Complex man-made systems are ubiquitous in modern technological society. The national air transportation infrastructure and the aircraft that operate within it, the highways stretching coast-to-coast and the vehicles that travel on them, and global communications networks and the computers that make them possible are all complex systems. It is impossible to fully validate a systems analysis or a design process. Systems are too large, complex, and expensive to build test and validation articles. Furthermore, the operating conditions throughout the life cycle of a system are impossible to predict and control for a validation experiment. Error is introduced at every point in a complex systems design process. Every error source propagates through the complex system in the same way information propagates, feedforward, feedback, and coupling are all present with error. As with error propagation through a single analysis, error sources grow and decay when propagated through a complex system. These behaviors are made more complex by the complex interactions of a complete system. This complication and the loss of intuition that accompanies it make proper error propagation calculations even more important to aid the decision maker. Error allocation and fidelity trade decisions answer questions like: Is the fidelity of a complex systems analysis adequate, or is an improvement needed, and how is that improvement best achieved? Where should limited resources be invested for the improvement of fidelity? How does knowledge of the imperfection of a model impact design decisions based on the model and the certainty of the performance of a particular design? In this research, a fidelity trade environment was conceived, formulated, developed, and demonstrated. This development relied on the advancement of enabling techniques including error propagation, metamodeling, and information management. A notional transport aircraft is modeled in the fidelity trade environment. Using the environment, the designer is able to make design decisions while considering error and he is able to make decisions regarding required tool fidelity as the design problem continues. These decisions could not be made in a quantitative manner before the fidelity trade environment was developed.

In spectral methods for numerical PDEs, when the solutions are periodical, the Fourier functions may be used. However, when the solutions are non-periodical, the Legendre and Chebyshev polynomials are recommended, reported in many papers and books. There seems to exist few reports for the study of non-periodical solutions by spectral Fourier methods under the Dirichlet conditions and other boundary conditions. In this paper, we will explore the spectral Fourier methods(SFM) and collocation Fourier methods(CFM) for elliptic and eigenvalue problems. The CFM is simple and easy for computation, thus for saving a great deal of the CPU time. The collocation Fourier methods (CFM) can be regarded as the spectral Fourier methods (SFM) partly with the trapezoidal rule. Furthermore, the error bounds are derived for both the CFM and the SFM. When there exist no errors for the trapezoidal rule, the accuracy of the solutions from the CFM is as accurate as the spectral method using Legendre and Chebyshev polynomials. However, once there exists the truncation errors of the trapezoidal rule, the errors of the elliptic solutions and the leading eigenvalues the CFM are reduced to O(h^2), where h is the mesh length of uniform collocation grids, which are just equivalent to those by the linear elements and the finite difference method (FDM). The O(h^2) and even the superconvergence O(h4) are found numerically. The traditional condition number of the CFM is O(N^2), which is smaller than O(N^3) and O(N^4) of the collocation spectral methods using the Legendre and Chebyshev polynomials. Also the effective condition number is only O(1). Numerical experiments are reported for 1D elliptic and eigenvalue problems, to support the analysis made. The simplicity of algorithms and the promising numerical computation with O(h^4) may grant the CFM to be competent in application in numerical physics, chemistry, engineering, etc., see [7].

The error analysis is made for the simple annular domain with the circular boundaries having the same origin. The error bounds are derived, and the optimal convergence rates can be archived. For circular domains with circular boundaries, the same convergence rates can be achieved by strict proof. Moreover, the NFM algorithms and its conservative schemes can be applied to very small holes, which are difficult for other numerical methods to handle. Both the NFM and the collocation Trefftz method(CTM) are used for very small circular holes, the CTM is superior to the NFM in accuracy and stability.

The collocation Trefftz method (CTM) proposed in [36] is employed to annular shaped domains, and new error analysis is made to yield the optimal convergence rates. This popular method is then applied to the special case: the Dirichlet problems on circular domains with circular holes, and comparisons are made with the null field method (NFM) proposed , and new interior field method (IFM) proposed in [35], to find out that both errors and condition numbers are smaller. Recently, for circular domains with circular holes, the null fields method (NFM) is proposed by Chen and his groups. In NFM, the fundamental solutions (FS) with the source nodes Q outside of the solution domains are used in the Green formulas, and the FS are replaced by their series expansions. The Fourier expansions of the known or the unknown Dirichlet and Neumann boundary conditions on the circular boundaries are chosen, so that the explicit discrete equations can be easily obtained by means of orthogonality of Fourier functions. The NFM has been applied to elliptic equations and eigenvalue problems in circular domains with multiple holes, reported in many papers; here we cite those for Laplace¡¦s equation only (see [18, 19, 20]). For the boundary integral equation (BIE) of the first kind, the trigonometric functions are used in Arnold [4, 5], and error analysis is made for infinite smooth solutions, to derive the exponential convergence rates. In Cheng¡¦s Dissertation [21, 22], for BIE of the first kind, the source nodes are located outside of the solution domain, the linear combination of fundamental solutions are used, and error analysis is made only for circular domains. This fact implies that not only can the CTM be applied to arbitrary domains, but also a better numerical performance is provided. Since the algorithms of the CTM is simple and its programming is easy, the CTM is strongly recommended to replace the NFM for circular domains with circular holes in engineering problems.

In this thesis, sensitivity and error analysis of a differential rectification method were performed by using digital images taken by a frame camera onboard BILSAT and pushbroom scanner on ASTER. Three methods were implemented for Sensitivity and Uncertainty analysis: Monte Carlo, covariance analysis and FAST (Fourier Amplitude Sensitivity Test). A parameter estimation procedure was carried out on the basis of so called Mixed Model extended by some suitable additional regularization parameters to stabilize the solution for improper geometrical conditions of the imaging system. The effectiveness and accuracy of the differential rectification method were compared with other rectification methods and the results were analyzed. Furthermore the differential method is adapted to the pushbroom scanners and software which provides rectified images from raw satellite images was developed.

In this thesis, an error analysis based method is proposed to calculate single shot hit probability (PSSH) values of a fire control system. The proposed method considers that a weapon and a threat are located in three dimensional space. They may or may not have relative motion in three dimensions with respect to each other. The method accounts for the changes in environmental conditions. It is applicable in modeling and simulation as well as in top down design of a fire control system to reduce the design cost. The proposed method is applied to a specific fire control system and it is observed that PSSH values highly depend on the distance between the weapon and the threat, hence they are time varying. Monte Carlo simulation is used to model various defense scenarios in order to evaluate a heuristic developed by G&uuml / lez (2007) for weapon-threat assignment and scheduling of weapons&rsquo / shots. The heuristic uses the proposed method for PSSH and time of flight computation. It is observed that the difference between the results of simulation and heuristic depends on the scenario used.

In this thesis, we consider a projection-based stabilization method for solving buoyancy driven flows (natural convection problems). The method consists of adding global stabilization for all scales and then anti-diffusing these effects on the large scales defined by projections into appropriate function spaces. In this way, stabilization acts only on the small scales. We consider two different variations of buoyancy driven flows based on the projection-based stabilization. First, we focus on the steady-state natural convection problem of heat transport through combined solid and fluid media in a classical enclosure. We present the mathematical analysis of the projection-based method and prove existence, uniqueness and convergence of the approximate solutions of the velocity, temperature and pressure. We also present some numerical tests to support theoretical findings. Second, we consider a system of combined heat and mass transfer in a porous medium due to the natural convection. For the semi-discrete problem, a stability analysis of the projectionbased method and a priori error estimate are given for the Darcy-Brinkman equations in double-diffusive convection. Then we provide numerical assessments and a comparison with some benchmark data for the Darcy-Brinkman equations. In the last part of the thesis, we present a fully discrete scheme with the linear extrapolation of convecting velocity terms for the Darcy-Brinkman equations.

<p>The purpose of this essay was to see what mistakes Swedish university students make when writing English essays and to focus on one specific mistake, namely the use of capital letters. Fifty essays written by students of Swedish origin were taken from the SWICLE (the Swedish Component of the International Corpus of Learner English), corrected and the mistakes were subsequently analysed. Furthermore, six Swedish school book series were examined in order to find examples of how Swedish pupils are taught how to use capital letters in English. The results showed that mistakes concerning capital letters were very common compared to other mistakes and that the students in the study seemed to have grasped some grammatical rules on the matter, but not all. Other common mistakes made in the essays were spelling mistakes and choice of words. Most common among the mistakes concerning capital letters were overuse of capital lettering and the lack of initial capital letters when writing weekdays, months and holidays. Only one out of the six school book series went deeper into the matter of when to use capital letters in English, which suggests that one of the reasons why capital letter mistakes are so common might be that the students are not extensively taught on the matter.</p>

Thesis (M.S.)--Mississippi State University. Department of Computational Engineering. / Title from title screen. Includes bibliographical references.

Substantial evidence emphasizing the importance of linguistic systems in reading acquisition, as well as emerging literature identifying the contribution of executive function to linguistic-based difficulties, underscores the importance of clarifying the neurocognitive mechanisms affecting reading performance. Research demonstrating the interrelationship between reading and spelling, coupled with neurocognitive theories of spelling, suggests that analysis of children’s spelling attempts may capture more subtle differences in their understanding of how to decode text. This study aimed to determine the utility of applying a spelling error analysis system as a method for differentiating between reading difficulties resulting from executive dysfunction or language deficits in a sample of children at risk for reading failure. The present study examined the relationship between executive function, language, and spelling achievement in a sample of 82 children aged 6-15 years identified as having a reading deficit and/or diagnosed with Attention-Deficit/Hyperactivity Disorder (ADHD). Hierarchical regression analyses indicated language-based skills, particularly word reading, and age significantly predicted the phonemic equivalency of misspellings. Tasks of executive functioning were not found to significantly contribute to performance on phonological spelling; however, analysis of group differences suggest that ADHD and Reading Deficit groups demonstrated unique cognitive profiles, including distinct performances on executive functioning tasks. Exploratory analyses also revealed that ADHD and Reading Deficit groups differed significantly in phonological spelling performance. Results from the current study provide evidence for the presence of two distinct underlying cognitive processes affecting spelling and, in effect, reading. Current findings have implications for the need to further examine characteristic deficits in language and executive functioning affecting children at risk for reading failure. Findings also provide support for the validity of further investigating the potential to infer differential diagnostic categories using a phonological spelling analysis. The use of an analysis of spelling errors as a diagnostic data source holds promise for a better understanding of reading failure and, ultimately, may contribute to more effective intervention practices. / text