176 resultados para Planting density
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The case study 3 team viewed the mitigation of noise and air pollution generated in the transport corridor that borders the study site to be a paramount driver of the urban design solution. These key urban planning strategies were adopted: * Spatial separation from transport corridor pollution source. A linear green zone and environmental buffer was proposed adjacent to the transport corridor to mitigate the environmental noise and air quality impacts of the corridor, and to offer residents opportunities for recreation * Open space forming the key structural principle for neighbourhood design. A significant open space system underpins the planning and manages surface water flows. * Urban blocks running on east-west axis. The open space rationale emphasises an east-west pattern for local streets. Street alignment allows for predominantly north-south facing terrace type buildings which both face the street and overlook the green courtyard formed by the perimeter buildings. The results of the ESD assessment of the typologies conclude that the design will achieve good outcomes through: * Lower than average construction costs compared with other similar projects * Thermal comfort; A good balance between daylight access and solar gains is achieved * The energy rating achieved for the units is 8.5 stars.
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Homo-and heteronuclear meso,meso-(E)-ethene-1,2-diyl-linked diporphyrins have been prepared by the Suzuki coupling of porphyrinylboronates and iodovinylporphyrins. Combinations comprising 5,10,15-triphenylporphyrin (TriPP) on both ends of the ethene-1,2-diyl bridge M 210 (M 2=H 2/Ni, Ni 2, Ni/Zn, H 4, H 2Zn, Zn 2) and 5,15-bis(3,5-di-tert-butylphenyl)porphyrinato-nickel(II) on one end and H 2, Ni, and ZnTriPP on the other (M 211), enable the first studies of this class of compounds possessing intrinsic polarity. The compounds were characterized by electronic absorption and steady state emission spectra, 1H NMR spectra, and for the Ni 2 bis(TriPP) complex Ni 210, single crystal X-ray structure determination. The crystal structure shows ruffled distortions of the porphyrin rings, typical of Ni II porphyrins, and the (E)-C 2H 2 bridge makes a dihedral angle of 50° with the mean planes of the macrocycles. The result is a stepped parallel arrangement of the porphyrin rings. The dihedral angles in the solid state reflect the interplay of steric and electronic effects of the bridge on interporphyrin communication. The emission spectra in particular, suggest energy transfer across the bridge is fast in conformations in which the bridge is nearly coplanar with the rings. Comparisons of the fluorescence behaviour of H 410 and H 2Ni10 show strong quenching of the free base fluorescence when the complex is excited at the lower energy component of the Soret band, a feature associated in the literature with more planar conformations. TDDFT calculations on the gas-phase optimized geometry of Ni 210 reproduce the features of the experimental electronic absorption spectrum within 0.1 eV. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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Sorghum (Sorghum bicolor (L.) Moench) is the world’s fifth major cereal crop and holds importance as a construction material, food and fodder source. More recently, the potential of this plant as a biofuel source has been noted. Despite its agronomic importance, the use of sorghum production is being constrained by both biotic and abiotic factors. These challenges could be addressed by the use of genetic engineering strategies to complement conventional breeding techniques. However, sorghum is one of the most recalcitrant crops for genetic modification with the lack of an efficient tissue culture system being amongst the chief reasons. Therefore, the aim of this study was to develop an efficient tissue culture system for establishing regenerable embryogenic cell lines, micropropagation and acclimatisation for Sorghum bicolor and use this to optimise parameters for genetic transformation via Agrobacterium-mediated transformation and microprojectile bombardment. Using five different sorghum cultivars, SA281, 296B, SC49, Wray and Rio, numerous parameters were investigated in an attempt to establish an efficient and reproducible tissue culture and transformation system. Using immature embryos (IEs) as explants, regenerable embryogenic cell lines (ECLs) could only be established from cultivars SA281 and 296B. Large amounts of phenolics were produced from IEs of cultivars, SC49, Wary and Rio, and these compounds severely hindered callus formation and development. Cultivar SA281 also produced phenolics during regeneration. Attempts to suppress the production of these compounds in cultivars SA281 and SC49 using activated charcoal, PVP, ascorbic acid, citric acid and liquid filter paper bridge methods were either ineffective or had a detrimental effect on embryogenic callus formation, development and regeneration. Immature embryos sourced during summer were found to be far more responsive in vitro than those sourced during winter. In an attempt to overcome this problem, IEs were sourced from sorghum grown under summer conditions in either a temperature controlled glasshouse or a growth chamber. However, the performance of these explants was still inferior to that of natural summer-sourced explants. Leaf whorls, mature embryos, shoot tips and leaf primordia were found to be unsuitable as explants for establishing ECLs in sorghum cultivars SA281 and 296B. Using the florets of immature inflorescences (IFs) as explants, however, ECLs were established and regenerated for these cultivars, as well as for cultivar Tx430, using callus induction media, SCIM, and regeneration media, VWRM. The best in vitro responses, from the largest possible sized IFs, were obtained using plants at the FL-2 stage (where the last fully opened leaf was two leaves away from the flag leaf). Immature inflorescences could be stored at 25oC for up to three days without affecting their in vitro responses. Compared to IEs, the IFs were more robust in tissue culture and showed responses which were season and growth condition independent. A micropropagation protocol for sorghum was developed in this study. The optimum plant growth regulator (PGR) combination for the micropropagation of in vitro regenerated plantlets was found to be 1.0 mg/L BAP in combination with 0.5 mg/L NAA. With this protocol, cultivars 296B and SA281 produced an average of 57 and 13 off-shoots per plantlet, respectively. The plantlets were successfully acclimatised and developed into phenotypically normal plants that set seeds. A simplified acclimatisation protocol for in vitro regenerated plantlets was also developed. This protocol involved deflasking in vitro plantlets with at least 2 fully-opened healthy leaves and at least 3 roots longer than 1.5 cm, washing the media from the roots with running tap water, planting in 100 mm pots and placing in plastic trays covered with a clear plastic bag in a plant growth chamber. After seven days, the corners of the plastic cover were opened and the bags were completely removed after 10 days. All plantlets were successfully acclimatised regardless of whether 1:1 perlite:potting mix, potting mix, UC mix or vermiculite were used as potting substrates. Parameters were optimised for Agrobacterium-mediated transformation (AMT) of cultivars SA281, 296B and Tx430. The optimal conditions were the use of Agrobacterium strain LBA4404 at an inoculum density of 0.5 OD600nm, heat shock at 43oC for 3 min, use of the surfactant Pluronic F-68 (0.02% w/v) in the inoculation media with a pH of 5.2 and a 3 day co-cultivation period in dark at 22oC. Using these parameters, high frequencies of transient GFP expression was observed in IEs precultured on callus initiation media for 1-7 days as well as in four weeks old IE- and IF-derived callus. Cultivar SA281 appeared very sensitive to Agrobacterium since all tissue turned necrotic within two weeks post-exposure. For cultivar 296B, GFP expression was observed up to 20 days post co-cultivation but no stably transformed plants were regenerated. Using cultivar Tx430, GFP was expressed for up to 50 days post co-cultivation. Although no stably transformed plants of this cultivar were regenerated, this was most likely due to the use of unsuitable regeneration media. Parameters were optimised for transformation by particle bombardment (PB) of cultivars SA281, 296B and Tx430. The optimal conditions were use of 3-7 days old IEs and 4 weeks old IF callus, 4 hour pre- and post-bombardment osmoticum treatment, use of 0.6 µm gold microparticles, helium pressure of 1500 kPa and target distance of 15 cm. Using these parameters for PB, transient GFP expression was observed for up to 14, 30 and 50 days for cultivars SA281, 296B and Tx430, respectively. Further, the use of PB resulted in less tissue necrosis compared to AMT for the respective cultivars. Despite the presence of transient GFP expression, no stably transformed plants were regenerated. The establishment of regenerable ECLs and the optimization of AMT and PB parameters in this study provides a platform for future efforts to develop an efficient transformation protocol for sorghum. The development of GM sorghum will be an important step towards improving its agronomic properties as well as its exploitation for biofuel production.
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We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.
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Purpose This thesis is about liveability, place and ageing in the high density urban landscape of Brisbane, Australia. As with other major developed cities around the globe, Brisbane has adopted policies to increase urban residential densities to meet the main liveability and sustainability aim of decreasing car dependence and therefore pollution, as well as to minimise the loss of greenfield areas and habitats to developers. This objective hinges on urban neighbourhoods/communities being liveable places, which residents do not have to leave for everyday living. Community/neighbourhood liveability is an essential ingredient in healthy ageing in place and has a substantial impact upon the safety, independence and well-being of older adults. It is generally accepted that ageing in place is optimal for both older people and the state. The optimality of ageing in place generally assumes that there is a particular quality to environments or standard of liveability in which people successfully age in place. The aim of this thesis was to examine if there are particular environmental qualities or aspects of liveability that test optimality and to better understand the key liveability factors that contribute to successful ageing in place. Method A strength of this thesis is that it draws on two separate studies to address the research question of what makes high density liveable for older people. In Chapter 3, the two methods are identified and differentiated as Method 1 (used in Paper 1) and Method 2 (used in Papers 2, 3, 4 and 5). Method 1 involved qualitative interviews with 24 inner city high density Brisbane residents. The major strength of this thesis is the innovative methodology outlined in the thesis as Method 2. Method 2 involved a case study approach employing qualitative and quantitative methods. Qualitative data was collected using semi-structured, in-depth interviews and time-use diaries completed by participants during the week of tracking. The quantitative data was gathered using Global Positioning Systems for tracking and Geographical Information Systems for mapping and analysis of participants’ activities. The combination of quantitative and qualitative analysis captured both participants’ subjective perceptions of their neighbourhoods and their patterns of movement. This enhanced understanding of how neighbourhoods and communities function and of the various liveability dimensions that contribute to active ageing and ageing in place for older people living in high density environments. Both studies’ participants were inner-city high density residents of Brisbane. The study based on Method 1 drew on a wider age demographic than the study based on Method 2. Findings The five papers presented in this thesis by publication indicate a complex inter-relationship of the factors that make a place liveable. The first three papers identify what is comparable and different between the physical and social factors of high density communities/neighbourhoods. The last two papers explore relationships between social engagement and broader community variables such as infrastructure and the physical built environments that are risk or protective factors relevant to community liveability, active ageing and ageing in place in high density. The research highlights the importance of creating and/or maintaining a barrier-free environment and liveable community for ageing adults. Together, the papers promote liveability, social engagement and active ageing in high density neighbourhoods by identifying factors that constitute liveability and strategies that foster active ageing and ageing in place, social connections and well-being. Recommendations There is a strong need to offer more support for active ageing and ageing in place. While the data analyses of this research provide insight into the lived experience of high density residents, further research is warranted. Further qualitative and quantitative research is needed to explore in more depth, the urban experience and opinions of older people living in urban environments. In particular, more empirical research and theory-building is needed in order to expand understanding of the particular environmental qualities that enable successful ageing in place in our cities and to guide efforts aimed at meeting this objective. The results suggest that encouraging the presence of more inner city retail outlets, particularly services that are utilised frequently in people’s daily lives such as supermarkets, medical services and pharmacies, would potentially help ensure residents fully engage in their local community. The connectivity of streets, footpaths and their role in facilitating the reaching of destinations are well understood as an important dimension of liveability. To encourage uptake of sustainable transport, the built environment must provide easy, accessible connections between buildings, walkways, cycle paths and public transport nodes. Wider streets, given that they take more time to cross than narrow streets, tend to .compromise safety - especially for older people. Similarly, the width of footpaths, the level of buffering, the presence of trees, lighting, seating and design of and distance between pedestrian crossings significantly affects the pedestrian experience for older people and impacts upon their choice of transportation. High density neighbourhoods also require greater levels of street fixtures and furniture for everyday life to make places more useable and comfortable for regular use. The importance of making the public realm useful and habitable for older people cannot be over-emphasised. Originality/value While older people are attracted to high density settings, there has been little empirical evidence linking liveability satisfaction with older people’s use of urban neighbourhoods. The current study examined the relationships between community/neighbourhood liveability, place and ageing to better understand the implications for those adults who age in place. The five papers presented in this thesis add to the understanding of what high density liveable age-friendly communities/ neighbourhoods are and what makes them so for older Australians. Neighbourhood liveability for older people is about being able to age in place and remain active. Issues of ageing in Australia and other areas of the developed world will become more critical in the coming decades. Creating livable communities for all ages calls for partnerships across all levels of government agencies and among different sectors within communities. The increasing percentage of older people in the community will have increasing political influence and it will be a foolish government who ignores the needs of an older society.
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Like other major cities, Brisbane (Australia) has adopted policies to increase residential densities to meet the liveability goal of decreasing car dependence. This objective hinges on urban neighbourhoods being amenity-rich spaces, reducing the need for residents to leave their neighbourhood for everyday living. While older people are attracted to urban settings, there has been little empirical evidence linking liveability satisfaction with older people's use of urban neighbourhoods. Using a case study approach employing qualitative (diaries, in-depth interviews) and quantitative (Global Positioning Systems and Geographical Information Systems mapping) methods,this paper explores the effect of the neighbourhood environment and its influence on liveability for older urban people. Reliance on motor vehicles and issues with availability and access to local amenities inhibit local participation for older people. Highlighting these issues furthers our understanding of the landscape planning and design factors that make urban neighbourhoods more liveable for older residents.
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Walking as an out-of-home mobility activity is recognised for its contribution to healthy and active ageing. The environment can have a powerful effect on the amount of walking activity undertaken by older people, thereby influencing their capacity to maintain their wellbeing and independence. This paper reports the findings from research examining the experiences of neighbourhood walking for 12 older people from six different inner-city high density suburbs, through analysis of data derived from travel diaries, individual time/space activity maps (created via GPS tracking over a seven-day period and GIS technology), and in-depth interviews. Reliance on motor vehicles, the competing interests of pedestrians and cyclists on shared pathways and problems associated with transit systems, public transport, and pedestrian infrastructure emerged as key barriers to older people venturing out of home on foot. GPS and GIS technology provide new opportunities for furthering understanding of the out-of-home mobility of older populations.
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The inner city Brisbane suburbs of the West End peninsula are poised for redevelopment. Located within walking distance to CBD workplaces, home to Queensland’s highest value cultural precinct, and high quality riverside parklands, there is currently a once-in-a-lifetime opportunity to redevelop parts of the suburb to create a truly urban neighbourhood. According to a local community association, local residents agree and embrace the concept of high-density living, but are opposed to the high-rise urban form (12 storeys) advocated by the City’s planning authority (BCC, 2011) and would prefer to see medium-rise (5-8 storeys) medium-density built form. Brisbane experienced a major flood event which inundated the peninsula suburbs of West End in summer January 2011. The vulnerability of taller buildings to the vagaries of climate and more extreme weather events and their reliance on main electricity was exposed when power outages immediately before, during and after the flood disaster seriously limited occupants’ access and egress when elevators were disabled. Not all buildings were flooded but dwellings quickly became unliveable due to disabled air-conditioning. Some tall buildings remained uninhabitable for several weeks after the event. This paper describes an innovative design research method applied to the complex problem of resilient, sustainable neighbourhood form in subtropical cities, in which a thorough comparative analysis of a range of multiple-dwelling types has revealed the impact that government policy regarding design of the physical environment has on a community’s resilience. The outcomes advocate the role of climate-responsive design in averting the rising human capital and financial costs of natural disasters and climate change.
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Purpose: To determine whether there is a difference in neuroretinal function and in macular pigment optical density between persons with high- and low-risk gene variants for age-related macular degeneration (AMD) and no ophthalmoscopic signs of AMD, and to compare the results on neuroretinal function to patients with manifest early AMD. Methods and Participants: Neuroretinal function was assessed with the multifocal electroretinogram (mfERG) for 32 participants (22 healthy persons with no AMD and 10 early AMD patients). The 22 healthy participants with no AMD had high- or low-risk genotypes for either CFH (rs380390) and/or ARMS2 (rs10490924). Trough-to-peak response densities and peak-implicit times were analyzed in 5 concentric rings. Macular pigment optical densitometry was assessed by customized heterochromatic flicker photometry. Results: Trough-to-peak response densities for concentric rings 1 to 3 were, on average, significantly greater in participants with high-risk genotypes than in participants with low-risk genotypes and in persons with early AMD after correction for age and smoking (p<0.05). The group peak- implicit times for ring 1 were, on average, delayed in the patients with early AMD compared with the participants with high- or low-risk genotypes, although these differences were not significant. There was no significant correlation between genotypes and macular pigment optical density. Conclusion: Increased neuroretinal activity in persons who carry high-risk AMD genotypes may be due to genetically determined subclinical inflammatory and/or histological changes in the retina. Neuroretinal function in healthy persons genetically susceptible to AMD may be a useful additional early biomarker (in combination with genetics) before there is clinical manifestation.
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There is a growing interest in the use of megavoltage cone-beam computed tomography (MV CBCT) data for radiotherapy treatment planning. To calculate accurate dose distributions, knowledge of the electron density (ED) of the tissues being irradiated is required. In the case of MV CBCT, it is necessary to determine a calibration-relating CT number to ED, utilizing the photon beam produced for MV CBCT. A number of different parameters can affect this calibration. This study was undertaken on the Siemens MV CBCT system, MVision, to evaluate the effect of the following parameters on the reconstructed CT pixel value to ED calibration: the number of monitor units (MUs) used (5, 8, 15 and 60 MUs), the image reconstruction filter (head and neck, and pelvis), reconstruction matrix size (256 by 256 and 512 by 512), and the addition of extra solid water surrounding the ED phantom. A Gammex electron density CT phantom containing EDs from 0.292 to 1.707 was imaged under each of these conditions. The linear relationship between MV CBCT pixel value and ED was demonstrated for all MU settings and over the range of EDs. Changes in MU number did not dramatically alter the MV CBCT ED calibration. The use of different reconstruction filters was found to affect the MV CBCT ED calibration, as was the addition of solid water surrounding the phantom. Dose distributions from treatment plans calculated with simulated image data from a 15 MU head and neck reconstruction filter MV CBCT image and a MV CBCT ED calibration curve from the image data parameters and a 15 MU pelvis reconstruction filter showed small and clinically insignificant differences. Thus, the use of a single MV CBCT ED calibration curve is unlikely to result in any clinical differences. However, to ensure minimal uncertainties in dose reporting, MV CBCT ED calibration measurements could be carried out using parameter-specific calibration measurements.
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Surveys were conducted in the Philippines from 1995 to 1997 to examine relationships between production environment variables (agroecosystem, synchrony of planting, and varieties planted) and the occurrence of rice tungro disease epidemics using correspondence analyses. The sites covered were Isabela, Nueva Ecija, North Cotabato, and Bohol provinces as well as Bicol region. Tungro disease incidence in farmers’ fields was assessed visually based on typical symptoms. In addition, leaf samples were collected from each field and indexed serologically by enzyme-linked immunosorbent assay for the presence of Rice tungro bacilliform (RTBV) and Rice tungro spherical (RTSV) viruses. Thus, relationships between the production environment variables and four disease variables — visual incidence and double RTBV and RTSV, single RTSV, and single RTBV infections — were examined. A higher association was observed between site and varieties planted as well as site and synchrony of planting than between site and agroecosystem or site and disease variables (visual incidence, double RTBV and RTSV and single RTSV infections). Disease variables depended on both varieties planted and synchrony of planting and correspondence analysis revealed that the low disease incidence in Nueva Ecija was associated with synchronous planting while the high disease incidence in Isabela was associated with the planting of susceptible varieties and asynchronous planting. Such findings suggest that the relationship between the last two factors at a given site is critical to predicting tungro occurrence. Moreover, correspondence analysis of the relationship among disease variables revealed that tungro incidence is associated with not only double RTBV and RTSV infections but also single RTSV infections. Implications of these results on tungro epidemiology and management are discussed.
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Optimisation of Organic Rankine Cycle (ORCs) for binary-cycle geothermal applications could play a major role in determining the competitiveness of low to moderate temperature geothermal resources. Part of this optimisation process is matching cycles to a given resource such that power output can be maximised. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration: the selection of working fluid and appropriate operating conditions as well as optimisation of the turbine design for those conditions will determine the amount of power that can be extracted from a resource. In this paper, we present the rationale for the use of radial-inflow turbines for ORC applications and the preliminary design of several radial-inflow machines based on a number of promising ORC systems that use five different working fluids: R134a, R143a, R236fa, R245fa and n-Pentane. Preliminary meanline analysis lead to the generation of turbine designs for the various cycles with similar efficiencies (77%) but large differences in dimensions (139–289 mm rotor diameter). The highest performing cycle, based on R134a, was found to produce 33% more net power from a 150 °C resource flowing at 10 kg/s than the lowest performing cycle, based on n-Pentane.
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Optimisation of Organic Rankine Cycles (ORCs) for binary-cycle geothermal applications could play a major role in the competitiveness of low to moderate temperature geothermal resources. Part of this optimisation process is matching cycles to a given resource such that power output can be maximised. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration. Due to the temperature differences in geothermal resources a one-size-fits-all approach to surface power infrastructure is not appropriate. Furthermore, the traditional use of steam as a working fluid does not seem practical due to the low temperatures of many resources. A variety of organic fluids with low boiling points may be utilised as ORC working fluids in binary power cycle loops. Due to differences in thermodynamic properties, certain fluids are able to extract more heat from a given resource than others over certain temperature and pressure ranges. This enables the tailoring of power cycle infrastructure to best match the geothermal resource through careful selection of the working fluid and turbine design optimisation to yield the optimum overall cycle performance. This paper presents the rationale for the use of radial-inflow turbines for ORC applications and the preliminary design of several radial-inflow turbines based on a selection of promising ORC cycles using five different high-density working fluids: R134a, R143a, R236fa, R245fa and n-Pentane at sub- or trans-critical conditions. Numerous studies published compare a variety of working fluids for various ORC configurations. However, there is little information specifically pertaining to the design and implementation of ORCs using realistic radial turbine designs in terms of pressure ratios, inlet pressure, rotor size and rotational speed. Preliminary 1D analysis leads to the generation of turbine designs for the various cycles with similar efficiencies (77%) but large differences in dimensions (139289 mm rotor diameter). The highest performing cycle (R134a) was found to produce 33% more net power from a 150°C resource flowing at 10 kg/s than the lowest performing cycle (n-Pentane).
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Australia’s urban form and planning has shifted from traditional individual dwellings on spacious suburban blocks towards higher density urban consolidation. Despite relatively strong market demand for inner city high density (ICHD) living, there is ongoing need to explore and understand the aspects that make this urban form liveable and sustainable. The purpose of this research is to explore the viewpoints of current ICHD residents to better understand the liveability and sustainability matters that affect their everyday experiences and perceptions of this urban form. Qualitative interviews with 24 ICHD Brisbane (Australia) residents illustrates their perceptions and experiences of liveability and the ways in which it is broadly understood within three main domains and nine key sub-concepts, including: individual dwelling (thermal comfort, natural light and balconies, noise mitigation), building complex (shared space, good neighbour protocols, environmental sustainability) and the community (transport, amenities, sense of community). Focussing on the experience of ICHD residents, this research highlights the ways in which multiple aspects of the immediate living environment, the dwelling, building complex and the community intertwine to provide residents with a liveable space. The results show that urban features that reflect current societal pressure for greater sustainability such as lower energy use are the exact same features sought by ICHD residents in determining their liveability. By highlighting the aspects current ICHD residents value most about their dwellings, buildings and communities, these findings will help inform policy-makers, planners, developers and designers as they create urban spaces and dwellings that are more liveable and sustainable.
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In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.