In this thesis, we explain the term CCZ-equivalence in more detail to- gether with an analysis of a special type of matrices of this equivalence. We also clarify the higher order differential cryptanalysis and its generalized ver- sion. To demonstrate this method we present several attacks on a simple five round Feistel cipher, two of these attacks are our own. We have implemented the most important attacks and results of these experiments can be found in the text. We also explore how to use a decomposition F = F2 ◦F−1 1 (where F1 and F2 are permutations) to construct a generalized higher order differential attack to a block cipher with an S-box F. This construction may be used while searching for an attack to F using the CCZ-equivalence which is gener- ally a hard question. The result of our research is a theorem which presents a necessary condition on a degree of F which is needed for an existence of such a decomposition. 1

In the thesis a new way of checking whether a function is CCZ-equivalent to a permutation is given. The results for known families of almost perfect nonlinear (APN) functions are presented for functions defined over GF(2n ), for even n ≤ 12. The ways how to reduce the number of polynomials from each family are studied. For functions of the form x3 + a-1 tr1(a3 x9 ) it is shown, that they cannot be CCZ-equivalent to a permutation on fields GF(24n ) for n ∈ ℕ .

This study explores perceptions of women’s freedom of movement since the 27 May 2015 Constitutional Court ruling CCZ 15/15, outlawing arbitrary arrests of women after dusk on grounds of loitering with intent to solicit for prostitution, focusing on Zimbabwe’s Avenues community. It traces issues surrounding women’s mobility under patriarchy since colonialism which through the 1960 Vagrancy Act marked the inception of its legal regulation premising stereotypic arrests by state agents. Guided by Pragmatic and Feminist philosophy the researcher adopts a Mixed Method Strategy to gather new knowledge on the complex issue. Employing Radical Feminist Theory under Feminism it critiques government efforts and their efficacy towards ensuring gender equality in mobility. The study argues that while useful legal mechanisms and laws have been adopted to enable women’s right to mobility, ideological and physical challenges continue to hamper this realisation. Empowering the Gender Commission with binding powers, ensuring sufficient security in public areas and educating women about their rights are some recommendations proffered to address challenges faced by women in the exercise of their right to movement. / Development Studies / M.A. (Development Studies)

Unconfined multiple interacting confluent round jets are interesting from a purely scientific point of view, as interaction between neighboring jets brings additional complexity to the flow field. Unconfined confluent round jets also exist in various engineering applications, such as ventilation supply devices, sewage disposal systems, combustion burners, chemical mixing or chimney stacks. Even so, little scientific attention has been paid to unconfined confluent round jets. The present work uses both advanced measurement techniques and computational models to provide deeper understanding of the turbulent flow field development of unconfined confluent round jets. Both Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV) have been used to measure mean velocity and turbulence properties within two setups, consisting of a single row of 1×6 jets and a square array of 6×6 confluent jets. Simulations using computational fluid dynamics (CFD) of the 6×6 setup were conducted using three different Reynolds Averaged Navier-Stokes (RANS) turbulence models: the standard k-ε, the RNG k-ε and the Reynolds Stress model (RSM). The results from the CFD simulations were compared with experimental data. The employed RANS turbulence models were all capable of accurately predicting mean velocities and turbulent properties in the investigated confluent jet array. In general the RSM and k-ε std. models provided smaller deviations between numerical and experimental results than the RNG k-ε model. In terms of mean velocity the second-order closure model (RSM) was not found to be superior to the less complex standard k-ε model. The validated CFD model was employed in a parametrical investigation, including five independent variables: inlet velocity, nozzle diameter, nozzle edge-to-edge spacing, nozzle height and the number of jets in the array. The parametrical investigations made use of statistical methods in the form of response surface methodology. The derived response surface models provided information on the principal influence and relative importance of the investigated parameters within the investigated design space. The positions of the jets within the array strongly influence both mean velocity and turbulence. In all investigated setups the jets experience merging and combining. Square arrays also include considerable jet convergence, which was not present in the 1×6 jet array. Due to the jet convergence in square arrays the turbulent flow field, especially for jets far away from the array center, is affected by mean flow curvature. Jets located along the sides of square jet arrays experience strong jet-to-jet interactions that result in considerable jet deformation, shorter potential core, higher turbulent kinetic energy and faster velocity decay compared to other jets. Jets located at the corners of the array do not interact as strongly with neighboring jets as do the jets along the sides. The locations of merging and combined points differ considerably between different jets and different jet configurations. As the jets combine a zone with uniform stream-wise velocity and low turbulence intensity forms in the center of square jet arrays. This zone has been called Confluent Core Zone (CCZ) due to its similarities with the potential core zone of a single jet. Within the CCZ the appropriate scaling length changes from nozzle diameter to the effective source diameter. The parametrical investigation showed that nozzle diameter and edge-to-edge nozzle spacing were the most important of the investigated parameters, reflecting a strong dependence on dimensionless jet spacing, S/d0. Higher S/d0 delays both merging and combining of the jets and leads to a CCZ with lower velocity and longer downstream extension. Increasing the array size leads to a reduced combined point distance, a stronger inwards displacement of jets in the outer part of the array, and reduced entrainment near the nozzles. A higher inlet velocity was found to increase the jet convergence in the investigated square confluent jet arrays. Nozzle height generally has minor impact on the investigated response variables.