purposes of this discussion we shall assume that the matrices [k] and [O] have already been calculated. The matrix function [<l>][exp[<I>] [7]]" 1 , denoted by [H], can be computed using Sylvester's expansion formula (see, however, below) so the immediate problem is the calculation of the column matrix ( / ) from (J)=c,[k][E](Ax) A.6.1 Arithmetic Operations Now, the multiplication of two square matrices of order m involves m 3 multiplication operations and m2(m 1) additions. However, the multiplication of a square and a column matrix involves m2 multiplications and m(m 1) additions and the multiplication of a square matrix with a scalar involves just m2 multiplications. With regard to Eq. A.6.2, there is, therefore, some incentive to computing ( / ) from right to left rather than from left to right, as written. A.6.2 Matrix Functions (A.6.2)

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, M 2 K * p M + 2, d K 0 0 K K K 0 K 1 0 0 K K K K * pM 2, d 1 0 0 0 0 K 0 pM 1, d * 1 ui, M ui, M +1 ui, M + 2 = K ui, M 2 ui, M 1 u i, M u * 1, M i+ u * 1, M +1 i+ u * 1, M + 2 i+ K u *+1, M 2 i u *+1, M 1 i u *+1, M i (516).

Whichever mode is used, the Control Word can be used to carry the value of the ATM Cell Loss Priority (CLP) bit from the ingress PE to the egress PE. The egress PE can copy the value of the bit into the regenerated ATM cell. Most implementations today support the N-to-one mode rather than the one-to-one mode. The latter is regarded as optional by the PWE3 ATM draft [PWE3-ATM] and is not mentioned in [MRT-ENC]. Whichever mode is used, the Header Error Check (HEC) field of each ATM cell is not sent across the core. Instead, it is regenerated by the egress PE. Either mode allows for multiple ATM cells to be sent in a single MPLS packet across the core. The number of cells that the user wishes to send is a tradeoff between bandwidth efficiency, delay variation and the number of cells that the user can afford to lose should an MPLS packet be lost.

(10.10)

To calculate value added, we take the periodic differences between the fund and benchmark returns, add the differences, and divide the sum by the total number of returns. To convert value added to an annualized equivalent, multiply it by the number of periodic observations in a year. ( RP i RM i ) Annualized value added = -------------------------------------- P N

It demonstrates that the communications between the servlet container and the EJB container are working. It provides us with a simple example of how to create and deploy a servlet that accesses an EJB. It provides us with an opportunity to create and test an implementation of the BusinessDelegate design pattern. We will reuse this Business Delegate object when we create a Struts-based application later in the chapter.

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