International audience
A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.
AbstractA new two-parameter family of analytical functions will be introduced for the modelling of loss distributions and exposure curves. The curve family contains the Maxwell-Boltzmann, the Bose-Einstein and the Fermi-Dirac distributions, which are well known in statistical mechanics. The functions can be used for the modelling of loss distributions on the finite interval [0, 1] as well as on the interval [0, ∞]. The functions defined on the interval [0, 1] are discussed in detail and related to several Swiss Re exposure curves used in practice. The curves can be fitted to the first two moments μ and σ of a loss distribution or to the first moment μ and the total loss probability p.
An approach to establish the no corrosion - fatigue curve is introduced. Based on this new approach, equations that describe the heat effect and life lost when determining the fatigue strength of metals may be established, also the reliability of the traditional fatigue curve can be assessed.
In this paper, a condition is obtained for the harmonic of the velocity vector field in the curve family passing through the fixed p and q points in Rn. It shows that the condition can be expressed in terms of the curvature functions. Finally, we give an example which provides the mentioned condition in this work and illustrates it with figures.
Plotting the "resource — energy conversion efficiency" compromise curve family for a centrifugal PUMP