The Application of Intelligent Technology on a Multi-Variable Dynamical System

Conventional control systems express control solutions by means of control expressions, usually mathematically based. To completely express the control solution, a vast amount of data is required. This is either difficult or virtually impossible to obtain. In contrast, knowledge-based solutions require far less plant data and mathematical expression. This reduces development time proportionately. A dynamical temperature control system is used in this project, within which a Fuzzy Logic Controller is used to maintain the system temperature. A Fuzzy Logic Control algorithm is implemented to test its performance in temperature control. An experimental analysis indicated that for approximately 50% decrease in flow rate, considering that the flow rate could not be increased to the desired value, owing to process problems, neither of the two temperature valves was subjected to oscillations. After approximately 30 s, the process temperature began to steady out. Mathematical reasoning would have increased the settling time tremendously.     

Generalized Lyapunov exponents in high-dimensional chaotic dynamics and products of large random matrices

We study the behavior of the generalized Lyapunov exponents for chaotic symplectic dynamical systems and products of random matrices in the limit of large dimensionsD. For products of random matrices without any particular structure the generalized Lyapunov exponents become equal in this limit and the value of one of the generalized Lyapunov exponents is obtained by simple arguments. On the contrary, for random symplectic matrices with peculiar structures and for chaotic symplectic maps the generalized Lyapunov exponents remains different forD , indicating that high dimensionality cannot always destroy intermittency.     

Renormalizing rectangles and other topics in random matrix theory

We consider random Hermitian matrices made of complex or realM×N rectangular blocks, where the blocks are drawn from various ensembles. These matrices haveN pairs of opposite real nonvanishing eigenvalues, as well asM–N zero eigenvalues (forM>N). These zero eigenvalues are kinematical in the sense that they are independent of randomness. We study the eigenvalue distribution of these matrices to leading order in the large-N, M limit in which the rectangularityr=M/N is held fixed. We apply a variety of methods in our study. We study Gaussian ensembles by a simple diagrammatic method, by the Dyson gas approach, and by a generalization of the Kazakov method. These methods make use of the invariance of such ensembles under the action of symmetry groups. The more complicated Wigner ensemble, which does not enjoy such symmetry properties, is studied by large-N renormalization techniques. In addition to the kinematical -function spike in the eigenvalue density which corresponds to zero eigenvalues, we find for both types of ensembles that if |r–1| is held fixed asN, theN nonzero eigenvalues give rise to two separated lobes that are located symmetrically with respect to the origin. This separation arises because the nonzero eigenvalues are repelled macroscopically from the origin. Finally, we study the oscillatory behavior of the eigenvalue distribution near the endpoints of the lobes, a behavior governed by Airy functions. Asr1 the lobes come closer, and the Airy oscillatory behavior near the endpoints that are close to zero breaks down. We interpret this breakdown as a signal thatr1 drives a crossover to the oscillation governed by Bessel functions near the origin for matrices made of square blocks.     

The limit-periodic finite-difference operator onl 2(ℤ) associated with iterations of quadratic polynomials

The limit-periodic discrete operator of the Schrödinger type on the axis associated with iterations of quadratic polynomials is investigated. It is proved that this operator has a singularly continuous simple spectrum. Connections with the Sinai-Bowen-Ruelle measure and the conformai map onto a special comblike domain are established.     

Analysis of individual natural pyrethrins in indoor matrices by HRGC/ECD

An HRGC/ECD method is presented which permits the identification and quantitation of individual components of pyrethrins (cinerin I, jasmolin I, pyrethrin I, cinerin II, jasmolin II, pyrethrin II) in indoor matrices (airborne particles, house dust) after application of an agent containing pyrethrum. In order to prepare calibration standards for the individual components of the pyrethrum extract, the pyrethrins were isolated hy semi-preparative HPLC and their content and purity were determined by ¹H-NMR spectroscopy.     

群链R3i-D4d-C2v及dN体系在C2v对称性场中的能量矩阵

R_(3i)—D_(4d)—C_(2v)是一条群链。本文讨论如何应用D_(4d)群的标准基函作为C_(2v)群的基函来写出d~N体系在C_(2v)对称性场中各配场谱项的能量矩阵H_1。H_1中的H_(el)。部分完全可以应用D_(4d)的H_1中的H_(el)。,因而简化了计算。所得能量矩阵H_1与前文列出的H_1等价。     

Corner transfer matrices of the eight-vertex model. I. Low-temperature expansions and conjectured properties

A corner transfer matrix (CTM) is defined for the zero-field, eight-vertex model on the square lattice. Its logarithm and its diagonal form are obtained to second order in a perturbation expansion of low-temperature type. They turn out to have a very simple form, apart from certain remainder contributions that can be ignored in the limit of a large lattice. It is conjectured that in this limit the operators have these simple forms for all temperatures less than the critical temperatureT _c. The spontaneous magnetization can then easily be obtained, and agrees with the expression previously proposed. It is intended to prove some of the conjectures in subsequent papers.     

Solution of nonsymmetric linear complementarity problems by iterative methods

Convergence is established for iterative algorithms for the solution of the nonsymmetric linear complementarity problem of findingz such thatMz+q0,z0,z ^T(Mz+q)=0, whereM is a givenn×n real matrix, not necessarily symmeetric, andq is a givenn-vector. It is first shown that, if the spectral radius of a matrix related toM is less than one, then the iterates generated by the general algorithm converge to a solution of the linear complementarity problem. It turns out that convergence properties are quite similar to those of linear systems of equations. As specific cases, two important classes of matrices, Minkowski matrices and quasi-dominant diagonal matrices, are shown to satisfy this convergence condition.The author is grateful to Professor O. L. Mangasarian and the referees for their substantive suggestions and corrections.     

Phase-fixed double-group 3-Γ symbols. I. A novel exposition of the general theory of 3-Γ symbols and coupling coefficients

The present paper is the first in a series aiming at the establishment of a transparent and readily applicable Wigner-Racah algebra for all the noncommutative double groups.Starting from the Wigner-Eckart theorem in a very general setting, the theory of the fundamental quantities called here triple coefficients — and the closely related coupling coefficients — is developed and leads through a careful discussion of permutational symmetries to the concept of 3- symbols. By basing the exposition on triple coefficients and by consistently using matrix representations, we obtain a notation and a terminology which enable a clear separation of permutational properties and problems concerning complex conjugation, and a more transparent discussion of tensor (Kronecker) product multiplicities.A particularly elegant formalism is obtained for a situation which generalizes that of the classical rotation-group Wigner-Racah algebra, viz., in which there is a fixed group element effecting (through the inner automorphism it defines) complex conjugation of all the standard irreducible matrix representations.