This paper examines asymptotic expansions of test statistics for dimensionality and additional information in canonical correlation analysis based on a sample of size N = n+1 on two sets of variables, i.e., xu; p1×1 and xv; p2×1. These problems are related to dimension reduction. The asymptotic approximations of the statistics have been studied extensively when dimensions p1 and p2 are fixed an...

Pavement frictional characteristics are commonly determined by conducting skid tests in accordance with ASTM Standard E274. The results of these tests [skid number (SN)] are used in ranking roads to establish construction priorities and to estimate tirepavement friction in accident analysis. The role of SN in these two applications is addressed. There are serious limitations constraining the us...

We consider the problem of automating the derivation of tight asymptotic complexity bounds for solving Horn clauses. Clearly, the solving time crucially depends on the “sparseness” of the computed relations. Therefore, our asymptotic runtime analysis is accompanied by an asymptotic sparsity calculus together with an asymptotic sparsity analysis. The technical problem here is that least fixpoint...

The enstrophy inertial range of a family of two-dimensional turbulent flows, so-called -turbulence, is investigated theoretically and numerically. Introducing the large-scale correction into Kraichnan–Leith– Batchelor theory, we derive a unified form of the enstrophy spectrum for the local and non-local transfers in the enstrophy inertial range of -turbulence. An asymptotic scaling behavior of ...