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It is a famous theorem of Iversen that if f(z) be a non-constant meromorphic transcendental function in the plane which assumes a value 'a' a finite number of times there, then there exists a path Γ tending to ∞, such that f(z) ⟶ a, as z ⟶ ∞ along Γ . The value a is called asymptotic value and Γ is called an asymptotic path; If we take a = ∞, we obtain the theorem that every integral function tends to infinity along some path. We investigate whether ah analogue of this holds for a general subharmonic function u(z) in the plane. We answer in the affirmative by proving Theorem 1.2. The entire Chapter I is devoted to our proof of this theorem.

Internationally, the relationship between homelessness and the increased risk of sexual transmission of HIV is well established. However, little is known about the social processes that shape homeless young people’s sexual choices, decisions, and practices in the context of Pakistan. To address this gap, semistructured interviews were conducted with twenty-nine homeless young people (aged 16-25 years old) from Rawalpindi, Pakistan, including nine cisgender heterosexual men, six cisgender heterosexual women, seven cisgender gay men, and seven transgender heterosexual women. Bourdieu's concepts of capital and social practice guided the analysis of interview data. The analysis revealed that participants’ pathways to homelessness were shaped by the decline of their families as a source of social capital including the poverty of the family, the stigma of being transgender or gay, and through experiences of domestic violence and illicit drug use. Once on the streets, participants improvised with the limited resources available to them by drawing on and reciprocating peer support, pursuing casual work and engaging in dance and/or sex work to accumulate needed resources. While sex helped some participants secure physical protection, social and emotional support and money, it carried risks of HIV/STI, violence, degradation, and social marginalisation. Participants were aware of their sexual health risks, but the social obligations of intimate partnerships, financial considerations, and fear of violence from clients collectively produced a context of competing risks, where protection from HIV/STI became secondary to maintaining relationships, income generation, and physical safety. Also, in relation to sex, participants adopted alternative strategies to protect themselves from HIV, including practices like only performing oral sex, post-sex anal douching, using the withdrawal method and adopting specific sexual positions when not using condoms. Nevertheless, these strategies were not always protective and sometimes inadvertently increased their risk of HIV/STI. The study’s identification of structural and contextual forces that shaped young people’s trajectories into street life, as well as their sexual risk-taking, have implications for policy and programs. An integrated health promotion approach that goes beyond the health sector may help to reduce young people's risk of homelessness and HIV/STI in Pakistan. Building healthy public policies, creating supportive environments, strengthening community actions, developing personal skills, and reorienting health services could help to improve young people’s socioeconomic status, which affects their capacity to practise safe sex and relationships.

The advent of new optical fibre technologies in recent years have revolutionized the telecommunications and sensing field. In particular the rapid development of microstructured fiber, also known as photonic crystal fiber (PCF), brings about remarkable features such as air guided mechanism, unique geometric structure and single material fibre structure that could overcome many limitations intrinsic to conventional standard optical fibers. This thesis reports my research and original results from the development and application of microstuctured fibre as fiber humidity sensors. My work covers the design and fabrication of the PCF-based sensors, development of experimental systems with related data generation and acquisition capabilities, novel sensing schemes and techniques as well as proof of concept experiments. I proposed and experimentally demonstrated several novel fibre humidity sensor schemes which do not require coating of any hygroscopic or sensitive film while most of previous reported fiber humidity sensors need the hygroscopic films to sense humidity. I also proposed and demonstrated a microstructured optical fibre based humidity sensor for respiration monitoring for possible application of PCF-based fiber sensors in the bio-medical engineering field.

Due to the enormous capacity and performance gains associated with the use of antenna arrays in wireless multi-input multi-output (MIMO) communication links, it is inevitable that these technologies will become an integral part of future systems. In order to assess the potential of such beam-oriented technologies, direct representation of the dispersion of multipath fading channel in angular and temporal domains is required. This representation can only be achieved with the use of spatial channel models. This thesis thus focuses on the issue of spatial channel modeling for cellular systems and on its use in the characteri-zation of multipath fading channels. The results of this thesis are presented mainly in five parts: a) modeling of scattering mechanisms, b) derivation of the closed-form expressions for the spatio-temporal characteristics, c) generalization of the quantitative measure of angular spread, d) investigation of the effect of mobile motion on the spatio-temporal characteristics, and e) characterization of fast fading channel and its use in the signature sequence adaptation for direct sequence code division multiple access (DS-CDMA) system. The thesis begins with an overview of the fundamentals of spatial channel modeling with regards to the specifics of cellular environments. Previous modeling approaches are discussed intensively and a generalized spatial channel model, the `Eccentro-Scattering Model' is proposed. Using this model, closed-form mathematical expressions for the distributions of angle and time of multipath arrival are derived. These theoretical results for the picocell, microcell and macrocell environments, when compared with previous models and available measurements, are found to be realistic and generic. In macrocell environment, the model incorporates the effect of distant scattering structures in addition to the local ones. Since the angular spread is a key factor of the second order statistics of fading processes in wireless communications, the thesis proposes a novel generalized method of quantifying the angular spread of the multipath power distribution. The proposed method provides almost all parameters about the angular spread, which can be further used for calculating more accurate spatial correlations and other statistics of multipath fading channels. The degree of accuracy in such correlation calculations can lead to the computation of exact separation distances among array elements required for maximizing capacity in MIMO systems or diversity antennas. The proposed method is also helpful in finding the exact standard deviation of the truncated angular distributions and angular data acquired in measurement campaigns. This thesis also indicates the significance of the effects of angular distribution truncation on the angular spread. Due to the importance of angular spread in the fading statistics, it is proposed as the goodness-of-fit measure in measurement campaigns. In this regard, comparisons of some notable azimuthal models with the measurement results are shown. The effect of mobile motion on the spatial and temporal characteristics of the channel is also discussed. Three mobile motion scenarios are presented, which can be considered to be responsible for the variations of the spatio-temporal statistical parameters of the multipath signals. Two different cases are also identified, when the terrain and clutter of the mobile surroundings have an additional effect on the temporal spread of the channel during mobile motion. The effect of increasing mobile-base separation on the angular and temporal spreads is elaborated in detail. The proposed theoretical results in spatial characteristics can be extended to characterizing and tracking transient behavior of Doppler spread in time-varying fast fading channels; likewise the proposed theoretical results in temporal characteristics can be utilized in designing efficient equalizers for combating inter-symbol interference (ISI) in time-varying frequency-selective fading channels. In the last part of the thesis, a linear state-space model is developed for signature sequence adaptation over time-varying fast fading channels in DS-CDMA systems. A decision directed adaptive algorithm, based on the proposed state-space model and Kalman filter, is presented. The algorithm outperforms the gradient-based algorithms in tracking the received distorted signature sequence over time-varying fast fading channels. Simulation results are presented which show that the performance of a linear adaptive receiver can be improved significantly with signature tracking on high Doppler spreads in DS-CDMA systems.