This thesis studies the effects of morphological factors of hexapod robots on their locomotion stability. In particular, an offset model for such robots is proposed. The stability margin as well as the error margin are used to indicate the stability of the hexapod robot, as it walks with different gaits in arbitrary directions. Two hexapod gaits are compared, which are the symmetric gait and the metachronal gait. The former is an artificial gait and the latter, on the contrary, is a natural gait which can be observed in many multiped animals. As we investigate advantages and disadvantages of the two gaits, we find that the stability of a hexapod robot can be enhanced by increasing the offset value. This is particularly true for a robot moving in the X and oblique directions with a symmetrical gait. However, altering the offset is less useful for metachronal gaits. In general, a hexapod robot moves most stably in the Y direction with a symmetrical gait, whereas it is most stable in the X direction with a metachronal gait.

<p>Stream ciphers are counted as an important part of symmetric encryption method. Their basic idea comes from One-Time-Pad cipher using XOR operator on the plain text and the key to generate the cipher. The present work brings a new idea in symmetric encryption method, which inherits stream key generation idea from synchronous stream cipher and uses division instead of xoring. The Usage of division to combine the plain text with stream key gives numerous abilities to this method that the most important one is using random factors to produce the ciphers.</p>

Recent wireless communication research faces the challenge of meeting a predicted 1000x increase in demand for wireless Internet data over the next decade. Among the key reasons for such explosive increase in demand include the evolution of Internet as a provider of high-definition video entertainment and two-way video communication, accessed via mobile wireless devices. One way to meet some of this demand is by using multiple antennae at the transmitter and receiver in a wireless device. For example, a system with 4 transmit and 4 receive antennae can provide up to a 4x increase in data throughput. Another key aspect of the overall solution would require sharing radio frequency spectral resources among users, causing severe amounts of interference to wireless systems. Consequently, wireless receivers with multiple antennae would be deployed in network environments that are rife with interference primarily due to wireless resource sharing among users. Other significant sources of interference include computational platform subsystems, signal leakage, and external electronics. Interference causes severe degradation in communication performance of wireless receivers. Having accurate statistical models of interference is a key requirement to designing, and analyzing the communication performance of, multi-antenna wireless receivers in the presence of interference. Prior work on statistical modeling of interference in multi-antenna receivers utilizes either the Gaussian distribution, or non-Gaussian distributions exhibiting either statistical independence or spherical isotropy. This dissertation proposes a framework, based on underlying statistical-physical mechanism of interference generation and propagation, for modeling multi-antenna interference in various network topologies. This framework can model interference which is spherically isotropic, or statistically independent, or somewhere on a continuum between these two extremes. The dissertation then utilizes the derived statistical models to analyze communication performance of multi-antenna receivers in interference-limited wireless networks. Accurate communication performance analysis can highlight the tradeoffs between communication performance and computational complexity of various multi-antenna receiver designs. Finally, using interference statistics, this dissertation proposes receiver algorithms that best mitigate the impact of interference on communication performance. The proposed algorithms include multi-antenna combining strategies, as well as, antenna selection algorithms for cooperative communications. / text

We study three different problems in non linear PDE. The first problem relates to finding equilibrium configurations in periodic media, more precisely, given an Area-Dirichlet functional J, which is periodic under integer translations and given three planes in R[superscript d], we proof there exists at least one minimizer such that it’s positive part, negative part and zero set remain at a uniform bounded distance of each plane. The second and third problem are related to non local diffusion, in the elliptic non symmetric case and parabolic case. In both cases we are interested in proving interior regularity for solutions of the aforementioned equations. / text

We study isometric maps between Teichmüller spaces and bounded symmetric domains in their Kobayashi metric. We prove that every totally geodesic isometry from a disk to Teichmüller space is either holomorphic or anti-holomorphic; in particular, it is a Teichmüller disk. However, we prove that in dimensions two or more there are no holomorphic isometric immersions between Teichmüller spaces and bounded symmetric domains and also prove a similar result for isometric submersions. / Mathematics

In this thesis, we set up a framework to define knot invariants for each choice of a symmetric space. In order to address this task, we start by defining appropriate notions of singular bundles and singular connections for a given symmetric space. We can associate a moduli space to any singular bundle defined over a compact 4-manifold with possibly non-empty boundary. We study these moduli spaces and show that they enjoy nice properties. For example, in the case of the symmetric space SU(n)/SO(n) the moduli space can be perturbed to an orientable manifold. Although this manifold is not necessarily compact, we introduce a comapctification of it. We then use this moduli space for singular bundles defined over 4-manifolds of the form YxR to define knot invariants. In another direction we mimic the construction of Donaldson invariants to define polynomial invariants for closed 4-manifolds equipped with smooth action of Z/2Z. / Mathematics

Electrolyte additives are generally used in commercial Li-ion cells to improve capacity retention and calendar life. Although it is apparent that electrolyte additives play an important role, the details of how they work are poorly understood. In order to be able to distinguish the effect of an additive on the positive or negative electrodes, an experimental method has been developed based on electrochemical impedance spectroscopy of symmetric cells constructed from electrodes of disassembled full cells similar to the method described by previous workers. This technique proved to be useful and showed that the effects of additives on both electrodes depend strongly on their concentration. It also showed that in some cases, when two additives are introduced in the same cell, both additives contribute to the formation of the surface layer of both electrodes. In other cases, each additive controls the formation of the surface layer of only one electrode.

Abstract is available from the print copy. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.

The goal of this thesis is to first give an overview of the modern approach, using the paper of A. Vershik and A. Okounkov, to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the group algebra. We index units first by partitions, and then by so called standard tableaux. We also present a new result and discuss future research exploring the connections between this theory and Quantum Information.

This thesis presents a probability model to predict the maximum rotation of rocking bodies exposed to seismic excitations given specific earthquake intensity measures. After obtaining the nonlinear equations of motion and clarification of the boundaries applied to a rocking body to avoid sliding, a complete discussion is provided on the estimation of approximate period and equivalent damping ratio for the rocking motion. Thereafter, instead of using an iterative solution, which was previously proven defective, a new approximate technique is developed by finding the best representative ground motion intensities. Suitable transformation and normalization are applied to these intensities, and the Bayesian Updating approach is employed to construct a probability model. The proposed probability model is capable of accurately predicting the maximum rotation of a symmetric rocking block given displacement design spectra, peak ground acceleration, peak ground velocity, and arias intensity of an earthquake. This probabilistic model along with the approximate capacity of rocking blocks are used to estimate the fragility curves for rocking blocks with specific geometrical parameters. At the end, a comprehensive and practical form of fragility curves and numerical examples are provided for design purposes.