Checking well-posed

From Theorem 6.2.2, a constraint gr q)h is well-posed if and only if i4(v ) C A vj) for all e,j E, and the forward constraint graph G(V, E/) is acyclic. We describe an algorithm called checkWellposed that determines whether a constraint graph G(y,E) is well-posed. First, the constraint graph Go V,E), wh e all data-dependent delays are set to zero, is checked for positive cycles to ensure the constraint graph is feasible. The algorithm then checks the anchor sets associated with the ends of every edge in G for containment 

The worst-case complexity of checkWellposed is dominated by the check for cycles, which is 0 V 1) [BN86]. The check for containment requires worst-case complexity of 0 Et i4 ). 

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Checking Well-posed - The constraint graph is checked for well-posedness using Theorem 6.2.2, using an algorithm called checkWellposed. 

First we should check to see if this problem is soluble (i.e.., well-posed in the sense of the Gibbs phase rule). The Gibbs phase rule, eqn. (6.9-6) is F = C-M-P + 2. Thus here we have F = 3-0-2 + 2 = 3 degrees of freedom. Since the temperature, and two independent liquid-phase mole fractions are specified, the problem is well posed. 

Unfortunately, for a given domain of interest boundary conditions can be chosen that over- or underspecify the problem. An example of an over-specified problem is a constant area duct, with a fixed fluid velocity at the inlet and but different at the outlet. Naturally, for an incompressible fluid both conditions cannot be physically satisfied in the absence of a mass source. In the same sense, a closed box with only heat flux boundary conditions is under specified since the temperature level is not constrained, and therefore unpredictable. It becomes clear that defining well posed boundary conditions is quite important for the proper solution of a flow problem. An easy way to check for well posed boundary conditions is to ask yourself Could the chosen configuration be physically recreated in the laboratory . 

In each step of the whole procedure, we can also check if the computed z e U, thus if it remains in the admissible region. If z tends to escape from the admissible region then the solution gets lost and the reconciliation procedure has failed. If it is a single case in a series of measurements, most likely the initial guess (in particular the measured value x ) was too bad (perhaps due to a gross measurement error). If the case occurs frequently then, most likely, the reconciliation problem is not well-posed. 

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. 

Then the program separates the two words by looking for one or more spaces between them. (It s best that it be tolerant of more than one space between words as well as spaces after the command. INPUT automatically strips leading spaces, so they don t pose a problem.) The above program section receives the player s INPUT (line 1000) and creates two strings, Cl and C2 (lines 1080 and 1085). Spaces between words are also checked for in line 1050. 

In this method the topics for discussion is announced to the students well in advance. The teacher gives a brief introduction about the contents of the topic and them suggests to his students various reference books, text books and other books. Students are then required to go through the relevant pages of these books and come prepared for a discussion of the topic on a specified day. During actual discussion period teachers poses a lew problems and thus provides the necessary motivation. The students are then asked to answer the question one by one and when ever thinks fit advises some students not to go out of the scope of a particular question or topic under consideration. This check is essential otherwise immature students may go out of the scope of the topics. 

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