• On some results concerning the polygonal polynomials.

      Andrica, Dorin; Bagdasar, Ovidiu; Babeș-Bolyai University; University of Derby (Technical University of Cluj-Napoca., 2019-02-13)
      In this paper we define the $n$th polygonal polynomial $P_n(z) = (z-1)(z^2-1)\cdots(z^n-1)$ and we investigate recurrence relations and exact integral formulae for the coefficients of $P_n(z)$ and for those of the Mahonian polynomials $Q_n(z)=(z+1)(z^2+z+1)\cdots(z^{n-1}+\cdots+z+1)$. We also explore numerical properties of these coefficients, unraveling new meanings for old sequences and generating novel entries to the Online Encyclopedia of Integer Sequences (OEIS). Some open questions are also formulated.
    • Behavioural Digital Forensics Model: Embedding Behavioural Evidence Analysis into the Investigation of Digital Crimes

      Al Mutawa, Noora; Bryce, Joanne; Franqueira, Virginia N.L.; Marrington, Andrew; Read, Janet C.; University of Derby (Elsevier, 2019-03)
      The state-of-the-art and practice show an increased recognition, but limited adoption, of Behavioural Evidence Analysis (BEA) within the Digital Forensics (DF) investigation process. Yet, there is currently no BEA-driven process model and guidelines for DF investigators to follow in order to take advantage of such an approach. This paper proposes the Behavioural Digital Forensics Model to fill this gap. It takes a multidisciplinary approach which incorporates BEA into in-lab investigation of seized devices related to interpersonal cases (i.e., digital crimes involving human interactions between offender(s) and victim(s)). The model was designed based on the application of traditional BEA phases to 35 real cases, and evaluated using 5 real digital crime cases - all from Dubai Police archive. This paper, however, provides details of only one case from this evaluation pool. Compared to the outcome of these cases using a traditional DF investigation process, the new model showed a number of benefits. It allowed a more effective focusing of the investigation, and provided logical directions for identifying the location of further relevant evidence. It also enabled a better understanding and interpretation of victim/offender behaviours (e.g., probable offenders' motivations and modus operandi), which facilitated a more in depth understanding of the dynamics of the specific crime. Finally, in some cases, it enabled the identification of suspect's collaborators, something which was not identified via the traditional investigative process.
    • Mathematical model of a constructional coanda effect nozzle.

      Trancossi, Michele; Stewart, Jill; Subhash, M; Angeli, Diego; Sheffield Hallam University (Physics Society of Iran., 2016)
      This paper analyses the ACHEON Coanda effect nozzle for aircraft propulsion, based on the dynamic equilibrium of two jet streams. The ACHEON concept, and, in particular, the HOMER nozzle, which is its main component, are presented, together with the literature milestones from which the idea originally stems. A subsystem analysis inspired by the principles of Constructal Theory is presented for the current architecture. A mathematical model of a 2D case of the system is developed, focusing on the combined effect of the mixing of the two streams and the Coanda adhesion over a convex surface. A validation of the model is also reported, based on 2D CFD analyses, under the hypothesis of incompressible flow. Results highlight that, in spite of its relative simplicity, the model produces accurate results.
    • Constructal design of an entropic wall With circulating water inside.

      Trancossi, Michele; Stewart, Jill; Dumas, Antonio; Madonia, Mauro; Marques, Jose Pascoa; Sheffield Hallam University (ASME, 2016-04-26)
      An entropic wall with circulating water inside could be a solution for acclimatizing a new building with high-energy efficiency and high levels of internal comfort. If circulating water is thermally stabilized by exchanging in the ground such has it happens in geothermal plants, a thermal shield could be realized keeping walls in comfort conditions and minimizing energy needs for further temperature regulations. This paper presents optimization guidelines of such a wall with the objective of maximizing the performances of the wall for reaching optimal internal wellness conditions. Optimization has been realized by a constructal law based method, which has been personalized by a step-by-step process and has been named constructal design for efficiency (CDE). The optimization of the system has been produced at different levels. It starts from a preliminary analysis at system levels, which allow defining the best objectives that could be reached. After this preliminary process, the system has been divided into modules, and the critical ones which have higher influence on the performances of the system have been evaluated. This analysis has been coupled also with an industrial analysis with the goal of defining an effective layout, which could be also manufactured with acceptable costs. The result has produced a final solution with a very good compromise between energetic performances and minimization of costs at industrial level. The results open interesting perspectives for the constructal law to become the core of an effective methodology of an industrial design which can couple perfectly with the modular approach which is currently the major part of industrial companies.
    • Increasing the impact of mathematics support on aiding student transition in higher education.

      Gallimore, M.; Stewart, J.; University of Lincoln (Oxford University Press, 2014-04-10)
      The ever growing gap between secondary and university level mathematics is a major concern to higher education institutions. The increase in diversity of students’ background in mathematics, with entry qualifications ranging from the more traditional A-level programmes to BTEC or international qualifications is compounded where institutions attempt to widen participation. For example, work-based learners may have been out of education for prolonged periods and, consequently, are often unprepared for the marked shift in levels, and catering for all abilities is difficult in the normal lecture, tutorial format. Lack of sufficient mathematical knowledge not only affects students’ achievement on courses but also leads to disengagement and higher drop-out rates during the first 2 years of study. Many universities now offer a maths support service in an attempt to overcome these issues, but their success is varied. This article presents a novel approach to maths support designed and adopted by the University of Lincoln, School of Engineering, to bridge this transition gap for students, offer continued support through Assessment for Learning and Individual Learning Plans, and ultimately increase student achievement, engagement and retention. The article then extends this proven approach and discusses recently implemented enhancements through the use of online diagnostic testing and a ‘student expert’ system to harness mathematical knowledge held by those gifted and talented students (often overlooked by higher education institutions) and to promote peer-to-peer mentoring. The article shows that with the proven system in place, there is a marked increase in student retention compared with national benchmark data, and an increase in student engagement and achievement measured through student feedback and assessments. Although the online enhancements are in the early stages of implementation, it is expected, based on these results, that further improvements will be shown.
    • Integrated flight/thrust vectoring control for jet-powered unmanned aerial vehicles with ACHEON propulsion.

      Cen, Zhaohui; Smith, Tim; Stewart, Paul; Stewart, Jill; University of Lincoln; University of Hull; University of Chester (SAGE, 2014-07-29)
      As a new alternative to tilting rotors or turbojet vector mechanical oriented nozzles, ACHEON (Aerial CoandaHigh Efficiency Orienting-jet Nozzle) has enormous advantages because it is free of moving elements and highly effective for Vertical/Short-Take-Off and Landing (V/STOL) aircraft. In this paper, an integrated flight/ thrust vectoringcontrol scheme for a jet powered Unmanned Aerial Vehicle (UAV) with an ACHEON nozzle is proposed to assess its suitability in jet aircraft flight applications. Firstly, a simplified Thrust-Vectoring (TV) population model is built based on CFD simulation data and parameter identification. Secondly, this TV propulsion model is embedded as a jet actuatorfor a benchmark fixed-wing ‘Aerosonde’ UAV, and then a four “cascaded-loop” controller, based on nonlinear dynamic inversion (NDI), is designed to individually control the angular rates (in the body frame), attitude angles (in the wind frame), track angles (in the navigation frame), and position (in the earth-centered frame) . Unlike previous research on fixed-wing UAV flight controls or TV controls, our proposed four-cascaded NDI control law can not only coordinatesurface control and TV control as well as an optimization controller, but can also implement an absolute self-position control for the autopilot flight control. Finally, flight simulations in a high-fidelity aerodynamic environment are performed to demonstrate the effectiveness and superiority of our proposed control scheme.
    • Man-In-The-Middle attacks in Vehicular Ad-Hoc Networks: Evaluating the impact of attackers’ strategies.

      Ahmad, Farhan; Adnane, Asma; Franqueira, Virginia N. L.; Kurugollu, Fatih; Liu, Lu; University of Derby; Loughborough University (MDPI, 2018-11-20)
      Vehicular Ad-Hoc Network (VANET), a vital component of Intelligent Transportation Systems (ITS) technology, relies on communication between dynamically connected vehicles and static Road Side Units (RSU) to offer various applications (e.g., collision avoidance alerts, steep-curve warnings and infotainment). VANET has a massive potential to improve traffic efficiency, and road safety by exchanging critical information between nodes (vehicles and RSU), thus reducing the likelihood of traffic accidents. However, this communication between nodes is subject to a variety of attacks, such as Man-In-The-Middle (MITM) attacks which represent a major risk in VANET. It happens when a malicious node intercepts or tampers with messages exchanged between legitimate nodes. In this paper, we studied the impact on network performance of different strategies which attackers can adopt to launch MITM attacks in VANET, such as fleet or random strategies. In particular, we focus on three goals of MITM attacks—message delayed, message dropped and message tampered. The simulation results indicate that these attacks have a severe influence on the legitimate nodes in VANET as the network experience high number of compromised messages, high end-to-end delays and preeminent packet losses.
    • Experimental and numerical investigation of fuel–air mixing in a radial swirler slot of a dry low emission gas turbine combustor.

      Agbonzikilo, Festus Eghe; Owen, Ieuan; Stewart, Jill; Sadasivuni, Suresh Kumar; Riley, Mike; Sanderson, Victoria; University of Lincoln; Sheffield Hallam University (ASME, 2015-11-17)
      This paper presents the results of an investigation in which the fuel/air mixing process in a single slot within the radial swirler of a dry low emission (DLE) combustion system is explored using air/air mixing. Experimental studies have been carried out on an atmospheric test facility in which the test domain is a large-scale representation of a swirler slot from a Siemens proprietary DLE combustion system. Hot air with a temperature of 300 °C is supplied to the slot, while the injected fuel gas is simulated using air jets with temperatures of about 25 °C. Temperature has been used as a scalar to measure the mixing of the jets with the cross-flow. The mixture temperatures were measured using thermocouples while Pitot probes were used to obtain local velocity measurements. The experimental data have been used to validate a computational fluid dynamics (CFD) mixing model. Numerical simulations were carried out using CFD software ansys-cfx. Due to the complex three-dimensional flow structure inside the swirler slot, different Reynolds-averaged Navier–Stokes (RANS) turbulence models were tested. The shear stress transport (SST) turbulence model was observed to give best agreement with the experimental data. The momentum flux ratio between the main air flow and the injected fuel jet, and the aerodynamics inside the slot were both identified by this study as major factors in determining the mixing characteristics. It has been shown that mixing in the swirler can be significantly improved by exploiting the aerodynamic characteristics of the flow inside the slot. The validated CFD model provides a tool which will be used in future studies to explore fuel/air mixing at engine conditions.
    • Analytical tools for blockchain: review, taxonomy and open challenges.

      Balaskas, Anastasios; Franqueira, Virginia N. L.; University of Derby (IEEE Computer Society, 2018-12-06)
      Bitcoin has introduced a new concept that could feasibly revolutionise the entire Internet as it exists, and positively impact on many types of industries including, but not limited to, banking, public sector and supply chain. This innovation is grounded on pseudo-anonymity and strives on its innovative decentralised architecture based on the blockchain technology. Blockchain is pushing forward a race of transaction-based applications with trust establishment without the need for a centralised authority, promoting accountability and transparency within the business process. However, a blockchain ledger (e.g., Bitcoin) tend to become very complex and specialised tools, collectively called “Blockchain Analytics”, are required to allow individuals, law enforcement agencies and service providers to search, explore and visualise it. Over the last years, several analytical tools have been developed with capabilities that allow, e.g., to map relationships, examine flow of transactions and filter crime instances as a way to enhance forensic investigations. This paper discusses the current state of blockchain analytical tools and presents a thematic taxonomy model based on their applications. It also examines open challenges for future development and research.
    • LQR controller design for quad-rotor helicopters.

      E. Okyere; A. bousbaine; G. T. Poyi; A.K. Joseph; J.M. Andrade; University of Derby (The Institute of Engineering and Technology., 2018-06-22)
      This paper presents an analysis and performance of a LQR control algorithm for quadrotor helicopters. For a successful analysis, first the dynamic model has been developed for the quadcopter and then the controller was designed, tuned and tested. In tuning the LQR, much attention was given to the feedback gain matrix (K). The controller’s performance wasverified in terms of delay time, rise time, overshoot, settling time and tolerance limits. The overall performance of theLQR controller was analysed.
    • Blockchain-Based Distributed Marketplace.

      Kabi, Oliver R.; Franqueira, Virginia N. L.; University of Derby (Springer Nature, 2019-01-03)
      Developments in Blockchain technology have enabled the creation of smart contracts; i.e., self-executing code that is stored and executed on the Blockchain. This has led to the creation of distributed, decentralised applications, along with frameworks for developing and deploying them easily. This paper describes a proof-of-concept system that implements a distributed online marketplace using the Ethereum framework, where buyers and sellers can engage in e-commerce transactions without the need of a large central entity coordinating the process. The performance of the system was measured in terms of cost of use through the concept of ‘gas usage’. It was determined that such costs are significantly less than that of Amazon and eBay for high volume users. The findings generally support the ability to use Ethereum to create a distributed on-chain market, however, there are still areas that require further research and development.
    • A generating function approach to the automated evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations.

      Larcombe, Peter J.; O'Neill, Sam T.; University of Derby (The Fibonacci Association, 2018-05)
      Based on a previous technique deployed in some specific low order cases, we develop an automated computational procedure to evaluate instances within a class of infinite series comprising exponentiated multiples of generalized linear combinations of Catalan numbers. The methodology is explained, and new results given.
    • New proofs of linear recurrence identities for terms of the Horadam sequence.

      Larcombe, Peter J.; Fennessey, Eric J.; University of Derby (Palestine Polytechnic University, 2019)
      We state, and prove using matrices, two (related) linear recurrence identities for termsofthesocalledHoradamsequence;eachresultexpressesthegeneraltermofthesequence as a linear combination of terms with particular initial values. First offered by A.F. Horadam himself in the 1960s, our approach to their formulation is quite different and, we believe, new.
    • On the notion of mathematical genius: rhetoric and reality.

      Larcombe, Peter J.; University of Derby (Palestine Polytechnic University, 2019)
      The existential hypothesis of mathematical ‘genius’ rests irrefutably with the affirmative. We can’t all be one of course—that sublime solopreneur in creativity—but we may still contribute to research as lesser mortals. This short essay attempts to explore what the notion means to both us and non-mathematicians.
    • On generalised multi-index non-linear recursion identities for terms of the Horadam sequence.

      Larcombe, Peter J.; Fennessey, Eric J.; University of Derby (Palestine Polytechnic University, 2019)
      We state and prove a non-linear recurrence identity for terms of the so called Horadamsequence,andthenofferitsgeneralisationwhichisavailablefromthesamemethodology. We illustrate how the overarching idea may be used to sequentially produce extended versions, each in turn with an extra level of non-linearity and term index complexity. These identities can all be captured in matrix determinant form.
    • A note on two rational invariants for a particular 2 x 2 matrix.

      Larcombe, Peter J.; Fennessey, Eric J.; University of Derby (Palestine Polytechnic University, 2018)
      We state and prove the invariance, with respect to matrix power, of both the diagonals and anti-diagonals ratio of a special case 2×2 matrix. The proof methodology is new, contrasting with those deployed previously in establishing anti-diagonals matrix invariants.
    • A new non-linear recurrence identity class for Horadam sequence terms.

      Larcombe, Peter J.; Fennessey, Eric J.; University of Derby (Palestine Polytechnic University, 2018)
      We state, and prove by a succinct matrix method, a non-linear recurrence identity class for terms of the so called Horadam sequence. A particular instance was established (in equivalent form) over half a century ago by A.F. Horadam, which provides a starting point for the discussion and an introduction to our formulation technique.
    • On two derivative sequences from scaled geometric mean sequence terms.

      Larcombe, Peter J.; Rabago, Julius, F. T.; Fennessey, Eric J.; University of Derby (Palestine Polytechnic University, 2018)
      The so called geometric mean sequence recurrence, with additional scaling variable, produces a sequence for which the general term has a known closed form. Two types of derivative sequence—comprising products of such sequence terms—are examined. In particular, the general term closed forms formulated are shown to depend strongly on a mix of three existing sequences, from which sequence growth rates are deduced and other results given.
    • A new tri-diagonal matrix invariance property.

      Larcombe, Peter J.; Fennessey, Eric J.; University of Derby (Palestine Polytechnic University, 2018)
      We state and prove an invariance property, with respect to matrix power, for those n−1 immediate off-diagonal ratios of a tri-diagonal n-square matrix. Illustrative examples are given.
    • A few thoughts on the aesthetics of mathematics in research and teaching.

      Larcombe, Peter J.; University of Derby (Palestine Polytechnic University, 2018)
      Mathematical aesthetic, having a variety of forms, is commonly experienced by mathematicians as a genuine reality and is available at every level of study. This short essay in hopefully moving beyond standardised hermeneutic critique attests to its authenticity through the words of some mathematical proponents, and reminds us that it should be promoted to children and students as a phenomenon that is as accessible as it is incontestable.