228,270 research outputs found

    Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero

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    Let Xp=(s1,...,sn)=(Xij)p×n\mathbf{X}_p=(\mathbf{s}_1,...,\mathbf{s}_n)=(X_{ij})_{p \times n} where XijX_{ij}'s are independent and identically distributed (i.i.d.) random variables with EX11=0,EX112=1EX_{11}=0,EX_{11}^2=1 and EX114<∞EX_{11}^4<\infty. It is showed that the largest eigenvalue of the random matrix Ap=12np(XpXp′−nIp)\mathbf{A}_p=\frac{1}{2\sqrt{np}}(\mathbf{X}_p\mathbf{X}_p^{\prime}-n\mathbf{I}_p) tends to 1 almost surely as p→∞,n→∞p\rightarrow\infty,n\rightarrow\infty with p/n→0p/n\rightarrow0.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ381 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    Analysis of elastically tailored viscoelastic damping member

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    For more than two decades, viscoelastic materials have been commonly used as a passive damping source in a variety of structures because of their high material loss factors. In most of the applications, viscoelastic materials are used either in series with or parallel to the structural load path. The latter is also known as the constrained-layer damping treatment. The advantage of the constrained-layer damping treatment is that it can be incorporated without loss in structural integrity, namely, stiffness and strength. However, the disadvantages are that: (1) it is not the most effective use of the viscoelastic material when compared with the series-type application, and (2) weight penalty from the stiff constraining layer requirement can be excessive. To overcome the disadvantages of the constrained-layer damping treatment, a new approach for using viscoelastic material in axial-type structural components, e.g., truss members, was studied in this investigation

    Temperature variation of the resistivity of metallic strain gauge materials Final report

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    Temperature effects on electrical resistivity of metallic strain gage material

    Behavior of the collective rotor in wobbling motion

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    The behavior of the collective rotor in wobbling motion is investigated within the particle-rotor model for the nucleus 135^{135}Pr by transforming the wave functions from the KK-representation to the RR-representation. After reproducing the experimental energy spectra and wobbling frequencies, the evolution of the wobbling mode in 135^{135}Pr, from transverse at low spins to longitudinal at high spins, is illustrated by the distributions of the total angular momentum in the intrinsic reference frame (azimuthal plot). Finally, the coupling schemes of the angular momenta of the rotor and the high-jj particle for transverse and longitudinal wobbling are obtained from the analysis of the probability distributions of the rotor angular momentum (RR-plots) and their projections onto the three principal axes (KRK_R-plots).Comment: 21 pages, 9 page

    Effective field theory for triaxially deformed nuclei

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    Effective field theory (EFT) is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. A Hamiltonian, called the triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO) within the EFT formalism. Its applicability is examined by comparing with a five-dimensional collective Hamiltonian (5DCH) for the description of the energy spectra of the ground state and γ\gamma band in Ru isotopes. It is found that by taking into account the NLO corrections, the ground state band in the whole spin region and the γ\gamma band in the low spin region are well described. The results presented here indicate that it should be possible to further generalize the EFT to triaxial nuclei with odd mass number.Comment: 21 pages, 9 figure
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