No description available.

Nesta dissertação estudamos sob que condições um módulo de comprimento finito pode ser imerso em um módulo injetivo de comprimento finito. Também apresentamos a caracterização, dada por Hirano em [8], para os anéis sobre os quais todo módulo de comprimento finito tem um fecho injetivo de comprimento finito, os chamados de ¶-V-anéis. Além disso, mostramos que as extensões normais finitas de ¶-V-anéis são também ¶-V-anéis. / In this dissertation we study under what conditions a module of finite length can be embedded in an injective module of finite length. Also, we present a charactization, given by Hirano in [8], for the rings over which all module of finite length has an injective hull of finite length, the so called ¶-V-rings. Moreover, we show that finite normalizing extensions of ¶-V-rings are also ¶-V-rings.

Nesta dissertação estudamos sob que condições um módulo de comprimento finito pode ser imerso em um módulo injetivo de comprimento finito. Também apresentamos a caracterização, dada por Hirano em [8], para os anéis sobre os quais todo módulo de comprimento finito tem um fecho injetivo de comprimento finito, os chamados de ¶-V-anéis. Além disso, mostramos que as extensões normais finitas de ¶-V-anéis são também ¶-V-anéis. / In this dissertation we study under what conditions a module of finite length can be embedded in an injective module of finite length. Also, we present a charactization, given by Hirano in [8], for the rings over which all module of finite length has an injective hull of finite length, the so called ¶-V-rings. Moreover, we show that finite normalizing extensions of ¶-V-rings are also ¶-V-rings.

Nesta dissertação estudamos sob que condições um módulo de comprimento finito pode ser imerso em um módulo injetivo de comprimento finito. Também apresentamos a caracterização, dada por Hirano em [8], para os anéis sobre os quais todo módulo de comprimento finito tem um fecho injetivo de comprimento finito, os chamados de ¶-V-anéis. Além disso, mostramos que as extensões normais finitas de ¶-V-anéis são também ¶-V-anéis. / In this dissertation we study under what conditions a module of finite length can be embedded in an injective module of finite length. Also, we present a charactization, given by Hirano in [8], for the rings over which all module of finite length has an injective hull of finite length, the so called ¶-V-rings. Moreover, we show that finite normalizing extensions of ¶-V-rings are also ¶-V-rings.

Axisymmetric radial Bernstein modes are known to exist in non-neutral plasmas and have been studied theoretically and computationally in 1D, but detection of these modes has still proven to be difficult due to self-shielding. To help advance the work on this front we created a 2D particle-in-cell (PIC) code that simulates a non-neutral plasma in a Malmberg-Penning trap. A detailed description of the PIC code itself has been included that highlights the benefits of using an $r^2$--$z$ grid and how it can be tested. The focus of the PIC simulation was to discover how best to drive and detect these modes. While it is improbable that radial Bernstein modes will be detected in long plasmas, we show that it may be a possible due to the axial nodal structure in the potential and electric field generated by confining plasmas of any finite-length. Additionally, we find that for a short plasma the strongest detection signal along the trap wall occurs at the plasma's midpoint rather than near the ends. Results show that oscillating the confinement potentials is sufficient to excite the fundamental radial Bernstein mode, but not any of the higher order modes. The higher order modes can be seen in the simulation, however, by sinusoidally driving the radial electric field. Unfortunately, the individual modes are difficult to isolate which we suspect is due to mode mixing. Finally, we report frequencies and mode shapes for the fundamental mode and the (lower) first higher order mode.

The overall aim of this project was to study 'functionalised' calcium carbonates (FCCs) for use as a carrier for the controlled release of 'actives,' by permeation and diffusion, and is being proposed as an environmentally friendly and non-toxic pharmaceutical excipient, nutraceutical, and flavour carrier. The delivery of a drug to its target site in the appropriate amount and time-frame in order for it to have a controlled release effect whilst achieving the maximum therapeutic effect remains a topic of design and development for novel drug delivery systems. FCCs encompass a family of new pharmaceutical excipients in which the conditions of manufacture follow strict process regulations with respect to the grade of reagents that are employed and the microbiological environment under which they are produced, and include freedom from organic polymers. Adjustments to the FCC production process can be used to produce a wide range of different morphologies, and raise the possibility of tailoring the void structures of the particles to provide controlled release delivery vehicles for actives across many fields, including drugs and flavours. However, such tailoring can only be fully optimised by a fundamental characterisation of the way in which a drug, loaded into an FCC, then flows and diffuses out over a period of time to provide the delayed release. It was found that adsorption on the FCC surface is selective, for example, saccharin does not become adsorbed from 4-(2-hydroxyethyl)piperazine-1-ethanesulfonic acid (HEPES) buffer solution, and neither does anethole from ethanol. FCC also does not adsorb the cationic probe benzyltrimethylammonium bromide (BTMAB) or the anionic probe sodium 2-naphthalenesulphonate (Na2NS). However, it was found that vanillin adsorbs onto the FCC in an amount of 2.00 ± 0.59 mg g^-1. Aspirin and vanillin adsorption from ethanolic solutions with various additions of water onto FCC TP was investigated and fitted with the Tóth isotherm. It was estimated that vanillin adsorbed onto around 17 %, and aspirin onto around 39 %, of the overall FCC TP surface area without the addition of any water. An equation was formulated in order to approximate the adsorption as a function of the FCC's surface coverage by the water. This is discussed in Chapter 4 and has also been published in a peer-reviewed academic journal (Levy et al., 2017). Chapter 5 discusses the preliminary steps of the loading of vanillin and saccharin into FCC, and the results were inconclusive for a majority of samples, concluding that the loading and analysis methods need refining. The modelling of the diffusion profiles of vanillin loaded FCC S07 and S10 was successful, and resulted in diffusion coefficients of 231.9 x 10^-16 m^2 s^-1 and 248.44 x 10^-16 m^ s^-1, respectively. This is outlined in Chapter 6. Chapter 7 describes the 'zero length column' (ZLC) technique, which was used as a way to characterise the diffusivity of the intraparticle pores of each FCC grade. However, it was established that there are many experimental artefacts present with such a method. This work outlines the development of the novel 'finite length column' (FLC), which was developed as a means to overcome the limitations of the ZLC (Levy et al., 2015). Effective diffusivity coefficients in the long-term region of the diffusion curves of the FCC samples range from 1.06-106 x 10 ^-16 m ^2 s^-1. The FLC was then used in preliminary trials to dilute FCC with an inert solid in order to further refine the ZLC technique, and is discussed in Chapter 8. Two mathematical methods were also developed to aid in the refinement. The reported effective diffusivity coefficient for FCC 03 in the long-term region of the diffusion curve is 49.5 x 10^-16 m^2 s^-1. In conclusion, this work confirms that FCC has potential for use as a carrier for the controlled release of 'actives' by diffusion. The utilisation of mathematical modelling in conjunction with experimental methods in the study of drug release and delivery is steadily increasing due to its enormous future potential; it will enable the optimisation of novel dosage forms and the elucidation of release mechanisms at a major reduction in cost and time compared with the number of experimental studies required to do so.

With the advent of power electronics, inverter-driven induction motor are finding increased use in industries because of applications that demand variable speed operations and because of the potential savings in energy usage. However, these drives sometimes produce unacceptably high levels in vibration and acoustic noise. A literature survey has revealed that while there has been intensive research on the design of inverters to minimize acoustic noise radiation from these drives, the vibro-acoustic behaviour of an induction motor structure has received relatively little attention. The primary objective of this research project, therefore, is to develop a general strategy/algorithm for estimating the acoustic noise radiated from inverter-driven induction motors. By using a three-phase, 2.2 kW induction motor, the vibration modes due to various structural components (such as the rotor, the stator/casing, the endshields and the base plate) of the motor structure were analysed by experimental modal testing. Results indicate that the vibration modes due to the rotor are only important at low frequencies. It has been found that the power injection method gives more accurate measurement of the damping of a motor structure than the modal testing and the time decay methods. If a point force excitation is used, then it is more accurate to measure the sound radiation efficiency than the power conversion efficiency for motor structures. The effect of three different inverter designs (an ideal ???almost sinusoidal??? controller and two commercially available PWM inverters) on the radiated acoustic power were assessed for both no-load and load conditions using sound intensity measurements conducted in an anechoic room. The results indicate that although the sound power level due to aerodynamic and mechanical noise increases at a rate of 12 dB per doubling of the motor speed, the electromagnetic noise dominates at low motor speeds and is still a significant noise source even at high motor speeds. For inverters with low switching frequencies, the radiated sound power level is almost 15 dB higher than the ideal case at low speeds and is relatively insensitive to the motor speed. For inverters that implement the random modulation technique, the change in the total sound power level with the level of the random modulation is very small but the tonal nature of the noise is greatly reduced. The vibration behaviour of a motor structure was modeled using the finite element method (FEM) and validated using the experimental modal testing results. It has been found that it is essential to model the laminated stator as an orthotropic structure. While the details of other structural components (such as the endshields, the teeth in the stator and the windings) are not so important, it is essential that they are incorporated into the structural model as simplified structures to account for their mass, stiffness and boundary conditions imposed on the motor structure. Based on this structural model, the radiated acoustic power for various operating conditions has been predicated using the boundary element (BEM) and the electromagnetic force calculated from an electromagnetic finite element model. The predicted results agree reasonably well with experimental measurements. Despite the success of the FEM/BEM approaches, they can be prohibitively expensive (in terms of computer resources required) to apply to large motors and high frequencies. Thus the feasibility of using a statistical method, namely, the statistical energy analysis (SEA), to estimate the radiated acoustic sound power from an inverter-driven induction motor has been examined. In order to carry out this analysis, analytical expressions for calculating the natural frequencies and radiation efficiency of finite length circular cylindrical shells (which are simplified models of the stator and casing of a motor structure) were firstly derived. The internal loss factors and coupling loss factors of the motor structure were determined experimentally using the power injection method. Then by introducing an equivalent surface mobility of circular cylindrical shells for the electromagnetic force, the vibration response and the acoustic noise radiated from each part of the motor structure were estimated. Results indicate that SEA method is potentially an efficient and effective tool in estimating the noise radiated from inverter-driven induction motors.

With the advent of power electronics, inverter-driven induction motor are finding increased use in industries because of applications that demand variable speed operations and because of the potential savings in energy usage. However, these drives sometimes produce unacceptably high levels in vibration and acoustic noise. A literature survey has revealed that while there has been intensive research on the design of inverters to minimize acoustic noise radiation from these drives, the vibro-acoustic behaviour of an induction motor structure has received relatively little attention. The primary objective of this research project, therefore, is to develop a general strategy/algorithm for estimating the acoustic noise radiated from inverter-driven induction motors. By using a three-phase, 2.2 kW induction motor, the vibration modes due to various structural components (such as the rotor, the stator/casing, the endshields and the base plate) of the motor structure were analysed by experimental modal testing. Results indicate that the vibration modes due to the rotor are only important at low frequencies. It has been found that the power injection method gives more accurate measurement of the damping of a motor structure than the modal testing and the time decay methods. If a point force excitation is used, then it is more accurate to measure the sound radiation efficiency than the power conversion efficiency for motor structures. The effect of three different inverter designs (an ideal ???almost sinusoidal??? controller and two commercially available PWM inverters) on the radiated acoustic power were assessed for both no-load and load conditions using sound intensity measurements conducted in an anechoic room. The results indicate that although the sound power level due to aerodynamic and mechanical noise increases at a rate of 12 dB per doubling of the motor speed, the electromagnetic noise dominates at low motor speeds and is still a significant noise source even at high motor speeds. For inverters with low switching frequencies, the radiated sound power level is almost 15 dB higher than the ideal case at low speeds and is relatively insensitive to the motor speed. For inverters that implement the random modulation technique, the change in the total sound power level with the level of the random modulation is very small but the tonal nature of the noise is greatly reduced. The vibration behaviour of a motor structure was modeled using the finite element method (FEM) and validated using the experimental modal testing results. It has been found that it is essential to model the laminated stator as an orthotropic structure. While the details of other structural components (such as the endshields, the teeth in the stator and the windings) are not so important, it is essential that they are incorporated into the structural model as simplified structures to account for their mass, stiffness and boundary conditions imposed on the motor structure. Based on this structural model, the radiated acoustic power for various operating conditions has been predicated using the boundary element (BEM) and the electromagnetic force calculated from an electromagnetic finite element model. The predicted results agree reasonably well with experimental measurements. Despite the success of the FEM/BEM approaches, they can be prohibitively expensive (in terms of computer resources required) to apply to large motors and high frequencies. Thus the feasibility of using a statistical method, namely, the statistical energy analysis (SEA), to estimate the radiated acoustic sound power from an inverter-driven induction motor has been examined. In order to carry out this analysis, analytical expressions for calculating the natural frequencies and radiation efficiency of finite length circular cylindrical shells (which are simplified models of the stator and casing of a motor structure) were firstly derived. The internal loss factors and coupling loss factors of the motor structure were determined experimentally using the power injection method. Then by introducing an equivalent surface mobility of circular cylindrical shells for the electromagnetic force, the vibration response and the acoustic noise radiated from each part of the motor structure were estimated. Results indicate that SEA method is potentially an efficient and effective tool in estimating the noise radiated from inverter-driven induction motors.

No description available.

<p dir="ltr"> The general design goal of low latency communication systems is to minimize the end-to-end delay while attaining the predefined reliability and throughput requirements. The burgeoning demand for low latency communications motivates a renewed research interest of the tradeoff between delay, throughput, and reliability. In this dissertation research, we consider slotted-based systems and explore the potential advantages of the so-called sequential codes in low latency network communications.</p><p dir="ltr"> The first part of this dissertation analyzes the exact error probability of random linear streaming codes (RLSCs) in the large field size regime over the stochastic independently and identically distributed (i.i.d.) symbol erasure channels (SECs). A closed-form expression of the error probability <i>p</i>_<em>e</em> of large-field-size RLSCs is derived under, simultaneously, the finite memory length α and decoding deadline Δ constraints. The result is then used to examine the intricate tradeoff between memory length (complexity), decoding deadline (delay), code rate (throughput), and error probability (reliability). Numerical evaluation shows that under the same code rate and error probability requirements, the end-to-end delay of RLSCs is 40-48% of that of the optimal block codes (i.e., MDS codes). This implies that switching from block codes to streaming codes not only eliminates the queueing delay completely (which accounts for the initial 50% of the delay reduction) but also improves the reliability (which accounts for the additional 2-10% delay reduction).</p><p dir="ltr"> The second part of this dissertation focuses on the asymptotics of the error probability of RLSCs in the same system model of the first part. Two important scenarios are analyzed: (i) tradeoff between Δ and <i>p</i>_<em>e</em> under infinite α; and (ii) tradeoff between α and <i>p</i>_<em>e</em> under infinite Δ. In the first scenario, the asymptote of <i>p</i>_<em>e</em>(Δ) is shown to be <i>ρ</i>Δ^-1.5<i>e</i>^-^<em>η</em>^Δ. The asymptotic power term Δ^-1.5 of RLSCs is a strict improvement over the Δ^-0.5 term of random linear block codes. A pair of upper and lower bound on the asymptotic constant <i>ρ</i> is also derived, which are tight (i.e., identical) for one specific class of SECs. In the second scenario, a refine approximation is proposed by computing the parameters in a multiterm asymptotic form, which closely matches the exact error probability even for small memory length (≈ 20). The results of the asymptotics can be further exploited to find the <i>c</i>-optimal memory length <i>α</i>_<em>c</em>^*(Δ), which is defined as the minimal memory length α needed for the resulting <i>p</i>_<em>e</em> to be within a factor of <i>c</i>>1 of the best possible <i>p</i>_<em>e</em>^<em>*</em>_{<em> </em>}for any Δ, an important piece of information for practical implementation.</p><p dir="ltr"> Finally, we characterize the channel dispersions of RLSCs and MDS block codes, respectively. New techniques are developed to quantify the channel dispersion of sequential (non-block-based) coding, the first in the literature. The channel dispersion expressions are then used to compare the levels of error protection between RLSCs and MDS block codes. The results show that if and only if the target error probability <i>p</i>_<em>e</em> is smaller than a threshold (≈ 0.1774), RLSCs offer strictly stronger error protection than MDS block codes, which is on top of the already significant 50% latency savings of RLSCs that eliminate the queueing delay completely.</p>