Novel criteria for exponential stability of linear neutral time-varying differential systems

Using a novel approach, we get explicit criteria for exponential stability of linear neutral time-varying differential systems. A brief discussion to the obtained results is given. To the best of our knowledge, the results of this paper are new.

Applications of symbolic computing for symmetry analysis of differential equations

 This thesis presents a number of applications of symbolic computing to the study of differential equations. In particular, three packages have been produced for the computer algebra system MAPLE and used to find a variety of symmetries (and corresponding invariant solutions) for a range of differential systems.

Differential encoding technique for multi-antenna systems with correlated Rayleigh fading channels

Differential space-time modulation (DSTM) techniques developed for multi-antenna systems allow the receiver to detect the transmitted signal without the knowledge of the fading channels. It can be viewed as an extension of differential phase-shift keying (DPSK) in single antenna systems. In this paper, we derived the pairwise error probability upper bound of differential space-time coded systems with spatially correlated Rayleigh fading channels. Based on the performance analysis, we develop a novel DSTM scheme which can exploit the spatial correlation in the fading channels. It is found that by carefully designing the initial transmitted signal matrix, the performance of the differential space-time coded systems can be significantly improved.

Robust strictly positive real synthesis of polynomial segments for discrete time systems

By using the result of robust strictly positive real synthesis of polynomial segments for continuous time systems, it is proved that, for any two n-th order polynomials a(z) and b(z), the Schur stability of their convex combination is necessary and sufficient for the existence of an n-th order polynomial c(z) such that c(z)/a(z) and c(z)/b(z) are both strictly positive real. We also provide the construction method of c(z). Illustrative examples are provided to show the effectiveness of this method.

Use of geographical information systems as a tool for predicting fish yield in tropical reservoirs : case study on Sri Lankan reservoirs

Use of geographical information systems (GIS) in inland fisheries has hitherto been essentially restricted to site evaluation for aquaculture development and assessment of limnological changes in time and space in individual water bodies. The present GIS study was conducted on the land-use pattern of the catchments of nine reservoirs in Sri Lanka, for which detailed fishery data, viz. yield, fishing intensity, landing size of major constituent species, together with selected limnological data such as conductivity and chlorophyll-a, were available. Potential statistical relationships (linear, curvilinear, exponential and second-order polynomial) of fish yield (FY, in kg ha−1 yr−1) to different land-use patterns, such as forest cover (FC, in km2) and shrub-land (SL, in km2), either singly, or in combination, and/or the ratio of each land type to reservoir area (RA in km2) and reservoir capacity (RC in km3), were explored. Highly significant relationships were evident between FY to the ratio of SL and/or FC+SL to RA and/or RC. Similarly, the above land-use types to RA and RC ratios were significantly related to limnological features of the reservoirs. The relationships of FY to various parameters obtained in this study were much better correlated than those relationships of FY to limnological and biological parameters used in yield prediction in tropical and temperate lacustrine waters previously.

A comparative study of some computer algebra packages which determine the lie point symmetries of differential equations

The study seeks to determine which of five computer algebra packages is best at finding the Lie point symmetries of systems of partial differential equations with minimal user intervention. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. A series of systems of partial differential equations are used in the study. The paper concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie point symmetries of systems of partial differential equations.

An observer design procedure for a class of nonlinear time-delay systems

This paper considers a class of uncertain, nonlinear differential state delayed control systems and presents a reduced-order observer design procedure to asymptotically estimate any vector state functionals. The method proposed involves decomposition of the delayed portion of the system into two parts: a matched and mismatched part. Provided that the rank of the mismatched part is less than the number of the outputs, a reduced-order linear functional observer, with any prescribed stability margin, can be constructed by using a simple procedure. A numerical example is given to illustrate the new design procedure and its features.

Precoder design for multi-antenna systems with temporally and spatially correlated fading channels

This paper addresses the problem of the design of a precoder for multiple transmit antenna communication systems with spatially and temporally correlated fading channels. Using the theories of matrix differential calculus, the paper derives a precoder for unitary space-time codes that can exploit the spatio-temporal correlation in the time-varying fading channels. The design criterion is based on minimizing the mean square error of the channel estimates. Computer simulation results show that a significant performance gain can be achieved by using the designed precoder.

Conditions to ensure the 2-D characteristic polynomial of uncertain matrix is very strict Hurwitz

This article derives some new conditions for the bivariate characteristic
polynomial of an uncertain matrix to be very strict Hurwitz. The uncertainties are assumed of the structured and unstructured type. Using the two-dimensional inverse Laplace transform, we derive the bounds on the uncertainties, which will ensure that the bivariate characteristic polynomial is very strict Hurwitz. Two numerical examples are given to illustrate the results.

Lie symmetries of partial differential equations using symbolic computing

This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.

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.

Intestinal microbiota associated with differential feed conversion efficiency in chickens

Analysis of model systems, for example in mice, has shown that the microbiota in the gastrointestinal tract can play an important role in the efficiency of energy extraction from diets. The study reported here aimed to determine whether there are correlations between gastrointestinal tract microbiota population structure and energy use in chickens. Efficiency in converting food into muscle mass has a significant impact on the intensive animal production industries, where feed represents the major portion of production costs. Despite extensive breeding and selection efforts, there are still large differences in the growth performance of animals fed identical diets and reared under the same conditions. Variability in growth performance presents management difficulties and causes economic loss. An understanding of possible microbiota drivers of these differences has potentially important benefits for industry. In this study, differences in cecal and jejunal microbiota between broiler chickens with extreme feed conversion capabilities were analysed in order to identify candidate bacteria that may influence growth performance. The jejunal microbiota was largely dominated by lactobacilli (over 99% of jejunal sequences) and showed no difference between the birds with high and low feed conversion ratios. The cecal microbial community displayed higher diversity, and 24 unclassified bacterial species were found to be significantly (<0.05) differentially abundant between high and low performing birds. Such differentially abundant bacteria represent target populations that could potentially be modified with prebiotics and probiotics in order to improve animal growth performance.

Finding higher symmetries of differential equations using the MAPLE package DESOLVII

We present and describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade of DESOLV. DESOLVII now includes new routines allowing the determination of higher symmetries (contact and Lie-Backlund) for systems of both ordinary and partial differential equations.