This paper is concerned with a study of approximation order and construction of locally supported elements for the space S41 (Δ) of Cl quartic pp (piecewise polynomial) functions on a triangulation Δ of a connected polygonal domain Ω in R2. It is well known that, when Δ is a three-directional mesh Δ(1), the order of approximation of S41(Δ(1)) is only 4, not 5. Though a local Clough-Tocher refinement procedure of an arbitrary triangulation A yields the optimal (fifth) order of approximation from the space S41(Δ) (see [1]), it needs more data points in addition to the vertex set of the triangulation A. In this paper, we will introduce a particular mixed three-directional mesh Δ(3)) and construct so-called mixed three-directional elements. We prove that the space S41(Δ(3)) achieves its optimal-order of approximation by constructing an interpolation scheme using mixed three-directional elements.

The IEEE802.11 standard for wireless networks includes a Wired Equivalent Privacy (WEP) protocol, which is a popular wireless secure communication stream cipher protocol approach to network security used to protect link-layer communications from eavesdropping and other attacks. It allows user to communicate with the user; sharing the public key over a network. It provides authentication and encrypted communications over unsecured channels. However, WEP protocol has an inherent security flaw. It is vulnerable to the various attacks, various experiments has proved that WEP fails to achieve its security goals. This thesis entails designing, evaluating and prototyping a wireless security infrastructure that can be used with the WEP protocol optionally, thus reducing the security vulnerabilities. We have studied the flaws of WEP and the reasons for their occurrence, and we provide the design and implementation of a novel scheme in Matlab and VHDL to improve the security of WEP in all aspects by a degree of 1000. The architecture was designed with a consideration for least increment in hardware, thus achieving power and cost efficiency. It also provides flexibility for optional implementation with the available technology by being able to be bypassed by the technology, which allows for non-replacement of existing hardware, common on both, the WEP and the proposed protocols, on the fly.

Sampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified Pal´ Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter, we introduce a new interpolation process, the modified Pal interpolation, based on papers by P ´ al, J ´ oo´ and Szabo, and we establish the existence and uniqueness of interpolation polynomials of modified ´ Pal type. ´ The paradigm to recover signals with finite rate of innovation from their samples is a fairly recent field of study. In the second chapter, we show that causal bilevel signals with finite rate of innovation can be stably recovered from their samples provided that the sampling period is at or above the maximal local rate of innovation, and that the sampling kernel is causal and positive on the first sampling period. Numerical simulations are presented to discuss the recovery of bilevel causal signals in the presence of noise.

Aircraft structures have varying stiffness levels making them flexible. Consequently, this elastic property becomes increasingly important at high speeds affecting the flight dynamics of the aircraft. In high speed aircraft such as the F/A-18, elastic structural properties must be accounted for to ensure confidence in predicted flight dynamics in order to avoid adverse aeroelastic phenomena throughout flight. Data from the F/A-18 Active Aeroelastic Wing (AAW) program was used to create aeroservoelastic (ASE) models at varying flight conditions. The discretized ASE models were integrated into the NASA Dryden F/A-18 simulator in parallel with the traditional 6-DOF (degrees-of-freedom) flight dynamics calculations to ensure minimal disruption to the existing operating framework of the simulator. An interpolation scheme was used to construct ASE models within the known flight condition models. Data was processed through the state-space ASE models to compute the elastic effects during flight. Total flight dynamics from the simulation were analyzed and showed expected behavior for the combined elastic and rigid-body components in flight.

Exoskeletons are getting popular day by day due to their abilities in helping people. Exoskeletons can be used to help people gain motor senses through rehabilitation. It can also help healthy people to augment their abilities. These exoskeletons need to be strong yet light, so that the human body can support the exoskeleton, while the exoskeleton can support the activity that is being performed. This calls for under-actuated systems, which help in avoiding unnecessary mass due to additional actuators, while providing the same movement capabilities. This thesis describes in detail about two such under-actuated upper body exoskeletons which can be used for lifting loads. The design of such exoskeletons and novel control techniques for comfortable usage is discussed in detail. / Master of Science / Exoskeletons are assistive devices which can help people in several ways. An exoskeleton can help people who are affected with stroke by enabling them to walk through rehabilitation and physiotherapy. It can also help people to perform beyond their capacity in terms of physical activities. This could be to lift more load than possible, run faster than usual. This thesis describes the design and working two such exoskeletons which can be attached to the upper body. These exoskeletons can be used by people to lift loads which would require a lot of effort and muscle activity. The addition of these exoskeletons potentially reduce the muscle activity on the user and helps avoiding injuries in long term. Such exoskeletons have to be light weight so that they do not defeat the purpose of reducing muscle activity. This problem is solved by using under-actuated systems, because a significant mass of the exoskeleton is taken by the actuators such as the motors. Using under-actuated systems help in lowering the mass of the exoskeleton, while still being able to perform the same kinds of motion. This thesis also talks about how these exoskeletons can be controlled such that the load is being lifted with minimal efforts, and being aware of the loads it is lifting to provide the correct amount of torque, above or below which can lead to the motor shooting up or down causing muscular discomfort and injuries in the arm.

<p> In this thesis we study convexity theorems on the interpolation of linear operators between LP-spaces. An extension of the Riesz-Thorin Theorem to spaces constructed from countably many LP-spaces is given. In addition, results involving analytic families of linear operators between these spaces are obtained. </p> / Thesis / Master of Science (MSc)

Many real-world engineering problems require large amounts of data in order to accurately model and predict outcomes. However, this data is often noisy, sampled and discontinuous, making the data difficult to process and giving rise to incorrect models. In order to address this issue, different interpolation techniques are commonly used to make the data continuous. This can then followed by a filtering process in order to reduce noise and further reduce discontinuities. In this report, our approach to filtering is the use of convolution kernels, which smooths out the data. By doing so, a better visual representation of the limited data available can be obtained. For instance, in the specific case of studying streamlines and vortices, filtering techniques have been used to produce more realistic plots. While the use of filters can be beneficial, it is important to note that the choice of filter and its parameters can greatly impact the results obtained. In particular, we found that, for the filters we studied, applying these to analytical functions can actually increase the error. On the other hand, when filters are applied to discontinuous functions, they can improve the accuracy of the data. Overall, when analyzing stream functions with filters, significant improvements can be seen in the quality of the data. This underscores the importance of careful selection and application of filtering techniques in engineering problems that involve large amounts of noisy and discontinuous data.

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