On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

Actuator fault detection and isolation in linear systems

A scheme for the detection and isolation of actuator faults in linear systems is proposed. A bank of unknown input observers is constructed to generate residual signals which will deviate in characteristic ways in the presence of actuator faults. Residual signals are unaffected by the unknown inputs acting on the system and this decreases the false alarm and miss probabilities. The results are illustrated through a simulation study of actuator fault detection and isolation in a pilot plant doubleeffect evaporator.

Power System Stability Enhancement by Single Network Adaptive Critic Stabilizers

This paper proposes a Single Network Adaptive Critic (SNAC) based Power System Stabilizer (PSS) for enhancing the small-signal stability of power systems over a wide range of operating conditions. SNAC uses only a single critic neural network instead of the action-critic dual network architecture of typical adaptive critic designs. SNAC eliminates the iterative training loops between the action and critic networks and greatly simplifies the training procedure. The performance of the proposed PSS has been tested on a Single Machine Infinite Bus test system for various system and loading conditions. The proposed stabilizer, which is relatively easier to synthesize, consistently outperformed stabilizers based on conventional lead-lag and linear quadratic regulator designs.

Investigations on Bi2CuO4: a quasi-one-dimensional oxide system

The potential of Bi2CuO4 as the first oxide system to show a linear-chain magnetic behaviour is examined. Electron diffraction studies do not resolve the previously reported ambiguity regarding its space group. The magnetic susceptibility data at high temperatures are best fitted to a uniform antiferromagnetic spin-1/2 Heisenberg chain. At low temperatures, however, neither the uniform nor the alternating Heisenberg antiferromagnetic model fits the data. Magnetic susceptibility data over the entire temperature range can be fitted if one assumes dimeric units with a nearly degenerate second singlet state close to the ground state, these states being separated from an excited triplet state by an energy gap. A simple heuristic model of a dimer that gives such an energy level spectrum is examined.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Risk minimization in water quality control problems of a river system

Methodologies are presented for minimization of risk in a river water quality management problem. A risk minimization model is developed to minimize the risk of low water quality along a river in the face of conflict among various stake holders. The model consists of three parts: a water quality simulation model, a risk evaluation model with uncertainty analysis and an optimization model. Sensitivity analysis, First Order Reliability Analysis (FORA) and Monte-Carlo simulations are performed to evaluate the fuzzy risk of low water quality. Fuzzy multiobjective programming is used to formulate the multiobjective model. Probabilistic Global Search Laussane (PGSL), a global search algorithm developed recently, is used for solving the resulting non-linear optimization problem. The algorithm is based on the assumption that better sets of points are more likely to be found in the neighborhood of good sets of points, therefore intensifying the search in the regions that contain good solutions. Another model is developed for risk minimization, which deals with only the moments of the generated probability density functions of the water quality indicators. Suitable skewness values of water quality indicators, which lead to low fuzzy risk are identified. Results of the models are compared with the results of a deterministic fuzzy waste load allocation model (FWLAM), when methodologies are applied to the case study of Tunga-Bhadra river system in southern India, with a steady state BOD-DO model. The fractional removal levels resulting from the risk minimization model are slightly higher, but result in a significant reduction in risk of low water quality. (c) 2005 Elsevier Ltd. All rights reserved.

An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.

Two-dimensional NMR spectroscopy of connected transitions by linear combination of flip angle dependent cosy: An alternative scheme for E.COSY

An alternative pulse scheme which simplifies and improves the recently proposed P.E.COSY experiment is suggested for the retention of connected or unconnected transitions in a coupled spin system. An important feature of the proposed pulse scheme is the improved phase characteristics of the diagonal peaks. A comparison of various experiments designed for this purpose, namely COSY-45, E.COSY, P.E.COSY and the present scheme (A.E.COSY), is also presented. The suppression of unconnected transitions and the measurement of scalar coupling constants and their relative signs are illustrated from A.E.COSY spectra of 2,3-dibromopropionic acid and 2-(2-thienyl)pyridine.

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. II. Results of parametric study

Based on a method presented in detail in a previous work by the authors, similar solutions have been obtained for the steady inviscid quasi‐one‐dimensional nonreacting flow in the supersonic nozzle of a CO2–N2 gasdynamic laser system, with either H2O or He as the catalyst. It has been demonstrated how these solutions could be used to optimize the small‐signal gain coefficient on a specified vibrational‐rotational transition. Results presented for a wide range of mixture compositions include optimum values for the small‐signal gain, area ratio, reservoir temperature, and a binary scaling parameter, which is the product of reservoir pressure and nozzle shape factor.

Kinetic studies on the interaction of gold(III) with nucleic acids. I. Native DNA-Au(III) system-spectrophotometric studies

Kinetics of the interaction of Au(III) with native calf thymus DNA has been studied spectrophotometrically to determine the kinetic parameters and to examine their dependency on the concentrations of DNA and Au(III), temperature, ionic strength and pH. The reaction is of the first order with respect to both the nucleotide unit of DNA and Au(III) in the stoichiometry of 2∶1 respectively. The rate constants vary with the initial ratio of DNA to Au(III) and is attributed to the effect of free chloride ions and the existence of a number of reaction sites with slight difference in the rate constants. The activation energies of this interaction have been found to be 14–16 kcal/mol. From the effect of ionic strength the reaction is found to occur between a positive and a negative ion in the rate-limiting step. The logarithm of rate constants are the linear function of pH and the slopes are dependent on ther-values. A plausible mechanism has been proposed which involves a primary dissociation of the major existing species (AuCl2(OH)2)−, to give (AuCl2)+ which then reacts with a site in the nucleotide unit of DNA in the rate-liminting step followed by a rapid binding to another site on the complementary strand of the DNA double helix. There exist a number of binding sites with slight difference in reactivity.

Polarization studies in electromagnetic scattering by small Solar-system particles

In remote-sensing studies, particles that are comparable to the wavelength exhibit characteristic features in electromagnetic scattering, especially in the degree of linear polarization. These features vary with the physical properties of the particles, such as shape, size, refractive index, and orientation. In the thesis, the direct problem of computing the unknown scattered quantities using the known properties of the particles and the incident radiation is solved at both optical and radar spectral regions in a unique way. The internal electromagnetic fields of wavelength-scale particles are analyzed by using both novel and established methods to show how the internal fields are related to the scattered fields in the far zone. This is achieved by using the tools and methods that were developed specifically to reveal the internal field structure of particles and to study the mechanisms that relate the structure to the scattering characteristics of those particles. It is shown that, for spherical particles, the internal field is a combination of a forward propagating wave with the apparent wavelength determined by the refractive index of the particle, and a standing wave pattern with the apparent wavelength the same as for the incident wave. Due to the surface curvature and dielectric nature of the particle, the incident wave front undergoes a phase shift, and the resulting internal wave is focused mostly at the forward part of the particle similar to an optical lens. This focusing is also seen for irregular particles. It is concluded that, for both spherical and nonspherical particles, the interference at the far field between the partial waves that originate from these concentrated areas in the particle interior, is responsible for the specific polarization features that are common for wavelength-scale particles, such as negative values and local extrema in the degree of linear polarization, asymmetry of the phase function, and enhancement of intensity near the backscattering direction. The papers presented in this thesis solve the direct problem for particles with both simple and irregular shapes to demonstrate that these interference mechanisms are common for all dielectric wavelength-scale particles. Furthermore, it is shown that these mechanisms can be applied to both regolith particles in the optical wavelengths and hydrometeors at microwave frequencies. An advantage from this kind of study is that it does not matter whether the observation is active (e.g., polarimetric radar) or passive (e.g., optical telescope). In both cases, the internal field is computed for two mutually perpendicular incident polarizations, so that the polarization characteristics can then be analyzed according to the relation between these fields and the scattered far field.

Epoch extraction from linear prediction residual for identification of closed glottis interval

In voiced speech analysis epochal information is useful in accurate estimation of pitch periods and the frequency response of the vocal tract system. Ideally, linear prediction (LP) residual should give impulses at epochs. However, there are often ambiguities in the direct use of LP residual since samples of either polarity occur around epochs. Further, since the digital inverse filter does not compensate the phase response of the vocal tract system exactly, there is an uncertainty in the estimated epoch position. In this paper we present an interpretation of LP residual by considering the effect of the following factors: 1) the shape of glottal pulses, 2) inaccurate estimation of formants and bandwidths, 3) phase angles of formants at the instants of excitation, and 4) zeros in the vocal tract system. A method for the unambiguous identification of epochs from LP residual is then presented. The accuracy of the method is tested by comparing the results with the epochs obtained from the estimated glottal pulse shapes for several vowel segments. The method is used to identify the closed glottis interval for the estimation of the true frequency response of the vocal tract system.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.