The O'Nan-Scott Theorem classifies finite primitive permutation groups into one of five isomorphism classes. This theorem is very useful for answering questions about finite permutation groups since four out of the five isomorphism classes are well understood. The proof of this theorem currently relies upon the classification of the finite simple groups, as it requires a consequence of this classification, the Schreier Conjecture. After reviewing some needed group theoretic concepts, I give a detailed proof of the O'Nan-Scott Theorem. I then examine how the techniques of this proof have been applied to an open problem which asks whether every finite lattice can be embedded as an interval into the subgroup lattice of a finite group.

Advancements in electronic performance lead to a decrease in device size and an increase in power density. Because of these changes, current cooling mechanisms for electronic devices are beginning to be ineffective. Microchannels, with their large heat transfer surface area to volume ratio, cooled with either gas or liquid coolant, have shown some potential in adequately maintaining a safe surface temperature. By modifying the walls of the microchannel with fins, the cooling performance can be improved. Using computational fluid dynamics software, microfins placed in a staggered array on the bottom surface of a rectangular minichannel are modeled in order to optimize microstructure geometry and maximize heat transfer dissipation through convection from a heated surface. Fin geometry, dimensions, spacing, height, and material are analyzed. Correlations describing the Nusselt number and the Darcy friction factor are obtained and compared to recent studies. These correlations only apply to short fins in the laminar regime. Triangular fins with larger fin height, smaller fin width, and spacing double the fin width maximizes the number of fins in each row and yields better thermal performance. Once the effects of microfins were found, an experiment with multi-walled carbon nanotubes (MWNTs) grown on the surface were tested using both water and Al2O3/H2O nanofluid as the working medium. Minichannel devices containing two different MWNT structures – one fully coated surface of MWNTs and the other with a circular staggered fin array of MWNTs - were tested and compared to a minichannel device with no MWNTs. It was observed that the sedimentation of Al2O3 nanoparticles on a channel surface with no MWNTs increases the surface roughness and the thermal performance. Finally, using the lattice Boltzmann method, a two dimensional channel with suspended particles is modeled in order to get an accurate characterization of the fluid/particle motion in nanofluid. Using the analysis based on an ideal fin, approximate results for nanofluids with increase surface roughness was obtained. Microchannels have proven to be effective cooling systems and understanding how to achieve the maximum performance is vital for the innovation of electronics. Implementation of these modified channel devices can allow for longer lasting electronic systems.

I detta exjobb har en trådlös enhet för vibrationsmätning på maskiner konstruerats. Arbetet har gällt både hårdvara ochmjukvara. I arbetet ingår bland annat implementering av olika digitala filter i den mikrokontroller som valts ochframtagning och implementering av ett kommunikationsprotokoll för trådlös kommunikation. Resultatet har blivit att enkomplett fungerande prototyp på en mätenhet med lovande egenskaper kunnat tas fram.

The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most widely known and widely used public-key cryptosystem in the world today. Compared to other public-key cryptosystems, such as elliptic curve cryptography, RSA requires longer keylengths and is computationally more expensive. In order to address these shortcomings, many variants of RSA have been proposed over the years. While the security of RSA has been well studied since it was proposed in 1977, many of these variants have not. In this thesis, we investigate the security of five of these variants of RSA. In particular, we provide detailed analyses of the best known algebraic attacks (including some new attacks) on instances of RSA with certain special private exponents, multiple instances of RSA sharing a common small private exponent, Multi-prime RSA, Common Prime RSA and Dual RSA.

The O'Nan-Scott Theorem classifies finite primitive permutation groups into one of five isomorphism classes. This theorem is very useful for answering questions about finite permutation groups since four out of the five isomorphism classes are well understood. The proof of this theorem currently relies upon the classification of the finite simple groups, as it requires a consequence of this classification, the Schreier Conjecture. After reviewing some needed group theoretic concepts, I give a detailed proof of the O'Nan-Scott Theorem. I then examine how the techniques of this proof have been applied to an open problem which asks whether every finite lattice can be embedded as an interval into the subgroup lattice of a finite group.

Quantum information is a growing field showing exciting possibilities for computational speed-up and communications. For the successful implementation of quantum computers, high-precision control is required to reach fault-tolerant thresholds. Control of quantum systems pertains to the manipulation of states and their evolution. In order to minimize the effects of the environment on the control operations of the qubits, control pulses should be made time-optimal. In addition, control pulses should be made robust to noise in the system, dispersion in energies and coupling elements, and uncertain parameters. In this thesis, we examine a robust time-optimal gradient ascent technique which is used to develop controls of the motional degrees of freedom for an ensemble of neutral atoms in a one-dimensional optical lattice in the high dispersion regime with shallow trapping potentials. As such, the system is analyzed in the delocalized basis. The system is treated as an ensemble of atoms with a range of possible quasimomenta across the first Brillouin zone. This gives the ensemble of Hamiltonians, indexed by the quasimomenta, a distinct spectra in their motional states and highly inhomogeneous control Hamiltonians. Thus, the optical lattice is seen as a model system for robust control. We find optimized control pulses designed using an ensemble modification of gradient-ascent pulse engineering robust to any range of quasimomentum. We show that it is possible to produce rotation controls with fidelities above 90\% for half of the first Brillouin zone with gate times in the order of several free oscillations. This is possible for a spectrum that shows upwards of 75\% dispersion in the energies of the band structure. We also show that NOT controls for qubit rotations on the entire Brillouin zone fidelities above 99\% were possible for 0.6\% dispersion in energies. The gate times were also in the order of several free oscillations. It is shown that these solutions are palindromic in time due to phase differences in some of the energy couplings when comparing one half of the Brillouin zone to another. We explore the limits of discretized sampling of a continuous ensemble for control.

Online mining sequential patterns over data streams is an important problem in data mining. There are many applications of using sequential patterns in data streams, such as market analysis, network security, sensor networks and web track- ing. Previous studies have shown mining closed patterns provides more benefits than mining the complete set of frequent patterns, since closed pattern mining leads to compact results. A sequential pattern is closed if the sequential pattern does not have any supersequence which has the same support. Chang et al. proposed a time- based sliding window model. The time-based sliding window has two features, the new item is inserted in front of a sequence, and the obsolete item is removed from of tail of a sequence. For solving the problem of data mining in the time-based sliding window, Chang et al. proposed an algorithm called SeqStream. It uses a data struc- ture IST (Inverse Closed Sequence Tree) to keep the result. IST can incrementally be updated by the SeqStream algorithm. Although the SeqStream algorithm has used the technique of dividing the time-based sliding window to speed up the updating of IST, the SeqStream algorithm still scans the sliding window many times when IST needs to be updated. In this thesis, we propose an obstruction-check approach to maintain the result of closed sequential patterns. Our approach is designed based on the lattice structure. The feature of the lattice structure is that the parent is a supersequence of its children. By utilizing this feature, we decide the obstruction link between the parent and child if their support is the same. If a node does not have any obstruction link parent, the node is a closed sequential pattern. Then we can utilize this feature to locally travel the lattice structure. Moreover, we can fully utilize the features of the time-based sliding window model to locally travel the lat- tice structure. Based on the lattice structure, we propose the EULB (Exact Update based on Lattice structure with Bit stream)-Lattice algorithm. The EULB-Lattice algorithm is an exact method for mining data streams. We record additional informa- tion, instead of scanning the entire sliding window. We conduct several experiments using different synthetic data sets. The simulation results show that the proposed algorithm outperforms the SeqStream algorithm.

Online mining the maximal frequent itemsets over data streams is an important problem in data mining. The maximal frequent itemset is the itemset which the support is large or equal to the minimal support and the itemset is not the subset or superse of each itemset. Previous algorithms to mine the maximal frequent itemsets in the traditional database are not suitable for data streams. Because data streams have some characteristics: (1) continuous (2) fast (3) no data limit (4) real time (5) searching once, mining data streams have many new challenges. First, they are unrealistic to keep the entire stream in the main memory or even in a secondary storage area, since a data stream comes continuously and the amount of data is unbounded. Second, traditional methods of mining on stored datasets by multiple scans are infeasible, since the streaming data is passed only once. Third, mining streams requires fast, real-time processing in order to keep up with the high data arrival rate and mining results are expected to be available within short response time. In order to solve mining maximal frequent itemsets from data streams using the landmark window model, Mao et. al. propose the INSTANT algorithm. In the landmark window model, knowledge discovery is performed based on the values between the beginning time and the present. The advantage of using the landmark window model is that the results are correct as compared to the other models. The structure of the INSTANT algorithm is simple and it can save many memory space. But it takes long time in mining the maximal frequent itemsets. When the new transactions comes, the number of comparisons between the old transactions of INSATNT algorithm is too much. In this thesis, we propose the Set-Checking algorithm to mine frequent itemsets from data streams using the landmark window model. We use the structure of lattice to store our information. The structure of lattice records the subset relationship between the child node and the father node. For every node, we can record the itemset and the support. When the new transaction comes, we consider five relations: (1) equivalent (2) superset (3) subset (4) intersection (5) empty relations. According to the lattice structure of the five sets , we can add the transaction and the renew support efficiently. From our simulation result, we find that the process time of our Set-Checking algorithm is faster than that of the INSTANT algorithm.

We study the properties of m-plane GaN structure on LiAlO 2 substrate grown by plasma-assisted molecular-beam epitaxy (PAMBE). Lattice parameters of LiAlO 2 are close to GaN, the interface between LiAlO 2 and GaN showed a good lattice matching. Low lattice mismatch can reduce the defect generation, improve crystal quality. However, lattice mismatch still exist, more or less density of defect still can be observed. The density of defect was reduced in the sample at high temperature. In this study, we investigate GaN on LiAlO 2 by scanning electron microscope (SEM), atomic force microscope (AFM), photoluminescence (PL) and X-ray diffraction (XRD) for different growth temperatures.

In this study, we researched three kinds of surface treatment (no surface treatment, homogeneous alignment (HA) and vertical alignment (VA)) effect for the optoelectronic properties of cholesteric blue phase liquid crystals (BPLCs). We demonstrate the surface treatments have influence on the temperature range of BPLCs. The VA-BPLC possesses the widest temperature range, about 6.0 ¢J. The temperature range of both no surface treatment BPLC and HA-BPLC are about 5.5 ¢J. In the process of cooling, the surface treatments will restrain the change of the pitch of BPLC. Besides, surface treatment will let the crystalline of BPLC shipshape, so that it can reduce the scattering of the reflection light of BPLC. In the vertical electric field, the reflection wavelength of BPLC will be red-shift when the applied voltage increased. The reflection wavelength of the HA-BPLC can be tuned about 90 nm. The reflection wavelength of the VA-BPLC can be tuned about 120 nm. We have demonstrated the treatment of vertical alignment will reduce the operating voltage of BPLC.