**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2505

# Search results for: Eigenvalue problems

##### 2505 Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem

**Authors:**
Benshi Zhu

**Abstract:**

**Keywords:**
Discrete eigenvalue problems,
positive solutions,
semipositone,
three critical points theorem

##### 2504 Restarted Generalized Second-Order Krylov Subspace Methods for Solving Quadratic Eigenvalue Problems

**Authors:**
Liping Zhou,
Liang Bao,
Yiqin Lin,
Yimin Wei,
Qinghua Wu

**Abstract:**

**Keywords:**
Quadratic eigenvalue problem,
Generalized secondorder Krylov subspace,
Generalized second-order Arnoldi process,
Projection technique,
Refined technique,
Restarting.

##### 2503 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

**Authors:**
Lv Yuhua

**Abstract:**

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Cone,
fixed point index,
eigenvalue problem,
p-Laplace operator,
positive solutions.

##### 2502 The Inverse Eigenvalue Problem via Orthogonal Matrices

**Authors:**
A. M. Nazari,
B. Sepehrian,
M. Jabari

**Abstract:**

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

**Keywords:**
Householder matrix,
nonnegative matrix,
Inverse eigenvalue problem.

##### 2501 Solving Stochastic Eigenvalue Problem of Wick Type

**Authors:**
Hassan Manouzi,
Taous-Meriem Laleg-Kirati

**Abstract:**

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

**Keywords:**
Eigenvalue problem,
Wick product,
SPDEs,
finite
element,
Wiener-Itô chaos expansion.

##### 2500 Numerical Computation of Sturm-Liouville Problem with Robin Boundary Condition

**Authors:**
Theddeus T. Akano,
Omotayo A. Fakinlede

**Abstract:**

**Keywords:**
Sturm-Liouville problem,
Robin boundary condition,
finite element method,
eigenvalue problems.

##### 2499 An Estimation of the Performance of HRLS Algorithm

**Authors:**
Shazia Javed,
Noor Atinah Ahmad

**Abstract:**

**Keywords:**
HRLS algorithm,
eigenvalue spread,
misalignment.

##### 2498 Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

**Authors:**
Jing Li,
Guang Zhou

**Abstract:**

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

**Keywords:**
Hadamard product,
Fan product; nonnegative matrix,
M-matrix,
Spectral radius,
Minimum eigenvalue,
1-path cover.

##### 2497 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

**Authors:**
Chao Yuan,
Bao Guang Tian

**Abstract:**

**Keywords:**
Generalized linear model,
generalized relative coefficient,
least eigenvalue,
relative efficiency.

##### 2496 Small Signal Stability Assessment of MEPE Test System in Free and Open Source Software

**Authors:**
Kyaw Myo Lin

**Abstract:**

This paper presents small signal stability study carried over the 140-Bus, 31-Machine, 5-Area MEPE system and validated on free and open source software: PSAT. Well-established linearalgebra analysis, eigenvalue analysis, is employed to determine the small signal dynamic behavior of test system. The aspects of local and interarea oscillations which may affect the operation and behavior of power system are analyzed. Eigenvalue analysis is carried out to investigate the small signal behavior of test system and the participation factors have been determined to identify the participation of the states in the variation of different mode shapes. Also, the variations in oscillatory modes are presented to observe the damping performance of the test system.

**Keywords:**
Eigenvalue analysis,
Mode shapes,
MEPE test
system,
Participation factors,
Power System oscillations.

##### 2495 Very-high-Precision Normalized Eigenfunctions for a Class of Schrödinger Type Equations

**Authors:**
Amna Noreen ,
Kare Olaussen

**Abstract:**

We demonstrate that it is possible to compute wave function normalization constants for a class of Schr¨odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P in decimals.

**Keywords:**
Eigenvalue problems,
bound states,
trapezoidal rule,
poisson resummation.

##### 2494 Modal Analysis of Power System with a Microgrid

**Authors:**
Burak Yildirim,
Muhsin Tunay Gençoğlu

**Abstract:**

A microgrid (MG) is a small power grid composed of localized medium or low level power generation, storage systems, and loads. In this paper, the effects of a MG on power systems voltage stability are shown. The MG model, designed to demonstrate the effects of the MG, was applied to the IEEE 14 bus power system which is widely used in power system stability studies. Eigenvalue and modal analysis methods were used in simulation studies. In the study results, it is seen that MGs affect system voltage stability positively by increasing system voltage instability limit value for buses of a power system in which MG are placed.

**Keywords:**
Eigenvalue analysis,
microgrid,
modal analysis,
voltage stability.

##### 2493 Eigenwave Analysis and Simulation of Disc Loaded Interaction Structure for Wideband Gyro-TWT Amplifier

**Authors:**
R. K. Singh,
P. K. Jain

**Abstract:**

**Keywords:**
Broadbanding,
Disc-loaded interaction structure,
Eigenvalue,
Gyro-TWT,
HFSS.

##### 2492 Linear-Operator Formalism in the Analysis of Omega Planar Layered Waveguides

**Authors:**
António L. Topa

**Abstract:**

**Keywords:**
Metamaterials,
linear operators,
omega media,
layered waveguide,
orthogonality relations

##### 2491 Optimal Design of UPFC Based Damping Controller Using Iteration PSO

**Authors:**
Amin Safari,
Hossein Shayeghi

**Abstract:**

This paper presents a novel approach for tuning unified power flow controller (UPFC) based damping controller in order to enhance the damping of power system low frequency oscillations. The design problem of damping controller is formulated as an optimization problem according to the eigenvalue-based objective function which is solved using iteration particle swarm optimization (IPSO). The effectiveness of the proposed controller is demonstrated through eigenvalue analysis and nonlinear time-domain simulation studies under a wide range of loading conditions. The simulation study shows that the designed controller by IPSO performs better than CPSO in finding the solution. Moreover, the system performance analysis under different operating conditions show that the δE based controller is superior to the mB based controller.

**Keywords:**
UPFC,
Optimization Problem,
Iteration ParticleSwarm Optimization,
Damping Controller,
Low FrequencyOscillations.

##### 2490 Generalized Inverse Eigenvalue Problems for Symmetric Arrow-head Matrices

**Authors:**
Yongxin Yuan

**Abstract:**

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.

**Keywords:**
Partially prescribed spectral information,
symmetric arrow-head matrix,
inverse problem,
optimal approximation.

##### 2489 Multimachine Power System Stabilizers Design Using PSO Algorithm

**Authors:**
H. Shayeghi,
A. Safari,
H. A. Shayanfar

**Abstract:**

In this paper, multiobjective design of multi-machine Power System Stabilizers (PSSs) using Particle Swarm Optimization (PSO) is presented. The stabilizers are tuned to simultaneously shift the lightly damped and undamped electro-mechanical modes of all machines to a prescribed zone in the s-plane. A multiobjective problem is formulated to optimize a composite set of objective functions comprising the damping factor, and the damping ratio of the lightly damped electromechanical modes. The PSSs parameters tuning problem is converted to an optimization problem which is solved by PSO with the eigenvalue-based multiobjective function. The proposed PSO based PSSs is tested on a multimachine power system under different operating conditions and disturbances through eigenvalue analysis and some performance indices to illustrate its robust performance.

**Keywords:**
PSS Design,
Particle Swarm Optimization,
Dynamic
Stability,
Multiobjective Optimization.

##### 2488 Method for Determining the Probing Points for Efficient Measurement of Freeform Surface

**Authors:**
Yi Xu,
Zexiang Li

**Abstract:**

In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.

**Keywords:**
eigenvalue-optimal optimization,
freeform surface inspection,
sampling size and location,
sampled points.

##### 2487 Damping Power System Oscillations Improvement by FACTS Devices: A Comparison between SSSC and STATCOM

**Authors:**
J. Barati,
A. Saeedian,
S. S. Mortazavi

**Abstract:**

**Keywords:**
Power system stability,
PSS,
SSSC,
STATCOM,
Coordination,
Optimization,
Damping Oscillations.

##### 2486 Investigation of SSR Characteristics of SSSC With GA Based Voltage Controller

**Authors:**
R. Thirumalaivasan,
M.Janaki,
Nagesh Prabhu

**Abstract:**

**Keywords:**
FACTS,
SSR,
SSSC,
damping torque,
GA.

##### 2485 A New Perturbation Technique in Numerical Study on Buckling of Composite Shells under Axial Compression

**Authors:**
Zia R. Tahir,
P. Mandal

**Abstract:**

**Keywords:**
CFRP Composite Cylindrical Shell,
Finite Element
Analysis,
Perturbation Technique,
Asymmetric Meshing Technique,
Linear Eigenvalue analysis,
Non-linear Riks Analysis

##### 2484 A Critical Study of Media Profiling on Society-s Social Problems from a British Perspective

**Authors:**
Cj Gletus Matthews Cn Jacobs,
Kogilah Narayanasamy

**Abstract:**

**Keywords:**
Media Profiling,
Policy Response,
Social Problems

##### 2483 Numerical Buckling of Composite Cylindrical Shells under Axial Compression Using Asymmetric Meshing Technique (AMT)

**Authors:**
Zia R. Tahir,
P. Mandal

**Abstract:**

This paper presents the details of a numerical study of buckling and post buckling behaviour of laminated carbon fiber reinforced plastic (CFRP) thin-walled cylindrical shell under axial compression using asymmetric meshing technique (AMT) by ABAQUS. AMT is considered to be a new perturbation method to introduce disturbance without changing geometry, boundary conditions or loading conditions. Asymmetric meshing affects both predicted buckling load and buckling mode shapes. Cylindrical shell having lay-up orientation [0^o/+45^o/-45^o/0^o] with radius to thickness ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is analysed numerically. A series of numerical simulations (experiments) are carried out with symmetric and asymmetric meshing to study the effect of asymmetric meshing on predicted buckling behaviour. Asymmetric meshing technique is employed in both axial direction and circumferential direction separately using two different methods, first by changing the shell element size and varying the total number elements, and second by varying the shell element size and keeping total number of elements constant. The results of linear analysis (Eigenvalue analysis) and non-linear analysis (Riks analysis) using symmetric meshing agree well with analytical results. The results of numerical analysis are presented in form of non-dimensional load factor, which is the ratio of buckling load using asymmetric meshing technique to buckling load using symmetric meshing technique. Using AMT, load factor has about 2% variation for linear eigenvalue analysis and about 2% variation for non-linear Riks analysis. The behaviour of load end-shortening curve for pre-buckling is same for both symmetric and asymmetric meshing but for asymmetric meshing curve behaviour in post-buckling becomes extraordinarily complex. The major conclusions are: different methods of AMT have small influence on predicted buckling load and significant influence on load displacement curve behaviour in post buckling; AMT in axial direction and AMT in circumferential direction have different influence on buckling load and load displacement curve in post-buckling.

**Keywords:**
CFRP Composite Cylindrical Shell,
Asymmetric
Meshing Technique,
Primary Buckling,
Secondary Buckling,
Linear
Eigenvalue Analysis,
Non-linear Riks Analysis.

##### 2482 Integral Operators Related to Problems of Interface Dynamics

**Authors:**
Pa Pa Lin

**Abstract:**

This research work is concerned with the eigenvalue problem for the integral operators which are obtained by linearization of a nonlocal evolution equation. The purpose of section II.A is to describe the nature of the problem and the objective of the project. The problem is related to the “stable solution" of the evolution equation which is the so-called “instanton" that describe the interface between two stable phases. The analysis of the instanton and its asymptotic behavior are described in section II.C by imposing the Green function and making use of a probability kernel. As a result , a classical Theorem which is important for an instanton is proved. Section III devoted to a study of the integral operators related to interface dynamics which concern the analysis of the Cauchy problem for the evolution equation with initial data close to different phases and different regions of space.

**Keywords:**
Evolution,
Green function,
instanton,
integral operators.

##### 2481 Singular Value Decomposition Based Optimisation of Design Parameters of a Gearbox

**Authors:**
Mehmet Bozca

**Abstract:**

**Keywords:**
Singular value,
optimisation,
gearbox,
torsional
vibration.

##### 2480 A Fast Block-based Evolutional Algorithm for Combinatorial Problems

**Authors:**
Huang,
Wei-Hsiu Chang,
Pei-Chann,
Wang,
Lien-Chun

**Abstract:**

The problems with high complexity had been the challenge in combinatorial problems. Due to the none-determined and polynomial characteristics, these problems usually face to unreasonable searching budget. Hence combinatorial optimizations attracted numerous researchers to develop better algorithms. In recent academic researches, most focus on developing to enhance the conventional evolutional algorithms and facilitate the local heuristics, such as VNS, 2-opt and 3-opt. Despite the performances of the introduction of the local strategies are significant, however, these improvement cannot improve the performance for solving the different problems. Therefore, this research proposes a meta-heuristic evolutional algorithm which can be applied to solve several types of problems. The performance validates BBEA has the ability to solve the problems even without the design of local strategies.

**Keywords:**
Combinatorial problems,
Artificial Chromosomes,
Blocks Mining,
Block Recombination

##### 2479 Classification and Resolving Urban Problems by Means of Fuzzy Approach

**Authors:**
F. Habib,
A. Shokoohi

**Abstract:**

Urban problems are problems of organized complexity. Thus, many models and scientific methods to resolve urban problems are failed. This study is concerned with proposing of a fuzzy system driven approach for classification and solving urban problems. The proposed study investigated mainly the selection of the inputs and outputs of urban systems for classification of urban problems. In this research, five categories of urban problems, respect to fuzzy system approach had been recognized: control, polytely, optimizing, open and decision making problems. Grounded Theory techniques were then applied to analyze the data and develop new solving method for each category. The findings indicate that the fuzzy system methods are powerful processes and analytic tools for helping planners to resolve urban complex problems. These tools can be successful where as others have failed because both incorporate or address uncertainty and risk; complexity and systems interacting with other systems.

**Keywords:**
Classification,
complexity,
Fuzzy theory,
urban problems.

##### 2478 Minimization Problems for Generalized Reflexive and Generalized Anti-Reflexive Matrices

**Authors:**
Yongxin Yuan

**Abstract:**

Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., RH = R = R−1 = ±Im and SH = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize AX−Z2+Y HA−WH2, and, given an arbitrary A˜ ∈ Cm×n, we find a unique matrix among the minimizers of AX − Z2 + Y HA − WH2 in ρ that minimizes A − A˜. We also obtain sufficient and necessary conditions for existence of A ∈ ρ such that AX = Z, Y HA = WH, and characterize the set of all such matrices A if the conditions are satisfied. These results are applied to solve a class of left and right inverse eigenproblems for generalized reflexive (anti-reflexive) matrices.

**Keywords:**
approximation,
generalized reflexive matrix,
generalized
anti-reflexive matrix,
inverse eigenvalue problem.

##### 2477 Fast Factored DCT-LMS Speech Enhancement for Performance Enhancement of Digital Hearing Aid

**Authors:**
Sunitha. S.L.,
V. Udayashankara

**Abstract:**

**Keywords:**
Hearing Impairment,
DCT Adaptive filter,
Sensorineural loss patients,
Convergence rate.

##### 2476 Consensus of Multi-Agent Systems under the Special Consensus Protocols

**Authors:**
Konghe Xie

**Abstract:**

**Keywords:**
Consensus,
multi-agent systems,
directed spanning
tree,
the Laplacian matrix.