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Using the same Y outcome vector and applying the same least squares calculation now gives b2 = (1111.11, 11.89, 1104.11) and Y = (11.22, 2.11, 2.78, 2.00) . However, the variance covariance matrix reacts sharply to the movement toward singularity as seen in the standardized correlation matrix: 1196.70 0.48 0.99 0.48 . Cs = 0.48 13.70 0.99 0.48 1193.00 Indeed, if X3 = 2.999, X X is singular (with regard to precision in Gauss and Splus) and we must use the generalized inverse. This produces b3 = GX Y = (1.774866, 5.762093, 1.778596) and Y = XGX Y = (11111.11, 11.89, 11104.11) . The resulting pseudovariance matrix (calculated now from G 2 ) produces larger standard deviations for the rst and third explanatory variables, re ecting greater uncertainty, again displayed as a standardized correlation matrix: 11967.0327987 0.4822391 0.9999999 13.698 0.4818444 . Cs = 0.4822391 0.9999999 0.4818444 11963.3201730 6.8 GENERALIZED CHOLESKY DECOMPOSITION We now describe the classic Cholesky decomposition and recent generalizations designed to handle nonpositive de nite matrices. A matrix C is positive de nite if for any x vector except x = 0, x Cx > 0, or in other words, if C has all positive eigenvalues. Symmetric positive de nite matrices are nonsingular, have only positive numbers on the diagonal, and have positive determinants for all principal leading submatrices. The Cholesky matrix is de ned as V in the decomposition C = V V. We thus construct our pseudovariance matrix as V V, where V = GCHOL(H ), GCHOL( ) is the generalized Cholesky described below, and H is the Moore Penrose generalized inverse of the Hessian.

Select parameter: Select the linear parameter by clicking its label. Specify parameter point to associate with action or enter [sTart point/Second point] <Start>: Pass the cursor over the right grip and click. Specify first corner of stretch frame or [CPolygon]: Click at 1 in Figure 18-24. Specify opposite corner: Click at 2. Specify objects to stretch. Select objects: Click close to but not on top of 2. Specify opposite corner: Click close to but not on top of 1. Select objects: Specify action location or [Multiplier/Offset]: Place the action label to the right of the grip on the right side of the desk.

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Transformer differential protection protects against short-circuits between turns of a winding and between windings that correspond to phase-to-phase or threephase type short-circuits. If there is no earthing connection at the transformer location point, this protection can also be used to protect against earth faults. If the earth fault current is limited by an impedance, it is generally not possible to set the current threshold to a value less than the limiting current. The protection must be then carried out by a high impedance differential protection. Transformer differential protection operates very quickly, roughly 30 ms, which allows any transformer deterioration in the event of a short-circuit between windings to be avoided. Transformers cannot be differentially protected using high impedance differential protection for phase-to-phase short-circuit due to the natural differential currents that occur: the transformer inrush currents. The operating speed required means that a time delay longer than the duration of this current cannot be used (several tenths of a second); the action of the on-load tap changer causes a differential current. The characteristics of transformer differential protection are related to the transformer specifications: transformation ratio between the current entering I in and the current leaving I out ; primary and secondary coupling method; inrush current; permanent magnetizing current. The block diagram is shown in Figure 7-49.

4.19 The observations w = (w1.. N - ~ ) are multinomially distributed with W N = .W ~ w, and expectations Ew, = g,(e). Show that their Fisher information matrix Fe is described by

The class diagram for the Active Object pattern is shown below:

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Just as with WordPress, it is critical that you add a podcast category; this will allow you to provide a separate RSS 2.0 feed that has only enclosures. This screen can be found by clicking Preferences Categories New Category Page. Once that is set up, you will need to make changes in the News Aggregator section. Figure 11-9 shows the RSS Enclosures page open. You can reach this page by clicking Preferences RSS Enclosure. The critical element to choose is the Check this box. . . if you want to be able to add enclosures to your own output channels. After you have done this and submitted the changes, click the Home menu item, and you will be back to your home page. The enclosures block will be enabled.

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