Undetermined system

Step 1 Compute the general solution to the undetermined system (AiX = 0). Using the procedure outlined in the previous chapter, the Q-R orthogonal factorization of Ai produces Qx, Rx, IIX matrices, which allows the calculation of Qxi, QX2, Rxi, Rx2, xfx, xg—rx such that... 

The systems with added iron-containing materials would amount to mineral buffer systems which should define the fugacities of oxygen and sulfur until one or more of the components of the buffer has been consumed. In general, all of the experiments have been made on thermodynamically undetermined systems, that is, not enough information has been obtained to define the systems. 

This distinction is rarely important, as V v is normally very small in t3q)ical reactor flow problems, nevertheless adopting the rigorous form of the constitutive relation (1.69) the bulk viscosity pg appears as an undetermined system parameter. 

The problem is finding the vector z that solves the undetermined system (8.3). 

The field equations and jump conditions form an undetermined system, insufficient to yield specific answers unless further equations are supplied. 

This law is showing that the mean pressure in a deforming viscous fluid is not exactly equal to the thermodynamic property called pressure (i.e., apparently the constitutive relation is not consistent with the local equilibrium assumption). This distinction is rarely important, as V v is normally very small in typical reactor flow problems, nevertheless adopting the rigorous form of the constitutive relation (1.77) the bulk viscosity fiB appears as an undetermined system parameter. Stokes [144] solved this problem by introducing the novel assumption that = 0. Adopting this... 

The mechanism for this photoreaction has not been elucidated, although it has been ascertained that these products are not observed in the dark reaction with acetone under the same conditions as used in the photolysis. The source of the isopropylidene unit is undetermined, but since all extraneous organic sources were excluded in the experiment, it seems clear that it originates from the azulene system itself, presumably from the five-membered ring. 

Although several approaches to stroke classification have been described, the most common mechanism-based classification in current use is the system described by the TOAST investigators." This classification describes five major subtypes of ischemic stroke based on the results of neuroimaging and other medical investigations, namely (1) LAA, (2) cardioembolism, (3) small-vessel occlusion, (4) stroke of other determined etiology, and (5) stroke of undetermined etiology. Inter-rater reliability of the TOAST scheme has been reported as moderate-to-substantial K 0.5-0.7). 

The procedure is schematically shown in Fig. 34.29. Equation (34.10) represents a homogeneous system of equations with a trivial solution r, = 0. Because component / is absent in the concentration vector, this component does not contribute to the matrix T °. As a consequence the rank of T is one less than its number of rows. A non-trivial solution therefore can be calculated. The value of one element of r, is arbitrarily chosen and the other elements are calculated by a simple regression [17]. Because the solution depends on the initially chosen value, the size (scale) of the true factors remains undetermined. By repeating this procedure for all columns c, (t = 1 to p), one obtains all columns of R, the entire rotation matrix. 

The other variable time, t, can vary from zero to some undetermined value, but the system is also represented by the characteristic time, x. Note that the value of 1/k also represents a characteristic time for the process. 

The terminal spectrum is furnished by cooperative motions which extend beyond slow points on chain in the equivalent system. The modulus associated with the terminal relaxations is vEkT, which is smaller by a factor of two than the value from a shifted Rouse spectrum. It is consistent with a front factor g = j given by some recent theories of rubber elasticity (Part 7). The terminal spectrum for E 1 has the Rouse spacings for all practical purposes, shifted along the time axis by an undetermined multiplying factor (essentially the slow point friction coefficient). Thus, the model does not predict the terminal spectrum narrowing which is observed experimentally. 

Here n is the number of moles of the fcth component. The equilibrium composition is found as the set of nt values (k = 1,..., K) that minimizes the function G, with the constraints of the mass balance of the system. The problem of a constrained minimization can be solved by a number of methods [369] frequently the method of undetermined Lagrange multipliers is used [368]. 

The malfunction or failure of system components, incorrect documentation, or improper operation that makes the proper use of the system impossible for an undetermined period, characterizes some of the incidents that can affect the correct operation of a computer system. These system incidents are also nonconformances. 

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