Basis Expansions for Functional Snippets

Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed approach allows one to consistently estimate an infinite-rank covariance function from functional snippets. We establish the convergence rates for the proposed estimators and illustrate their finite-sample performance via simulation studies and two data applications.Comment: 51 pages, 10 figure

Ordered Self-Assembling of Tetrahedral Oxide Nanocrystals

©1997 The American Physical Society. The electronic version of this article is the complete one and can be found online at: http://link.aps.org/doi/10.1103/PhysRevLett.79.2570DOI: 10.1103/PhysRevLett.79.2570Self-assembling of size, shape, and phase controlled nanocrystals into superlattices with translational and even orientational ordering is a new approach for engineering nanocrystal materials and devices. High purity tetrahedral nanocrystals of CoO, with edge lengths of 4.4±0.2 nm, were synthesized and separated from Co nanocrystals, using a novel magnetic field phase-selection technique. Self-assembling of the faceted CoO nanocrystals forms ordered superlattices, the structures of which are determined

The expanded Maxwell's equations for a mechano-driven media system that moves with acceleration

In classical electrodynamics, by motion for either the observer or the media, it always naturally assumed that the relative moving velocity is a constant along a straight line (e.g., in inertia reference frame), so that the electromagnetic behavior of charged particles in vacuum space can be easily described using special relativity. However, for engineering applications, the media have shapes and sizes and may move with acceleration, and recent experimental progresses in triboelectric nanogenerators have revealed evidences for expanding the Maxwell's equations to include media motion that could be time and even space dependent. Therefore, we have developed the expanded Maxwell's equations for a mechano-driven media system (MEs-f-MDMS) by neglecting relativistic effect. This article first presents the updated progresses made in the field. Secondly, we extensively investigated the Faraday's law of electromagnetic induction for a media system that moves with an acceleration. We concluded that, the newly developed MEs-f-MDMS are required for describing the electrodynamics inside a media that has a finite size and volume and move with and even without acceleration. The classical Maxwell's equations are to describe the electrodynamics in vacuum space when the media in the nearby are moving.Comment: 35 pages,8 figure

Maxwell's equations for a mechano-driven, shape-deformable, charged-media system, slowly moving at an arbitrary velocity field v(r,t)

The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which the medium has a time-dependent volume, shape and boundary and may move at an arbitrary velocity field v(r,t) and along a general trajectory, we derived the Maxwell's equations for a mechano-driven slow-moving media system directly starting from their integral forms, which should be accurate enough for describing the coupling among mechano-electro-magnetic interactions of a general system in practice although it may not Lorentz covarance. Our key point is from the integral expressions of the four physics laws by describing all of the fields, the space and the time in the frame where the observation is done. The equations should be applicable to not only moving charged solid and soft media, but also charged fluid/liquid media, e.g., fluid electrodynamics. General strategies for solving the Maxwell's equations for mechano-driven slowing moving medium are presented using the perturbation theory both in time and frequency spaces. Finally, approaches for the electrodynamics of moving media are compared, and related discussions are given about a few interesting questions.Comment: 32 pages, 4 figure

Dual-mode mechanical resonance of individual ZnO nanobelts

©2003 American Institute of Physics. The electronic version of this article is the complete one and can be found online at: http://link.aip.org/link/?APPLAB/82/4806/1DOI:10.1063/1.1587878The mechanical resonance of a single ZnO nanobelt, induced by an alternative electric field, was studied by in situ transmission electron microscopy. Due to the rectangular cross section of the nanobelt, two fundamental resonance modes have been observed corresponding to two orthogonal transverse vibration directions, showing the versatile applications of nanobelts as nanocantilevers and nanoresonators. The bending modulus of the ZnO nanobelts was measured to be ~52 GPa and the damping time constant of the resonance in a vacuum of 5×10–8 Torr was ~1.2 ms and quality factor Q = 500

Induced Growth of Asymmetric Nanocantilever Arrays on Polar Surfaces

©2003 The American Physical Society. The electronic version of this article is the complete one and can be found online at: http://link.aps.org/doi/10.1103/PhysRevLett.91.185502DOI: 10.1103/PhysRevLett.91.185502We report that the Zn-terminated ZnO (0001) polar surface is chemically active and the oxygenterminated (0001) polar surface is inert in the growth of nanocantilever arrays. Longer and wider "comblike" nanocantilever arrays are grown from the (0001)-Zn surface, which is suggested to be a self-catalyzed process due to the enrichment of Zn at the growth front. The chemically inactive (0001)-O surface typically does not initiate any growth, but controlling experimental conditions could lead to the growth of shorter and narrower nanocantilevers from the intersections between (0001)-O with (0110) surfaces