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There are DC transmission lines from generator G2 s interconnection bus, a substantial distance from the control area, to bus B4 within the control area As previously noted, DC lines are superior for transmitting power over long distances DC lines do not require reactive power support and DC lines have higher power transfer capacity than AC lines There are converters (not shown) on the delivery and receiving sides of the DC lines On the delivery side, a converter converts power from AC to DC, while on the receiving side at bus B2 a converter converts DC to AC In the schematic, not all the power from generator G2 ows across the DC lines A portion of the power ows to another control area across the 750-kV lines that interconnect with bus B2 Power from the distant generators, G1 and G11, is supplied via 750-kV lines.



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Place a crystal on a page of printed text and rotate the crystal while looking down on it from above One ray does not move as the crystal is rotated (the O ray), whereas the other ray (the E ray) rotates around the fixed ray according to the angle of rotation of the crystal (Fig 8-6) The O ray does not move because it obeys the laws of normal refraction and passes through the crystal on a straight, undeviated trajectory The E ray, in contrast, travels along a tilted or oblique path, and its point of emergence at the surface of the crystal changes depending on the orientation of atoms in the crystal and therefore on the orientation of the crystal itself.





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The function f is (i) scale invariant, if for every d DS and every > 0 we have f (d) = f ( d); (ii) rich, if Ran(f ) = PART(S); (iii) consistent, if for every d, d DS and PART(S) such that f (d) = and d is a -transformation of d we have f (d ) = , Unfortunately, as we shall see in Theorem 14, established in the work by Kleinburg [8], there is no clustering function that enjoys all three properties The following de nition will be used in the proof of Lemma 2 De nition 11 A dissimilarity d DS is (a, b)-conformant to a clustering if x y implies d(x, y) a and x y implies d(x, y) b A dissimilarity is conformant to a clustering if it is (a, b)-conformant to for some pair of numbers (a, b).

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Because the angle of divergence is so great, wedges of calcite crystal can be cut and glued together in such a way that one of the two components is reflected and removed while the other is transmitted, making calcite an ideal linear polarizer Examine the crystal resting on a black spot on a blank page through a dichroic polarizing filter held close to the eye, while rotating the crystal through 360 First one ray and then the other ray alternately comes into view and becomes extinguished, and the black spot appears to jump back and forth as the filter is rotated through increments of 90 The double images correspond to the O and E rays, each of which is linearly polarized and vibrates in a plane perpendicular to the other.

Note that if d is a -transformation of d, and d is (a, b)-conformant to , then d is also (a, b)-conformant to De nition 12 Let PART(S) be a partition on S and f be a clustering function on S A pair of positive numbers (a, b) is -forcing with respect to f if for every d DS that is (a, b)-conformant to we have f (d) = Lemma 2 If f is a consistent clustering function on a set S, then for any partition Ran(f ) there exist a, b R>0 such that the pair (a, b) is -forcing..

For most crystals the two rays are close together and must be magnified to be observed, but in calcite the rays are so widely separated that no magnification is necessary As we will see, this is due to large differences in the refractive index along different paths through the crystal Notice too that polarized light cannot be distinguished from ordinary random light and that an analyzer is required to distinguish the different planes of polarization..

Note that these are the highest-rated AC lines in the system High-voltage lines are more ef cient than low-voltage lines because for a given real power transfer, the reactive inductance of a high-voltage transmission line is lower than the reactive inductance of a low-voltage power line As noted above, reactive inductance in the power line limits the ef ciency of power transfer and requires reactive power providers Aside from the distant generators there are several generators within the control area The ratings of the transmission lines that couple these generators with the substations are lower than those of the 750-kV lines that connect generators from outside the control area While higher-voltage lines are always superior in transmission ef ciency, it is not always feasible to construct high-voltage lines Pathways for high-voltage lines must be much wider than those for low-voltage lines.

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