51 resultados para Solution of mathematical problems

em Deakin Research Online - Australia


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Although e-government offers unique opportunities for streamlining good governance, there remains considerable skepticism about its applicability in developing countries due to their lack of required level of infrastructural, technological, legal and human development. This paper argues that developing countries can introduce e-government practices by re-engineering their existing infrastructure rather than waiting for massive investments and perfect technological advancements. Using Bangladesh- a developing country- as an exemplar, this paper assesses the applicability and prospects of e-government practices in dealing with the problems in the agricultural input sector which is predominantly associated with poor, marginalised and semi-illiterate farmers. The utilization of the Bangladesh case study has important implications for examining and highlighting the probable introduction of e-government practices in developing countries.

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This thesis reviews progress toward an understanding of the processes involved in the solution of spatial problems. Previous work employing factor analysis and information processing analysis is reviewed and the emphasis on variations in speed and accuracy as the major contributers to individual differences is noted. It is argued that the strategy used by individuals is a preferable explanatory concept for identifying the cognitive substratum necessary for problem solving. Using the protocols obtained from subjects solving The Minnesota Paper Form Board (Revised), a test commonly regarded as measuring skill in spatial visualization, a number of different strategies are isolated. Assumptions as to the task variants which undergird these strategies are made and tested experimentally. The results suggest that task variants such as the size of the stimulus and the shape of the pieces interact with subject variables to produce the operating strategy. Skill in problem solving is revealed in the ability to structure the array, to hold a structured image and to reduce the number of answers requiring intensive processing. The interaction between task and subject variables results in appropriate or inappropriate strategies which in turn affect speed and accuracy. Results suggest that strategy formation and usage are the keys to explaining individual differences and an heuristic model is presented to explain the performance of individual subjects on the problems involved in the Minnesota Paper Form Board. The model can be used to predict performance on other tests; and as an aid to teaching subjects experiencing difficulties. The model presented incorporates strategy variation and is consequently mores complex than previously suggested models. It is argued that such complexity is necessary to explain the nature of a subject's performance and is also necessary to perform diagnostic evaluation. Certain structural -features of the Minnesota Paper Form Board are questioned and suggestions for improvement included. The essential explanatory function of the strategy in use makes the prevalent group administration approach suspect in the prediction of future performance in spatial or vocational activity.

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In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

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The current automotive industry and todays car drivers are faced with every increasing challenges, not previously experienced. Climate Change, financial issues, rising fuel prices, increased traffic congestion and reduced parking space in cities are all leading to changes in consumer preferences and the requirements of modern passenger vehicles. However, despite the shift in the industry dynamics, the principal layout of a car hasn’t changed since its invention. The design of a ’conventional’ vehicle is still principally a matchbox with four wheels, one at each corner. The concept has served its purpose well for over 100 years, but such a layout is not suited to solving today’s problems. To address the range of problems faced by the industry, a number of alternative commuting vehicles have been developed. Yet the commercialization of these ‘alternative’ vehicles has yet to be successful. This is largely due failure of these vehicles to meet the changing demands of the industry and the limited understanding of consumer behaviour, motivation and attitudes. Deakin University’s Tomorrow’s Car concept tackles all of these problems. The vehicle is a novel three-wheeler cross over concept between a car and a motorbike that combines the best of both worlds. The vehicle combines the low cost, small size and ‘fun’ factor of a motorbike together with the safety, comfort and easy to drive features of a car produce a vehicle with a fuel efficiency better than either car or scooter. Intensive market research has been conducted for various major potential markets of alternative vehicles including India, China and Australia. The research analysed consumer attitudes in relation to narrow tilting vehicles, and in particular towards Deakin’s Tomorrow’s Car (TC). The study revealed that a relatively large percentage of consumers find such a concept very appealing. For the other consumers, the overall appearance and perception of safety and not the actual safety performance were found to be the most impeding factors of such vehicles. By addressing these issues and marketing the vehicle accordingly the successful commercialization of Tomorrow’s Car can be ensured.

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A commercial roller-skating centre in southern Australia had condensation problems on both the roof and floor. The building is a typical warehouse-type structure with a high level of natural ventilation due to poor construction and permanently open vents. A computer model of the building, using the thermal simulation software TRNSYS, was calibrated from a sensitivity analysis of three key parameters, namely air exchange rate, roof surface heat transfer coefficient and deep ground temperature. The predicted times of condensation on the roof were compared with site observations. The time of year was predicted with acceptable accuracy, although earlier in the morning than had been observed. The effect of installing foil insulation in the roof was simulated. Under normal winter conditions, this modification was enough to stop the condensation. However, in unusually cold and humid conditions, condensation still occurred on both surfaces. This was overcome by heating the floor (15 W/m 2 ) for approximately eight hours. Subsequent modifications have demonstrated the value of the simulations.

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The syntheses of cyclo-[R2Sn(OPPh2O)2SnR2](O3SCF3)2 (R = Me (1), t-Bu (2)) by the consecutive reaction of R2SnO (R = Me, t-Bu) with triflic acid and diphenylphosphinic acid are presented. In the solid state, 1 and 2 were investigated by 119Sn MAS and 31P MAS NMR spectroscopy as well as X-ray crystallography and appear to exist as ion pairs of cyclo-[R2Sn(OPPh2O)2SnR2]2+ dications and triflate anions. In solution, 1 and 2 are involved in extensive equilibria processes featuring cationic diorganotin(IV) species with Sn-O-P linkages, as evidenced by 119Sn and 31P NMR spectroscopy, electrospray mass spectrometry, and conductivity measurements.

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The reaction of Me3SbCl2 and (Me2SnS)3 afforded the complex (Me3SbS)2Me2SnCl2 in high yields, whose molecular structure features both hypercoordinated tin and antimony atoms. In solution, (Me3SbS)2Me2SnCl2 undergoes a reversible dissociation and ligand interchange reaction to give Me3SbS, Me3SbCl2 and (Me2SnS)3.

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The condensation of [Ph2(OH)Sn(CH2)nSn(OH)Ph2] (1-3; n = 1-3) with HO3SCF3 and HO2PPh2 provided [Ph2Sn(CH2)nSnPh2(OH)](O3SCF3) (4-6; n = 1-3) and [Ph2(O2PPh2)Sn(CH2)nSn(O2PPh2)Ph2] (10-12; n = 1-3), respectively. The reaction of [Ph2Sn(CH2)nSnPh2(OH)](O3SCF3) (4-6; n = 1-3) with HO2PPh2 and NaO2PPh2 gave rise to the formation of [Ph2Sn(CH2)nSnPh2(O2PPh2)](O3SCF3) (7-9; n = 1-3) and [Ph2(OH)Sn(CH2)nSn(O2PPh2)Ph2] (13-15; n = 1-3), respectively. In the solid state, compounds 4-9 comprise ion pairs of cationic cyclo-[Ph2SnCH2SnPh2(OH)]22+, cyclo-[Ph2Sn(CH2)nSnPh2(OH)]+ (n = 2, 3), and cyclo-[Ph2Sn(CH2)nSnPh2(O2PPh2)]+ (n = 1-3) and triflate anions. In MeCN, the eight-membered-ring system cyclo-[Ph2SnCH2SnPh2(OH)]22+ appears to be in equilibrium with the four-membered-ring system cyclo-[Ph2SnCH2SnPh2(OH)]+. In contrast, compounds 10-15 show no ionic character. Compounds 1-15 were characterized by multinuclear NMR spectroscopy in solution and in the solid state, IR spectroscopy, conductivity measurements, electrospray mass spectrometry, osmometric molecular weight determinations, and X-ray crystallography (4, 5, 7, and 12).

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Much advice about teaching for understanding implies that teacher should help children to develop connections between aspects of their experience, knowledge, and skills. This paper outlines points from the literature about different types of connections and describes relevant points from four case study teachers said and did.

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Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.

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Game theory is a rapidly advancing approach to structure and understand complex management problems in the natural resources sector in both the developed and developing countries. Many natural resource problems are complex due to common property and public goods characteristics. Despite these limitations many researchers have used game theory to analyze water shed management, irrigation water management, grazing land management, and managing other ecological resources. The prisoner’s dilemma game has been widely used. The work of Runge shows that collective action is feasible if a critical mass of people can cooperate. The use of game theory is hindered by lack of information, paucity of empirical applications and the lack of interest by policy makers who wish quick answers to critical policy issues. The potential still remains high for game theory to be productively used both in developing and developed countries.