Effects of multiple blade interaction on the containment of blade fragments during a rotor failure

A finite element analysis is used to study the impact and the containment aspects of rotor blade fragments that are produced during a aircraft jet engine rotor failure. The impact and containment studies are performed on a ring-type containment structure and various fragment types are considered in this study. For each type of fragment, the ring thickness is varied incrementally and the ring response, residual kinetic energy level of the fragments, magnitude of impact forces and the overall containment or failure are determined. First, only a single fragment is considered and the rotor is assumed to contain no other blades. Next, the remaining blades are introduced and the effects of multiple collisions with the other blades on the containment are analyzed. The explicit, nonlinear finite element code Dyna3d is used for the numerical computations in this study and the results are compared with the experimental results performed on a T58 rotor at the spin facility of the Naval Air Propulsion Test Center.     

Third-order efficiency of conditional tests in exponential models: The lattice case

As is well known, in full rank multivariate exponential families, tests of Neyman structure are uniformly most powerful unbiased for one-sided problems. For the case of lattice distributions, the power of these tests—evaluated at contiguous alternatives—is approximated by asymptotic expansions up to errors of order o(n^?1). Surprisingly the tests with Neyman structure are not third-order efficient in the class of all asymptotically similar tests unless the problem is univariate.     

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 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.     

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights,which can be arbi- trarily dependent of each other.Then the applications to ruin probabilities in a discrete time risk model with dependent stochastic returns are considered.     

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.     

Strong and electromagnetic J/ψ and ψ(2S) decays into pion and kaon pairs

We discuss interference effects important for the form factors extraction in the vicinity of J/ψ andψ(2S)resonances in combination with resonance parameters determination.The implementation to the Monte Carlo event generator PHOKHARA of the J/ψ and ψ(2S)contributions to the muon,pion and kaon pairs production associated with a photon at next-to-leading order is also described.     

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.     

Dyck paths with a first return decomposition constrained by height

We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height $k$ with a flat (resp. with no flats) at the maximal height.