Constrained pole placement for linear systems using low-order output feedback controllers

The paper presents a simple approach to the problem of designing low-order output feedback controllers for linear continuous systems. The controller can place all of the closed-loop poles within a circle, C(- , 1/ β) , with centre at - and radius of 1/ β in the left half s-plane. The design method is based on transformation of the original system and then applying the bounded-real-lemma to the transformed system. It is shown that subjected to the solvability of an algebraic Riccati equation (ARE), output feedback controllers can then be systematically derived. Furthermore, the order of the controller is low and equals only the number of the open-loop poles lying outside the circle. A step-by-step design algorithm is given. Numerical examples are given to illustrate the design method.

The GHP II package with applications

We present an advanced version of the Maple package GHP called GHPII. In it we provide a number of additional sophisticated tools to assist with problems formulated in the Geroch-Held-Penrose (ghp) formalism. The first part of this article discusses these new tools while in the second part we shall apply the ghp formalism, using the GHPII routines, to vacuum Petrov type D spacetimes and shear-free perfect fluids. We prove that for all shear-free perfect fluids with a barotropic equation of state, where two of the principal null directions are coplanar with the fluid four-velocity and vorticity then either the expansion or vorticity of the fluid must be zero.

Algebra skills and traps and diagnostic teaching for the future

Explores on some research about teaching and learning algebra and related classroom issues. Diagnostic instruments that may be used by senior secondary teachers in teaching algebra to senior classes; Strategies for remediating algebraic difficulties and misconceptions; Impact of technology on the algebra curriculum; Usefulness of copying algebraic expressions while using Computer Algebra Systems or mathematics processing software in a calculus class.

MMSE precoder for unitary space–time codes in correlated time-varying channels

This letter addresses the problem of the design of a precoder for multiple transmit antenna communication systems with spatially and temporally correlated fading channels. By using the asymptotic (high signal-to-noise ratio) mean-square error of the channel estimates, the letter derives a precoder for unitary space-time codes that can exploit the spatiotemporal correlation in the time-varying fading channels. Simulation results illustrate that significant performance gains can be achieved by using the new precoder.

Extraction of structured programs from specification proofs

We present a method using an extended logical system for obtaining programs from specifications written in a sublanguage of CASL. These programs are “correct” in the sense that they satisfy their specifications. The technique we use is to extract programs from proofs in formal logic by techniques due to Curry and Howard. The logical calculus, however, is novel because it adds structural rules corresponding to the standard ways of modifying specifications: translating (renaming), taking unions, and hiding signatures. Although programs extracted by the Curry-Howard process can be very cumbersome, we use a number of simplifications that ensure that the programs extracted are in a language close to a standard high-level programming language. We use this to produce an executable refinement of a given specification and we then provide a method for producing a program module that maximally respects the original structure of the specification. Throughout the paper we demonstrate the technique with a simple example.

Evaluation of the robustness of predictive yield models based on catchment characteristics using GIS for reservoir fisheries in Sri Lanka

Land-use patterns in the catchment areas of Sri Lankan reservoirs, which were quantified using Geographical Information Systems (GIS), were used to develop quantitative models for yield prediction. The validity of these models was evaluated through the application to five reservoirs that were not used in the development of the models, and by comparing with the actual fish yield data of these reservoirs collected by an independent body. The robustness of the predictive models developed was tested by principal component analysis (PCA) on limnological characteristics, land-use patterns of the catchments and fish yields. The predicted fish yields in five Sri Lankan reservoirs, using the empirical models based on the ratios of forest cover and/or shrub cover to reservoir capacity or reservoir area were in close agreement with the observed fish yields. The scores of PCA ordination of productivity-related limnological parameters and those of land-use patterns were linearly related to fish yields. The relationship between the PCA scores of limnological characteristics and land-use types had the appropriate algebraic form, which substantiates the influence of the limnological factors and land-use types on reservoir fish yields. It is suggested that the relatively high predictive power of the models developed on the basis of GIS methodologies can be used for more accurate assessment of reservoir fisheries. The study supports the importance and the need for an integrated management strategy for the whole watershed to enhance fish yields.

MRD hashing

We propose two new classes of hash functions which are motivated by Maximum Rank Distance (MRD) codes. We analise the security of these schemes. The system setup phase is computationally expensive for general field extensions. To overcome this limitation we derive an algebraic solution which avoids computations in special extension fields in the intended operational range of the hash functions.

Sir, can x equal x plus two?

Technology in classrooms has brought opportunities to develop new ways of teaching and learning, as well as new ways of thinking and communicating. The author describes a lesson which aimed to have the grade four children in the class construct on the computer screen images of rectangles. The lesson provided the opportunity to learn about some powerful generalisations about rectangles as well to learn about their geometric and algebraic understandings.

A stable MCA learning algorithm

Minor component analysis (MCA) is an important statistical tool for signal processing and data analysis. Neural networks can be used to extract online minor component from input data. Compared with traditional algebraic  approaches, a neural network method has a lower computational complexity. Stability of neural networks learning algorithms is crucial to practical applications. In this paper, we propose a stable MCA neural networks learning algorithm, which has a more satisfactory numerical stability than some existing MCA algorithms. Dynamical behaviors of the proposed algorithm are analyzed via deterministic discrete time (DDT) method and the conditions are obtained to guarantee convergence. Simulations are carried out to illustrate the theoretical results achieved.

Differentiation from first principles using spreadsheets

The article demonstrates the ability of spreadsheets to fit a polynomial to a set of discrete points. It is noted that such an ability enables students to not just evaluate a gradient at a single point, but at a whole family of points, which generates the analytical global gradient function of secants without doing any algebraic manipulations. One of the advantages of such an approach is that it enables the class to focus on the concepts being taught, rather than being hindered by the mechanics of trying to factorise a cubic polynomial.

Dots versus antidots : computational exploration of structure, magnetism, and half-metallicity in boron-nitride nanostructures

Triangle-shaped nanohole, nanodot, and lattice antidot structures in hexagonal boron-nitride (h-BN) monolayer sheets are characterized with density functional theory calculations utilizing the local spin density approximation. We find that such structures may exhibit very large magnetic moments and associated spin splitting. N-terminated nanodots and antidots show strong spin anisotropy around the Fermi level, that is, half-metallicity. While B-terminated nanodots are shown to lack magnetism due to edge reconstruction, B-terminated nanoholes can retain magnetic character due to the enhanced structural stability of the surrounding two-dimensional matrix. In spite of significant lattice contraction due to the presence of multiple holes, antidot super lattices are predicted to be stable, exhibiting amplified magnetism as well as greatly enhanced half-metallicity. Collectively, the results indicate new opportunities for designing h-BN-based nanoscale devices with potential applications in the areas of spintronics, light emission, and photocatalysis. © 2009 American Chemical Society.

Identification of nonlinear systems using hybrid functions

Most real systems have nonlinear behavior and thus model linearization may not produce an accurate representation of them. This paper presents a method based on hybrid functions to identify the parameters of nonlinear real systems. A hybrid function is a combination of two groups of orthogonal functions: piecewise orthogonal functions (e.g. Block-Pulse) and continuous orthogonal functions (e.g. Legendre polynomials). These functions are completed with an operational matrix of integration and a product matrix. Therefore, it is possible to convert nonlinear differential and integration equations into algebraic equations. After mathematical manipulation, the unknown linear and nonlinear parameters are identified. As an example, a mechanical system with single degree of freedom is simulated using the proposed method and the results are compared against those of an existing approach.

The padding scheme for RSA signatures

The RSA scheme is used to sign messages; however, in order to avoid forgeries, a message can be padded with a fixed string of data P. De Jonge and Chaum showed in 1985 that forgeries can be constructed if the size of P (measured in bytes) is less than the size of N/3, where N is the RSA modulus. Girault and Misarsky then showed in 1997 that forgeries can be constructed if the size of P is less than the size of N/2. In 2001, Brier, Clavier, Coron and Naccache showed that forgeries can still be constructed when the size of P is less than two thirds the size of N. In this paper, we demonstrate that this padding scheme is always insecure; however, the complexity of actually finding a forgery is O(N). We then focus specifically on the next unsettled case, where P is less than 3/4 the size of N and show that finding a forgery is equivalent to solving a set of diophantine equations. While we are not able to solve these equations, this work may lead to a break-through by means of algebraic number theory techniques.

Structure effect on the oxygen permeation properties of barium bismuth iron oxide membranes

In this work, we investigated the oxygen permeation properties of barium bismuth iron oxide within the family of [Ba_2−3xBi_3x−1][Fe_2xBi_1−2x]O_2+3x/2 for x = 0.17–0.60. The structure changed progressively from cubic to tetragonal and then to hexagonal as function of x in accordance with the different relative amounts of bismuth on A-site and B-site of ABO_3−δ perovskite lattices. We found that the oxygen flux and electrical conductivity correlated strongly, and it was prevalent for the cubic structure (x = 0.33–0.40) which conferred the highest oxygen flux of 0.59 ml min⁻¹ cm⁻² at 950 °C for a disk membrane x = 0.33 with a thickness of 1.2 mm. By reducing the thickness of the disk membrane to 0.8 mm, the oxygen flux increased to 0.77 ml min⁻¹ cm⁻², suggesting both surface kinetics and ion diffusion controlled oxygen flux, though the former was more prominent at higher temperatures. For disk membranes x = 0.45–0.60, the perovskite structure changed to tetragonal and hexagonal, and the oxygen flux was insignificant below 900 °C, clearly indicating electron conduction properties only. However, for two compositions with relatively high bismuth content, e.g. x = 0.55 and 0.60, there was a sudden and significant rise of oxygen permeability above 900 °C, by more than one order of magnitude. These materials changed conduction behavior from metallic to semiconductor at around 900 °C. These results suggest the advent of mixed ionic electronic conducting properties caused by the structure transition as bismuth ions changed their valence states to compensate for the oxygen vacancies formed within the perovskite lattices.