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Thus, for any given path, the root-mean squared volatility for inst will simply be equal to (Ti) times the root-mean squared volatility for inst. Given the approximate, but highly accurate, linearity, the price implied by the Monte Carlo simulation will also be multiplied by the same scaling factor, thus ensuring correct pricing for each at-the-money caplet.27 The numerical implementation is quite ef cient as only one simulation is used to price all the caplets. For a given volatility path, all strikes are calculated, and different stopping times along a path are used for different maturities. European swaptions can also be quickly numerically priced in a similar manner to caplets using the displaced diffusion LIBOR model. Denote the instantaneous volatility of the kth swaption when the displacement of the diffusion has a value of by S(k)(t). Let n(k) denote the number of forward rates underlying the kth swap and let Sk be the kth swap rate. Then using a version of Rebonato s swap volatility approximation in equation (13.40),

Note that the total mortgage of $300,000 is used for the pv argument. This calculation can be checked using the calculated payment to determine the PV. This formula returns $299,999.43 (the rounding error is caused by using a rounded payment amount):

ii) clear weather in the uplink and atmospheric attenuation in the downlink, corresponding to a percentage pdw% of the total time. The percentage pup and pdw are such that their sum equals the percentage of time fixed by the performance objective: pup% + pdw% = p% The correct split between pup and pdw is that which makes the value of (C/T)total evaluated under configuration i) (attenuation in the uplink) equal to the value of (C/T)total evaluated under configuration ii) (attenuation in the downlink). The assessment of this split is usually performed by iteration on the computer letting pup vary from 0 to p, with pdw given by p pup, until the values of (C/T)total in the two configurations are equal. For pessimistic purposes, the TDMA link budgets for EUTELSAT II given here have been calculated for the case of the worst climatic conditions experienced in Europe. Table AN2-4c gives the values of pup and pdw and the values of the atmospheric attenuations corresponding to these percentages of time.

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F F dF (t)dF (t)

1 Special care has to be taken when estimating M, which can be done via another maximumlikelihood, or minimum-entropy, criterion.

contours to redistribute light that would be otherwise misdirected or trapped. Other reflector contours Compound contours, which provide asymmetric distribution or maximum beamspread with a shape of minimum dimension, are useful for producing uniformity of luminance from a position close to the surface being lighted; for example, to light the ceiling in a low-height room (figure 9.7). Innumerable other possible reflector contours can be mathematically defined and tailored for a particular function. These reflectors do not have a specific focal point. Reflectors Specular reflectors Almost all reflector design presumes a compact point source of light or a linear source of light at the focus or other precise location. The most compact source is an incandescent filament in a clear bulb. Large variations in beam control occur, however, with the use of lamps that emit

utilized summarizes a week or month of communication activities and content Generally speaking, there is no incentive to disconnect from the dial-up ADSL Internet connection, when there is no charge per time or volume Therefore, only a flat fee for basic services without special requirements will be incentive-compatible However, an always existing spending cap will limit the amount of services utilized over time As stated in Ferrari and Delgrossi [37], the following charging properties exist from a customer s perspective: comprehensibility, controllability, predictability, stability, and fairness With a commercial ISP, a high revenue maximization and best cost-recovery strategy should be achieved [122] Therefore, the pricing model applied and the service bundle offered in a given market situation determines the optimization dimensions for customers and providers.

Figure 8.3 Gasi cation paths to heat and power. (From Ref. [9].)

Excel also enables you to use expressions as arguments. Think of an expression as a formula within a formula. When Excel encounters an expression as a function s argument, it evaluates the expression and then uses the result as the argument s value. Here s an example: