基于EMD-HMM的故障诊断模型及应用

提出了基于经验模式分解(EMD)和隐马尔科夫模型(HMM)的故障诊断模型,为通过设备状态监测数据分析进行基于状态维修和维修决策提供了一种新途径.为了消除EMD的端点效应,使用神经网络拟合延拓原始数据序列端点极值,并通过定义序列复杂度来定性地确定延拓极点数.进一步,采用分解所得的固有模态(IMF)能谱熵作为HMM分类系统的输入,得到一种设备故障诊断方案.通过数值仿真和发动机故障诊断验证了该方法的有效性.     

Strong summability of Fourier series and Morrey spaces

This work is dedicated to the investigation of strong summability of Fourier series in the context of periodic Morrey spaces. First, we study the Hilbert transform in the periodic vector-valued context. Boundedness of the Hilbert transform implies uniform estimates of the operator norms of the partial sums of the Fourier series. Afterwards, we study the Lizorkin-Triebel-Morrey and Nikol’skij-Besov-Morrey spaces. Here we concentrate on Lizorkin representations and embeddings into the scale of Hölder-Zygmund spaces. In the final section, we study consequences for strong summability of Fourier series.     

Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz-Toeplitz isometries as a special case.     

Artinian level modules and cancellable sequences

In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain artinian modules. As in the case of algebras a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences involving Macaulay representations.     

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order $H^m(\mathbb {H}^n), m\in \mathbb {N}^n,$ under the heat kernel transform on $\mathbb {H}^n,$ using direct sum and direct integral of Bergmann spaces and certain unitary representations of $\mathbb {H}^n$ which can be realized on the Hilbert space of Hilbert‐Schmidt operators on $L^2(\mathbb {R}^n).$ We also show that the image of Sobolev space of negative order $H^{-s}(\mathbb {H}^n), s(>0) \in \mathbb {R}$ is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on $\mathbb {H}^n$ under the heat kernel transform.     

A Fractional Hilbert Transform for 2D Signals

The Hilbert transform is an important tool in image processing and optics. The Hilbert transform can be generalized to a fractional Hilbert transform. The generalization is driven by optics and image processing. We will generalize the fractional Hilbert transform into 2 dimensions by rotating the Hilbert transform in \({\mathbb{R}^{3}}\) . The definition of the Hilbert transform as well as of the rotations will be done by quaternions.     

On the interplay between the Hilbert transform and conjugate harmonic functions

As is well‐known, there is a close and well‐defined connection between the notions of Hilbert transform and of conjugate harmonic functions in the context of the complex plane. This holds e.g. in the case of the Hilbert transform on the real line, which is linked to conjugate harmonicity in the upper (or lower) half plane. It also can be rephrased when dealing with the Hilbert transform on the boundary of a simply connected domain related to conjugate harmonics in its interior (or exterior). In this paper, we extend these principles to higher dimensional space, more specifically, in a Clifford analysis setting. We will show that the intimate relation between both concepts remains, however giving rise to a range of possibilities for the definition of either new Hilbert‐like transforms, or specific notions of conjugate harmonicity. Copyright © 2006 John Wiley & Sons, Ltd.     

Q_p上的共轭温度系

本文用于构造p-adic共轭温度系.首先,说明了热核及其Hilbert变换所适合的估计,描述了它们的正则性.并且对热核及其Hilbert变换在各个方向的导数进行了估计.然后,利用热核的卷积理论,得到了共轭温度系的边值特性.最后,通过共轭温度系解释了Hardy空间.     

Hilbert space with non-associative scalars II

The theory of a Hilbert space over a finite associative algebra is formulated, and the spectral resolution theorem for bounded Hermitian operators on this space is obtained. The properties of series representations are discussed and are found to be analogous to the usual ones of the complex Hilbert space. It is then shown that the theory of the non-associative Hilbert space developed in our previous paper is contained in the more general theory for the special case in which the finite algebra is chosen to be the Cayley ring.     

Hilbert空间上算子W-加权Drazin逆的刻画及表示

该文研究了Hilbert空间上线性算子的W-加权Drazin逆,利用算子的分块矩阵表示,给出了W-加权Drazin逆的刻画及表示,所获结果推广了魏益民等的相关结果.     

Investigations on the approximability and computability of the Hilbert transform with applications

It was recently shown that on a large class of important Banach spaces there exist no linear methods which are able to approximate the Hilbert transform from samples of the given function. This implies that there is no linear algorithm for calculating the Hilbert transform which can be implemented on a digital computer and which converges for all functions from the corresponding Banach spaces. The present paper develops a much more general framework which also includes non-linear approximation methods. All algorithms within this framework have only to satisfy an axiom which guarantees the computability of the algorithm based on given samples of the function. The paper investigates whether there exists an algorithm within this general framework which converges to the Hilbert transform for all functions in these Banach spaces. It is shown that non-linear methods give actually no improvement over linear methods. Moreover, the paper discusses some consequences regarding the Turing computability of the Hilbert transform and the existence of computational bases in Banach spaces.     

Wavelets and Hilbert Modules

A Hilbert C^*-module is a generalization of a Hilbert space for which the inner product takes its values in a C^*-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert C^*-modules over a group C^*-algebra which is generated by the group of translations associated with a wavelet. We shall investigate bracket products and their Fourier transform in the space of square integrable functions in Euclidean space. We will also show that some wavelets are associated with Hilbert C^*-modules over the space of essentially bounded functions over higher dimensional tori.     

Some properties of analytic in a disk functions with applications to the study of the behavior of singular integrals

We obtain representations for an analytic in a disc function such that its real part has a zero of an integer order at a fixed boundary point. We consider certain applications of these representations for studying properties of singular integrals with Hilbert kernel.     

The Lappo-Danilevskii method and trivial intersections of radicals in lower central series terms for certain fundamental groups

In this paper, it is proved that the intersection of the radicals of nilpotent residues for the generalized pure braid group corresponding to an irreducible finite Coxeter group or an irreducible imprimitive finite complex reflection group is always trivial. The proof uses the solvability of the Riemann—Hilbert problem for analytic families of faithful linear representations by the Lappo-Danilevskii method. Generalized Burau representations are defined for the generalized braid groups corresponding to finite complex reflection groups whose Dynkin—Cohen graphs are trees. The Fuchsian connections for which the monodromy representations are equivalent to the restrictions of generalized Burau representations to pure braid groups are described. The question about the faithfulness of generalized Burau representations and their restrictions to pure braid groups is posed.     

Dirichlet to Neumann operator on differential forms

We define the Dirichlet to Neumann operator on exterior differential forms for a compact Riemannian manifold with boundary and prove that the real additive cohomology structure of the manifold is determined by the DN operator. In particular, an explicit formula is obtained which expresses Betti numbers of the manifold through the DN operator. We express also the Hilbert transform through the DN map. The Hilbert transform connects boundary traces of conjugate co-closed forms.     

A Parametrization of the Irreducible Representations of a Compact Inverse Semigroup

The aim in this article is to provide a parametrization of the finite dimensional irreducible representations of a compact inverse semigroup in terms of the irreducible representations of maximal subgroups and order theoretic properties of the idempotent set. As a consequence, we obtain a new, and more conceptual, proof of the following theorem of Shneperman: a compact inverse semigroup has enough finite dimensional irreducible representations to separate points if and only if its idempotent set is totally disconnected. Moreover, we also prove that every norm continuous irreducible *-representation of a compact inverse semigroup on a Hilbert space is finite dimensional.     

Coherent Transforms and Irreducible Representations Corresponding to Complex Structures on a Cylinder and on a Torus

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of antiholomorphic sections in which the irreducible Hermitian representations of the original algebra are realized. The reproducing kernels of these spaces are expressed in terms of the Riemann theta function and its modifications. They generate quantum Kähler structures on the surface and the corresponding quantum reproducing measures. We construct coherent transforms intertwining abstract representations of an algebra with irreducible representations, and these transforms are also expressed via the theta function.     

Kaplansky Density and Kadison Transitivity Theorems for Irreducible Representations of Real C＊-Algebras

We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.     

Generalising Group Algebras

We generalise group algebras to other algebraic objects withbounded Hilbert space representation theory; the generalisedgroup algebras are called ‘host’ algebras. The mainproperty of a host algebra is that its representation theoryshould be isomorphic (in the sense of the Gelfand–Raikovtheorem) to a specified subset of representations of the algebraicobject. Here we obtain both existence and uniqueness theoremsfor host algebras as well as general structure theorems forhost algebras. Abstractly, this solves the question of whena set of Hilbert space representations is isomorphic to therepresentation theory of a C*-algebra. To make contact withharmonic analysis, we consider general convolution algebrasassociated to representation sets, and consider conditions fora convolution algebra to be a host algebra.     

Self-adjoint extensions of commuting Hermite operators

It is proved that it is possible to commuting self-adjoint operators two formally commuting Hermite operators, one of which is self-adjoint after closure and the other has equal defect numbers. The operators act in a Hilbert space constructed from the tensor product of two Hilbert spaces by completion with respect to a norm defined by a positive definite kernel which satisfies a certain majorizability condition. The result can be applied to a problem of integral representations and extensions of positive definite kernels.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 695–697, May, 1990.