MacMahon's Master Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. We give a complete proof of MacMahon's Master Theorem based on MacMahon's original 1960 proof. We also study a specific infinite dimensional matrix inverse due to C. Krattenthaler.

Cyber-attack on synchrophasor data has become a widely explored area. However, GPS-spoofing and FDIA attacks require different responsive actions. State-estimation based attack detection method works similar way for both types of attacks. It implies that using state-estimation based detection alone doesn’t give the control center enough information about the attack type. This scenario is specifically more critical for those attack detection methods which consider GPS-spoofing attack as another FDIA with falsified phase angle data. Since identifying correct attack type is paramount, we have attempted to develop an algorithm to distinguish these two attacks. Previous researchers exploited low-rank approximation of Hankel Matrix to differentiate between FDIA and physical events. We have demonstrated that, together with angle unwrapping algorithm, low-rank approximation of Hankel Matrix can help us separating GPS-spoofing attack with FDIA. The proposed method is verified with simulation result. It has been demonstrated that the GSA with 3 second time-shift creates a low-rank approximation error 700% higher than that of normal condition, whereas FDIA doesn’t produce any significant change in low-rank approximation error from that of normal condition. Finally, we have proposed a real-time method for successful identification of event, FDIA and GSA. / M.S. / Cyber-attack on synchrophasor data has become a widely explored area. However, GPS-spoofing and FDIA attacks require different responsive actions. State-estimation based attack detection method works similar way for both types of attacks. It implies that using state-estimation based detection alone doesn’t give the control center enough information about the attack type. This scenario is specifically more critical for those attack detection methods which consider GPS-spoofing attack as another FDIA with falsified phase angle data. Since identifying correct attack type is paramount, we have attempted to develop an algorithm to distinguish these two attacks. Previous researchers exploited low-rank approximation of Hankel Matrix to differentiate between FDIA and physical events. We have demonstrated that, together with angle unwrapping algorithm, low-rank approximation of Hankel Matrix can help us separating GPS-spoofing attack with FDIA. The simulation result verifies the next chapter discusses our proposed algorithm on GPS-spoofing attack detection and its ability to distinguish this type of attack from conventional FDIA. The proposed method is verified with simulation result. It has been demonstrated that the GSA with 3 second time-shift creates a low-rank approximation error 700% higher than that of normal condition, whereas FDIA doesn’t produce any significant change in low-rank approximation error from that of normal condition. Finally, we have proposed a real-time method for successful identification of event, FDIA and GSA.

No / The complexity of automotive systems has increased dramatically, driven by the requirement to address environmental and safety concerns and the pressure to offer higher level consumer technologies. This places a great challenge on product development organizations to manage the multidisciplinary systems integration in a reliable and robust manner. Engineering changes, which are integral part of the iterative automotive product development process, need to be managed in a way that efficiently addresses the integration requirements of complex multidisciplinary systems. The aim of this paper is to present a structured approach for engineering change management which is based on an enhanced interface analysis method which aims to identify comprehensively the system integration functional requirements as the basis for both engineering change prediction and support of robust engineering change design. The framework will be illustrated with an industrial case study on the development of an electric vehicle powertrain. The effectiveness of the proposed approach will be discussed in contrast with other methods for engineering change management.

<p> This thesis presents a derivation of a method to obtain two-body, diagonal and non-diagonal, reaction matrix elements for central and tensor forces respectively directly from nucleon-nucleon scattering phase shifts. This procedure eliminates the necessity for constructing a nuclear potential.</p> / Thesis / Master of Science (MSc)

<p> Using the reference spectrum method the G-matrix elements, and hence the binding energy of an infinite nucleus is calculated. Three modern potentials. two of which are hard core and one soft core are used. This formalism is then extended to a finite nuclei and spin orbit splittings around some closed shell nuclei are calculated. Both for binding energy and spin orbit splittings fairly good agreement with experiment is obtained. </p> / Thesis / Doctor of Philosophy (PhD)

<p> A highly parallel computing system capable of computing transcendental functions, matrix operations and iterative calculations has been devised and a typical cell has been implemented. The system consists of an array of cells, a control unit, a PDP-11 computer and an interface unit. The array uses modified SOLOMON type of communication between cells. Each cell consists of 15 words and arithmetic hardware. Arithmetic and logic operations, on words or bytes, may be performed serially between pairs of these words. Division and floating-point arithmetic are under software control. Parallel algorithms have been developed. A set of instructions and mnemonics permits a practical use of the system. The possibility of using the array as an associative-memory processor is also considered. The system has been tested by using the software package prepared. Although only one cell has actually been constructed a complete array has been simulated on a PDP-11 computer.</p> / Thesis / Master of Engineering (MEngr)

<p> Even with a good fit to nucleon-nucleon scattering data, there is considerable freedom in the off-energy-shell behaviour of the nuclear reaction matrix because of (1) the unavailability of the elastic scattering data in the high energy region and (2) the assumptions about the non-locality of the interaction. We have investigated off-energy shell behaviour by developing 'super' soft core potentials and several pairs of phase shift equivalent separable, local and momentum dependent potentials. Nuclear matter calculations were done using these potentials in order to study the sensitivity of the binding energy to the differences in the off-energy-shell behaviour. The effective range formula has been extended to the off-energy-shell case.</p> / Thesis / Doctor of Philosophy (PhD)

<p> In this thesis a systematic and short method for computing the expected values of mean squares has been developed. One chapter is devoted to the theory of regression analysis by the method of least squares using matrix notation and a proof is given that the method of least squares leads to an absolute minimum, a result which the author has not found in the literature. For two-way classifications the results have been developed for proportional frequencies, a subject which again has been neglected in the literature except for the Type II model. Finally, the methods for computing the expected values of the mean squares are applied to nested classifications and Latin square designs.</p> / Thesis / Master of Arts (MA)

In this dissertation, we investigate the Riccati diagonal stability and explore some extensions of this notion. Riccati diagonal stability plays an important role in the stability analysis of linear time-delay systems. It is known that if a linear time-delay system is Riccati diagonally stable then it admits a diagonal Lyapunov-Krasovskii functional. The existence of such a functional implies the asymptotic stability of the linear time-delay system. This diagonal stability problem has other applications in applied areas such as physical sciences and population dynamics. We also study the Lyapunov diagonal stability, which has a clear connection to the Riccati diagonal stability. Using a separation theorem, we first provide new proofs for some existing results on the Lyapunov-type diagonal stability. We also construct a new, shorter, and more transparent proof for a well-known result by Kraaijevanger that gives explicit conditions for the Lyapunov diagonal stability on matrices in $\mathbb{R}^{3 \times 3}$. In addition, we give several necessary and sufficient conditions for matrices in $\mathbb{R}^{3 \times 3}$ to be Lyapunov diagonally stable. Furthermore, we present an extension of the so-called Riccati diagonal stability to the Riccati $\alpha$-scalar stability. We derive two new characterizations regarding the Riccati $\alpha$-scalar solution of the Riccati matrix inequality so as to expand and broaden the relevant existing results. We also generalize this notion to consider a common $\alpha$-scalar solution for a family of Riccati matrix inequalities. We shall refer to this new generalization as common Riccati $\alpha$-scalar stability. As an application for the main results, we further explore families of block triangular matrices. Finally, motivated by recent developments, we formulate the problem of Riccati $\alpha$-stability. We present a necessary and sufficient condition for this type of stability and study the connection between Riccati $\alpha$-stability of a pair of $\alpha$-block matrices and Riccati stability of the diagonal block pairs. Moreover, we generalize the Riccati $\alpha$-stability by considering a family of pairs of $\alpha$-block matrices and give a new characterization for this new case.

Fall armyworm larvae (FAW), which are serious pests in the southern United States, show retarded growth when they feed on insect-resistant maize inbreds Mp704 and Mp708. These maize genotypes are not only resistant to FAW, but to a number of other lepidopteran pests. In these genotypes, a unique, extracellular, 33-KDa cysteine protease (Mir1-CP) rapidly accumulates in the whorl in response to insect feeding. Initial morphological studies on larvae feeding on resistant maize plants over-expressing the cysteine protease showed severe damage in insect?s first line of defense, the peritrophic matrix (PM). But it is not known whether the cysteine protease has unprecedented effect on insect defense mechanisms. This study focuses on understanding the functional involvement of the cysteine protease (Mir1-CP) in a plant-herbivore defense mechanism. I used purified, recombinant 33-KDa cysteine protease (Mir1-CP) and its two mutated forms (Mut1 and Mut2) to determine their effects on the permeability of PMs from fall armyworm and other lepidopteran larvae. The purified Mir1-CP was also used to determine its minimal effective dosage on lepidopteran larval growth as well as to qualitatively determine their direct morphological effects on PM and gut regions of fall armyworm larvae. In vitro permeability studies demonstrated that the recombinant Mir1-CP directly permeabilized the PM and requires both cysteine at the active site and the terminal 25 amino acids to achieve complete permeabilization. Dose response study suggested that physiologically relevant concentrations of Mir1-CP in the maize whorl would be effective in controlling a broad range of lepidopteran pests. The study also suggested that stacking Mir1-CP and Bt-toxin (Bt-CryIIA) genes in transgenic plants could broaden the normal range of both Mir1-CP and Bt-toxin. Morphological studies using three different microscopic techniques showed damaged PM in larvae fed on Mir1-CP diet. These results suggest that by directly permeabilizing and damaging the PM, the Mir1-CP provides critical defense in host plants against lepidopteran pests.