Relative scheduling properties

Section 6.3 presents polynomial-time algorithms to check for well-posedness, make the constraints well-posed with minimal serialization, remove redundant anchors, and find the minimum relative schedule. Section 6.4 analyzes the properties of the algorithms. In particular, we show that the algorithms are guaranteed to yield a minimally serialized, well-posed, minimum schedule, if one exists. Finally, Section 6.5 summarizes the relative scheduling approach. 

In this section, we analyze several properties of relative scheduling. The following theorem states the existence criterion for making a constraint graph well-posed. 

We analyze in this section properties of the algorithms presented in Section 6.3. We prove first the makeWellposed algorithm can minimally serialize an ill-posed constraint graph in attempt to make it well-posed, if a well-posed solution exists. We then prove the iterative incremental scheduling algorithm can construct a minimum relative schedule, if one exists, in polynomial time. 

The iterative incremental scheduling algorithm constructs a minimum relative schedule, or detects the presence of inconsistent timing constraints, with at most i + 1 iterations. This is a very desirable property, since the number of maximum timing constraints i is in general small. The proof follows the outline in [LW83]. Note that in the sequel the full anchor set A(v <) for a valex Vi is used in the computation of the start time and offsets. By Theorem 6.2.4 and Theorem 6.2.6, the result is applicable when the relevant anchor set R vi) or the irredundant anchor set IR(vi) are used instead. 

In relative scheduling, the start time of an operation is defined as time offsets with respect to the completion of anchors. Constraints are feasible or well-posed depending on whether they can be satisfied under restricted or general input conditions, respectively. Redundancy of anchors was introduced to simplify the start time of operations by removing redundant anchor dependencies. This can lead to a more efficient control implementation because operations need to be synchronized to a fewer number of signals. Analysis of these properties was presented in this chapter. 

Another factor to be considered is the time required to fabricate additional liners if the initial supply is depleted. Recently, General Atomics claimed it was able to fabricate 20-mil thick liners of the required diameter for the reactor. General Atomics plans to float a precious-metal liner in a cylindrical Hastelloy pressure vessel and use cooled elastomeric O-rings that have performed satisfactorily on other SCWO systems to form the SCWO reactor. The annular space between the liner and the vessel wall will be monitored for leaks to indicate when change-out of the liner is required. No decision has been made yet on whether to use platinum or Pt-20%Ir. Because they have markedly different mechanical properties, these two liner materials may require significantly different fabrication methods. Platinum is relatively weak and very ductile Pt-20%Ir is less ductile but 10 times stronger. Final selection of the liner material for use at the NECDF was scheduled for early 2000. Fabrication... 

ASTM D-1344 describes a cross-lap specimen of the type shown in Fig. 2d for determining tensile properties of adhesive bonds. Wood, glass, sandwich, and honeycomb materials have been tested as samples in this general configuration. Even under the best of circumstances, one would not anticipate the stress distribution in such a case to be very uniform. The exact stress distribution is highly dependent on the relative flexibilities of both the cross beams and the adhesive. Certainly, caution must be exercised when comparing tensile strength from this test with data obtained from other tensile tests. Probably for these reasons, this test is scheduled by ASTM for discontinuation. 

Heat-cured adhesives. Heat curing by convection in box ovens is the most widely used and simplestmethod for curing adhesives. Heat is applied until a temperature is reached at which polymerization occurs and continues until the polymerization is complete. Time-temperature curing schedules are developed for each adhesive for which optimum properties are achieved. F or each of their adhesives, suppliers provide several cure schedules that are considered equivalent relative to final properties. The user may also develop... 

Prediction of battery life is not only difficulty but also expensive. Furthermore, the battery life is dependent on the number of charge and discharge cycles, materials used, and operation type (intermittent or constant). For starting, lighting, and ignition (SLI) applications, prediction of Pb-acid battery life is relatively simple, because the Pb-acid battery design is fully matured and the material cost and maintenance procedures are fully known. In case of batteries using solid electrodes and exotic solid-state materials, prediction of battery life is more complex. As stated earlier, prediction life is strictly dependent on the materials used for the cathodes and anodes, properties of the materials, and the maintenance procedures and schedules used. 

Some typical properties of the two families of polymer are listed in Table 3.2. It must be most strongly emphasized that the information is again indicative and will depend upon the exact system used and the cure schedule. For further details the manufacturers data sheets should be consulted. Among the important points are that all the systems have similar densities and relatively low strengths and moduli. 

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