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Dissertations / Theses on the topic 'Initial problem'
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Holt, M. W. "Localised symmetric instability : an initial value problem." Thesis, University of Reading, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253477.
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Webster, Stuart. "The barotropic initial value problem and atmospheric predictability." Thesis, University of Reading, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262485.
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Chihara, Hiroyuki. "The initial value problem for semilinear Schrödinger equations." Kyoto University, 1997. http://hdl.handle.net/2433/157012.
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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである<br>Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(工学)<br>甲第6965号<br>工博第1648号<br>新制||工||1084(附属図書館)<br>UT51-97-L186<br>京都大学大学院工学研究科数理工学専攻<br>(主査)教授 大矢 勇次郎, 教授 曾根 良夫, 教授 岩井 敏洋<br>学位規則第4条第1項該当
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Zhao, Kun. "Initial-boundary value problems in fluid dynamics modeling." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31778.
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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Pan, Ronghua; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Gangbo, Wilfrid; Committee Member: Yeung, Pui-Kuen. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Hanson-Hart, Zachary Aaron. "A Cauchy Problem with Singularity Along the Initial Hypersurface." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/126171.
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Mathematics<br>Ph.D.<br>We solve a one-sided Cauchy problem with zero right hand side modulo smooth errors for the wave operator associated to a smooth symmetric 2-tensor which is Lorentz on the interior and degenerate at the boundary. The degeneracy of the metric at the boundary gives rise to singularities in the wave operator. The initial data prescribed at the boundary must be modified from the classical Cauchy problem to suit the problem at hand. The problem is posed on the interior and the local solution is constructed using microlocal analysis and the techniques of Fourier Integral Operators.<br>Temple University--Theses
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Forgoston, Eric T. "Initial-Value Problem for Perturbations in Compressible Boundary Layers." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/195810.
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An initial-value problem is formulated for a three-dimensional perturbation in a compressible boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature factor effects. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using the analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using a Gaussian model as well as the method of steepest descent. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation. Using the inverse Fourier transform computations, the development of the wave packet is studied, including effects due to Reynolds number, Mach number and temperature factor.
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Papallo, Giuseppe. "Causality and the initial value problem in Modified Gravity." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/277416.
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Lovelock and Horndeski theories are natural generalisations of Einstein’s theory of General Relativity. They find applications in Astrophysics, Cosmology and String Theory. This dissertation discusses some issues regarding the mathematical consistency of these theories. In the first part of the thesis we study the Shapiro time delay for gravitons in spherically symmetric spacetimes in Einstein–Gauss–Bonnet gravity (a Lovelock theory). In Lovelock theories, gravitons can propagate faster or slower than light. We show that, thanks to this property, it is possible for them to experience a negative time delay. It was recently argued that this feature could be employed to construct closed causal curves, implying that the theory should be discarded as causally pathological. We show that this construction is unphysical, for it cannot be realised as the evolution of sensible initial data. The second part investigates the local well-posedness of the initial value problem for Lovelock and Horndeski theories. For the initial value problem to be well-posed it is necessary that the equations of motion be strongly hyperbolic. It is known that when the background fields are large, even weak hyperbolicity may fail. Hence, we consider the weak field regime, in which these equations can be considered as small perturbations of the Einstein equations. We prove that both Lovelock and Horndeski theories are weakly hyperbolic in a generic weak field background in harmonic and generalised harmonic gauge, respectively. We show that Lovelock theories fail to be strongly hyperbolic in this setting. We also prove that the most general Horndeski theory which is strongly hyperbolic is simply a “k-essence” theory coupled to Einstein gravity and that any more general theory would necessarily fail to be so. Our results imply that the standard methods used to prove the well-posedness of the initial value problem for the Einstein equations cannot be extended to Lovelock or Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields and hence might not constitute a valid alternative to General Relativity.
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Viguria, Jimenez Luis Antidio. "Distributed Task Allocation Methodologies for Solving the Initial Formation Problem." Thesis, Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24731.
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Mobile sensor networks have been shown to be a powerful tool for enabling a number of activities that require recording of environmental parameters at various spatial and temporal distributions. These mobile sensor networks could be implemented using a team of robots, usually called robotic sensor networks.
This type of sensor network involves the coordinated control of multiple robots to achieve specific measurements separated by varied distances. In most formation measurement applications, initialization involves identifying a number of interesting sites to which mobility platforms, instrumented with a variety of sensors, are tasked. This process of determining which
instrumented robot should be tasked to which location can be viewed as solving the task allocation problem.
Unfortunately, a centralized approach does not fit in this type of application due to the fault tolerance requirements. Moreover, as the size of the network grows, limitations in bandwidth severely limits the possibility of conveying and using global information. As such, the utilization of decentralized techniques for forming new sensor topologies and configurations is a highly desired quality of robotic sensor networks.
In this thesis, several distributed task allocation algorithms will be explained and compared in different scenarios. They are based on a market approach since our interest is not only to obtain a feasible solution, but also an efficient one. Also, an analysis of the efficiency of those algorithms using probabilistic techniques will be explained.
Finally, the task allocation algorithms will be implemented on a real system consisted of a team of six robots and integrated in a complete robotic system that considers obstacle avoidance and path planning. The results will be validated in both simulations and real experiments.
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Thornburg, Jonathan. "Coordinates and boundary conditions for the general relativistic initial data problem." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/25060.
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Techniques for numerically constructing initial data in the 3+1 formalism of general relativity (GR) are studied, using the theoretical framework described in Bowen and York (1980), Physical Review D 21(8), 2047-2056. The two main assumptions made are maximal slicing and 3-conformal flatness of the generated spaces. For ease of numerical solution, axisymmetry is also assumed, but all the results should extend without difficulty to the non-axisymmetric case.
The numerical code described in this thesis may be used to construct vacuum spaces containing arbitrary numbers of black holes, each with freely specifyable (subject to the axisymmetry assumption) position, mass, linear momentum, and angular momentum. It should be emphasised that the time evolution of these spaces has not yet been attempted.
There are two significant innovations in this work: the use of a new boundary condition for the surfaces of the black holes, and the use of multiple coordinate patches in the numerical solution.
The new boundary condition studied herein requires the inner boundary of the numerical grid to be a marginally trapped surface. This is in contrast to the approach used in much previous work on this problem area, which requires the constructed spaces to be conformally isometric under a "reflection mapping" which interchanges the interior of a specified black hole with the remainder of the space. The new boundary condition is found to be easy to implement, even for multiple black holes. It may also prove useful in time evolution problems.
The coordinate choice scheme introduced in this thesis uses multiple coordinate patches in the numerical solution, each with a coordinate system suited to the local physical symmetries of the region of space it covers. Because each patch need only cover part of the space, the metrics on the individual patches can be kept simple, while the overall patch system still covers a complicated topology. The patches are linked together by interpolation across the interpatch boundaries. Bilinear interpolation suffices to give accuracy comparable with that of common second order difference schemes used in numerical GR.
This use of multiple coordinate patches is found to work very well in both one and two black hole models, and should generalise to a wide variety of other numerical GR problems. Patches are also found to be a useful (if somewhat over-general) way of introducing spatially varying grid sizes into the numerical code. However, problems may arise when trying to use multiple patches in time evolution problems, in that the interpatch boundaries must not become spurious generators or reflectors of gravitational radiation, due to the interpolation errors. These problems have not yet been studied.
The code described in this thesis is tested against Schwarzschild models and against previously published work using the Bowen and York formalism, reproducing the latter within the limits of error of the codes involved. A number of new spaces containing one and two black holes with linear or angular momentum are also constructed to demonstrate the code, although little analysis of these spaces has yet been done.<br>Science, Faculty of<br>Physics and Astronomy, Department of<br>Graduate
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Fotouhi, A. R. "Longitudinal data analysis : the initial conditions problem in random effects modelling." Thesis, Lancaster University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387647.
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DE, SANTI FRANCESCA. "Perturbation dynamics in laminar and turbulent flows. Initial value problem analysis." Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2613156.
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Stability and turbulence are often studied as separate branches of fluid dynamics, but they are actually the two faces of the same coin: the existence of equilibrium, laminar in one case and steady in the mean in the other. The link between these two faces is transition. Initial value problems are considered to analyse the dynamics of disturbances in the three phases.
In the context of stability, linearised equations of motion can be used. Although this is a substantial simplification, the results that are obtained with this
analysis are far from being trivial. The transition to turbulence through the dynamics of disturbances is discussed in the context of the zig-zag instability: a particular kind of instability that occurs in geophysical flows. Eventually, the perturbations dynamics in turbulent flows is used to analyse the mixing process between water-vapour in clouds and clear air in the surroundings, in the presence of a meteorological inversion.
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Kazemi, Iraj. "The initial conditions problem in dynamic panel data models with random effects." Thesis, Lancaster University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.431463.
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Tee, Key Yong. "Twistor methods to the initial value problem of gravitational plane waves interaction." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268161.
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Adkins, Jacob. "A Robust Numerical Method for a Singularly Perturbed Nonlinear Initial Value Problem." Kent State University Honors College / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1513331499579714.
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Graaff, Erik de. "Simulation of initial medical problem-solving studies on a new measure for the assessment of medical problem-solving ability /." Haarlem : Maastricht : Thesis ; University Library, Maastricht University [Host], 1989. http://arno.unimaas.nl/show.cgi?fid=5460.
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Gale, Andrew Dent 1955. "Dynamic point relocation: An enhancement for traveling salesman problem initial tour construction procedures." Thesis, The University of Arizona, 1993. http://hdl.handle.net/10150/292024.
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Traditional solving techniques for the traveling salesman problem are carried out in two phases. First an initial tour is constructed, then this tour is improved using some form of optimization. The procedure introduced in this research applies a simple optimization technique which minimally increases the runtime of the initial tour construction procedure. At the same time it greatly improves the quality of the tour which is constructed. It does this by globally searching the tour after each insertion for points which require repositioning and performing point relocations where necessary.
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Ran, Yu. "Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/47930.
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The dissertation focuses on the initial boundary value problems (IBVPs) of a class of nonlinear Schrodinger equations posed on a half plane R x R+ and on a strip domain R x [0,L] with Dirichlet nonhomogeneous boundary data in a two-dimensional plane. Compared with pure initial value problems (IVPs), IBVPs over part of entire space with boundaries are more applicable to the reality and can provide more accurate data to physical experiments or practical problems. Although there is less research that has been made for IBVPs than that for IVPs, more attention has been paid for IBVPs recently. In particular, this thesis studies the local well-posedness of the equation for the appropriate initial and boundary data in Sobolev spaces H^s with non-negative s and investigates the global well-posedness in the H^1-space. The main strategy, especially for the local well-posedness, is to derive an equivalent integral equation (whose solution is called mild solution) from the original equation by semi-group theory and then perform the Banach fixed-point argument. However, along the process, it is essential to select proper auxiliary function spaces and prepare all the corresponding norm estimates to complete the argument. In fact, the IBVP posed on R x R+ and the one posed on R x [0,L] are two independent problems because the techniques adopted are different. The first problem is more related to the initial value problem (IVP) posed on the whole plane R^2 and the major ingredients are Strichartz's estimate and its generalized theory. On the other hand, the second problem can be studied as an IVP over a half-line and periodic domain, which is established on the analysis for series inspired by Bourgain's work. Moreover, the corresponding smoothing properties and regularity conditions of the solution are also considered.<br>Ph. D.
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Shalaev, Ivan. "Initial-Value Problem for Small Perturbations in an Idealized Detonation in a Circular Pipe." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/194709.
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The thesis is devoted to the investigation of the initial-value problem for linearized Euler equations utilizing an idealized one-reaction detonation model in the case of three-dimensional perturbations in a circular pipe.The problem is solved using the Laplace transform in time, Fourier series in the azimuthal angle, and expansion into Bessel's functions of the radial variable.For each radial and azimuthal mode, the inverse Laplace transform can be presented as an expansion of the solution into the normal modes of discrete and continuous spectra. The dispersion relation for the discrete spectrum requires solving the homogeneous ordinary differential equations for the adjoint system and evaluation of an integral through the reaction zone.The solution of the initial-value problem gives a convenient tool for analysis of the flow receptivity to various types of perturbations in the reaction zone and in the quiescent gas.
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Parton, G. J. "Problem-based learning in initial teacher education : the construction and adaption of professional identity." Thesis, Leeds Beckett University, 2015. http://eprints.leedsbeckett.ac.uk/2278/.
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The aim of this thesis was to investigate whether problem-based learning as a learning model has the potential to develop and adapt students’ professional identity. I argue that in an ever-changing educational environment and a consistent neo-liberal ideology of educational policy, that teachers’ professionalism is a vital component within teacher education. The research took place within a four-year undergraduate teacher education degree in a university located in the South-East of England. The purposive sample of eight students in the second year of their studies was chosen from a year group of 256. Professional studies was a core module that ran throughout the four years of the degree and was seen as the ‘spine’ of the degree. Problem-based learning was located within the second year professional studies module. The sample of eight students were interviewed four times using a qualitative methodology; before, during and after their experience of problem-based learning. The first interviews investigated the sample’s previous educational experiences, the second and third examined the sample’s experience of problem-based learning and the fourth considered the sample’s emerging professional identity and the transferable nature of the skills and attitudes that were nurtured within a problem-based learning environment. The main findings, which emerged from the interviews of the sample of eight students, were the ways that learner identity was constructed and deconstructed throughout the student teachers educational life. Learner identity and professional identity were inextricably linked and learner identity was seen, within the analysis of the interviews, as a powerful precursor to the construction of professional identity. I argue that the discourses associated with problem-based learning acts as organising structure that can, in the safe, critical and supportive environment, promote a collaborative, critical and reflective professional identity that, I argue is vital in the ever changing environment of education in the United Kingdom.
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Qiao, Yongyuan. "On the determinants of initial public offering underpricing." Thesis, St Andrews, 2008. http://hdl.handle.net/10023/575.
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Sbierski, Jan. "On the initial value problem in general relativity and wave propagation in black-hole spacetimes." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/248837.
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The first part of this thesis is concerned with the question of global uniqueness of solutions to the initial value problem in general relativity. In 1969, Choquet-Bruhat and Geroch proved, that in the class of globally hyperbolic Cauchy developments, there is a unique maximal Cauchy development. The original proof, however, has the peculiar feature that it appeals to Zorn’s lemma in order to guarantee the existence of this maximal development; in particular, the proof is not constructive. In the first part of this thesis we give a proof of the above mentioned theorem that avoids the use of Zorn’s lemma. The second part of this thesis investigates the behaviour of so-called Gaussian beam solutions of the wave equation - highly oscillatory and localised solutions which travel, for some time, along null geodesics. The main result of this part of the thesis is a characterisation of the temporal behaviour of the energy of such Gaussian beams in terms of the underlying null geodesic. We conclude by giving applications of this result to black hole spacetimes. Recalling that the wave equation can be considered a “poor man’s” linearisation of the Einstein equations, these applications are of interest for a better understanding of the black hole stability conjecture, which states that the exterior of our explicit black hole solutions is stable to small perturbations, while the interior is expected to be unstable. The last part of the thesis is concerned with the wave equation in the interior of a black hole. In particular, we show that under certain conditions on the black hole parameters, waves that are compactly supported on the event horizon, have finite energy near the Cauchy horizon. This result is again motivated by the investigation of the conjectured instability of the interior of our explicit black hole solutions.
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Barnholdt, Jacob, and Filip Carlsson. "Convergence Properties for Different Null Space Bases When Solving the Initial Margin Optimization Problem Using CMA-ES." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-273628.
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This thesis evaluates how the evolutionary algorithm CMA-ES (Covariance Matrix Adaption Evolution Strategy) can be used for optimizing the total initial margin for a network of banks trading bilateral OTC derivatives. The algorithm is a stochastic method for optimization of non-linear and, but not limited to, non-convex functions. The algorithm searches for an optimum by generating normally distributed samples and iteratively updating the mean and covariance matrix of the search distribution using the best candidate solutions in the sampled population. In this thesis, feasible solutions are represented by the null space obtained from the constraint of keeping all banks' market exposure unchanged throughout the optimization, and the generated samples for each iteration correspond to linear combinations of the base vectors spanning this null space. In particular, this thesis investigates how different representations of this null space affect the convergence speed of the algorithm. By applying the algorithm to problems of varying sizes, using several different null space representations coming from different matrix decomposition methods, it is found that as long as an orthonormal representation is used it does not matter which matrix decomposition method it comes from. This is found to be because, given any orthonormal null space representation, the algorithm will at start generate a rotationally invariant sample space in its search for the optimal solution, independent of the specific null space representation. If the representation is not orthogonal, the initial sample will in contrast be in the shape of an ellipsoid and thus biased in certain directions, which in general affects the performance negatively. A non-orthonormal representation can converge faster in specific optimization problems, if the direction of the solution is known in advance and the sample space is pointed towards that direction. However, the benefit of this aspect is limited in a realistic scenario and an orthonormal representation is recommended. Furthermore, as it is shown that different orthonormal representations perform equally, it is implied that other characteristics can be considered when deciding which matrix decomposition method to use; such as the importance of fast computation or desire for a sparse representation.<br>Denna avhandling utvärderar hur CMA-ES (Covariance Matrix Adaption Evolution Strategy) kan användas för att optimera en total "initial margin" för ett nätverk av banker som handlar bilaterala OTC derivat. Algoritmen är en stokastisk metod för optimering av icke-linjära och, men inte enbart, icke-konvexa funktioner. Algoritmen söker efter ett optimum genom att generera normalfördelade utfall och iterativt uppdatera medelvärdet och kovariansmatrisen för sök-fördelningen med hjälp av de bästa lösningarna i varje iteration. I detta arbete representeras tillåtna lösningar till problemet av nollrummet från bivillkoret att alla bankers marknadsexponering ska vara oförändrade genom optimeringen och de genererade utfallen består av slumpade linjärkombinationer av nollrummets basvektorer. I synnerhet undersöks hur olika representationer av nollrummet påverkar konvergenshastigheten för algoritmen. Algoritmen har applicerats med flera olika nollrumsrepresentationer, framtagna genom olika matrisfaktoriseringsmetoder, och det kan konstateras att så länge nollrummsrepresentationen är ortonormal är valet av faktoreringsmetod obetydlig. Detta då användande av orthornormala nollrumsrpresentationer i algoritmen leder till en initialt symmetrisk, rotationsmässigt invariant, sökning efter den optimala lösningen. Om representationen inte är ortogonal kommer det resulterande sökområdet i varje iteration att ha formen av en ellipsoid och sålunda viktas i vissa riktningar, vilket i allmänhet påverkar prestandan negativt. Emellertid kan en icke-ortonormal representation konvergera snabbare i specifika scenarier, givet att lösningens riktning är känd i förväg och sökområdet kan pekas mot den riktningen. Vidare, eftersom det har visats att olika ortonormala representationer konvergerar lika fort, innebär resultatet att andra egenskaper kan beaktas vid val av matrisfaktoriseringsmetod, såsom vikten av snabb beräkning eller önskan om en gles representation.
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Nedialkov, Nedialko Stoyanov. "Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0005/NQ41256.pdf.
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MONTANARI, Piera. "Local and Global Existence results for the Characteristic Problem for Linear and Semi-linear Wave Equations." Doctoral thesis, Università degli studi di Ferrara, 2010. http://hdl.handle.net/11392/2389334.
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The thesis concerns the well posedness of the Characteristic Initial
Value Problem for the Semilinear Wave Equation, with initial data on
a light cone. In the first part of the thesis, an explicit representation
formula for the solution of the linear equation is given, extending the
results known for the homogeneous equation and the trace on the time
axis of the solution.
Further, Energy Estimates are derived. In constructing such Estimates
one encounters several difficulties due to the presence of a
geometrical singularity at the tip of the cone. To manage the construction
of the Energy Estimate, one introduces suitable Sobolev-like
norms characterized by weights, which mitigates the difficulties in the
origin. These Estimates are well posed only for functions which vanish
of order high enough at the origin. This fact brings us to split the initial
data in the sum of two terms. The first term consists of the Taylor
polynomial of the initial datum, the second one consist of remainder
regular function with the required vanishing order at the origin.
An interesting phenomenon observed here is a gap of differentiability
between the solution and the initial data.
The solution obtained using the Energy method is still incomplete,
because of the splitting of the initial data. This fact brings us to solve
the problem for purely polynomial data. For this purpose, it is used a
generalization of the well-known harmonic polynomials.
The last part of the thesis is devoted to the semi-linear problem,
for which the tools developed in the previous chapters are generalized.
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Beyer, Carrie Austin. "Exact synchronized simultaneous uplifting over arbitrary initial inequalities for the knapsack polytope." Thesis, Kansas State University, 2011. http://hdl.handle.net/2097/8782.
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Master of Science<br>Department of Industrial & Manufacturing Systems Engineering<br>Todd W. Easton<br>Integer programs (IPs) are mathematical models that can provide an optimal solution to a variety of different problems. They have been used to reduce costs and optimize organizations. Additionally, IPs are NP-complete resulting in many IPs that cannot be
solved. Cutting planes or valid inequalities have been used to decrease the time required
to solve IPs.
Lifting is a technique that strengthens existing valid inequalities. Lifting inequalities can result in facet defining inequalities, which are the theoretically strongest valid inequalities. Because of these properties, lifting procedures are used in software to reduce the time required to solve an IP. The thesis introduces a new algorithm for exact synchronized simultaneous uplifting over an arbitrary initial inequality for knapsack problems. Synchronized Simultaneous Lifting (SSL) is a pseudopolynomial time algorithm requiring O(nb+n[superscript]3) effort to solve. It exactly uplifts two sets simultaneously into an initial arbitrary valid inequality and creates multiple inequalities of a particular form. This previously undiscovered class of inequalities generated by SSL can be facet defining.
A small computational study shows that SSL is quick to execute, requiring on average less than a quarter of a second. Additionally, applying SSL inequalities to a knapsack problem enabled commercial software to solve problems that it could not solve without them.
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Velkur, Chetan Babu. "Initial assessment of the "compressible poor man's Navier-Stokes (CPMNS) equation" for subgrid-scale models in large-eddy simulation." Lexington, Ky. : [University of Kentucky Libraries], 2006. http://lib.uky.edu/ETD/ukymeen2006t00502/Cbvelkur.pdf.
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Thesis (M.S.)--University of Kentucky, 2006.<br>Title from document title page (viewed on January 5, 2007). Document formatted into pages; contains: x, 128 p. : ill. (some col.). Includes abstract and vita. Includes bibliographical references (p. 116-127).
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Young, Alex D. "Problem construction in initial sessions of psychotherapy : a meta-synthesis of existing literature and a critical discourse analysis." Thesis, University of Sheffield, 2016. http://etheses.whiterose.ac.uk/15711/.
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This thesis consists of a literature review and a research study. The review used a meta-synthesis to integrate the findings of existing literature on problem construction in initial sessions of psychotherapy. Five main themes were constructed from the studies reviewed: Problems are defined by therapists, Therapists employ rhetorical strategies, Therapists’ use of power and clients’ resistance, Problems are structured and ordered through language, and Problems exist in socio-historical context. A new explanatory model for problem construction in psychotherapy was proposed. Therapists’ problem schemas that were shaped by socio-historical factors and rhetorical strategies involved in realising these schemas were central to the process of problem construction. Epistemological differences in research methodologies generated difficulties in the synthesis of existing research. For the research study, a critical discourse analysis was used to analyse therapist-client problem construction in first sessions of therapy in a trial comparing two psychotherapies for depression. Four stages of analysis were conducted, with the following findings: (1) discursive constructs included how problems were experienced and made sense of; (2) rhetorical strategies were used to pursue agendas by both clients and therapists; (3) subject positions were interactive and could be contradictory for both therapists and clients, they were generally more problem focused for clients and powerful for therapists; (4) therapists and clients reproduced normative discourses from institutions and ideologies shaping their subjectivity. Methodological limitations and recommendations for practice were outlined.
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Montealegre, Scott Juan. "Initial value problem for a coupled system of Kadomtsev-Petviashvili II equations in Sobolev spaces of negative indices." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95255.
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SCARSOGLIO, STEFANIA. "Hydrodynamic linear stability of the two-dimensional bluff-body wake through modal analysis and initial-value problem formulation." Doctoral thesis, Politecnico di Torino, 2008. http://hdl.handle.net/11583/2499922.
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The stability of the two-dimensional wake behind a circular cylinder - a free flow of general interest in differing applications (from aerodynamics to environmental physics and biology) - is studied by means of two different but complementary theoretical methods.
The first part of the work is focused on the asymptotic evolution of disturbances described through modal analysis, a method which allows the determination of the asymptotic stability of a flow. The stability of the intermediate and far near-parallel wake is studied by means of a multiscale approach. The disturbance is defined as the local wavenumber at order zero in the longitudinal direction and is associated to a classical spatio-temporal WKBJ analysis. The inverse of the Reynolds number is taken as the small parameter for the multiscaling. It takes into account non-parallelism effects related to the transversal dynamics of the base flow. The first order corrections find absolute instability pockets in the first part of the intermediate wake (and not in the near wake, where the recirculating eddies are, as usually seen in literature in contrast with the near-parallelism hypothesis). These regions are present for Reynolds numbers larger than $Re=35$. That is in agreement with the general notion of critical Reynolds number for the onset of the first instability of about $Re=47$. In particular, for Re=50 and Re=100, the angular frequency obtained is in agreement with global data in literature concerning numerical and experimental results. The instability is convective throughout the domain. All the stability characteristics are vanishing in the far field, a fact that is independently confirmed by the asymptotic analysis of the Orr-Sommerfeld operator.
Using asymptotic Navier-Stokes expansions for the wake inner field the entrainment evolution in the intermediate and far domain is evaluated in terms of asymptotic expansion. The maximum of entrainment is reached in the region where the absolute instability pockets are found. Downstream of this region the entrainment is decreasing and eventually vanishing in the far wake. This point confirms the validity of the multiscale approach.
In the second part of the thesis the stability analysis is studied as an initial-value problem to observe the transient behaviour and the asymptotic state of perturbations initially imposed. The initial-value problem allows the formulation to be extended to the near-parallel flow configuration. The initial-value method is, however, less general than the modal analysis, since many parameters, such as the polar wavenumber, the spatial damping rate, the angle of obliquity and the symmetry of the perturbation, are involved. An exploratory analysis of these parameters permits the study of different transient configurations. Before the asymptotic (stable or unstable) state is reached, maxima and minima of the perturbation energy are observed for transients lasting hundreds of time scales. In the temporal asymptotics, the initial-value problem well reproduces modal results in terms of angular frequency and temporal growth rate. Moreover, for Reynolds numbers larger than the critical one (Re_{cr} = 47), the present method gives a good prediction, in terms of wavelength and pulsation, of the vortex shedding observed in experiments. In the framework of the initial-value problem formulation, a multiscale analysis for the stability of long waves
is then proposed. Even to the lowest order, the multiscaling - whose small parameter is defined as the polar wavenumber -
approximates sufficiently well the full problem solution with a
relevant reduction of the computational cost. The two (modal and
non-modal) analyses combined together lead to a quite complete
description of the bluff-body wake stability.
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Nordin, Syarifah Zyurina. "Task scheduling in parallel processor systems." Thesis, Curtin University, 2011. http://hdl.handle.net/20.500.11937/2510.
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Task scheduling in parallel processing systems is one of the most challenging industrial problems. This problem typically arises in the manufacturing and service industries. The task scheduling problem is to determine a set of task assignments to a set of parallel processors for execution so as to optimize a specified performance measure. The difficulty of the problem is that the scheduling needs to satisfy a set of requirements as well as a range of environmental constraints. The problem is known to be NP-complete.In this study, we consider a non-preemtive task scheduling problem on iden- tical and unrelated parallel processor systems. We are interested in the objective function that minimizes the maximum of the completion time of the entire set of tasks (i.e makespan) so as to ensure a good load balance on the parallel proces- sors. We consider three different task characteristics to the classical task scheduling problem that has a set of n independent tasks to be assigned to m parallel processors.The first task characteristic that we consider is an on-line scheduling with release date specifications on an identical parallel processing system with a centralized queue and no splitting structure. We focus on developing simple and efficient heuristics for this problem. Three heuristic algorithms are proposed to solve this non-deterministic problem with scheduling over time where the availability of each task is restricted by release date. Our approach uses a multi-step method in the task selection phase and a greedy search algorithm in the processor selection phase. The multi-step method is used to reduce the non-determinism in on-line scheduling by partitioning the scheduling process into several procedures. We introduce two procedures in the priority rule loop which we refer to as Cluster Insertion and Local Cluster Interchange.Computational testing on randomly generated data is conducted using Microsoft Visual C++ 6.0 to examine the effectiveness of the proposed multi-step method against the optimal solution. Different size of problems are tested in the experiment involving 3 processors by 200 tasks up to 5 processors by 1000 tasks with five clusters ranging from 10 to 50. The computational results show that all the three heuristics performed very well with the value of the average gaps are improved as the number of the tasks in the system is increases. The average gap for all the three heuristics are less than 1.04% for the largest tested cases (i.e for 1000 tasks run on 5 processors).In the second problem, we address priority consideration as an added feature to the basic task characteristics of unrelated parallel processors scheduling. The priority consideration is defined by a list of ordered independent tasks with priority. A task requires to start processing after another task is finished on the same processor based on priority but may require to start earlier if processed on other machine. Our aim is to develop Mixed Integer Linear Programming models to obtain optimal solutions for three type of priority lists which are ascending order, descending order and general priority list. We validate the model using a case study taken from the literature. Then, computational testing is implemented on the general priority list using AIMMS 3.10 package and CPLEX 12.1 as the solver. Computational results show that the proposed MILP model is effective and produces optimal results for all tested cases. The model is very efficient as 95% of all the instances, which are problem up to 80 tasks assigned on 5 processors, have been solved within 5 minutes of CPU time.In the final problem, we address a further problem for the task scheduling with a disruption problem that occurs on the parallel processor system. The disruption is causes by the unavailability of the processor during a certain time and it is called resource disruption. Our recovery solution for the disruption problem is a rescheduling approach. A MILP model is developed for the rescheduling model for the case of non-resumable tasks. Recovery model for the disrupted initial schedule with dummy insertion is proposed for predictive disruption management and match up schedule for post-disruption management. To evaluate the model, computational testing is performed with different sets of data.Different levels of disruptions are considered with different weights in the objective function to observe the stability of the model. The optimum initial schedule and the rescheduling model is performed using CPLEX 12.1 solver in AIMMS 3.10 package. In our computational results we measure the stability rate which is to observe the stability condition of the current schedule compared to the initial schedule in term of the task migration. From the results, the stability is improved when the number of tasks in the system increases within a reasonable amount of time. Another interesting observation is that our model yields small average gaps that are less than 7.99% within 300 seconds of the CPU time for a large data set that reach 200 tasks by 10 processors. The average gaps are considerably small for the disruption problem since the rescheduling model have to match up with the optimum initial schedule.
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Oti, Vincent Bediako. "Numerické metody pro řešení počátečních úloh zlomkových diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445462.
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Tato diplomová práce se zabývá numerickými metodami pro řešení počátečních problémů zlomkových diferenciálních rovnic s Caputovou derivací. Jsou uvedeny dva numerické přístupy spolu s přehledem základních aproximačních formulí. Dvě verze Eulerovy metody jsou realizovány v Matlabu a porovnány na základě numerických experimentů.
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Gonçalves, Reinaldo Bellini. "Development and validation of new methods of distribution of initial population on genetic algorithms for the problem of protein-ligand docking." Laboratório Nacional de Computação Científica, 2008. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=154.
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The methods of protein-ligand docking are computational methods usedto predict the mode of binding of molecules into drug candidates for its receptor. The docking allows tests of hundreds of compounds in ashort space of time, assisting in the discovery of new drug candidates. The great complexity that involves the binding of protein-ligand complex, makes the problem of docking computationally difficult to be solved. In this work, we used the Genetic Algorithms which is a technique of optimization based on the theory of biological evolution of Darwin. The proposed algorithm was implemented and tested initially by Camila S. de Magalhães in her doctoral thesis, with the Group of Molecular Modeling of Biological Systems at LNCC, with a range of 5 ligands of HIV-1 protease. It was built a new set used for test with 49 structures with several physico-chemical properties, distributed in 22 different families of protein, allowing for a broader test of the algorithm It was conducted a detailed study of the dependence of the genetic algorithm in relation to the distribution of its initial population and it was also investigated ways more efficient and robust to generate the same. Among these, the proposal to distribute the initial population based on the coordinates of individuals of lower energy in the population (proposal 5), it is very promising. This distribution has allowed the algorithm to obtain good results, finding solutions of lower energy in the population very close to experimental structure optimized, without having specific information about the experimental structure. This fact is very important, because the algorithm makes it more realistic in view that in the rational design of drugs, it has not the trial structure.<br>Os métodos de docking proteína-ligante, são métodos computacionais usados para predizer o modo de ligação de moléculas candidatas a fármaco em seu receptor. O docking permite o teste de centenas de compostos em um curto espaço de tempo, auxiliando na descoberta de novos candidatos a fármacos. A grande complexidade que envolve a ligação do complexo ligante-proteína, torna o problema de docking difícil de ser resolvido computacionalmente. Neste trabalho, são usados os Algoritmos Genéticos, que são uma técnica de otimização baseada na teoria da evolução biológica de Darwin. O algoritmo proposto foi implementado e testado inicialmente por Camila S. de Magalhães em sua tese de doutorado, junto ao Grupo de Modelagem Molecular de Sistemas Biológicos do LNCC, com um conjunto de 5 ligantes de HIV-1 protease.
Foi construido um novo conjunto utilizado para teste, agora com 49 estruturas com propriedades físico-químicas diversas, distribuidos em 22 famílias distintas de proteínas, permitindo um teste mais amplo do algoritmo. Foi realizado um estudo aprofundado sobre a dependência do Algoritmo Genético em relação à distribuição da sua população inicial e investigou-se formas mais eficientes e robustas de gerar a mesma. Dentre estas, a proposta de distribuir a população inicial baseada nas coordenadas dos indivíduos de menor energia na população (proposta 5), é muito promissora. Esta distribuição permitiu o algoritmo obter bons resultados, encontrando soluções de menor energia na população muito próximas a estrutura experimental otimizada, sem possuir informações específicas sobre a estrutura experimental. Este fato é muito importante, pois torna o algoritmo mais realista, tendo em vista que no desenho racional de fármacos real não se dispoe da estrutura experimental.
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Campbell, Jesse. "A discourse analysis of the initial negotiation of therapeutic parameters and the development of new problem descriptions, in two different psychological therapies." Thesis, University of East London, 2009. http://roar.uel.ac.uk/3730/.
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This thesis uses discourse analysis to compare systemic and cognitive-behavioural therapies, in terms of, the process of initial negotiation between client and therapist over therapeutic parameters, and the development of new problem descriptions. It also compares the theoretical description of the application of each therapy with the actual application of each therapy. The first section develops an argument for an approach to process research which is based on bottom-up naturalistic analysis of the way language is used in therapy. In doing so, it highlights the limitations of the positivist process and outcome research traditions, and provides an account of the range of established approaches to discourse analysis. The approach to analysis used draws on traditions of conversation analysis and discourse analysis. Several sub-themes are discussed within each of the two main analytic foci; negotiation of parameters and development of problem descriptions. The final section summarises the findings according to the analytic foci, and discusses the implications of the findings for clinical practice, and topical professional and political developments. Further indicated research and validity issues are also discussed.
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Rivas, Ivonne. "Analysis and Control of the Boussinesq and Korteweg-de Vries Equations." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321371582.
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Lundvall, Johan. "Data Assimilation in Fluid Dynamics using Adjoint Optimization." Doctoral thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-9684.
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Nunes, Célia Barros [UNESP]. "O processo ensino-aprendizagem-avaliação de geometria através da resolução de problemas: perspectivas didático-matemáticas na formação inicial de professores de matemática." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/102122.
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nunes_cb_dr_rcla.pdf: 3789615 bytes, checksum: dcaee776ef4788b9aa3cd4ba26eefddb (MD5)<br>Toda pesquisa começa com uma curiosidade do pesquisador e se apresenta como um ponto de partida para uma investigação. Assim, esta pesquisa tem como fenômeno de interesse trabalhar a Geometria Euclidiana, numa abordagem dinâmica, com alunos, futuros professores, do curso de Licenciatura em Matemática da Universidade do Estado da Bahia – UNEB, Campus X. Seu objetivo é o de investigar, compreender e evidenciar as potencialidades didático-matemáticas da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas nos processos de ensinar e aprender Geometria. É uma pesquisa de natureza qualitativa que foi desenvolvida seguindo orientações metodológicas de Thomas A. Romberg. Usou-se como procedimentos metodológicos na coleta de dados: a observação, o material escrito pelos alunos, questionários, filmagens, gravações e diário de campo. Dois projetos de ensino foram criados e aplicados nas disciplinas Didática da Matemática e Laboratório de Ensino de Matemática II, respectivamente. Na junção desses dois projetos, depois de aplicados, concluiu-se que essa é mais uma pesquisa no contexto da Educação Matemática que une as disciplinas trabalhadas como uma dupla necessária para a formação de professores. Ademais, sugere um trabalho feito com professores em formação inicial visando a sua própria formação e propicia momentos de reflexão e análise sobre as potencialidades que a Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas oferece no sentido de incrementar a aprendizagem e melhorar os processos de ensino de Matemática, sobretudo o de Geometria.<br>Every search begins with a curiosity of the researcher and it is presented as a starting point for an investigation. This research has the phenomenon of interest to work Euclidean geometry, a dynamic approach, with students, future teachers, the Degree in Mathematics at the University of Bahia - UNEB, Campus X. Its goal is to investigate, understand and highlight the potential of teaching math-Teaching Methodology-Evaluation of Learning Mathematics through Problem Solving in the processes of teaching and learning geometry. . It is a qualitative research that was developed following methodological guidelines of Thomas A. Romberg. It used as instruments to collect data: observation, material was written by students, quizzes, films, recordings and field diary. Two education projects were created and applied in the disciplines of Didactics of Mathematics and Laboratory of Mathematics II, respectively. At the junction of these two projects, once implemented, it was concluded that this is another research in the context of mathematics education that unites the disciplines worked as a dual need for teacher training. Moreover, it suggests a work that was done with teachers in training to become self-training and provides moments of reflection and analysis on the potential that the methodology of Teaching-Learning-Evaluation of Mathematics through Problem Solving offers to enhance their learning and improve the processes of teaching mathematics, especially in geometry.
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ROSSI, ELENA. "Balance Laws: Non Local Mixed Systems and IBVPs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/103090.
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Scalar hyperbolic balance laws in several space dimensions play a central role in this thesis. First, we deal with a new class of mixed parabolic-hyperbolic systems on all R^n: we obtain the basic well-posedness theorems, devise an ad hoc numerical algorithm, prove its convergence and investigate the qualitative properties of the solutions. The extension of these results to bounded domains requires a deep understanding of the initial boundary value problem (IBVP) for hyperbolic balance laws. The last part of the thesis provides rigorous estimates on the solution to this IBVP, under precise regularity assumptions.
In Chapter 1 we introduce a predator-prey model. A non local and non linear balance law is coupled with a parabolic equation: the former describes the evolution of the predator density, the latter that of prey. The two equations are coupled both through the convective part of the balance law and the source terms. The drift term is a non local function of the prey density. This allows the movement of predators to be directed towards the regions where the concentration of prey is higher. We prove the well-posedness of the system, hence the existence and uniqueness of solution, the continuous dependence from the initial data and various stability estimates.
In Chapter 2 we devise an algorithm to compute approximate solutions to the mixed system introduced above. The balance law is solved numerically by a Lax-Friedrichs type method via dimensional splitting, while the parabolic equation is approximated through explicit finite-differences. Both source terms are integrated by means of a second order Runge-Kutta scheme. The key result in Chapter 2 is the convergence of this algorithm. The proof relies on a careful tuning between the parabolic and the hyperbolic methods and exploits the non local nature of the convective part in the balance law.
This algorithm has been implemented in a series of Python scripts. Using them, we obtain information about the possible order of convergence and we investigate the qualitative properties of the solutions. Moreover, we observe the formation of a striking pattern: while prey diffuse, predators accumulate on the vertices of a regular lattice.
The analytic study of the system above is on all R^n. However, both possible biological applications and numerical integrations suggest that the boundary plays a relevant role. With the aim of studying the mixed hyperbolic-parabolic system in a bounded domain, we noticed that for balance laws known results lack some of the estimates necessary to deal with the coupling. In Chapter 3 we then focus on the IBVP for a general balance law in a bounded domain. We prove the well-posedness of this problem, first with homogeneous boundary condition, exploiting the vanishing viscosity technique and the doubling of variables method, then for the non homogeneous case, mainly thanks to elliptic techniques. We pay particular attention to the regularity assumptions and provide rigorous estimates on the solution.
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Guimarães, José Osvaldo de Souza. "Computação evolutiva na resolução de equações diferenciais ordinárias não lineares no espaço de Hilbert." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-29062009-154349/.
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A tese apresenta um método para a solução dos problemas do valor inicial (PVIs) com margens de erro comparáveis às de métodos numéricos consagrados (MN), tanto para a função quanto para suas derivadas. O método é aplicável a equações diferenciais (EDs) lineares ou não, sendo o ferramental desenvolvido até a quarta ordem, que pode ser expandido para ordens superiores. A solução é uma expressão polinomial de alto grau com coeficientes expressos pela razão entre dois inteiros. O método se mostra eficaz mesmo em alguns casos em que os MN não conseguiram dar a partida. As resoluções são obtidas considerando que o espaço de soluções é um espaço de Hilbert, equipado com a base completa dos polinômios de Legendre. Em decorrência do método aqui desenvolvido, os majorantes de erros para a função e derivadas são determinados analiticamente por um cálculo matricial também deduzido nesta tese. Paralelamente a toda fundamentação analítica, foi desenvolvido o software SAM, que automatiza todas as tarefas na busca de soluções dos PVIs. A tese propõe e verifica a validade de um novo critério de erro no qual pesam tanto os erros locais quanto os erros globais, simultaneamente. Como subprodutos dos resultados já descritos, igualmente integrados ao SAM, obtiveram-se também: (1) Um critério objetivo para analisar a qualidade de um MN, sem necessidade do conhecimento de seu algoritmo; (2) Uma ferramenta para aproximações polinomiais de alta precisão para funções de quadrado integrável em determinado intervalo limitado, com um majorante de erro; (3) Um ferramental analítico para transposição genérica (linear ou não) dos PVIs até 4ª ordem, nas mudanças de domínio; (4) As matrizes de integração e diferenciação genéricas para todas as bases polinomiais do espaço de Hilbert.<br>This thesis shows a new method to get polynomial solutions to the initial value problems (IVP), with an error margin comparable to the consecrate numerical methods (NM), for both the function and its derivatives. The method works with differential equations (DEs) linear or not, beeing the developed tolls available until 4th order, whose can be expanded to higher orders. The solution is a polynomial high degree expression with coefficients expressed by the ratio between two integers. The method behaves efficiently even in some cases that NM cannot get started. The resolutions are gotten considering that, the solution space is a Hilbert space, equipped with a complete set basis of Legendre Polynomials. Due the method here developed, the errors majoratives for the function and its derivatives are found analytically by a matrix calculus, also derived in this thesis. Beside all analytical foundation, a software (SAM) was developed to automate the whole process, joining all the tasks involved in the search for solutions to the IVP. This thesis proposes, verifies and validates a new error criterion, which takes in account simultaneously the local and global errors. As sub-products of the results described before, also integrated to the SAM, the following achievements should be highlighted: (1) An objective criterion to analyze the quality of any NM, despite of the knowledge of its algorithm; (2) A tool for a polynomial approximation, of high precision, for functions whose square is integrable in a given limited domain, with an errors majorative; (3) A tool-kit for a generically transpose (linear or not) of the IVPs domain and form, taking into account its derivatives, until the 4th order; (4) The generic matrices for integration and differentiation for all the polynomial basis of the Hilbert space.
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Ferreira, Nilton Cezar [UNESP]. "Uma proposta de ensino de álgebra abstrata moderna, com a utilização da metodologia de ensino-aprendizagem-avaliação de matemática através da resolução de problemas, e suas contribuições para a formação inicial de professores de matemática." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/149213.
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Previous issue date: 2017-03-03<br>Este trabalho teve como principal objetivo investigar as contribuições que a Álgebra Abstrata Moderna (onde se trabalham as teorias de Grupos, Anéis e Corpos, dentre outras), ministrada como uma disciplina em cursos de Licenciatura em Matemática no Brasil, poderia dar à Formação Inicial de Professores de Matemática. Esta pesquisa teve caráter qualitativo e foi apoiada no Modelo Metodológico de Romberg-Onuchic. Visando alcançar esse objetivo, propusemos uma pesquisa de campo, desenvolvida em 2015, com uma turma do quinto período de Licenciatura em Matemática do Instituto Federal de Goiás (IFG). Para isso, elaboramos e implementamos um projeto de ensino com o propósito de levar os alunos dessa turma a construírem um conhecimento satisfatório de Álgebra Abstrata Moderna e mostrar a relação de seus conteúdos com os da Educação Básica. Para a construção desse conhecimento, fizemos uso da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas, figurada no campo da Educação Matemática e consolidada por diversas pesquisas como eficiente no processo de ensino, aprendizagem e avaliação de Matemática em diversos níveis – Fundamental, Médio e Superior. A correlação entre os conteúdos de Álgebra Abstrata Moderna e os da Educação Básica se deu através da proposição, aos estudantes da referida turma, de atividades extraclasse, que, sempre, em um momento posterior, eram discutidas, em sala de aula, por todos os integrantes desse processo: alunos, pesquisador e professor da disciplina. Contou, ainda, com dois encontros exclusivos para se trabalhar, discutir e analisar essa associação – Álgebra Abstrata Moderna e Educação Básica. A coleta de evidências foi feita através da observação do pesquisador durante a aplicação do projeto; materiais produzidos pelos alunos; mídias (gravações em áudio e vídeo dos encontros realizados); e uma avaliação diagnóstica que teve como foco: Formação de Professores, Álgebra e Resolução de Problemas. Os resultados confirmaram que a Álgebra Abstrata, se trabalhada de forma adequada, poderá trazer contribuições significativas à formação de professores de Matemática.<br>The main purpose of the present work was to investigate the contributions that Modern Abstract Algebra (which the theories of Groups, Rings and Fields, among others, are worked on), as a discipline in Degree courses in Mathematics in Brazil, might give to initial Teacher Education in Mathematics. The present research has a qualitative approach and it was grounded on the Methodological Model of Romberg-Onuchic. In order to achieve that goal, we proposed a field research, developed in 2015, involving a class of fifth semester students of Degree in Mathematics at Instituto Federal de Goiás (IFG). To that end, we elaborated and implemented a teaching project with the purpose of enabling that group of students to build satisfactory knowledge on Modern Abstract Algebra and showing the relationship of its contents to the ones of Elementary Education. In order to build such knowledge, we used the Methodology of Teaching-Learning-Evaluation in Mathematics through Problem Solving, found in the field of Mathematics Education and consolidated by several researches as effective in the process of Mathematics teaching, learning and evaluation in several levels – Elementary, Middle and Higher Education. The correlation between the contents of Modern Abstract Algebra and the ones of Elementary Education came about through the proposition to that group of students of extracurricular activities which were always discussed further in classroom by all people involved in that process: students, researcher and teacher. There were also two meetings with the only purpose of working, discussing and analysing this association – Modern Abstract Algebra and Elementary Education. The evidence-gathering was made through the researcher’s observation during the project application, the materials produced by the students, the media (audio and video recordings of the meetings) and a diagnostic evaluation focused on Teacher Education, Algebra and Problem Solving. The results confirmed that Abstract Algebra, if properly worked on, might bring significant contributions to Teacher Education in Mathematics.
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Freire, Melquesedeque da Silva. "A estrat?gia did?tica de resolu??o de problemas na forma??o de professores de qu?mica." Universidade Federal do Rio Grande do Norte, 2010. http://repositorio.ufrn.br:8080/jspui/handle/123456789/16061.
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Previous issue date: 2010-07-05<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>In this work it is presented a research developed in the initial training of teachers of the chemistry graduation course at the Universidade Federal do Rio Grande do Norte (UFRN). The intervention was realized in two classes in the context of a discipline in the curricular structure with nineteen undergraduate students of chemistry. The study utilizes characteristics of the qualitative approach and uses observation, questionnaires, interviews and examination papers. The experiment involved a sequence of activities fundamented on the Problem Solving (PS) teaching strategy to approach chemical concepts. The proposal was planned and organized according to the theoretical presupposition of the work developed by the authors of the Science Education in PS, of teaching experience and from the initial hypotheses of the research. The goal was that the future teachers could experience the strategy and advance to the new meanings. The themes addressed in the activities were the difference between exercises and problems, exercises turning into problems, the steps of problem solving and some implications of the teaching strategy for the work of the teacher. The results showed evidence that through a process of collective reflection, and from the difficulties experienced in the strategy practice, the undergraduates are introduced to new perspectives of reflection and action of teaching practice, and understanding some benefits of innovative proposals for the teaching of chemistry. It also showed that, although this theme is approached, in some moments of the graduation, the future teachers don‟t know when or how to realize activities in this perspective. From the aspects that rose in research we highlighted the difficulties in the problem solving steps, the use of the strategy in school and the knowledge and skills of the teacher for planning activities in Problem Solving<br>Neste trabalho ? apresentada uma experi?ncia desenvolvida durante a forma??o inicial de professores no curso de Licenciatura em Qu?mica da Universidade Federal do Rio Grande do Norte (UFRN). A interven??o se deu em duas turmas no contexto de uma disciplina da estrutura curricular com dezenove licenciandos de qu?mica. A pesquisa traz elementos da abordagem qualitativa e fez uso da observa??o, de question?rios, entrevistas e prova pedag?gica. A experi?ncia envolveu uma sequ?ncia de atividades fundamentadas na estrat?gia de ensino por Resolu??o de Problemas (RP) para abordar conceitos qu?micos. A proposta foi planejada e organizada de acordo com os pressupostos te?ricos dos trabalhos desenvolvidos por autores da Did?tica das Ci?ncias em RP, da experi?ncia docente e de hip?teses iniciais da investiga??o. O objetivo era que os futuros professores pudessem vivenciar a estrat?gia e avan?ar para os novos significados. Os temas abordados nas atividades foram as diferen?as entre os exerc?cios e problemas, a transforma??o de exerc?cios em problemas, as etapas de resolu??o de problemas e algumas implica??es da estrat?gia de ensino para o trabalho docente. Os resultados evidenciaram que, atrav?s de um processo de reflex?o coletiva, e a partir das dificuldades encontradas na pr?tica da estrat?gia, os licenciandos s?o introduzidos em novas perspectivas de reflex?o e a??o da pr?tica de ensino e de compreens?o de alguns benef?cios de propostas inovadoras para o ensino de qu?mica. Revela tamb?m que apesar do tema RP ser abordado, em alguns momentos durante o curso de gradua??o, os futuros professores sinalizaram que n?o sabem como e quando realizar atividades nessa perspectiva. Dos aspectos que emergiram na investiga??o destacamos as dificuldades nas etapas de resolu??o de problemas, a utiliza??o da estrat?gia no contexto escolar e os conhecimentos e habilidades do professor para planejar atividades em RP
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Laier, Simone Simionato dos Santos. "Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop." Universidade Federal de Mato Grosso, 2014. http://ri.ufmt.br/handle/1/318.
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Previous issue date: 2014-04-15<br>A presente pesquisa de mestrado tem por objetivo estudar Aspectos do Pensamento Algébrico revelados por acadêmicos da Licenciatura em Ciências Naturais e Matemática, com Habilitação em Matemática, da UFMT - Campus de Sinop/MT. Trata-se de uma pesquisa de natureza qualitativa, exploratória e investigativa, em que buscamos estudar as manifestações dos acadêmicos em relação à Álgebra, usando como procedimento a Resolução de Problemas matemáticos. Os instrumentos utilizados para a produção de dados incluíram a aplicação de questionários para a caracterização do perfil dos sujeitos; oito problemas matemáticos e registros audiovisuais. A partir do que foi produzido pelos sujeitos, organizamos os dados e procedemos à análise em dois enfoques: o primeiro para identificar aspectos do pensamento algébrico revelados na resolução dos problemas matemáticos, elementos na resolução que evidenciassem uma sequência de etapas ou procedimentos para chegarem à resposta, além de verificarmos se haveria a produção de algum significado para a atividade em questão; o segundo enfoque visou considerar as concepções de Álgebra apresentadas e o posicionamento em relação à Resolução de Problemas matemáticos. Diante disso, para o primeiro enfoque, identificamos nos registros apresentados, que os sujeitos procederam com certa regularidade nas operações, desenvolveram algum tipo de processo de generalização nos problemas, além de usar linguagem algébrica ao expressarem-se matematicamente. No que tange às etapas para a resolução dos problemas, percebemos que cada sujeito manteve uma regularidade nas soluções apresentadas, ou seja, lançaram mão dos mesmos recursos que utilizaram para resolver um problema, nos demais, como se fosse uma característica pessoal para organizarem suas ideias. Para o segundo enfoque, o que apresentaram, acerca de seus conhecimentos algébricos, nos ofereceu a possibilidade de refletir sobre como esses futuros professores lidam com a Álgebra e atividades envolvendo a Resolução de Problemas matemáticos. Disto, conseguimos identificar que os sujeitos não tiveram experiências que proporcionassem o trabalho com a Resolução de Problemas a favor de uma nova forma de trabalhar e explorar os conteúdos matemáticos. Em relação à aprendizagem da matemática por meio da Resolução de Problemas, não identificaram, de fato, a possibilidade de aprender com essa metodologia, mesmo considerando-a importante para o processo de desenvolvimento do raciocínio e pensamento algébrico. Sobre os Aspectos do Pensamento Algébrico que foram revelados, podemos concluir que, em relação às dimensões da Álgebra, predominantemente ela se destaca como aritmética generalizada com uso das letras para expressar um modelo aritmético em seu aspecto funcional. Operaram com a variação de grandezas, com o uso de letras expressando relações e funções e para o estabelecimento de equações que utilizam letras como incógnitas.<br>This master's research is aimed at studying the aspects of algebraic thinking shown by the students of the Licentiate’s Degree program in Natural Sciences and Mathematics, with specialization in Mathematics, of UFMT (The Federal University of Mato Grosso) – Sinop Campus, MT. This is a qualitative, exploratory and investigative research, in which we seek to study the manifestations of students in relation to algebra, using the procedure of mathematical problem solving. Data for this research were collected through questionnaires aimed at the profiling of subjects, eight mathematical problems and audiovisual records. From what was produced by the subjects, the data were organized and the analysis proceeded in two distinct approaches: the first one intended to identify aspects of algebraic thinking revealed by solving mathematical problems and the elements of the problem solving that could reveal a sequence of steps or procedures used to reach the answer, as well as check whether there would be a production of meaning for the activity in question; the second approach aimed to consider the concepts of algebra presented and the stance in relation to mathematical problem solving. For the first approach, we identified in the records presented, that the subjects proceeded with some regularity in operations and developed some kind of generalization process for the problems, in addition to using algebraic language to express themselves mathematically. Regarding the steps taken to solve the problems, we noted that each subject maintained a regularity of the solutions presented, i.e., they applied the same resources used to solve a problem to the other ones, as if it were a personal characteristic to organize their own ideas. For the second approach, what the subjects presented about their algebraic knowledge provided some support for our reflecting on how these prospective teachers perceive algebra and the activities involving mathematical problem solving. These results suggest that the subjects had had no experiences that provided the opportunity to work with problem solving encouraging a new way of working and exploring mathematical content. In what learning mathematics through problem solving is concerned, the possibility of learning from this methodology was not, in fact, identified, even though they consider it important for the development process of reasoning and algebraic thinking. Regarding the aspects of algebraic thinking that were revealed, we can conclude that, in relation to the extent of algebra, it predominantly stands out as generalized arithmetic, using letters to express a mathematical model in its functional aspect. The subjects operated with variables, using letters to express relations and functions, in order to establish equations that use letters as unknowns.
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Sanja, Ružičić. "Dopustiva singularna rešenja sistema gasne dinamike sa nepozitivnim pritiskom." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2020. https://www.cris.uns.ac.rs/record.jsf?recordId=114114&source=NDLTD&language=en.
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Karakteristika hiperboličnih sistema zakona odrržanja je da čak i u slučaju glatkog po-četnog uslova rešenja uglavnom razvijaju prekide u konačnom vremena. Zbog toga se posmatraju slaba rešenja koja dati sistem zadovoljavaju u distributivnom smislu i mogu biti čak i neograničena što se ispoljava kroz pojavu Dirakove delta funkcije u rešenju. U ovoj disertaciji se akcenat stavlja na analizu protoka stišljivog neviskoznog fluida koji ne menja pravac prilikom kretanja. Protok je opisan Ojlerovim sistemom iz gasne dinamike koji se sastoji iz zakona održanja mase, količine kretanja i energije, dok su karakteristike fluida određene konstitutivnim relacijama. U slučaju izentropskog ili izotermnog protoka sistem se svodi na zakone održanja mase i količine kretanja. Glatka rešenja takvog sistema automatski zadovoljavaju zakon održanja energije, dok prelaskom na slabu formulaciju dolazi do gubitka energije. Za predstavnike sistema gasne dinamike sa nepozitivnim pritiskom su uzeti sistem gasne dinamike bez pritiska i model za Čapliginov gas i njegova uopštenja. Data su rešenja Rimanovih problema za te sisteme koja se mogu predstaviti kao kombinacija klasičnih elementarnih talasa i senka talasa koji aproksimiraju rešenja u obliku delta udarnih talasa i koji omogućavaju rešavanje početnog problema koji u početnom uslovu sadrži delta funkciju. Na primeru modela za uopšten Čapliginov gas dokazano je da uslov prekompresivnosti nije jači od entropijskog uslova, što je prvi takav rezultat u literaturi. Dalje su korišćena rešenja Rimanovih problema, kao i problema singularne interakcije i dat je algoritam za konstrukciju globalnog dopustivog približnog rešenja početnog problema za sistem gasne dinamike bez pritiska. Algoritam je univerzalan i ideja se može proširiti na veliki broj sistema zakona održanja i veliki broj početnih uslova. Diskutovane su promene energije u približnom rešenju i posle interakcija. Dobijeno približno rešenje slabo konvergira u prostoru Radonovih mera sa predznakom.<br> A solutions to hyperbolic conservation laws systems starting out as smooth often develop singularities in a finite time. As a consequence, we are forced to look for weak solutions that satisfy the system in distributional sense. Those solutions are often unbounded, which is expressed through the appearance of Dirac delta function. In this theses we study a one-dimensional, compressible and inviscid flow of a fluid. The process is described by compressible Euler gas dynamics system which consists of conservation laws of mass, linear momentum and energy, while the characteristics of the fluid are described using constitutive relations. In the case of isentropic or isothermal flow the system reduces to conservation laws of mass and linear momentum. The energy is conserved for smooth solutions to such systems, but while passing to the weak formulation the energy is being dissipated. As representatives, we consider pressureless gas dynamics system, as well as Chaplygin gas model and its generalizations. We give the solutions to Riemann problems which can be represented as a combinations of classical elementary waves and shadow waves that approximate the solutions in the form of delta shock and allow as to solve the problems with initial data containing delta function. We use generalized Chaplygin gas model as demonstration of the fact that overcompressibility condition is not stronger that entropy condition, which is the first result of that kind in the literature. Further, we use solutions to the Riemann problems, as well as singular interaction problems to give the algorithm for construction of global admissible approximate solution to the pressureless gas dynamics initial value problem. The algorithm is universal and idea can be applied to large number of conservation laws systems and large number of initial data. We discuss energy changes in approximate solution and after the interactions. The constructed approximate solution converges in the space of signed Radon measures.
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Rana, Muhammad Sohel. "Analysis and Implementation of Numerical Methods for Solving Ordinary Differential Equations." TopSCHOLAR®, 2017. https://digitalcommons.wku.edu/theses/2053.
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Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It includes discussion what are the advantages and disadvantages of implicit methods over explicit methods, the accuracy and stability of methods and how the order of various methods can be approximated numerically. Also, semidiscretization of some partial differential equations and stiff systems which may arise from these semidiscretizations are examined.
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Hussein, Sayed A. "Implicit methods in initial value problems." Thesis, University of Essex, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302882.
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Martins, Egídio Rodrigues. "Possibilidades do uso da metodologia de ensino-aprendizagem-avaliação de Matemática através da resolução de problemas em um curso de licenciatura Matemática na Rede Federal de Educação Tecnológica no Estado de São Paulo /." Rio Claro, 2019. http://hdl.handle.net/11449/181825.
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Orientador: Lourdes de la Rosa Onuchic<br>Resumo: Esta pesquisa de doutorado está dividida em dois momentos: o primeiro foi realizado em seis campi do IFSP e seu objetivo era o de investigar, junto aos professores que atuam nos cursos de Licenciatura em Matemática do IFSP, como eles percebem a possibilidade de atuação como formador e como professor de matemática em uma mesma instituição. A segunda etapa deu-se com a incorporação da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através de Resolução de Problemas e teve como objetivo analisar a possibilidade do uso da referida metodologia na Formação de Professores de Matemática no IFSP, além de compreender como os professores formadores e os licenciandos em Matemática veem a possibilidade da utilização da referida metodologia em diferentes níveis de ensino. Esta pesquisa teve como mote uma discussão teórica acerca dos temas: Institutos Federais de Educação e Ciência e Tecnologia - IFs, formação de professores e Resolução de Problema. Realizaram-se, também, pesquisas de cunho bibliográfico para discutir os temas supracitados e trazer novos debates e diálogos para a cena, aqui, construída. Isso se fez a partir de trabalhos de referência e impacto e, também, uma análise sobre documentos oficiais tanto do cenário nacional quanto do internacional sobre os temas: IFs, Formação de Professores, Formação de Professores de Matemática, Resolução de Problemas, dentre outros. Para alcançar os objetivos propostos, adotou-se a metodologia de pesquisa de abordagem qualitativa, se... (Resumo completo, clicar acesso eletrônico abaixo)<br>Abstract: This PhD research is divided into two phases: The first one was carried out on six campuses of the IFSP and its objective was to investigate how teachers working in the degree courses in Mathematics of the IFSP perceive the possibility of acting as trainer and as professor of mathematics in the same institution. The second step was to incorporate the Teaching-Learning-Assessment-Mathematics Methodology through Problem Solving, which had the objective of analyzing the possibility of the use of said methodology in the Training of Mathematics Teachers in the IFSP, besides understanding how teacher trainers and mathematics graduates are affected by the possibility of using this methodology at different levels of education. This research had as motto a theoretical discussion about the themes: Federal Institutes of Education and Science and Technology - IFs, teacher training and Problem Solving. Bibliographical research was also carried out to discuss the aforementioned themes and to bring new debates and dialogues to the scene, built here. This was done from reference and impact works and also an analysis of official documents from both the national and the international scenario on the themes: IFs, Teacher Training, Mathematics Teacher Training, Problem Solving, among others. In order to achieve the proposed objectives, a qualitative approach was adopted. Data collection was done through interviews and the application of a project at one of the campuses of the IFSP, the Araraquar... (Complete abstract click electronic access below)<br>Doutor
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Tiwari, Ganesh. "Numerical Analysis of Non-Fickian Diffusion with a General Source." ScholarWorks@UNO, 2013. http://scholarworks.uno.edu/honors_theses/49.
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The inadequacy of Fick’s law to incorporate causality can be overcome by replacing it with the Green–Naghdi type II (GNII) flux relation. Combining the GNII assumption and conservation of mass leads to [see document for equation] where r (x, t) is the density function, S(p) is a source term and c¥ is a positive constant which carries (SI) units of m/sec. A general source term given by [see document for equation] is proposed. Here, the constants y and ps are the rate coefficient and saturation density respectively. The travelling wave solutions and numerical analysis of four special cases of equation (2), namely: Pearl-Verhulst Growth law, Zel’dovich Law, Newmann Law and Stefan- Boltzmann Law are investigated. For both analysis, results are compared with the available literature and extended for other cases. The numerical analysis is carried out by imposing well-studied Initial Boundary Value Problem and implementing a built-in method in the software package Mathematica 9. For Pearl-Verhulst source type, the results are compared to those found in literature [1]. Confirming the validity of built-in method for Pearl-Verhulst law, the generic built-in method is extended to study the transient signal response for similar initial boundary value problems when the source terms are Zel’dovich law, Newmann law and Stefan-Boltzmann law.
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Nascimento, Marcio Lemos do. "Unicidade e discretiza??o para problemas de valor inicial." Universidade Federal do Rio Grande do Norte, 2013. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18648.
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Previous issue date: 2013-08-13<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>This paper has two objectives: (i) conducting a literature search on the criteria
of uniqueness of solution for initial value problems of ordinary differential equations.
(ii) a modification of the method of Euler that seems to be able to converge to a
solution of the problem, if the solution is not unique<br>O presente trabalho tem dois objetivos: (i) a realiza??o de uma pesquisa bibliografifica sobre os crit?rios de unicidade de solu??o para problemas de valor inicial
de equa??es diferenciais ordin?rias. (ii) Introduzir uma modifica??o do m?todo de Euler que parece ser capaz de convergir a uma das solu??es do problema, caso a solu??o n?o seja ?nica
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Nunes, Célia Barros. "O processo ensino-aprendizagem-avaliação de geometria através da resolução de problemas : perspectivas didático-matemáticas na formação inicial de professores de matemática /." Rio Claro : [s.n.], 2010. http://hdl.handle.net/11449/102122.
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Orientador: Lourdes de la Rosa Onuchic<br>Banca: Adair Mendes Nacarato<br>Banca: Kátia Cristina Stocco Smole<br>Banca: Norma Suely Gomes Allevato<br>Banca: Rosana Giaretta Sguerra Miskulin<br>Resumo: Toda pesquisa começa com uma curiosidade do pesquisador e se apresenta como um ponto de partida para uma investigação. Assim, esta pesquisa tem como fenômeno de interesse trabalhar a Geometria Euclidiana, numa abordagem dinâmica, com alunos, futuros professores, do curso de Licenciatura em Matemática da Universidade do Estado da Bahia - UNEB, Campus X. Seu objetivo é o de investigar, compreender e evidenciar as potencialidades didático-matemáticas da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas nos processos de ensinar e aprender Geometria. É uma pesquisa de natureza qualitativa que foi desenvolvida seguindo orientações metodológicas de Thomas A. Romberg. Usou-se como procedimentos metodológicos na coleta de dados: a observação, o material escrito pelos alunos, questionários, filmagens, gravações e diário de campo. Dois projetos de ensino foram criados e aplicados nas disciplinas Didática da Matemática e Laboratório de Ensino de Matemática II, respectivamente. Na junção desses dois projetos, depois de aplicados, concluiu-se que essa é mais uma pesquisa no contexto da Educação Matemática que une as disciplinas trabalhadas como uma dupla necessária para a formação de professores. Ademais, sugere um trabalho feito com professores em formação inicial visando a sua própria formação e propicia momentos de reflexão e análise sobre as potencialidades que a Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas oferece no sentido de incrementar a aprendizagem e melhorar os processos de ensino de Matemática, sobretudo o de Geometria.<br>Abstract: Every search begins with a curiosity of the researcher and it is presented as a starting point for an investigation. This research has the phenomenon of interest to work Euclidean geometry, a dynamic approach, with students, future teachers, the Degree in Mathematics at the University of Bahia - UNEB, Campus X. Its goal is to investigate, understand and highlight the potential of teaching math-Teaching Methodology-Evaluation of Learning Mathematics through Problem Solving in the processes of teaching and learning geometry. . It is a qualitative research that was developed following methodological guidelines of Thomas A. Romberg. It used as instruments to collect data: observation, material was written by students, quizzes, films, recordings and field diary. Two education projects were created and applied in the disciplines of Didactics of Mathematics and Laboratory of Mathematics II, respectively. At the junction of these two projects, once implemented, it was concluded that this is another research in the context of mathematics education that unites the disciplines worked as a dual need for teacher training. Moreover, it suggests a work that was done with teachers in training to become self-training and provides moments of reflection and analysis on the potential that the methodology of Teaching-Learning-Evaluation of Mathematics through Problem Solving offers to enhance their learning and improve the processes of teaching mathematics, especially in geometry.<br>Doutor
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Mugnolo, Delio. "Second order abstract initial-boundary value problems." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971647674.
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Nkosana-Nyawata, Idah Dzanisa. "Understanding delay : a grounded theory examination of the pre-diagnostic journey of individuals with malignant melanoma : an analysis of the experiences of individuals subsequently diagnosed with high risk malignant melanoma from problem identification through to initial specialist treatment." Thesis, University of Bradford, 2008. http://hdl.handle.net/10454/4314.
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