An integer sequence a(n) is called a jump sequence if a(1) = 1 and 1 ≤ a(n) < n for n ≥ 2. Such a sequence has the property that ak(n) = a(a(· · · (a(n)) · · · )) goes to 1 in finitely many steps. We call the pattern (n, a(n), a2(n), . . . , al(n) = 1) a jumping pattern from n down to 1. In this paper we look at jumping sequences that are weight minimizing with respect to various weight functio...

Hydrological jump characteristics in a rectangular open channel flume with sluice gates at both ends are the focus of this article. Among many aspects hydraulic that have been examined analytically and experimentally are: (i) Sequent depth relation (y2y1), (ii) Length jump, (iii) Relative loss energy (ELE1), (iv) Water profile jump. There was total 15 inflow tests conducted. With values between...

A hydraulic jump is a sudden, rapid transition from a supercritical flow to a subcritical flow. At large inflow Froude numbers, the jump is characterized by a significant amount of entrained air. For this paper, the bubbly two-phase flow properties of steady and strong hydraulic jumps were investigated experimentally. The results demonstrate that the strong air entrainment rate and the depth-av...

Let r ≥ 2 be an integer. A real number α ∈ [0, 1) is a jump for r if there exists c > 0 such that for any ǫ > 0 and any integer m, m ≥ r, there exists an integer n0 such that any r-uniform graph with n > n0 vertices and density ≥ α + ǫ contains a subgraph with m vertices and density ≥ α+ c. It follows from a theorem of Erdős and Stone that every α ∈ [0, 1) is a jump for r = 2. Erdős asked wheth...

Let X be a Turing oracle. A function f(n) is said to be boundedly limit recursive in X if it is the limit of an X-recursive sequence of X-recursive functions f̃(n, s) such that the number of times f̃(n, s) changes is bounded by a recursive function of n. Let us say that X is BLR-low if every function which is boundedly limit recursive in X is boundedly limit recursive in 0. This is a lowness prop...

A jump system is a set of integer points with an exchange property, which is a generalization of a matroid, a delta-matroid, and a base polyhedron of an integral polymatroid (or a submodular system). Recently, the concept of M-convex functions on constant-parity jump systems is introduced by Murota as a class of discrete convex functions that admit a local criterion for global minimality. M-con...

Scott, Jon. The locust jump: an integrated laboratory investigation. Adv Physiol Educ 288: 21–26, 2005; doi:10.1152/advan.00037.2004.— The locust is well known for its ability to jump large distances to avoid predation. This class sets out a series of investigations into the mechanisms underlying the jump enabling students to bring together information from biomechanics, muscle physiology, and ...

Recent theoretical and experimental studies suggested the large-amplitude angular jump mechanism of the reorientational motions of water molecules. In this paper, we study the correlation effects of such angular jump motions, which are important for understanding a number of biological processes involving the motions of water molecules, by using molecular dynamics simulations. The results show ...