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Communication of video data is increasingly dominating mobile traffic. However, compressed video can be very sensitive to bit errors and data losses. Since mobile devices rely on wireless connections for network access, improving video delivery over such networks is becoming more important. Therefore, this Thesis presents several techniques to enhance video delivery over wireless networks. Particularly, cross-layer techniques are proposed to overcome many shortcomings of conventional layered protocol stacks. The Thesis investigates in detail some of the available error-resilience tools and presents some original findings and recommendations. Several video packet prioritization schemes are proposed. Specifically, two low-complexity prioritization schemes are presented for video with cyclic intra-refresh lines. Another scheme is proposed based on the distortion effect of dropped video slices. For data-partitioned video streams with intra- refresh, a modified prioritization is recommended. These prioritization schemes are applied to quality-of-service supported networks in a cross-layer manner with results showing a considerable video quality improvement. In addition, a cross- layer scheme is proposed to improve scalable video delivery over such networks. To limit the effect of burst errors on video delivered over 'lossy' channels, a scheme is suggested based on multiple description video with network path diversity. Finally, a modified transport scheme is proposed. Using this transport scheme, different protection schemes are presented for both scalable and non- scalable video delivery over wireless broadband networks.

Adequate information is already available on flow through pipes and on flat plates under constant pressure. In pipes, where the stress does not vary along the wall, the velocity distribution is logarithmic for most of the flow region. For flat plates, where the wall stress decreases systematically in the downstream direction, the velocity profile concaves around the logarithmic law. Between these two cases remains a gap to be closed. This thesis concerns a theoretical and experimental investigation on a turbulent boundary layer where the pressure distribution is so arranged to give a constant stress along the wall as in pipes. Various sand roughnesses were used, and the distributions of mean velocity, pressure, and turbulence were measured at various sections. Chapter II concerns the theoretical and experimental study of the flow in this particular type of boundary layer, whereas in Chapter III the mean velocity distributions are examined in the light of earlier work on both rough and smooth walls, and the effect of roughness is investigated. Also a law for the velocity profile close to a smooth wall id derived, and an experiment on separation from a rough wall is reported. Chapter IV deals with turbulence measurements near rough walls, whereas Chapter V examines the usual methods of calculation for turbulent boundary layers under pressure gradients. In Chapter VI, loose sand was used for the boundary and the movement of grains was examined and compared with that in parallel flow.

Combinatorial optimization problems (COPs) are well-known NP-hard realistic ones. Due to the drawbacks of existing approaches, many researchers proposed different evolutionary algorithms (EAs) for solving them. Differential evolution (DE) is primarily used to solve continuous-based optimization problems and has been considered unsuitable for solving many permutation-based combinatorial ones. However, several efforts to design an efficient discrete DE algorithm have been made in recent years. In this thesis, to efficiently solve COPs, an algorithmic framework involving DE and multiple methodologies is introduced. Firstly, a new best-matched value (BMV) mapping method consisting of a new heuristic for converting solutions with continuous variables to ones with discrete/binary variables and directing the mapped solution towards optimality is developed. Secondly, a complete DE incorporating the BMV and problem-specific components for solving knapsack problems (KPs) is proposed. Also, a new fitness evaluation for calculating and repairing knapsack solutions is introduced. Then, an improved complete DE that uses 1) an improved BMV, 2) a k-means clustering repairing method, 3) an ensemble of mutation and 4) two well-known local searches is developed to solve discrete traveling salesman problems (TSPs). Finally, motivated by the promising performances of the proposed versions of DE, a discrete-binary DE (DBDE) algorithm that uses the good search features of the BMV and most effective introduced components to solve the complex traveling thief problem (TTP) which consists of a TSP and KP is proposed. All the proposed DE versions are tested on three sets of well-known COPs, namely, KPs, TSPs and TTPs. It is found that: 1) the BMV improves the solution quality of the traditional DE by 45.04% and saves 66.56% of the times required to solve them; 2) using extra functions in DE to solve KPs leads to define new better solutions and 98.38% faster performances; 3) adopting a repairing method and ensemble of mutations improves the quality of solutions; 4) the DBDE algorithm exhibits a promising performance for solving generic COPs (TTPs). Finally, as the experimental results discussed in this thesis confirm the suitability of the DBDE algorithm for tackling generic COPs, it is expected that it will significantly advance knowledge of DE by extending the research work previously undertaken on it in the continuous domain to developing DEs that can solve complex COPs.

Resource constrained project scheduling problems (RCPSPs) are well-known NP hard combinatorial problems. Due to the drawbacks of existing solution approaches, many researchers have proposed different evolutionary algorithms (EAs) for solving them. Although EAs are able to achieve near-optimal solutions, they cannot guarantee optimality and, in fact, no single EA has consistently been able to solve all types of problems. This has led to the emergence of hybrid methods which have shown good performances but their search capabilities for solving RCPSPs have not yet been fully explored. In this thesis, to efficiently solve RCPSPs, an algorithmic framework involving multiple methodologies is introduced. Firstly, a memetic algorithm (MA) consisting of a new heuristic for converting infeasible solutions to feasible ones in the initial population and multiple local search (MLS) strategies for increasing the exploitation capability of the algorithm is proposed. Secondly, an improved differential evolution (DE) algorithm containing new search operators that can guarantee the generation of feasible solutions, even from infeasible ones, is introduced. Finally, motivated by the encouraging performances of the proposed MA and DE, a bi-evolutionary algorithm (bi-EA) that utilizes the good search features of both these algorithms by automatically switching between them according to their performance, which implies placing more emphasis on the best-performing one during the evolutionary process, is proposed. In addition, two heuristic approaches developed to guide the solutions in both the initial population and every generation towards feasibility are adopted. All the algorithms proposed in this thesis are tested on a set of well-known project scheduling problems taken from the PSPLIB, with the results for instances of 30, 60, 90 and 120 activities compared with both each other and state-of-the-art algorithms. It is found that: (1) the heuristic method improves the performance of the traditional GA by 80.66% in terms of quality of solutions; (2) the use of MLS techniques leads to much better solutions (11.83%) and saves 20.21% of the GA’s computational time; (3) adopting the heuristic method in DE improves the quality of solutions by 28.96% and saves 10.62% of CPU time; (4) the improved DE operators provide much better solutions and greater savings in computational time than a traditional one; (5) bi-EA outperforms both MA and DE in terms of solution quality, especially for large-scale problems as, on average, it obtains 4.33% and 3.5% higher-quality solutions than MA and DE, respectively, and also provides competitive solutions compared with those from state-of-the-art-algorithms.

In this paper we consider the question of uniqueness of positive solutions for Dirichlet problems of the form - Δ u(x)= g(λ,u(x)) in B, u(x) = 0 on ϑB, where A is the Laplace operator, B is the unit ball in RˆN, and A>0. We show that if g(λ,u)=uˆ(N+2)/(N-2) + λ, that is g has "critical growth", then large positive solutions are unique. We also prove uniqueness of large solutions when g(λ,u)=A f(u) with f(0) < 0, f "superlinear" and monotone. We use a number of methods from nonlinear functional analysis such as variational identities, Sturm comparison theorems and methods of order. We also present a regularity result on linear elliptic equation where a coefficient has critical growth.