Nonholonomic Theory of Principal-direction Orthonormal Basis for a Layer of Surfaces

In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A novel kind of field theory termed as the nonholonomic theory of the Principal-Direction Orthonormal Basis(PDOB)is presented systematically in the present paper,in which the formal Christoffel symbols are related directly to the principal and geodesic curvatures with respect to the principal directions of the surface.Furthermore,a systematic and simple way to determine the curvatures of the surface are presented with some examples.It provides a way to recognize qualitatively the bending property of a surface.

Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops

A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincare map of the system is constructed. Using the Poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.

A Note on Tight Frames

Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.

Approximation to NLAR(p) with Wavelet Neural Networks

Recently, wavelet neural networks have become a popular tool for non-linear functional approximation. Wavelet neural networks, which basis functions are orthonormal scalling functions, are more suitable in approximating to function. Based on it, approximating to NLAR(p) with wavelet neural networks is studied.

A CHARACTERIZATION OF ORTHONORMAL WAVELET FAMILIES IN SOBOLEV SPACES

In this paper, a characterization of orthonormal wavelet families in Sobolev spaces H s （R） is established.

Identification of Coherent Structures of Turbulence at the Atmospheric Surface Layer

A parameter-free method based on orthonormal wavelet transforms is recommended for calculating the principal time scale of coherent structures in atmospheric boundary-layer measurements. First, the atmospheric turbulent signal is decomposed into the small scale vortex that has approximate isotropy and the large scale vortex with the digital filter. Then, the large scale vortex is used to detect coherent structures with this method. The principal time scale and profile of coherent structures for velocity components (u, v, w above rice fields are obtained. In order to testify the validity of this method, the correlation of coherent structures and non-coherent structures are also calculated.

MULTIDIMENSIONAL MULTI-KNOTS PIECEWISE LINEAR SPECTRAL SEQUENCES

Motivated by representing multidimensional periodic nonlinear and non-stationary signals （functions）, we study a class of orthonormal exponential basis for L2（Id） with I ：= [0, 1）, whose exponential parts are piecewise linear spectral sequences with p-knots. It is widely applied in time-frequency analysis.

AN MRA YIELDS AN ORTHONORMAL WAVELET BASIS——AN OPERATOR THEORETIC PROOF

In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.

Comparative Analysis of Quantum based Receivers with Linear and Nonlinear Adaptive Receivers

In this paper,we propose a new linear multiuser receiver for synchronous code-division multiple-access (CDMA) systems,referred to as the orthogonal multiuser(OMU) receiver.Unlike the linear minimum mean-squared error(MMSE) receiver,the OMU receiver depends only on the signature vectors and does not require knowledge of the received amplitudes or the channel signal-to-noise ratio(SNR).Here we develop methods that construct an optimal set of vectors with a specified inner product structure,from a given set of vectors in a complex Hilbert space.The optimal vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors.An algorithm has been developed using the principles of quantum parameters and some of its axioms and constraints.In place of the classical matched filter(MF) receiver we propose a modified receiver.This approach assumes that improving the accuracy will necessarily result in im- proved performance.The simulation results provided here suggests that in certain cases the OMU and POMU receivers can significantly increase the probability of correct detection with low error rate over the MF receiver.

Inversion Method for Sound Velocity Profile of Eddy in Deep Ocean

The modal wave number tomography approach is used to obtain sound speed profile of water column in deep ocean. The approach consists of estimation of the local modal eigenvalues from complex pressure field and use of these data as input to modal perturbative inversion method for obtaining the local sound speed profile. The empirical orthonormal function (EOF) is applied to reduce the parameter search space. The ocean environment used for numerical simulations includes the Munk profile as the unperturbed background speed profile and a weak Gaussian eddy as the sound speed profile perturbation. The results of numerical simulations show the method is capable of monitoring the oceanic interior structure.

A New Kind of k-Quantum Nonlinear Coherent States： Their Generation and PhysicalMeaning

A new kind of k-quantum nonlinear coherent states,i.e.,the k eigenstates of the k-th power~k (k≥3) of the generalized annihilation operator=1/f() of f-oscillators,are obtained and their properties are discussed.The completeness of the k states is investigated.An alternative method to construct them is proposed.It is shown that these states may form a complete Hilbert space,and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states.Physically,they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.

What can routh table offer in addition to stability?

Routh stability test is covered in almost all undergraduate control texts. It determines the stability or, a little beyond, the number of unstable roots of a polynomial in terms of the signs of certain entries of the Routh table constructed from the coefficients of the polynomial. The use of the Routh table, as far as the common textbooks show, is only limited to this function. We will show that the Routh table can actually be used to construct an orthonormal basis in the space of strictly proper rational functions with a common stable denominator. This orthonormal basis can then be used for many other purposes, including the computation of the H2 norm, the Hankel singular values and singular vectors, model reduction, H∞ optimization, etc. Keywords Routh stablity criterion - Orthonormal basis - Root-mean-squared value - Hankel operater - Nehari problem - Model reduction This work was supported by the Hong Kong Research Grants Council.

Kautz Function Based Continuous-Time Model Predictive Controller for Load Frequency Control in a Multi-Area Power System

A continuous-time Model Predictive Controller was proposed using Kautz function in order to improve the performance of Load Frequency Control(LFC).A dynamic model of an interconnected power system was used for Model Predictive Controller(MPC)design.MPC predicts the future trajectory of the dynamic model by calculating the optimal closed loop feedback gain matrix.In this paper,the optimal closed loop feedback gain matrix was calculated using Kautz function.Being an Orthonormal Basis Function(OBF),Kautz function has an advantage of solving complex pole-based nonlinear system.Genetic Algorithm(GA)was applied to optimally tune the Kautz function-based MPC.A constraint based on phase plane analysis was implemented with the cost function in order to improve the robustness of the Kautz function-based MPC.The proposed method was simulated with three area interconnected power system and the efficiency of the proposed method was measured and exhibited by comparing with conventional Proportional and Integral(PI)controller and Linear Quadratic Regulation(LQR).

Three Levels of Tensor Theory

There are many forms of tensor theory which are quite different. Discussions are put forward and their relationships are found. The differences between them depend on whether there is metric on the space and the basis is orthonormal.

Construction of nonseparable orthonormal compactly supported wavelet bases for L^2(R^d)

Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a（r＋s） ×（r＋s） dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr＋s/Zr＋s areΓΩ={[γT h,ζ T q] T：γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton＇s condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2（Rr＋s）.Properties,including Lawton＇s condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2（Rr＋1） are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].

A Property of MRA of Multiplicity r with an Arbitrary Dilation Matrix

In this paper, we give a property for multivariate multiresolution analysis of multiplicity r with an arbitrary dilatiion matrix.

A Modified Homotopy Analysis Method for Solving Boundary Layer Equations

A new modification of the Homotopy Analysis Method (HAM) is presented for highly nonlinear ODEs on a semi-infinite domain. The main advantage of the modified HAM is that the number of terms in the series solution can be greatly reduced;meanwhile the accuracy of the solution can be well retained. In this way, much less CPU is needed. Two typical examples are used to illustrate the efficiency of the proposed approach.

Representation of Functions in <i>L</i>¹<sub style="margin-left:-6px"><i>μ</i></sub>Weighted Spaces by Series with Monotone Coefficients in the Walsh Genrealized System

Let is the Walsh generalized system. In the paper constructed a weighted space , and series in the Walsh generalized system with monotonically decreasing coefficient such that for each function in the space one can find a subseries that converges to in the weighted and almost everywhere on [0,1].

Irregular Segmented Region Compression Coding Based on Pulse Coupled Neural Network

An irregular segmented region coding algorithm based on pulse coupled neural network(PCNN) is presented. PCNN has the property of pulse-coupled and changeable threshold, through which these adjacent pixels with approximate gray values can be activated simultaneously. One can draw a conclusion that PCNN has the advantage of realizing the regional segmentation, and the details of original image can be achieved by the parameter adjustment of segmented images, and at the same time, the trivial segmented regions can be avoided. For the better approximation of irregular segmented regions, the Gram-Schmidt method, by which a group of orthonormal basis functions is constructed from a group of linear independent initial base functions, is adopted. Because of the orthonormal reconstructing method, the quality of reconstructed image can be greatly improved and the progressive image transmission will also be possible.

The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures

Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).