By Daveau C., Zaghdani A.
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Extra resources for A hp-discontinuous Galerkin method for the time-dependent Maxwell’s equation: a priori error estimate
A related unpublished paradox, also discovered by Moser, concerns n-dimensional chessboards. All the black squares of a chessboard are enclosed with circumscribed circles [see Figure 221. Assume that each cell is of side 2 and area 4. Each circle has a radius of fland an area of 2 ~ The . 71 I n the analogous situation for a cubical chessboard, the black cubical cells of edge 2 are surrounded by spheres. The volume of each black cell is 8 and the volume of each sphere, +. FIGURE 22 Leo Moser's hyperchessboard problem which has a radius of \% is 477\3 but the volume of the unenclosed portion of each white cube is not so easy to calculate because the six surroundirlg spheres intersect one another.
If the first player plays the vertical bar of a possible L, the second player plays the horizontal bar. If the first player forms the horizontal part of a possible L, the second player forms the vertical part. This guarantees at least a draw for the second player. Answers to the seven match puzzles are given in Figure 16. Several readers found an alternate solution to the sixth puzzle. The VI on the left is changed to XI, the Roman equivalent of the Arabic 11 on the other side. " -Children's sick joke, circa 1955 A CIRCLE is the locus of all points on the plane at a given distance from a fixed point on the plane.
The basis for ordering the Master Pattern is intimately bound up with the Designer's estimate of the abilities of the other players because, as we shall see, he makes his highest score when one player does very well and another very poorly. Can the reader discern the simple basis for the nonsymmetrical ordering shown in Figure 24? The Designer puts his sheet face down on the table. Any player may now make inquiries by drawing on his own grid a small slant line in the lower left-hand corner of any cell about which he seeks information.
A hp-discontinuous Galerkin method for the time-dependent Maxwell’s equation: a priori error estimate by Daveau C., Zaghdani A.