Mathematics, Department of
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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.

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Recent Submissions

A comparative thermodynamic analysis of air handling units at variable reference temperature

Ventilation and air conditioning systems are emerging as the major energy consumers in low energy buildings. The objective of this paper is to present new methodology for assessment of Air Handling Units (AHUs) taking into account the variations of reference temperature. The methodology using the concept of coenthalpy, developed for heat exchangers and published by the authors previously has been used. Four AHUs that comprise energy transfer devices, such as: Water-to-Air Heater (WAH), Heat R...

Martinaitis, Vytautas; Streckiene, Giedre; Bagdanavicius, Audrius; Bielskus, Juozas

Gaussian process methods for nonparametric functional regression with mixed predictors

Gaussian process methods are proposed for nonparametric functional regression for both scalar and functional responses with mixed multidimensional functional and scalar predictors. The proposed models allow the response variables to depend on the entire trajectories of the functional predictors. They inherit the desirable properties of Gaussian process regression, and can naturally accommodate both scalar and functional variables as the predictors, as well as easy to obtain and express uncert...

Wang, Bo; Xu, Aiping

Explicit Representations Of Periodic Solutions Of Nonlinearly Parameterized Ordinary Differential Equations And Their Applications To Inverse Problems

Developing mathematical models involves joining theory and experimental or observational data. The models often depend on parameters which are not always known or measured. A major task in this process is therefore to determine parameters fitting empirical observations. In this work we consider the fundamental challenge of inferring parameters of systems of ordinary differential equations (ODEs) from the values of their solutions and/or their continuous mappings. To achieve this aim we develo...

Al-Ameri, Jehan M. K.

Quantum mechanics approach to option pricing

Options are financial derivatives on an underlying security. The Schrodinger and
Heisenberg approach to the quantum mechanics together with the Dirac matrix
approaches are applied to derive the Black-Scholes formula and the quantum Cox-
Rubinstein formula.
The quantum mechanics approach to option pricing is based on the interpretation
of the option price as the Schrodinger wave function of a certain quantum mechanics
model determined by Hamiltonian H. We apply this approach to continuou...

Hao, Wenyan

Homotopy of planar Lie group equivariant presheaves

We utilise the theory of crossed simplicial groups to introduce a collection of local Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site. As an application, we give a characterisation of equivariant cohomology theories on a site as derived mapping spaces in these model categories.

Balchin, Scott

Crossed Simplicial Group Categorical Nerves

We extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first considering a generalised bar construction of a group before looking at twisted versions of some of these nerves. As an application we show how we can use the twisted nerves to give equivariant versions of certain derived stacks.

Balchin, Scott

Optimization of the non-axisymmetric stator casing of a 1.5 stage axial turbine

The interaction of secondary flows with the main passage flow in turbomachines results in entropy generation and in aerodynamic loss. This loss source is most relevant to low aspect ratio blades. One approach for reducing this flow energy loss is by endwall contouring. However, limited work has been reported on using non-axisymmetric endwalls at the stator casing and on its interaction with the tip leakage flow. In this paper, a non-axisymmetric endwall design method for the stator casing is ...

Kadhim, Hakim T.; Rona, Aldo; Gostelow, J. Paul; Leschke, Katrin

Mobility cost and degenerated diffusion in kinesis models

A new critical effect is predicted in population dispersal. It is based on the fact that a trade-off between the advantages of mobility and the cost of mobility breaks with a significant deterioration in living conditions. The recently developed model of purposeful kinesis (Gorban & Çabukoǧlu, Ecological Complexity 33, 2018) is based on the “let well enough alone” idea: mobility decreases for high reproduction coefficient and, therefore, animals stay longer in good conditions and leave quicke...

Gorban, Alexander N.; Çabukoǧlu, Nurdan

Knowledge Transfer Between Artificial Intelligence Systems

We consider the fundamental question: how a legacy “student” Artificial Intelligent (AI) system could learn from a legacy “teacher” AI system or a human expert without re-training and, most importantly, without requiring significant computational resources. Here “learning” is broadly understood as an ability of one system to mimic responses of the other to an incoming stimulation and vice-versa. We call such learning an Artificial Intelligence knowledge transfer. We show that if internal vari...

Tyukin, Ivan Y.; Gorban, Alexander N.; Sofeykov, Konstantin I.; Romanenko, Ilya

A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients

A new stochastic collocation finite element method is proposed for the numerical solution of elliptic boundary value problems (BVP) with random coefficients, assuming that the randomness is well-approximated by a finite number of random variables with given probability distributions. The proposed method consists of a finite element approximation in physical space, along with a stochastic collocation quadrature approach utilizing the recent Multilevel Sparse Kernel-Based Interpolation (MuSIK) ...

The Convective Instability of BEK Family of Non-Newtonian Rotating Boundary-Layer Flows

The BEK family of flows have many important practical applications such as centrifugal pumps, steam turbines, turbo-machinery and rotor-stator devices. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. The convective instability of the BEK family of rotating boundary-layer flows has been considered for generalised Newtonian fluids, power-law and Carreau fluids. A linear stability analysis is conducted using a Chebyshev collocation method in order to investigate...

Abdulameer, Mohammed Alaa

Measure concentration in computer vision applications

We live in the Information Age. In this age technological industry allows individuals to explore their personalized needs, therefore simplifying the procedure of making decisions. It also allows big global market players to leverage amounts of information they collect over time in order to excel in the markets they are operating in. Huge and often incomprehensive volumes of information collected to date constitute the phenomenon of Big Data. Big Data is a term used to describe datasets that a...

Sofeikov, Konstantin Igorevich

Jordan-Lie Inner Ideals of Finite Dimensional Associative Algebras

A subspace B of a Lie algebra L is said to be an inner ideal if [B, [B,L]] ⊆ B. Suppose that L is a Lie subalgebra of an associative algebra A. Then an inner ideal B of L is said to be Jordan-Lie if B2 = 0.
In this thesis, we study Jordan-Lie inner ideals of finite dimensional associative algebras (with involution) and their corresponding Lie algebras over an algebraically closed field F of characteristic not 2 or 3.
Let A be a finite dimensional associative algebra over F. Recall that A be...

Shlaka, Hasan Mohammed Ali Saeed

Model Selection, Union And Assembling In Practical Data Analysis: Methods And Case Study

The main problem in KDD (Knowledge Discovery and Data Mining) is always two-fold: we have to discover knowledge in real data and we need to develop methods for KDD. This thesis is also two-fold. First, I participated in the support and maintenance of the project ‘Personality traits and drug consumption’. The real data from almost 2000 respondents have been analysed. My role was in data analysis and risk assessment. The central problem is in the search and validation of psychological predictor...

Muhammad, Awaz K.

Generalized Root Graded Lie Algebras

Let g be a non-zero finite-dimensional split semisimple Lie algebra with root system
Δ. Let Γ be a finite set of integral weights of g containing Δ and {0}. We say that a Lie
algebra L over F is generalized root graded, or more exactly (Γ,g)-graded, if L contains
a semisimple subalgebra isomorphic to g, the g-module L is the direct sum of its weight
subspaces Lα (α ∈ Γ) and L is generated by all Lα with α ̸= 0 as a Lie algebra. If g is the
split simple Lie algebra and Γ = Δ∪{0} then L is...

Yaseen, Hogar M.

Short-Time Velocity Identification and Coherent-Like Detection of Ultra-High Speed Targets

Finding a balance between observation duration
and detection rates is the ultimate goal of the detection of
ultra high speed targets. However, short observation durations,
both across range unit (ARU) and Doppler frequency migration
(DFM), may severely limit the detection performance of ultra
high speed targets. Although traditional coherent integration
methods can efficiently accumulate signal energy to produce a
high signal to noise ratio (SNR) measurement, they often need
to search...

Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework.

Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a clear understanding about all possible types of dynamical regimes in classical reaction-diffusion models, such as Lotka-Volterra competition models with spatial dependence. In this study, we demonstrate some new types of wave propagation and pattern formatio...

Cangiani, Andrea; Georgoulis, Emmanuil H.; Morozov, Andrey Y.; Sutton, O. J.

Decomposition spaces and restriction species

We show that Schmitt's restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated coalgebras are an instance of the general construction of incidence coalgebras of decomposition spaces. We introduce the notion of directed restriction species that subsume Schmitt's restriction species and also induce decomposition spaces. Whereas ordinary restriction species are presheaves on the category of finit...

Gálvez-Carrillo, Imma; Kock, Joachim; Tonks, Andrew

Global Warming Can Lead to Depletion of Oxygen by Disrupting Phytoplankton Photosynthesis: A Mathematical Modelling Approach

We consider the effect of global warming on the coupled plankton-oxygen dynamics in the ocean. The net oxygen production by phytoplankton is known to depend on the water temperature and hence can be disrupted by warming. We address this issue theoretically by considering a mathematical model of the plankton-oxygen system. The model is generic and can account for a variety of biological factors. We first show that sustainable oxygen production by phytoplankton is only possible if the net produ...

Sekerci, Yadigar; Petrovskii, Sergei

A compact minimal space Y such that its square YxY is not minimal

The following well known open problem is answered in the negative:
Given two compact spaces X and Y that admit minimal homeomorphisms,
must the Cartesian product X × Y admit a minimal homeomorphism
as well? Moreover, it is shown that such spaces can be realized as minimal sets
of torus homeomorphisms homotopic to the identity. A key element of our construction
is an inverse limit approach inspired by combination of a technique of
Aarts & Oversteegen and the construction of Slovak spaces...