Let λ = (λ1, λ2, . . . , λl), λ1 ≥ λ2 ≥ . . . ≥ λl > 0, be a partition of n, λ ⊢ n, and let [λ] = {(i, j) ∈ Z : 1 ≤ i ≤ l, 1 ≤ j ≤ λi} be the corresponding Young diagram. The conjugate partition λ is defined by λj = max{i : λi ≥ j}. We will freely use implications such as i ≤ j ⇒ λi ≥ λj. The hook Hz ⊆ [λ] is the set of squares weakly to the right and below of z = (i, j) ∈ [λ], and the hook len...

1. INTRODUCTION. There is obvious value in finding the most efficient ways to arrange objects like balls or polyhedra in a given container. There is more scope for rich mathematics in having the " container " be all of space, so there are no boundaries to spoil the potential symmetry of the optimal arrangements, and this is the type of problem we will consider (see Figure 1 for an efficient and...

For instance, in Table 1 one observes three bid insertions between 10:30:08.35 and 10:30:12.56, where the best bid in this period was bid 7 at limit 97.53 due to the price-time priority rule of the Xetra system. The insertion of an ask at 10:30:12.56 led to a transaction price of 97.53 and full execution of order 7, 10 and 11. This is illustrated in Figure 1 which contains the information shown...

Overview Let ∆ABC be a triangle, and let the radian measure of these angles bem(]CAB) = 3α, m(]ABC) = 3β, and m(]BCA) = 3γ, so that α+ β + γ = π/3.1 We trisect each (interior) angle of the triangle, and take the intersections of the proximal or adjacent trisectors; for example, to choose the intersection between a trisector of the angle at A and the angle at B, we choose the trisector from A cl...

Research on regional variation in the sound system of American English has focused almost exclusively on vowel quality (e.g., Labov et al. 2005; Thomas, 2001). However, several recent studies have provided preliminary evidence for regional variation in temporal organization, including speaking rate and pause distribution. The results of these studies suggest that Southerners speak more slowly (...

Ross Paterson, Ron Wyatt, and other young-earth creationists (YEC), claim in four videos that they have found the remains of five ancient cities (e.g., Sodom and Gomorrah) that were destroyed by a biblical “fire and brimstone” storm (Genesis 18:16 to 19:29). See Figure 1 and these links: https://www.youtube.com/watch?v=KBCs4wexgRk&index=23&list=WL https://www.youtube.com/watch?v=L7uHKn2ijKw htt...

0 0 1 8 9 1 6 2 / 1 6 / $ 3 3 . 0 0 © 2 0 1 6 I E E E S tandards touch our lives every day. They keep us safe, make our products work together, and ensure repeatable processes. Hundreds, if not thousands, of organizations develop standards. While the methods they use might vary, I’ve found commonalities across the world of standardization. Creating standards is interesting and sometimes strange...

Article history: Received 6 September 2007 Received in revised form 14 January 2009 Accepted 2 March 2009

To illustrate the problem, see Figure 1, where a short Chinese sentence was translated into English by ten different human translators. Each came up with a different translation. This is a very typical example. Given any sentence of non-trivial length, a group of ten translators will come up with ten different translations. In fact, if presented with the same sentence the next day, they will co...

The first step in our story is to inscribe a square PQRS in a given triangle ABC. Since the square has four vertices and the triangle has only three sides, some side of the triangle must contain two of the vertices of the square (Figure 1). How to construct such a square is an interesting problem in its own right and it gives us a chance to dust off a very useful observation about similar figures.