Title: Hadamard matrices and their applications in cryptography Author: Jan Luber Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc., Department of Algebra Abstract: This thesis takes interest in Hadamard matrices, their constructions and application in cryptography. Firstly, we introduce basic properties of Hadamard matrices and selected summary of classical constructions is presented. Then we show a table of constructions that can be used to construct Hadamard matrix of given order. In the next part, we get concerned with Hadamard matrices with circulant cores with detailed description of construction Hadamard matrices with two circulant cores from GL-pair. In the end, we present cryptosystem using Hadamard matrices, we show its essential weaknesses and simple attacks. We propose several improvements in the form of adding other security elements. Keywords: Hadamard matrix, Hadamard conjecture, symmetric cryptography

The primary intent of this thesis is to uncover the presence of matrices in polynomials and also to demonstrate that wherever there are vast numbers of interlocking relationships that must be handled, it is reasonable to guess that matrices will appear on the scene and lend their strength to facilitate the process. Most important of all, I seriously expose this omnipresent ability of matrices in polynomials and matrix equations. Matrix polynomials and equations are, in the main, a part of algebra, but it has become increasingly clear that they possess a utility that extends beyond the domain of algebra into other regions of mathematics. More than this, we have discovered that they are exactly the means necessary for expressing many ideas of applied mathematics. My thesis illustrates this for polynomials and equations of matrices.

In this report, we focus on Biofluids problems, specifically the Stokes Equation. The method of regularized Stokeslets can be derived from bound- ary integral equations derived from the Lorentz reciprocal identity. When body forces are known, this is a direct numerical approximation of an in- tegral, resulting in a summation to determine the fluid velocity. In certain cases, which this report is focused on, we know the velocity and want to determine the forces on a structure immersed in a fluid. This results in a lin- ear system Af = u, where A is a square dense matrix. We study different methods to solve this system of equations to determine the force f on the structure. For solving a linear system with a dense coefficient matrix, the backslash command in MATLAB can be used. This will use an efficient and robust direct method for solving a smaller matrix, but this is not an efficient method for a large, dense coefficient matrix. For a large, dense coefficient ma- trix, we will explore other direct methods as well as several iterative methods to determine computation time and error on a test case with an exact solu- tion. For direct methods, we will study backslash, LU factorization and QR factorization methods. For iterative methods, we stuied Jacobi, Gauss-Seidel, SOR, GMRES, CG, CGS, BICGSTAB and Schulz CG methods for these bioflu- ids applications. All of these methods have different requirements. For our coefficient matrix A, we identified specific properties and then used proper methods, both direct and iterative. Result showed that iterative methods are more efficient then direct method for large size A. Schulz CG was slower but had a smaller error for the test case where there was an exact solution.

Several research efforts have been directed towards in-situ fabrication of titanium matrix composites (TMCs) from Ti and B4C powder mixtures as one of the ways to improve the physical and mechanical properties of titanium and its alloys. In this perspective, the present study reports the development of in-situ particulate reinforced titanium matrix composites from TiH2-B4C and Ti-B6O powder mixtures The relationship between densification and microstructure and mechanical properties (hardness and fracture toughness) of pure Ti and in-situ reinforced titanium matrix composites have been studied in detail using pressureless and hot-pressing techniques. Titanium hydride powder was compacted into cylindrical pellets that were used to produce pure Ti through dehydrogenation and pressureless sintering technique. Various composition of TiH2-B4C powder mixtures were initially milled using alumina balls in a planetary mill. The milling was to achieve homogeneous mixing and distribution of the ceramic partially in the TiH2 powder, as well as uniform distribution of reinforcing phases on the resulting Ti matrix. Dehydrogenation and conversion of loose powder and compacts of TiH2 powder was carried out in argon atmosphere and complete removal of hydrogen was achieved at 680 and 715oC for loose and compacted powder respectively. Pressureless sintering of pure Ti from TiH2 was carried out between 750-1400oC, while pressureless sintering and hot pressing of TiH2-B4C was carried out in the temperature range1100-1400oC using 30MPa for hot pressed samples in argon atmosphere. Different sintering times were considered. The microstructure and phase composition of the sintered and hot-pressed materials were characterized using scanning electron microscopy (SEM) and X-ray diffractometry (XRD). Densities of the sintered and hotpressed materials were measured to determine the extent of densification, while Vickers hardness and indentation fracture toughness were used to measure the mechanical properties of the sintered and hot-pressed materials. Pure Ti from TiH2 showed higher densification of above 99% of theoretical density compared to literature where lower densification and swelling was observed. Its Vickers hardness is higher than that of commercial Ti sintered under the same conditions. Titanium matrix composites (TMCs) with different volume content of in-situ formed reinforcements (TiB + TiC) were successfully produced. The amount of reinforcements formed increases with increased amount of B4C used in the starting powder mixtures, while the amount of needle-type TiB decrease and size and amount of blocky-type TiB increase with increasing volume fraction of TiB. Dense materials and improved Vickers hardness were achieved by the hot-pressed composites especially at 1400oC compared to the pressureless sintered composites under the same conditions and to the relevant literature. TMCs produced in this study show higher Vickers hardness compared to available data in the literature. The hardness was found to depend on the volume content of the reinforcing phases. However, the fracture toughness obtained is low (5.3MPa.m1/2) in comparison to pure Ti but is comparable with reported data in the literature. The mechanisms leading to the achievement of improved densification and higher hardness and the reasons for lower fracture toughness with different sintering temperature and composition of reinforcements in the composites are critically analysed. It has been shown that pure Ti can be pressureless sintered using TiH2 and reinforced Ti matrix composites with improved densification and mechanical properties can be produced from TiH2-B4C powder mixtures. Further work on the comprehensive study of the mechanical properties of these composites would enhance the industrial potential of using these materials and the processing route to produce economically feasible titanium matrix composites

Este estudo apresentou uma metodologia para inferir hidrometeoros a partir de medidas polarimétricas de um radar meteorológico de dupla polarização banda X. A metodologia consiste em uma abordagem teórica baseada em simulações numéricas com um modelo de espalhamento Mie (T M atrix e M ueller) e uma experimental pautada na aplicação de um algoritmo de classificação de hidrometeoros (Dolan and Rutledge [2009]). As si- mulações teóricas foram utilizadas para estudar os efeitos da distribuição de tamanho de gotas, temperatura dos hidrometeoros, ângulo de elevação e mistura de hidrometeoros a partir do fator de refletividade do radar (Z), refletividade diferencial (Z DR ), fase diferen- cial especifica (K DP ) e coeficiente de correlação( HV ). Os valores de Z DR são 0.5 dBZ maior para a frequência de banda X do que para um banda S. A partir de Z maior que 45 dBZ K DP começa a ficar maior que 0. Já HV começa a diminuir quando Z é maior que 25 dBZ. Não se observa variações significativas para o graupel, porém para granizo K DP é maior que 0 quando Z é maior que 15 dBZ, entretanto, para água, os valores são consideravelmente menores. Os efeitos de temperatura só são notados quando Z é maior que 60 dBZ. Ao analisar o efeito da elevação, observa-se que Z DR diminui com o aumento da elevação, sendo mais sensível para Z maiores, o mesmo efeito é observado para K DP e HV . Estas variações são mais sensíveis para água e granizo do que para o graupel. Comparando as distribuições exponencial e gama para considerar os efeitos da distribuição do tamanho de gotas para o caso da chuva, nota-se que a distribuição exponenciais é maior que a gama quando as gotas aumentam seu tamanho e diminui sua concentração, devido que na simulação teórica foi utilizado N 0 fixo.Ao analisar os efeitos da co-existência de água e graupel, temos que as gotas de água dominam o sinal de Z quando Z for maior que 30 dBZ, já K DP será positivo(negativo) quando Z for maior(menor) que 35 dBZ da água, desde que Z do graupel seja menor que 10 dBZ, já HV tende a ficar próximo de 1 quanto mais graupel é observado. Para a mistura de granizo e água, Z da água domina o do granizo quando Z é maior que 45 dBZ, K DP é maior(menor) que zero quando Z for maior (menor) que 25 dBZ desde que Z do granizo seja menor que 10 dBZ, já Z DR da água(granizo) domina o do granizo(água) quando Z for maior(menor) que 45 dBZ. Na parte experimental, dois casos observados durante o experimento de campo do Projeto CHUVA no Vale do Paraíba em 8 de Fevereiro e 22 de Março de 2012 foram utilizados. A classificação de hidrometeoros segundo Dolan and Rutledge [2009] indicaram a presença de chuva próximo da superfície proveniente de graupel e granizo. Acima dos 5 km foram identificados a presença de graupel,granizo e cristais de gelo. Ao examinar as regiões classificadas como granizo e graupel dentro da região de 0 e 15 C com os resultados teóricos, é possível explicar a presença concomitante de água e granizo e água e graupel nestas regiões. / This study presents a methodology for inferring hydrometeors from polarimetric mea- surements of a X band double polarization meteorological radar. The methodology consists of a theoretical approach based on numerical simulations with a Mie scattering model (T-Matrix and Mueller) and an experimental approach based on the application of a classification algorithm of hydrometeors (Dolan and Rutledge [2009]). The theoretical simulations were used to study the effects of droplet size distribution, hydrometeor tem- perature, elevation angle and mixture of hydrometeors from radar reflectivity factor (Z), differential reflectivity (Z DR ), specific differential phase (K DP ) and correlation coefficient ( HV ). The values of Z DR are 0.5 dBZ higher for the X band frequency than for the S band frequency. From Z greater than 45 dBZ, K DP starts to get higher than 0. When Z is greater than 25 dBZ, HV starts to decrease. No significant variations are observed for the graupel, however for hail, K DP is greater than 0 when Z is greater than 15 dBZ, but these values were much lower than for water. Temperature effects are only noticed when Z is greater than 60 dBZ. When analyzing the effect of elevation, it is observed that Z DR decreases with increasing elevation, being more sensitive to Z larger; the same effect is observed for K DP and HV . These variations are more sensitive to water and hail than to the graupel. Comparing the exponential and gamma distributions to consider the effects of droplet size distribution in the case of rain, it is noted that the exponential distribution is larger than the gamma when the droplets increase in size and decrease in concentration, due to the fact that in the simulation was used N 0 fixed. When analyzing the effects of co-existence of water and graupel, we have that the water droplets dominate the Z signal when Z is greater than 30 dBZ, K DP will be positive (negative) when Z is greater (lower) than 35 dBZ of water, since Z of the graupel is less than 10 dBZ and HV tends to be close to 1 when more graupel is observed. For the mixture of hail and water, Z of water dominates that of hail when Z is greater than 45 dBZ, K DP is larger (smaller) than zero when Z is larger (smaller) than 25 dBZ since Z of hail is less than 10 dBZ and Z DR of water (hail) dominates hail (water) when Z is greater (lower) than 45 dBZ. In the experimental part, two cases observed during the field experiment of the RAIN Project in Vale do Paraíba on February 8 and March 22, 2012 were used. The classification of hydrometeors according to Dolan and Rutledge [2009] indicated the presence of rain near the surface coming of graupel and hail. Above 5 km were identified the presence of graupel, hail and ice crystals. When examining the regions classified as hail and graupel within the region of 0 and 15 C with the theoretical results, it is possible to explain the concomitant presence of water and hail and water and graupel in these regions.

Este estudo apresentou uma metodologia para inferir hidrometeoros a partir de medidas polarimétricas de um radar meteorológico de dupla polarização banda X. A metodologia consiste em uma abordagem teórica baseada em simulações numéricas com um modelo de espalhamento Mie (T M atrix e M ueller) e uma experimental pautada na aplicação de um algoritmo de classificação de hidrometeoros (Dolan and Rutledge [2009]). As si- mulações teóricas foram utilizadas para estudar os efeitos da distribuição de tamanho de gotas, temperatura dos hidrometeoros, ângulo de elevação e mistura de hidrometeoros a partir do fator de refletividade do radar (Z), refletividade diferencial (Z DR ), fase diferen- cial especifica (K DP ) e coeficiente de correlação( HV ). Os valores de Z DR são 0.5 dBZ maior para a frequência de banda X do que para um banda S. A partir de Z maior que 45 dBZ K DP começa a ficar maior que 0. Já HV começa a diminuir quando Z é maior que 25 dBZ. Não se observa variações significativas para o graupel, porém para granizo K DP é maior que 0 quando Z é maior que 15 dBZ, entretanto, para água, os valores são consideravelmente menores. Os efeitos de temperatura só são notados quando Z é maior que 60 dBZ. Ao analisar o efeito da elevação, observa-se que Z DR diminui com o aumento da elevação, sendo mais sensível para Z maiores, o mesmo efeito é observado para K DP e HV . Estas variações são mais sensíveis para água e granizo do que para o graupel. Comparando as distribuições exponencial e gama para considerar os efeitos da distribuição do tamanho de gotas para o caso da chuva, nota-se que a distribuição exponenciais é maior que a gama quando as gotas aumentam seu tamanho e diminui sua concentração, devido que na simulação teórica foi utilizado N 0 fixo.Ao analisar os efeitos da co-existência de água e graupel, temos que as gotas de água dominam o sinal de Z quando Z for maior que 30 dBZ, já K DP será positivo(negativo) quando Z for maior(menor) que 35 dBZ da água, desde que Z do graupel seja menor que 10 dBZ, já HV tende a ficar próximo de 1 quanto mais graupel é observado. Para a mistura de granizo e água, Z da água domina o do granizo quando Z é maior que 45 dBZ, K DP é maior(menor) que zero quando Z for maior (menor) que 25 dBZ desde que Z do granizo seja menor que 10 dBZ, já Z DR da água(granizo) domina o do granizo(água) quando Z for maior(menor) que 45 dBZ. Na parte experimental, dois casos observados durante o experimento de campo do Projeto CHUVA no Vale do Paraíba em 8 de Fevereiro e 22 de Março de 2012 foram utilizados. A classificação de hidrometeoros segundo Dolan and Rutledge [2009] indicaram a presença de chuva próximo da superfície proveniente de graupel e granizo. Acima dos 5 km foram identificados a presença de graupel,granizo e cristais de gelo. Ao examinar as regiões classificadas como granizo e graupel dentro da região de 0 e 15 C com os resultados teóricos, é possível explicar a presença concomitante de água e granizo e água e graupel nestas regiões. / This study presents a methodology for inferring hydrometeors from polarimetric mea- surements of a X band double polarization meteorological radar. The methodology consists of a theoretical approach based on numerical simulations with a Mie scattering model (T-Matrix and Mueller) and an experimental approach based on the application of a classification algorithm of hydrometeors (Dolan and Rutledge [2009]). The theoretical simulations were used to study the effects of droplet size distribution, hydrometeor tem- perature, elevation angle and mixture of hydrometeors from radar reflectivity factor (Z), differential reflectivity (Z DR ), specific differential phase (K DP ) and correlation coefficient ( HV ). The values of Z DR are 0.5 dBZ higher for the X band frequency than for the S band frequency. From Z greater than 45 dBZ, K DP starts to get higher than 0. When Z is greater than 25 dBZ, HV starts to decrease. No significant variations are observed for the graupel, however for hail, K DP is greater than 0 when Z is greater than 15 dBZ, but these values were much lower than for water. Temperature effects are only noticed when Z is greater than 60 dBZ. When analyzing the effect of elevation, it is observed that Z DR decreases with increasing elevation, being more sensitive to Z larger; the same effect is observed for K DP and HV . These variations are more sensitive to water and hail than to the graupel. Comparing the exponential and gamma distributions to consider the effects of droplet size distribution in the case of rain, it is noted that the exponential distribution is larger than the gamma when the droplets increase in size and decrease in concentration, due to the fact that in the simulation was used N 0 fixed. When analyzing the effects of co-existence of water and graupel, we have that the water droplets dominate the Z signal when Z is greater than 30 dBZ, K DP will be positive (negative) when Z is greater (lower) than 35 dBZ of water, since Z of the graupel is less than 10 dBZ and HV tends to be close to 1 when more graupel is observed. For the mixture of hail and water, Z of water dominates that of hail when Z is greater than 45 dBZ, K DP is larger (smaller) than zero when Z is larger (smaller) than 25 dBZ since Z of hail is less than 10 dBZ and Z DR of water (hail) dominates hail (water) when Z is greater (lower) than 45 dBZ. In the experimental part, two cases observed during the field experiment of the RAIN Project in Vale do Paraíba on February 8 and March 22, 2012 were used. The classification of hydrometeors according to Dolan and Rutledge [2009] indicated the presence of rain near the surface coming of graupel and hail. Above 5 km were identified the presence of graupel, hail and ice crystals. When examining the regions classified as hail and graupel within the region of 0 and 15 C with the theoretical results, it is possible to explain the concomitant presence of water and hail and water and graupel in these regions.

by Xiao-Qing Jin. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1986 / Bibliography: leaves 47-48

Stem cell therapies have shown promising capabilities in regaining the functionality of scar tissue following a myocardial infarction. Biological sutures composed of fibrin have been shown to more effectively deliver human mesenchymal stem cells (hMSCs) to the heart when compared to traditional cell delivery mechanisms. While the biological sutures do show promise, improvements can be made. To enhance the fibrin sutures, we propose to incorporate native cardiac extracellular matrix (ECM) into the fibrin microthreads to produce a more in vivo-like environment. This project investigated the effects that ECM incorporation has on fibrin microthread structure, mechanics, stem cell seeding, and pro-angiogenic potential. Single microthreads composed of fibrin or fibrin and ECM were subjected to uniaxial tensile testing. It was found that the microthreads consisting of both fibrin and ECM had significantly high elastic moduli than fibrin only microthreads. Cell seeding potential was evaluated by performing a 24-hour hMSC seeding experiment using sutures of the varying microthread types. A CyQuant cell proliferation assay was used to determine the number of cells seeded onto each suture type. The results determined that there was no statistical difference between the numbers of cells seeded on the types of sutures. To examine the pro-angiogenic potential the microthreads had, a 24-hour endothelial progenitor outgrowth cell (EPOC) outgrowth assay was used. Fibrin and 15% ECM-fibrin microthreads were placed within the scratch of an EPOC culture and evaluated every 6 hours for 24 hours. We found that the 15% ECM microthreads had significantly increased the EPOC outgrowth, approximately 16% more distance travelled than fibrin microthreads and 18% more than no microthreads. Our combined results suggest that ECM does not affect hMSC attachment to biological sutures but does increase the pro-angiogenic potential of the microthreads due to their increase in guiding EPOC outgrowth.

Typescript, etc. / Digitized by Kansas Correctional Industries

Lok Tsan Ming. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 82-83). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstract in Chinese.