Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer: principle and experimental considerations

The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of 10⁻¹⁰ of the Newtonian terms arising from the mass of the Earth. Due to the dragging of the local inertial frame by the spinning Earth, there are also secular terms, which grow in time. These fields can be detected in principle by a set of orbiting superconducting gravity gradiometers. The Riemann tensor components for various spacecraft orientations have been computed and the principle of detecting the gravitomagnetic tidal force has been published. In this paper, we review the conclusions of the earlier analyses and discuss the feasibility of the gravity gradiometer experiment.     

Minimum-energy wavelet frame on the interval with arbitrary integer dilation factor

In this paper, we study minimum-energy frame Ψ={ψ¹,ψ²,…,ψ^M} on the interval with arbitrary factor d for L²[0,1], Ψ corresponding to some refinable functions with compact support. We give the constructive proof as well as the necessary and sufficient conditions of minimum-energy frames for L²[0,1], present the decomposition and reconstruction formulas of minimum-energy frame on the interval [0,1], and some examples. The experimental results show that the proposed minimum-energy frame on the interval improves the performance in the application of image denoising significantly.     

Models for products

This paper explores how models can support productive thinking. For us a model is a thing, a tool to help make sense of something. We restrict attention to specific models for whole-number multiplication, hence the wording of the title. They support evolving thinking in large measure through the ways their users redesign them. They assume new forms, come to be seen and understood in different ways. We show how work that learners do with models can help them to transform, not simply their understanding of key concepts, but also how they come to view themselves as thinkers and learners, as collaborators in a social process that their work and thinking help to constitute. We draw on recent research on core knowledge, especially by Carey, Spelke, and Tomasello, to clarify how models, as we view them here, can underpin specific actions that support emerging understanding.     

地球同步轨道碎片观测图像分级检测方法

为了快速检测出地球同步轨道带光学观测图像中的空间碎片,提出了一种基于信噪比的分级检测方法.首先分析实测数据,得出观测图像中不同信噪比碎片运动相似的特性.对于高信噪比碎片,采取帧差法快速检测,并利用多帧图像计算速度信息;对于低信噪比碎片,根据高信噪比碎片检测结果得到的速度信息,采用改进的动态规划检测方法.实际图像检测结果表明：当递归方程的搜索窗口为5pixel×5pixel时,分级检测方法检测性能最好;当累积帧数大于5帧时,检测时间比传统动态规划方法减少了87%以上.分级检测方法具有检测率高、虚警率低、计算量小的优势,适合地球同步轨道带光学观测图像中空间碎片的检测.     

The construction of multivariate periodic wavelet bi-frames

This paper addresses periodic wavelet bi-frames associated with general expansive matrices. Periodization is an important method to obtain periodic wavelets from wavelets on R^d${\mathbb{R}}^d$. MEP and MOEP provide us with criteria for the construction of wavelet bi-frames on R^d${\mathbb{R}}^d$. Based on periodization techniques, MEP and MOEP, periodic wavelet bi-frames associated with the dyadic matrix have been constructed. However, the problem of constructing periodic wavelet bi-frames associated with general expansive matrices is still open. The geometry of a general expansive matrix is much more complicated than the dyadic matrix. In this paper, with the help of quasi-norms, MEP and MOEP we construct periodic wavelet bi-frames associated with general expansive matrices.     

用回传波射矩阵法分析框架的地震效应

结构在地震载荷作用下的瞬态响应分析对抗震设计很重要. 大部分地震效应 研究采用时程积分等数值方法. 回传波射矩阵法是桁架和框架结构瞬态响应的一种新的频域 矩阵分析法. 基于Bernulli梁理论的回传波射矩阵法扩展到地面加速度载荷的情形, 对一榀钢制框架在地面El Centro波加速度作用下的瞬态应力计算, 结果表明该方法 能准确有效地进行结构的地震效应分析.     

The road to equal-norm Parseval frames

The construction of equal-norm Parseval frames is fundamental for many applications of frame theory. We present a construction method based on a system of ordinary differential equations, which generates a flow on the set of Parseval frames that converges to equal-norm Parseval frames. We developed this method to address a question posed by Vern Paulsen: How close is a nearly equal-norm, nearly Parseval frame to an equal-norm Parseval frame? The distance estimate derived here can be used to substantiate numerically found, approximate constructions of equal-norm Parseval frames. The estimate is valid for a fairly general class of frames — requiring that the dimension of the Hilbert space and the number of frame vectors is relatively prime. In addition, we re-phrase our distance estimate to show that certain projection matrices which are nearly constant on the diagonal are close in Hilbert-Schmidt norm to ones which have a constant diagonal.     

Linear combinations of frame generators in systems of translates

A finitely generated shift invariant space V   is a closed subspace of L²(R^d)$L^2({\mathbb{R}}^d)$ that can be generated by the integer translates of a finite number of functions. A set of frame generators for V is a set of functions whose integer translates form a frame for V. In this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators. Surprisingly the results are very different from the recently studied case when the property to be a frame is not required.     

Intrinsic Localization of Frames

Several concepts for the localization of a frame are studied. The intrinsic localization of a frame is defined by the decay properties of its Gramian matrix. Our main result asserts that the canonical dual frame possesses the same intrinsic localization as the original frame. The proof relies heavily on Banach algebra techniques, in particular on recent spectral invariance properties for certain Banach algebras of infinite matrices. Intrinsically localized frames extend in a natural way to Banach frames for a class of associated Banach spaces which are defined by weighted ℓ^p-coefficients of their frame expansions. As an example, the time--frequency concentration of distributions is characterized by means of localized (nonuniform) Gabor frames.     

Frames and bases in tensor products of Hilbert spaces and Hilbert <Emphasis Type="Italic">C</Emphasis>*-modules

In this article, we study tensor product of Hilbert C*-modules and Hilbert spaces. We show that if E is a Hilbert A-module and F is a Hilbert B-module, then tensor product of frames (orthonormal bases) for E and F produce frames (orthonormal bases) for Hilbert A ⊗ B-module E ⊗ F, and we get more results. For Hilbert spaces H and K, we study tensor product of frames of subspaces for H and K, tensor product of resolutions of the identities of H and K, and tensor product of frame representations for H and K.