We study a hydrodynamic limit approach to move-to-front rules, namely, a scaling limit as the number of items tends to infinity, of the joint distribution of jump rate and position of items. As an application of the limit formula, we present asymptotic formulas on search cost probability distributions, applicable for general jump rate distributions.

We rigorously prove results on spiky patterns for the Gierer-Meinhardt system [5] with a large number of jump discontinuities in the diffusion coefficient of the inhibitor. Using numerical computations in combination with a Turing-type instability analysis, this system has been investigated by Benson, Maini and Sherratt [1], [3], [9]. We first review results on the case of two segments given in...

In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming CrouzeixRaviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality ...

In this paper we consider an extremal problem regarding multigraphs with edge multiplicity bounded by a positive integer q. Given a family F of q-multigraphs, define ex(n,F ) to be the maximum number of edges (counting multiplicities) that a q-multigraph on n vertices can have without containing a copy of any F ∈ F (not necessarily induced). It is well known that τ(F ) = limn→∞ ex(n,F )/ (n 2 )...

Purpose: Various kinematics and kinetics methods have been proposed for the assessment of jumping ability as a critical skill in professional volleyball players, but little is known about the accuracy and differences between these methods. Therefore, the objective of the current study was to answer the question “Is there any difference between the results of various kinetic methods in the asses...

There is a substantial evidence that plyometric training significantly increases muscular strength and vertical jump. Due to the vigorous nature of this type of training, however, there is a risk of incurring musculoskeletal injuries. Therefore, conducting plyometric exercise programs in an aquatic environment might lead to significant improvements in vertical jump with possibly a lower risk of...