The subject for this thesis is to find a basis which minimizes the number of bit operations involved in a finite field multiplication. The number of bases of a finite field increases quickly with the extension degree, and it is therefore important to find efficient search algorithms. Only fields of characteristic two are considered. A complexity measure is introduced, in order to compare bases. Different methods and algorithms are tried out, limiting the search in order to explore larger fields. The concept of equivalent bases is introduced. A comparison is also made between the Polynomial, Normal and Triangular Bases, referred to as known bases, as they are commonly used in implementations. Tables of the best found known bases for all fields up to GF(2^24) is presented. A list of the best found bases for all fields up to GF(2^25) is also given.

[pt] O presente trabalho desenvolve um sistema computacional que, baseado em conceitos algébricos bem simples, discretiza domínios planos de contornos irregulares em elementos triangulares equilaterais ou próximas a estes. A técnica utilizada consiste em gerar faixas consecutivas de elementos triangulares a partir do contorno externo, de tal forma a diminuir consecutivamente a área restante a ser discretizada. O método apresentado envolve várias modificações feitas sobre o método de Sadek como a atualização instantânea do contorno após o processo de geração, cortes sequenciais, teste de interferência, sequência do processo de geração e o cálculo da posição do nó gerado. Vários exemplos gráficos são mostrados. / [en] The development a computional algorithm for the generation of triangular meshes for plane surfaces with irregular boundarys is described. The method used is based on the generation of successive layers of elements starting from the external boundary and the consecutive reduction of the remaining area. It contains modifications of the method of Sadek such as continous update of the boundary, sequential cuts and test of interference. Several graphical examples are included.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22685号 / 理博第4626号 / 新制||理||1665(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)准教授 前里 光彦, 教授 吉村 一良, 教授 有賀 哲也 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

No description available.

This dissertation is directed towards improving the performance of 5G Wireless Fronthaul Networks and Wireless Sensor Networks, as measured by reliability, fault recovery time, energy consumption, efficiency, and security of transmissions, beyond what is achievable with conventional error control technology. To achieve these ambitious goals, the research is focused on novel applications of networking techniques, such as Diversity Coding, where a feedforward network design uses forward error control across spatially diverse paths to enable reliable wireless networking with minimal delay, in a wide variety of application scenarios. These applications include Cloud-Radio Access Networks (C-RANs), which is an emerging 5G wireless network architecture, where Remote Radio Heads (RRHs) are connected to the centralized Baseband Unit (BBU) via fronthaul networks, to enable near-instantaneous recovery from link/node failures. In addition, the ability of Diversity Coding to recover from multiple simultaneous link failures is demonstrated in many network scenarios. Furthermore, the ability of Diversity Coding to enable significantly simpler and thus lower-cost routing than other types of restoration techniques is demonstrated. Achieving high throughput for broadcasting/multicasting applications, with the required level of reliability is critical for the efficient operation of 5G wireless infrastructure networks. To improve the performance of C-RAN networks, a novel technology, Diversity and Network Coding (DC-NC), which synergistically combines Diversity Coding and Network Coding, is introduced. Application of DC-NC to several 5G fronthaul networks, enables these networks to provide high throughput and near-instant recovery in the presence of link and node failures. Also, the application of DC-NC coding to enhance the performance of downlink Joint Transmission-Coordinated Multi Point (JT-CoMP) in 5G wireless fronthaul C-RANs is demonstrated. In all these scenarios, it is shown that DC-NC coding can provide efficient transmission and reduce the resource consumption in the network by about one-third for broadcasting/multicasting applications, while simultaneously enabling near-instantaneous latency in recovery from multiple link/node failures in fronthaul networks. In addition, it is shown by applying the DC-NC coding, the number of redundant links that uses to provide the required level of reliability, which is an important metric to evaluate any protection system, is reduced by about 30%-40% when compared to that of Diversity Coding. With the additional goal of further reducing of the recovery time from multiple link/node failures and maximizing the network reliability, DC-NC coding is further improved to be able to tolerate multiple, simultaneous link failures with less computational complexity and lower energy consumption. This is accomplished by modifying Triangular Network Coding (TNC) and synergistically combining TNC with Diversity Coding to create enhanced DC-NC (eDC-NC), that is applied to Fog computing-based Radio Access Networks (F-RAN) and Wireless Sensor Networks (WSN). Furthermore, it is demonstrated that the redundancy percentage for protecting against n link failures is inversely related to the number of source data streams, which illustrates the scalability of eDC-NC coding. Solutions to enable synchronized broadcasting are proposed for different situations. The ability of eDC-NC coding scheme to provide efficient and secure broadcasting for 5G wireless F-RAN fronthaul networks is also demonstrated. The security of the broadcasting data streams can be obtained more efficiently than standardized methods such as Secure Multicasting using Secret (Shared) Key Cryptography.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19479号 / 理博第4139号 / 新制||理||1595(附属図書館) / 32515 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 戸塚 圭介, 教授 川上 則雄, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Many computer graphic API’s, including OpenGL, emphasize modeling with rectangular patches, which are especially useful in Computer Aided Geomeric Design (CAGD). However, not all shapes are rectangular; some are triangular or more complex. This paper extends the OpenGL library to support the modeling of triangular patches, Coons patches, and Box-splines patches. Compared with the triangular patch created from degenerate rectangular Bezier patch with the existing functions provided by OpenGL, the triangular Bezier patches can be used in certain design situations and allow designers to achieve high-quality results that are less CPU intense and require less storage space. The addition of Coons patches and Box splines to the OpenGL library also give it more functionality. Both patch types give CAGD users more flexibility in designing surfaces. A library for all three patch types was developed as an addition to OpenGL.

The ability to effectively adapt a mesh is a very important feature of high fidelity finite element modeling. In a finite element analysis, a relatively high node density is desired in areas of the model where there are high error estimates from an initial analysis. Providing a higher node density in such areas improves the accuracy of the model and reduces the computational time compared to having a high node density over the entire model. Node densities can be determined for any model using the sizing functions based on the geometry of the model or the error estimates from the finite element analysis. Robust methods for mesh adaptation using sizing functions are available for refining triangular, tetrahedral, and quadrilateral elements. However, little work has been published for adaptively refining all hexahedral meshes using sizing functions. This thesis describes a new approach to drive hexahedral refinement based upon an error sizing function and a mechanism to compare the sizes of the node after refinement.

Biomechanics research investigating the knee kinematics of youth participants is very limited. The most accurate method of measuring knee kinematics utilizes invasive procedures such as bone pins. However, various experimental techniques have improved the accuracy of gait kinematic analyses using minimally invasive methods. In this study, gait trials were conducted with two participants between the ages of 11 and 13 to obtain the knee flexion-extension (FE), adduction-abduction (AA) and internal-external (IE) rotation angles of the right knee. The objectives of this study were to (1) conduct pilot experiments with youth participants to test whether any adjustments were necessary in the experimental methods used for adult gait experiments, (2) apply a Triangular Cosserat Point Element (TCPE) analysis for Soft-Tissue Artifact (STA) correction of knee kinematics with youth participants, and (3) develop a code to conduct a Principal Component Analysis (PCA) to find the PCA-defined flexion axis and calculate knee angles with both STA and PCA-correction for youth participants. The kinematic results were analyzed for six gait trials on a participant-specific basis. The TCPE knee angle results were compared between uncorrected angles and another method of STA correction, Procrustes Solution, with a repeated measures ANOVA of the root mean square errors between each group and a post-hoc Tukey test. The PCA-corrected results were analyzed with a repeated measures ANOVA of the FE-AA correlations from a linear regression analysis between TCPE, PS, PCA-TCPE and PCA-PS angles. The results indicated that (1) youth experiments can be conducted with minor changes to experimental methods used for adult gait experiments, (2) TCPE and PS analyses did not yield statistically different knee kinematic results, and (3) PCA-correction did not reduce FE-AA correlations as predicted.

Subsonic wind tunnel investigations were conducted on a 60° swept, flat plate, delta wing with a leading edge vortex flap. The pressure distributions were measured over a range of angles of attack starting from zero to 40° in 5° interval and flap deflection angles from zero to 45° with 5° increments at a Reynolds number of about 2.14 x 10‘ based on the root chord. The flow visualization experiments were performed from zero degree to the stall angle, with ten different flap deflection angles at the same Reynolds number. The mean flow field was measured at angles of attack l0° and 15° with the flap deflection angles of l0° and 30° at a Reynolds number of about 1.50 x 10°. The experimental results shows that the leading edge vortex flap is an effective means to control the vortex flow over a delta wing. The optimum flap deflection angles were found where the primary vortex was confined to the leading edge vortex flap, thus producing a thrust on the flap. It was found that flap deflection could be used to restore a vortex flow from burst vortex condition. / Ph. D. / incomplete_metadata