Strong approximations of the Hoeffding,Blum, Kiefer,Rosenblatt multivariate empirical process

Hoeffding (Ann. Math. Statist. 1948) and Blum, Kiefer and Rosenblatt (Ann. Math. Statist. 1961) constructed distribution free tests of independence based on a multivariate empirical process. We establish strong invariance principles for the latter and also for appropriate functionals of it.     

A compact F-space not co-absolute with βN−N

We show that if every Parovi?enko space of weight $\text{c}$ is co-absolute with $\text{β}\text{N}\text{?}\text{N}$, then .     

A simple proof for the Chernoff-Savage theorem

A proof for the Chernoff-Savage theorem is given based on differentiable statistical functionals. It employs no second order differentiability condition.     

On the evaluation of some distributions that arise in simultaneous tests for the equality of the latent roots of the covariance matrix

In this paper, the authors consider the evaluation of the distribution functions of the ratios of the intermediate roots to the trace of the real Wishart matrix as well as the ratios of the individual roots to the trace of the complex Wishart matrix. In addition, the authors consider the evaluation of the distribution functions of the ratios of the extreme roots of the Wishart matrix in the real and complex cases. Some applications and tables of the above distributions are also given.     

First countable, countably compact spaces and the continuum hypothesis

We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah's iteration theorems appearing in Chapters V and VIII of Proper and improper forcing (1998), as well as Eisworth and Roitman's (1999) iteration theorem. We close the paper with a ZFC example (constructed using Shelah's club-guessing sequences) that shows similar results do not hold for closed pre-images of .

     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

Bioactivity of SiO2-CaO-P2O5-Na2O glasses containing zinc-iron oxide

Glasses with composition x(ZnO,Fe₂O₃)(65 − x)SiO₂20(CaO,P₂O₅)15Na₂O (6 ≤ x ≤ 21 mol%) were prepared by melt-quenching technique. Bioactivity of the glasses was investigated in vitro by examining apatite formation on the surface of glasses treated in acellular simulated body fluid (SBF) with ion concentrations nearly equal to those in human blood plasma. Formation of bioactive apatite layer on the samples treated in SBF was confirmed by using Fourier transform infrared reflection (FTIR) spectroscopy, grazing incidence X-ray diffraction (GI-XRD) and scanning electron microscope (SEM) equipped with energy dispersive X-ray spectrometer. Development of an apatite structure on the surface of the SBF treated glass samples as functions of composition and time could be established using the GI-XRD data. FTIR spectra of the glasses treated in SBF show features at characteristic vibration frequencies of apatite after 1-day of immersion in SBF. SEM observations revealed that the spherical particles formed on the glass surface were made of calcium and phosphorus with the Ca/P molar ratio being close to 1.67, corresponding to the value in crystalline apatite. Increase in bioactivity with increasing zinc-iron oxide content was observed. The results have been used to understand the evolution of the apatite surface layer as a function of glass composition and immersion time in SBF.     

Optimal testing strategies in overlapped design process

Testing is an important activity in product development. Past studies, which are developed to determine the optimal scheduling of tests, often focused on single-stage testing of sequential design process. This paper presents an analytical model for the scheduling of tests in overlapped design process, where a downstream stage starts before the completion of upstream testing. We derive optimal stopping rules for upstream and downstream stages’ testing, together with the optimal time elapsed between beginning the upstream tests and beginning the downstream development. We find that the cost function is first convex then concave increasing with respect to upstream testing duration. A one-dimensional search algorithm is then proposed for finding the unique optimum that minimizes the overall cost. Moreover, the impact of different model parameters, such as the problem-solving capacity and opportunity cost, on the optimal solution is discussed. Finally, we compare the testing strategies in overlapped process with those in sequential process, and get some additional results. The methodology is illustrated with a case study at a handset design company.     

On the effectiveness of a generalization of Miller’s primality theorem

Berrizbeitia and Olivieri showed in a recent paper that, for any integer r$r$, the notion of ω$\omega$-prime to base a$a$ leads to a primality test for numbers n≡1$n\equiv 1$ mod r$r$, that under the Extended Riemann Hypothesis (ERH) runs in polynomial time. They showed that the complexity of their test is at most the complexity of the Miller primality test (MPT), which is O((logn)^4+o(1))$O\left({(logn)}^{4+o\left(1\right)}\right)$. They conjectured that their test is more effective than the MPT if r$r$ is large.     

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.