Conditional demand

Conditioning Demands Other Than for Human Occupants... 

Efficient combustion of gas under varying conditions demands the use of a wide variety of burners. However, these can all be categorized as natural draft or forced draft. 

With regard to higher pressure industrial and power boilers, the more exacting waterside and operating conditions demanded generally dictate that an alternative approach to corrosion control be employed, which usually precludes the presence of free-caustic. 

The main utility of Peterson olefination lies in the contrasting stereochemical requirements (6) for elimination, use of base requiring a syn conformation whereas acid conditions demand an anti conformation, with complementary geometrical results ... 

Heterogeneous catalysis is by nature a surface phenomenon. An efficient catalytic system under reactive conditions demands a delicate energetic balance. For a catalytic reaction to occur, reactant molecules must adsorb on a surface, react, and... 

The term conditional demand is derived from the concept of conditional density and simply means the following Let a random variable be described by its density. What do we know about the outcome of the random variable, if we know that the outcome will be not less than a certain value The answer is, roughly speaking, that this additional knowledge in typical cases increases the mean value and reduces the standard deviation. This effect can be calculated precisely. 

Figure 6.5 below shows the construction of the conditional demand density from the original demand density, assuming that 50 units have already been ordered. 

Especially in an industrial environment conditional demand is an important concept. This is because orders usually allow for some delivery time. This delivery time is in many cases long enough to be taken into account in production scheduling. As the deadline for orders for a certain date of delivery comes closer one can compare the original forecast with the orders that were already received. It is intuitively clear that if many orders were already received this implies a somewhat increasing forecast with less uncertainty. Sometimes orders that were already received can be used to automate the forecast to a certain extent because one knows that usually 25% are ordered four weeks in advance, 50% are ordered two weeks in advance and the like. We assume here that there is a valid latest forecast at the point in time where a decision on the next production volume is necessary and the orders that were already received are taken into account at that fixed point in time. 

We only present the continuous version of the precise formulas for conditional demand, which makes this intuitive reasoning precise. 

The mean conditional demand is not smaller than the unconditional mean demand. 

In the first section we discussed random demand. Then we calculated the conditional demand and now finally we define conditional random service and conditional random shortage. These concepts are very important for optimization of service levels under capacity constraints. 

If the shortage is greater than zero, the service is equal to the inventory. If the shortage is zero then the conditional demand is at most the inventory. 

This section relates random services and random shortages to conditional demands as defined in Section 6.2.5. Conditional random service is the crucial quantity that has to be calculated when a safety stock level has to be determined. Conditional random service results from three quantities a demand density 5, an already ordered quantity r and an available inventory s. From these parameters we obtain two new densities, the conditional service density 5+,r,s and the conditional shortage density... 

The conditional service density derived from a continuous demand density is continuous almost everywhere but has one exceptional point which carries a discrete probability mass The probability that the whole inventory s goes to service is the integral of the conditional demand density from s to oo. In other words, the service is s if the demand is s or above. 

The conditional shortage x and the demand x + s have the same density (x > 0). The conditional shortage is zero with the same probability for the conditional demand to be at most s. 

The first term describes the situation when the available inventory is at least the conditional demand. The last term follows from these observations With total probability 1 — A (s) the demand is greater than s. With total probability the conditional demand is greater than s. In these cases there is a shortage and we... 

The key mathematical tool for the solution is the expected marginal service at a given stock s. If 5r as in Section 6.2.5.1 denotes the conditional demand density and Ar the corresponding conditional service distribution, then the expected marginal service is simply 1 — Ar. Indeed, if the stock s is 0 then 1 — Ar (s) = 1 — Ar (0) = 1 — 0 = 1. In other words, if we add a little bit (mathematically speaking, an infinitesimal small amount) to our stock 0, this little bit is sold... 

Finally, Fig. 5.15 relates derived potentials to gross electricity demand. More precisely, it depicts the total realisable mid-term potentials (up to 2020) for RES-E as the share of gross electricity demand in 2004 and 2020 - for all EU25 countries as well as the EU25 in total. (The total realisable mid-term potential comprises the already achieved (as of 2004) and the additional realisable potential up to 2020.) The impact of the expected demand increase is crucial if the indicated realisable mid-term potential for RES-E, covering all RES-E options, was fully exploited up to 2020, only 41% of gross consumption could be covered, if the demand increases as expected under business as usual conditions. (Demand figures for 2020 are taken from DG TREN s BAU forecast (Mantzos et al., 2003).) In contrast, if a stabilisation in demand is achieved, RES-E may contribute to meet about 53% of total demand. 

This may appear to be an unlikely situation to encounter until one recalls that there are a number of reactions involving two isolated and independently reacting centers. One might then anticipate that statistically A , = Ik and that Sg = l/2( + < ). These are precisely the conditions demanded by (1.91). It is worth noting that in this case the observed first-order rate constant is k2-... 

Many acid-labile linkers are used to assemble combinatorial libraries. Compounds are cleaved in the final step by TFA/DCM solution with various concentrations for a certain period of time. Mild cleavage conditions may lead to incomplete cleavage of the desired compound from a solid support. On the other hand harsh conditions may cause compound degradation and side reactions. Harsh conditions will also cause the partial breakdown of resin and the leaching of unidentified impurities into the final products. Harsh cleavage conditions demand the stabihty of all compounds under such conditions. This may limit the scope of combinatorial synthesis... 

Grahame derived an equation between a and based on the Gouy-Chapman theory. We can deduce the equation easily from the so-called electroneutrality condition. This condition demands that the total charge, i.e. the surface charge plus the charge of the ions in the whole double layer, must be zero. The total charge in the double layer is /0°° pe dx and we get [59]... 

In general, these conditions demand a method of preparing i A) and t/fB) that correlate the internal states A(/ )) and r/jB(/)> with their associated momenta kf, kf so as to obtain Eq. (7.17). Since the overall phase of the wave function is irrelevant to the state of the system, the dynamics is not sensitive to the overall phase of I Aa) I Ab ) However, the phases of the interference term must be well defined or the control will average to zero. 

Clinical investigations of A -tetrahydrocannabinol (4,5) and ll-hydroxy-A -tetrahydrocannabinol (6) have relied upon analysis by radioactive labeling. However, the study of distribution, metabolism and excretion of the drug and its metabolites under chronic or "street" conditions demands nonradioactive analytical procedures. When plasma suspensions of l c-A -tetrahydrocan-nabinol were administered intravenously to three dogs at doses of 0.1 - 2.0 mg/kg and plasma levels of 1 were followed for up to 7000 minutes, no significant differences were seen in 1 plasma levels as determined by liquid scintillation and electron capture detection (GLC) after HPLC collection. 

We can now introduce the condition demanded by the atomic nature of the medium. We shall do this only for the simplest case of a simple cubic lattice, but similar results hold in general. Let the atoms be spaced with lattice spacing d, such that X = Nd, Y = Nyd, Z — Nd, and... 

The condition u(0 ) = u prescribed by Equation 8, hereafter called the input condition states that every phase trajectory starts on a vertical line u = u. At the same time, the condition v(x ) = vt imposed by Equation 9 which we shall call the output condition demands that every trajectory ends on a horizontal line v = v- . Thus we have a point (u, v ) associated with each solution. The set of all such points constitutes a structure which we call the input - output space of the reactor. For the case of convex isotherm, this was done by Viswanathan and Aris (1). 

The 2+/3+ transition in the Marcus model or its successors involves only small Inner Sphere changes in solvation molecule coordinates in the radial direction to and from the ion. Electron transfer under FC or Born-Oppenheimer conditions demands that an activation energy in the outer Continuum should resist one-electron transfer via a continuum inertial term X = (e2/2r )(l/n2 - l/e0) where r is an effective intermediate reactant-product radius. To avoid error, X can be... 

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