Browsing Department of Electronics, Computing & Maths by Title
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A new formula for the coefficients of Gaussian polynomialsWe deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of their extensions is applied.

A new formulation of a result by McLaughlin for an arbitrary dimension 2 matrix powerWe obtain an existing 2004 result of J. McLaughlin which gives explicit entries for a general dimension 2 matrix raised to an arbitrary power. Our formulation employs so called Catalan polynomials related to the crucial parameter of McLaughlin’s statement, and is a new one running along a different line of argument.

A new graph construction of unbounded cliquewidth.We define permutationpartition graphs by replacing one part of a 2K2free bipartite graph (a bipartite chain graph) by an induced linear forest. We show that this hereditary graph class is of of unbounded cliquewidth (with a new graph construction of large cliquewidth). We show that this graph class contains no minimal graph class of unbounded cliquewidth, and give a conjecture for a contained boundary class for this property.

A new nonlinear recurrence identity class for Horadam sequence terms.We state, and prove by a succinct matrix method, a nonlinear 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.

New proofs of linear recurrence identities for terms of the Horadam sequence.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.

A new propelled wing aircraft configurationThis paper investigates by an energetic approach possible new configurations of aircrafts, which can rival in low speed operations against helicopters. It starts from an effective energy balance of helicopters during fundamental operations: takeoff, horizontal flight, hovering, and landing. The energy state of a helicopter can be written as: E = ½ mV2 + mgh + ½ I ω2 (1) where m is mass of helicopter, I is total rotor inertia, ω is rotor rotational speed. By taking the partial derivative with respect to time of equation 1, the power is expressed as dE/dt = ΔP = mV dV/dt + mg dh/dt (2) By optimizing the energy balance of the helicopter a new aircraft configuration has been obtained that allow a very high lift even at very low speed, but drastically reducing the energy consumption during horizontal flight. The total power required is obtained by rotor power and overall efficiency factor (η) and HPreq total = η HPreq rotor. By equations (1) and (2) it has been produced a preliminary optimization in different operative conditions considering a speed range from 0.5 (hovering conditions) to 50 m/s. By an accurate balance of the results, it has been identified that the most disadvantageous situation for a helicopter is forward flight. A new powered wing architecture has been specifically studied for replicating the behaviour of helicopters. Preliminary it has been defined by starting from the energy equations the main characteristics of the propelled wing. From those numerical results it has been defined a new configuration of propelled wing and the new aircraft configuration which allow adequate performance against helicopter. Those wings take a large advantage of two not common features: symmetry with respect to a vertical axis and possibility of optimizing the shape for specific missions. It has been designed and optimized in different configurations by CFD. In particular, an accurate analysis of fluiddynamic of the system allows quantifying the different effects that allows realizing an extraordinary ratio between lift and thrust producing an effective vehicle that can rival against helicopter also at very low speeds with a morphing configuration that will be presented in the final paper because of patenting reasons. Results show that the proposed innovative aircraft configuration allows hovering and very low speed flight. In particular, the conditions and the design for this kind of operation are presented even if still in initial design stage. The presented aircraft architecture can also allow inverting the direction of motion just by inverting the direction of the thrust. In this case, it will allow overcoming completely the performances of helicopters. The energetic balance of flight has been evaluated and the advantages with respect to helicopters have been finally expressed with surprising results.

New results and conjectures on 2partitions of multisets.The interplay between integer sequences and partitions has led to numerous interesting results, with implications in generating functions, integral formulae, or combinatorics. An illustrative example is the number of solutions at level n to the signum equation. Denoted by S(n), this represents the number of ways of choosing + and  such that ±1±2±3±···±n = 0 (see A063865 in OEIS). The AndricaTomescu conjecture regarding the asymptotic behaviour of S(n) was solved affirmatively in 2013, and new conjectures were formulated since then. In this paper we present recurrence formulae, generating functions and integral formulae for the number of ordered 2partitions of the multiset M having equal sums. Certain related integer sequences not currently indexed in the OEIS are then presented. Finally, we formulate conjectures regarding the unimodality, distribution and asymptotic behaviour of these sequences.

A new tridiagonal matrix invariance property.We state and prove an invariance property, with respect to matrix power, for those n−1 immediate offdiagonal ratios of a tridiagonal nsquare matrix. Illustrative examples are given.

A nonlinear identity for a particular class of polynomial familiesWe state and prove a new nonlinear identity for a class of polynomial families associated with integer sequences whose ordinary generating functions have quadratic governing equations with functional (polynomial) coefficients.

Nonlinear damper design for a vibration isolation systemIn this paper, vibration transmissibility of a singledegreeoffreedom (SDOF) for a massspringdamper system is presented. This is done with a linear damper having a configuration perpendicular to a linear vertical spring. The method is analyzed using a nonlinear frequency analysis approach. The concept of the output frequency response function (OFRF) is used to derive an explicit polynomial relationship between the system output response (relative displacement of the mass) and the nonlinear damping coefficient which is the parameter of interest. With the derived OFRF polynomial, various damping parameters were designed for desired output responses. Realtime experimental results are presented for the vibration isolation system validation with dampers orientated perpendicularly (at 90 degrees) to the linear spring. The experimental case studies are provided to demonstrate the new OFRFbased nonlinear system design and its significance in isolated vibration system applications. A force transmissibility graph showing the system output using both numerical and the OFRF methods are presented.

Nonlinear design and optimisation of a vibration energy harvesterNonlinear behavior has been exploited over the last decade towards improving the efficiency of most engineering systems. The effect of nonlinearities on a vibration energy harvester (VEH) has been widely studied. It has been reported in literature that a cubic damping nonlinearity extends the dynamic range (power/energy level) of a VEH system. It has also been widely shown that the operational bandwidth of a VEH system can be increased using a nonlinear hardening spring. As most energy harvesters have a maximum throw limited by the physical enclosure of the device, it is imperative to improve the operational conditions of the harvester within this limitation. This paper investigates the effects of a nonlinear hardening spring with cubic damping on a VEH system while assuming no limitation to the maximum throw (Practical VEH systems are constrained to a maximum throw and this is considered in a subsequent study). A frequencybased approach known as Output Frequency Response Function (OFRF) determined using the Associated Linear Equations (ALEs) of the nonlinear system model is employed. The OFRF polynomial is a representation of the actual system model hence used for the nonlinear VEH analysis and design. Based on the OFRF, optimal parameter values are designed to achieve any desired level of energy for the VEH.

A note on the invariance of the general $2 \times 2$ matrix antidiagonals ratio with increasing matrix power: Four proofsAn invariance matrix property, first observed empirically and seemingly absent from mainstream literature, is stated and established formally here. Four short, and different, proofs are given accordingly.

A note on two rational invariants for a particular 2 x 2 matrix.We state and prove the invariance, with respect to matrix power, of both the diagonals and antidiagonals ratio of a special case 2×2 matrix. The proof methodology is new, contrasting with those deployed previously in establishing antidiagonals matrix invariants.

NOTRINO: a NOvel hybrid TRust management scheme for INternetOfvehiclesInternetofVehicles (IoV) is a novel technology to ensure safe and secure transportation by enabling smart vehicles to communicate and share sensitive information with each other. However, the realization of IoV in reallife depends on several factors, including the assurance of security from attackers and propagation of authentic, accurate and trusted information within the network. Further, the dissemination of compromised information must be detected and vehicle disseminating such malicious messages must be revoked from the network. To this end, trust can be integrated within the network to detect the trustworthiness of the received information. However, most of the trust models in the literature relies on evaluating node or data at the application layer. In this study, we propose a novel hybrid trust management scheme, namely, NOTRINO, which evaluates trustworthiness on the received information in two steps. First step evaluates trust on the node itself at transport layer, while second step computes trustworthiness of the data at application layer. This mechanism enables the vehicles to efficiently model and evaluate the trustworthiness on the received information. The performance and accuracy of NOTRINO is rigorously evaluated under various realistic trust evaluation criteria (including precision, recall, Fmeasure and trust). Furthermore, the efficiency of NOTRINO is evaluated in presence of malicious nodes and its performance is benchmarked against three hybrid trust models. Extensive simulations indicate that NOTRINO achieve over 75% trust level as compared to benchmarked trust models where trust level falls below 60% for a network with 35% malicious nodes. Similarly, 92% precision and 87% recall are achieved simultaneously with NOTRINO for the same network, comparing to benchmark trust models where precision and recall falls below 87% and 85% respectively.

A novel contextbased risk assessment approach in vehicular networksVehicular Networks (VANET) are the largest real life application of adhoc networks where nodes are represented via fast moving vehicles. As VANET is characterised with several unique features such as the high mobility, random distribution and short connection times, etc. establishing security becomes very challenging, and identifying security threats and possible attacks become very critical. Thus, identifying, managing and exploiting risk across the different components of VANET have become increasingly important to ensure the success and the robustness of the VANET components and its applications. As VANET include different contexts, the risk posed by particular attack may have different impact, i.e., the risk caused by an attack in rural and urban area may have different consequences on the network. To this end, we propose a novel contextbased risk assessment methodology to identify attacks in different contexts of VANET. The main aim of the paper is twofold: 1) First, we identified vulnerabilities, threats and attacks on important assets in VANET, and (2) secondly, we proposed a novel contextbased risk assessment approach in VANET to identify the risks encountered by attacks in VANET in various contexts.