Mathematics, Department of
: [799]
Community home page

The Department of Mathematics has built a strong reputation for innovation and leadership in targeted areas of pure and applied mathematics. Indicators of success are:

- In Research Assessment Exercise 2001 the Department received ranking 5 in both pure and applied mathematics. Within the mathematical field, only a small number received a coveted 5/5*-rating which is characterised by forefront position within the international academic community 5-ranking in each unit.

- External funding: a stream of grants have been obtained in recent years in all main subject areas. In 2006, our Department was the best funded mathematics department per capita from EPSRC.

- Interdisciplinary research, linking mathematics with biology, chemistry, engineering, geology and physics. The Centre for Mathematical Modelling (MMC) coordinates this type of activity.

- Organisation of numerous international conferences and workshops both at Leicester and elsewhere.

When downloading papers please observe the normal copyright codes and conventions for their use.

Recent Submissions

Using partially specified models to detect and quantify structural sensitivity in biological systems

Mathematical models in ecology and evolution are highly simplified representations of a complex underlying reality. For this reason, there is always a high degree of uncertainty with regards to the model specificationâ€”not just in terms of parameters, but also in the form taken by the model equations themselves. This uncertainty becomes critical for models in which the use of two different functions fitting the same dataset can yield substantially different model predictionsâ€”a property known a...

Adamson, Matthew William

Optimum shape problems in distributed parameter control theory.

The work is concerned with optimum shape problems in the distributed parameter area and it consists of four parts. In Part I we consider first the basic variational theory due to Gelfand and Fomin emphasising the importance of the transversality condition in optimum shape situations; also in Part I we discuss an application of the basic theory in a particular problem where the state equations (the constraints) are hyperbolic in character. In Part II we consider a heat transfer problem between...

Girgis, Siham Boctor.

Distributed parameter theory in optimal control.

The main result of this work is the solution of open loop optimal control problems for counterflow diffusion processes, which occur very widely in chemical and mechanical engineering. In these processes two fluids pass each other moving in opposite directions separated by a membrane which is permeable to heat or a chemical solute. The membrane may also take the form of a liquid-gas interface. Subject to certain simplifying assumptions, the equations describing such processes are 01 (x,t), 02 ...

Gregson, M. J.

Applications of variational theory in certain optimum shape problems in hydrodynamics.

PART I In a recent paper Wu, T.Y. & Whitney, A.K., the authors studied optimum shape problems in hydrodynamics. These problems are stated in the form of a singular integral equation depending on the unknown shape and an unknown singularity distribution; the shape is then to be determined so that some given performance criterion has to be {lcub}maximized/minimized{rcub} In the optimum problem to be studied in this part we continue to assume that the state equation is a linear integral equation...

Essawy, Abdelrahman Hussein.

Optimum shape problems for distributed parameter systems.

In this thesis the variation of a functional defined on a variable domain has been studied and applied to the problem of finding the optimum shape of the domain in which some performance criterion has an extreme. The method most frequently used is one due to Gelf and Fomin. It is applied to problems governed by first and second order partial differential equations, unsteady one dimensional gas movements and the problem of minimum drag on a body with axial symmetry in Stokes flow.

Edwards, Janet M

Many-valued logics. a study of the relationship of propositional calculi and algebraic systems.

This thesis sets out to examine the possibility of devising a theory which will give a unified account of prepositional calculi and algebraic systems. Starting from a historical account of the principal ideas tributary to the main stream of theory from Boole to the present day, it presents a technical- language framework within which it is possible to develop in a uniform format substantial portions of the theories of both sorts of system. The idea of an Interpretation then leads to a discuss...

Cuninghame-Green, Raymond.

Parameter reduction in definition by multi-successor recursion.

It is well known that in primitive recursive arithmetic with a single successor the number of parameters in a definition by recursion may be successively reduced. In this thesis I examine the possibility of effecting a similar reduction in the number of parameters in a definition by recursion in a multi-successor arithmetic. The reduction process involves the discovery in multi-successor arithmetic of analogues of pairing functions and of functions which select the elements of an ordered pair...

Burville, J. C.

Composition algebras and their generators.

The aim of this thesis is to show how the study of composition algebras and their generators has developed from a simple observation in logic made by Henry Maurice Sheffer nearly 60 years ago. The results in the algebra on 2 marks, which corresponds to classical 2-value sentence logic, were firmly established when Emil Post wrote a monograph on the subject 30 years ago. In this dissertation, however, they are developed in a more coherent and systematic way than has been attempted before and i...

Wheeler, Roger F.

A formalisation of the arithmetic of transfinite ordinals in a multisuccessor Equation calculus.

This thesis presents a syntactic development of the arithmetic of ordinal numbers less than This is done by means of an Equation calculus v/here.all statements are given in the form of equations. There are rules of inference for deriving; one equation from another. Certain functions, including a countably infinite number of successor functions are taken as primitive. New functions are defined by substitution and primitive recursion starting with the primitive functions. Such definitions const...

Williams, H. P.

Towards a theory of multivariate interpolation using spaces of distributions.

The research contained in this thesis concerns the study of multivariate interpolation problems. Given a discrete set of possibly complex-valued data, indexed by a set of interpolation nodes in Euclidean space, it is desirable to generate a function which agrees with the data at the nodes. Within this general framework, this work pursues and generalizes one approach to the problem. Based on a variational theory, we construct a parameterised family of Hilbert spaces of tempered distributions, ...

Wayne, Henry.

Some problems in the kinetic theory of plasmas.

This thesis covers essentially two problems in the kinetic theory of plasmas. The first concerns the investigation of plasma oscillations in a constant electric field - a topic investigated by Akheizer and Sitenko as early as 1956 [1] More recently Stenflo [2] has considered the problem in which he replaces the collision integral of Boltzmann's equation by a Fokker-Planck term and a B.G.K. term. The dispersion relations derived by Stenflo contained a number of parameters the relative importan...

Tapp, M. C.

Incomplete data in event history analysis.

Incomplete data present a serious problem in the modelling of event histories. Two particular forms of incompleteness are in evidence for data of this form. The first is due to recording of event times in interval-censored form. For single non-repeatable events this can be accommodated by using methods for modelling grouped survival times, such as those of Prentice and Gloeckler (1978) and Finkel- stein (1986). The other, more serious, problem relates to incomplete recording of follow-up meas...

Sutton, Christopher Julian.

Alglat for modules over fsi rings and reflexivity.

For a bimodule RMDelta where R and Delta are rings with unity, alglat RMDelta is the ring of all Delta-endomorphisms of M leaving invariant every R-submodule of M. The bimodule is said to be reflexive if the elements of alglat RMDelta are precisely the left scalar multiplications by elements of R. For most of the thesis Delta = R, a commutative ring with unity. However, in the early work, some results on the general structure of alglat are obtained, and in particular, Theorem 1.9 shows that i...

Snashall, Nicole Jane.

Successor systems. An investigation into the primitive recursive functions of generalised multisuccessor arithmetics, with applications to constructive algebra.

An investigation into the primitive recursive functions of generalised multisuccessor arithmetics, with applications to constructive algebra.' Submitted for the degree of Doctor of Philosophy by Paul Hudson Stanford* at Leicester University, England, in 1975. The above named thesis is concerned with the extension of the notion of primitive recursion to structures other than the natural numbers. Successor systems are generalisations of the arithmetics of Vu?kovi? [2], and as a class are closed...

Stanford, Paul Hudson.

Functional-completeness criteria for finite domains.

Necessary and sufficient conditions for the functional completeness of a set F of functions with variables and values ranging over N = {lcub}0,1,...,n{rcub}, where n ? 1, are investigated and in particular, completeness criteria for a single function are determined. Complete solutions are known in the special cases n = 1,2, and results about these special cases which are of use in formulating general theorems are discussed. Proceeding to the general case some preliminary criteria (which presu...

Schofield, P. (Peter)

Formalisations of recursive arithmetic.

In this thesis we shall present a new formalisation of the theory of primitive recursive functions, which is called Ternary Recursive Arithmetic. In a recent paper, Alonzo Church described a formalisation of recursive arithmetic in which single axioms of recursion and composition (i.e. definition by explicit substitution) took the place of an infinity of such axioms in earlier codifications. Church's system, however, postulates axioms of the propositional calculus and of mathematical inductio...

Rose, H. E. (Harvey Ernest)

The metatheory of the elementary equation calculus.

Abstract not available.

Bundy, A.

The convective instability of the boundary-layer flow over families of rotating spheroids.

The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly t...

Samad, Abdul.

Logical systems with finitely many truth values.

Abstract not provided.

Rousseau, G.

Transmission of guided sound waves through a layer of fluid or solid.

The thesis considers the transmission of sound waves through a layer of fluid or solid contained in a wave-guide of a simple form. The main aim is to find the transmission coefficient for a lowest order incident mode and to fine the lengths of the layer for which the transmission is a maximum or minimum. The first part of the thesis gives the exact solution for transmission through a layer of inviscid fluid, and for transmission through a layer of viscous fluid when the boundaries of the guid...