MIMS EPrints
Not a member yet
2151 research outputs found
Sort by
Algebraic structures connected with pairs of compatible associative algebras
No full textWe study associative multiplications in semisimple associative algebras over ℂ compatible with the usual one or, in other words,
linear deformations of semi-simple associative algebras over ℂ. It turns out that these deformations are in one-to-one
correspondence with representations of certain algebraic structures,
which we call M-structures in the matrix case and PM-structures
in the case of direct sums of several matrix algebras. We also investigate various properties of PM-structures, provide numerous examples and describe an important class of PM-structures. The classification of these PM-structures naturally leads to affine Dynkin diagrams of A,D,E-types
Cryptographic Applications of Non-Commutative Algebraic Structures and Investigations of Nonlinear Recursions
Get PDFIn this thesis we investigate the application of non-commutative algebraic structures and nonlinear recursions in cryptography. To begin with, we demonstrate that the public key cryptosystem based on the word problem on the Grigorchuk groups, as proposed by M. Garzon and Y. Zalcstein [8], is insecure. We do this by exploiting information contained in the public key in order to construct a key which behaves like the private key and allows successful decryption of ciphertexts.
Further on, we present a new block cipher with key-dependent S-boxes, based on the Grigorchuk groups. To the best of our knowledge, it is the first time groups are used in a block cipher, whereas they have been extensively used in public key cryptosystems. The study of the cipher’s properties is, at this stage, purely theoretical.
Finally, we investigate the notion of nonlinear complexity, or maximal order complexity as it was first defined in 1989 [15], for sequences. Our main purpose is to begin classification of periodic binary sequences into nonlinear complexity classes. Previous work on the subject also includes approximation of the size of each class, found in [7]. Once the classification is completed, we can use it to show how to perform checks for short cycles in large nonlinear feedback shift registers using our proposed algorithm
Linking Landscape Fires and Local Meteorology—A Short Review
Get PDFFires burning on 18th January 2003 generated a series of cumulonimbus clouds that probably exacerbated a fire that reached suburban Canberra. Powerful whirlwinds were generated, at least one of which might have been a genuine tornado. We briefly review the development of plume theory over the last fifty years and a potential atmospheric stability index that may assist in the identification of conditions that are conducive to extreme fire behaviour in the environment. This information cab assist in deciding the location of future monitoring stations
Comparison of solution behaviour for three models of pressure-dependent plasticity: A simple analytical example
Get PDFThe main objective of the present paper is to compare, by means of a problem permitting a closed-form solution, qualitative behaviour of solutions based on three models of pressure-dependent plasticity, the coaxial model, the double-shearing model, and the double-slip and rotation model. The constitutive equations of each model reduce to classical metal plasticity at specific values of input parameters. Nevertheless, the solution behaviour essentially depends on the model chosen, independently of how close the input parameters are to these specific values. In particular, such features of the solutions as non-uniqueness, non-existence and singularity are emphasized. It is concluded that the double-slip and rotation model only retains all features inherent to classical plasticity
On the rational subset problem for groups
Get PDFWe use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automaton subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership
SDELab: stochastic differential equations with MATLAB
Get PDFWe introduce SDELab, a package for solving stochastic differential equations (SDEs) within MATLAB. SDELab features explicit and implicit integrators for a general class of Ito and Stratonovich SDEs, including Milstein's method, sophisticated algorithms for iterated stochastic integrals, and flexible plotting facilities
Symmetric Linearizations for Matrix Polynomials
Get PDFA standard way of treating the polynomial eigenvalue problem
P(\l)x = 0 is to convert it
into an equivalent matrix pencil---a process known as linearization.
Two vector spaces of pencils
\Ell_1(P) and \Ell_2(P), and their intersection \DL(P),
have recently been defined and studied by
Mackey, Mackey, Mehl, and Mehrmann.
The aim of our work is to gain new insight into these spaces
and the extent to which their constituent pencils inherit
structure from \@.
For arbitrary polynomials we show that every pencil in \DL(P)
is block symmetric
and we obtain a convenient basis for \DL(P) built from block Hankel matrices.
This basis is then exploited to
prove that
the first pencils in a sequence constructed by
Lancaster in the 1960s generate \DL(P).
When is symmetric, we show that
the symmetric pencils in \Ell_1(P) comprise
\DL(P),
while for Hermitian the Hermitian pencils in \Ell_1(P)
form a proper subset of \DL(P) that we explicitly characterize.
Almost all pencils in
each of these subsets are shown to be linearizations.
In addition to obtaining new results, this work provides a self-contained
treatment of some of the key properties of \DL(P)
together with some new, more concise proofs
Linear instability of planar shear banded flow of both diffusive and non-diffusive Johnson-Segalman fluids
No full textWe consider the linear stability of shear banded planar Couette flow of the Johnson–Segalman fluid, with and without the addition of stress diffusion to regularise the equations. In particular, we investigate the linear stability of an initially one-dimensional “base” flow, with a flat interface between the bands, to two-dimensional perturbations representing undulations along the interface. We demonstrate analytically that, for the linear stability problem, the limit in which diffusion tends to zero is mathematically equivalent to a pure (non-diffusive) Johnson–Segalman model with a material interface between the shear bands, provided the wavelength of perturbations being considered is long relative to the (short) diffusion lengthscale.
For no diffusion, we find that the flow is unstable to long waves for almost all arrangements of the two shear bands. In particular, for any set of fluid parameters and shear stress there is some arrangement of shear bands that shows this instability. Typically the stable arrangements of bands are those in which one of the two bands is very thin. Weak diffusion provides a small stabilising effect, rendering extremely long waves marginally stable. However, the basic long-wave instability mechanism is not affected by this, and where there would be instability as wavenumber k→0 in the absence of diffusion, we observe instability for moderate to long waves even with diffusion.
This paper is the first full analytical investigation into an instability first documented in the numerical study of Fielding [S.M. Fielding, Linear instability of planar shear banded flow, Phys. Rev. Lett. 95 (2005) 134501]. Authors prior to that work have either happened to choose parameters where long waves are stable or used slightly different constitutive equations and Poiseuille flow, for which the parameters for instability appear to be much more restricted.
We identify two driving terms that can cause instability: one, a jump in N1, as reported previously by Hinch et al. [E.J. Hinch, O.J. Harris, J.M. Rallison, The instability mechanism for two elastic liquids being coextruded, J. Non-Newtonian Fluid Mech. 43 (1992) 311–324]; the second, a discontinuity in shear rate. The mechanism for instability from the second of these is not thoroughly understood.
We discuss the relevance of this work to recent experimental observations of complex dynamics seen in shear-banded flows
On hypotheses testing for the selection of the spatio-temporal models
No full textSeveral models have been proposed in recent years for analysing spatial data and also, to some extent, spatio-temporal data. One of the important problems, namely the choice of an appropriate model for describing real data sets, remains unsolved. Here we consider the analysis of spatio-temporal processes from which observations over space and time are available. We propose statistical tests for discriminating between space-time autoregressive processes and multivariate autoregressive processes. The sampling properties of the proposed tests are considered. We illustrate the methods with a real example. We use the above tests to find the best model to describe spatio-temporal variations of hourly carbon monoxide measurements at four locations in London in January 2004
Regression models for covariance structures in longitudinal studies
No full textA convenient reparametrization of the marginal covariance matrix arising in longitudinal studies is discussed. The new parameters have transparent statistical interpretations, are unconstrained and may be modelled parsimoniously in terms of polynomials of time. We exploit this framework to model the dependence of the covariance structure on baseline covariates, time and their interaction. The rationale is based on the assumption that a homogeneous covariance structure with respect to the covariate space is a testable model choice. Accordingly, we provide methods for testing this assumption by incorporating covariates along with time into the model for the covariance structure. We also present new computational algorithms which can handle unbalanced longitudinal data, thereby extending existing methods. The new model is used to analyse Kenward's (1987) cattle data, and the findings are compared with published analyses of the same data set