Pseudo-orthogonality for graph 1-Laplacian eigenvectors and applications to higher Cheeger constants and data clustering

The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data.This is an NP-hard problem that can be relaxed in the spectral graph theory,where the optimal cuts of a graph are related to the eigenvalues of graph 1-Laplacian.In this paper,we first give new notations to describe the paths,among critical eigenvectors of the graph 1-Laplacian,realizing sets with prescribed genus.We introduce the pseudo-orthogonality to characterize m_(3)(G),a special eigenvalue for the graph 1-Laplacian.Furthermore,we use it to give an upper bound for the third graph Cheeger constant h_(3)(G),that is,h_(3)(G)≤m_(3)(G).This is a first step for proving that the k-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous k−1 Cheeger constants.Eventually,we apply these results to give a method and a numerical algorithm to compute m3(G),based on a generalized inverse power method.

BUECKNER'S WORK CONJUGATE INTEGRALS AND WEIGHT FUNCTIONS FOR A CRACK IN ANISOTROPIC SOLIDS

The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.

3D Woven Structures and Their Weave Design with Changing Cross-section on Warp and Weft Direction

With 3D orthogonal and pseudo-orthogonal weaves, woven sructures with lengthwise and widthwise changing cross section on one side or both sides of the structure can be constructed. The weave formation and the looming draft creation are discussed in this paper which can be used as references to manufacture woven preforms with changing cross sections.

PAPR Reduction in OFDM Systems with Large Number of Sub-Carriers by Carrier Interferometry Approaches

High Peak-to-Average Power Ratio(PAPR)is one of the major drawbacks of Orthogonal Frequency DivisionMultiplexing(OFDM)systems.This paper presents the structures of the particular bit sequences leading to the maximumPAPR(PAPR_(max))in Carrier-Interferometry OFDM(CI/OFDM)and Pseudo Orthogonal Carrier-Interferometry OFDM(PO-CI/OFDM)systems for Binary Phase Shift Keying(BPSK)modulation.Furthermore,the simulation and analysisof PAPR_(max) and PAPR cumulative distribution in CI/OFDM and PO-CI/OFDM systems with 2048 sub-carriers are pre-sented in this paper.The results show that the PAPR of OFDM system with large number of sub-carriers reduced evidentlyvia CI approaches.

Improvement and Analysis of Carrier-Interferometry Orthogonal Frequency Division Multiplexing System

This paper proposes to use Fast Fourier Transform （ FFT ） / Inverse Fast Fourier Transform （IFFT）, instead of vector-matrix multiplication, to implement the spreading/despreoding in Carrier-Interferometry Orthogonal Frequency Division Multiplexing （ CI/OFDM） and Pseudo-Orthogonal Carrier lnterferometry OFDM （PO-CI/OFDM）. That can improve the signal processing efficiency of CI/OFDM and PO-CI/OFDM systems by about 2N/log2N and 2N/（ 1 ＋ log2 N） times respectively and dose not make any difference to the system function and performance. Moreover, the effi- ciency benefits will increase with the increase of the number of sub-carriers. In addition to that, we point out that the transmitter of CI/OFDM is actually technically equivalent to that of a single-carrier system with cyclic-prefix and the receiver of CI/OFDM is a typical OFDM receiver with CI despreading. Hence the low Peak-to-Average Power Ratio （PA- PR） property and high anti-fading performance of CI/OFDM system can be well explained .

A PO-CI/MC-CDMA scheme for high modulation styles

Through analyzing the theoretical spreading principle,it has been proved in this paper that the benefit of pseudo-orthogonal carrier interferometry(PO-CI)spreading code is not supported when complex signal modulation(e.g.,quadrature phase-shift keying(QPSK)and quadrature amplitude modulation(QAM))types are employed.On this basis,a novel and feasible structure for this problem is brought forward.Within the structure mentioned,instead of complex modulation patterns,pulse amplitude modulation(PAM)combined with PO-CI spreading code is utilized.This allows us to maintain the throughput increase of a multi-carrier code division multiple access(MC-CDMA)system with minimal loss in performance and no bandwidth expansion.