No description available.

Optimized Schwarz methods are iterative domain decomposition procedures with greatly improved convergence properties, for solving second order elliptic boundary value problems. The enhanced convergence is obtained by replacing the Dirichlet transmission conditions in the classical Schwarz iteration with more general conditions that are optimized for performance. The convergence is optimized through the solution of a min-max problem. The theoretical study of the min-max problems gives explicit formulas or characterizations for the optimized transmission conditions for practical use, and it permits the analysis of the asymptotic behavior of the convergence. / In the first part of this work, we continue the study of optimized transmission conditions for advection-diffusion problems with smooth coefficients. We derive asymptotic formulas for the optimized parameters for small mesh sizes, in the overlapping and non-overlapping cases, and show that these formulas are accurate when the component of the advection tangential to the interface is not too large. / In a second part, we consider a diffusion problem with a discontinuous coefficient and non-overlapping domain decompositions. We derive several choices of optimized transmission conditions by thoroughly solving the associated min-max problems. We show in particular that the convergence of optimized Schwarz methods improves as the jump in the coefficient increases, if an appropriate scaling of the transmission conditions is used. Moreover, we prove that optimized two-sided Robin conditions lead to mesh-independent convergence. Numerical experiments with two subdomains are presented to verify the analysis. We also report the results of experiments using the decomposition of a rectangle into many vertical strips; some additional analysis is carried out to improve the optimized transmission conditions in that case. / On a third topic, we experiment with different coarse space corrections for the Schwarz method in a simple one-dimensional setting, for both overlapping and non-overlapping subdomains. The goal is to obtain a convergence that does not deteriorate as we increase the number of subdomains. We design a coarse space correction for the Schwarz method with Robin transmission conditions by considering an augmented linear system, which avoids merging the local approximations in overlapping regions. With numerical experiments, we demonstrate that the best Robin conditions are very different for the Schwarz iteration with, and without coarse correction.

Let Ω be a Lipschitz domain in Rᴺ,n ≥ 3, and L = divA∇ - B∇ be a second order elliptic operator in divergence form with real coefficients such that A is a bounded elliptic matrix and the vector field B ɛ L∞loc(Ω) is divergence free and satisfies the growth condition dist(X,∂Ω)|B(X)|≤ ɛ1 for ɛ1 small in a neighbourhood of ∂Ω. For these elliptic operators we will study on the basis of the theory for elliptic operators without drift terms the Dirichlet problem for boundary data in Lp(∂Ω), 1 < p < ∞, and the regularity problem for boundary data in W¹,ᵖ(∂Ω) and HS¹. The main result of this thesis is that the solvability of the regularity problem for boundary data in HS1 implies the solvability of the adjoint Dirichlet problem for boundary data in Lᵖ'(∂Ω) and the solvability of the regularity problem with boundary data in W¹,ᵖ(∂Ω for some 1 < p < ∞. In [KP93] C.E. Kenig and J. Pipher have proven for elliptic operators without drift terms that the solvability of the regularity problem with boundary data in W¹,ᵖ(∂Ω) implies the solvability with boundary data in HS1. Thus the result of C.E. Kenig and J. Pipher and our main result complement a result in [DKP10], where it was shown for elliptic operators without drift terms that the Dirichlet problem with boundary data in BMO is solvable if and only if it is solvable for boundary data in Lᵖ(∂Ω) for some 1 < p < ∞. In order to prove the main result we will prove for the elliptic operators L the existence of a Green's function, the doubling property of the elliptic measure and a comparison principle for weak solutions, which are well known results for elliptic operators without drift terms. Moreover, the solvability of the continuous Dirichlet problem will be established for elliptic operators L = div(A∇+B)+C∇+D with B,C,D ɛ L∞loc(Ω) such that in a small neighbourhood of ∂Ω we have that dist(X,∂Ω)(|B(X)| + |C(X)| + |D(X)|) ≤ ɛ1 for ɛ1 small and that the vector field B satisfies |∫B∇Ø| ≤ C∫|∇Ø| for all Ø ɛ Wₒ¹'¹ of that neighbourhood.

Children with impaired emotion knowledge are likely to also experience difficulties with social skills (Bukato, 2008) and internalising and externalising behaviour problems (Trentacosta & Fine, 2009, Fine et al, 2003). Given that children with developmental disabilities are both at risk of developing behaviour problems (Roberts & Lawton, 2001), and may have impairments in emotion knowledge (Wishart et al, 2007, Kasari et al, 2001, Sinzig et al, 2008; Bal et al, 2010), teaching emotion knowledge skills is likely to be beneficial in helping to ameliorate the risks faced by these children, for developing behaviour problems. The research question investigated in this study was; can using an adapted version of the PATHS programme with children and adolescents aged between 9 and 18, who have developmental disabilities, improve both their emotion knowledge and their behaviour problems? Four participants were recruited, aged between nine and 18 who had developmental disabilities, one of whom served as a pilot participant. The intervention was carried out in the participants’ homes, with two one hour-long sessions a week. The measurements used included the Vineland-II, a behaviour diary and the Emotion Knowledge Test (EKT) - designed specifically for this research by the researcher. All participants included in the main study made improvements on the sentence-labelling task but not on the photograph-labelling task of the EKT. Participants 2 and 4 improved in regards to the number of problem behaviours displayed each week, Participant 3’s problem behaviours did not occur often enough to determine whether improvements had been made. Participant 2 improved on both of the Socialisation and Maladaptive Behaviour domains of the Vineland-II, Participant 3 improved on the Socialisation domain and Participant 4 improved on the Maladaptive Behaviour Domain, however all improvements made were small. The results indicate that there may be promise with using the PATHS programme with children with developmental disabilities, in one-to-one settings. However this research involved several limitations, such as the reliability and sensitivity of the measures used and the short length of the baseline and intervention periods. More research is needed in this area, as there are many possible social, emotional and academic benefits for these children, using the skills taught in the PATHS programme.

The purpose of this study was to investigate the effectiveness of two teaching methods, based on diverse principles of psychotherapy, with groups of children manifesting disturbed behavioral patterns. One of the methods was based on principles of behavior modification and the other on high levels of facilitative conditions, or relationship therapy. The variables of experimental interest were arithmetic achievement, adaptive overt behavior and personality adjustment as indicated on several indices. The study attempted to elicit inferences regarding the teaching of adaptive behaviors and cognitive skills to a population of withdrawn children. The comparative effects of the two distinct sets of psychotherapeutic principles were of special interest in this study.The research was conducted in the Marion, Indiana Public Schools. A total of 20 children, 10 in each group, participated in this study. These children were all fourth-graders, selected from the regular classroom. Behaviors of the subjects qualified for the label "emotionally disturbed."They all displayed withdrawn behavior.Careful control was exercised in selecting the teachers for the two experimental groups. A teacher preferring structure and order assumed the instructional responsibility for the behavior modification group. The teacher selected for the relationship group was characterized as a highly sensitive, warm individual. Intermittent consultation was provided each teacher throughout the experiment.The subjects in the experimental groups were compared, on pre and post measures, on the basis of group means and standard deviations, as to IQ, achievement level, grade level, and degree of personality adjustment. Personality adjustment was contingent upon three measures; teacher ratings, peer perceptions, and performance on selective factors on a standardized inventory. The experiment continued for thirteen weeks.In testing for significant differences on educational achievement, the analysis of covariance was used. The Mann-Whitney U was used to test for significant differences on all indices of personality adjustment. Overt adaptive responses during the experimental period were presented graphically. Assessments for variables within each group were also treated graphically.Findings1. The behavioristic educative method was superior to the relationship educative method in enhancing educational achievement. The significance level was established at the .05 level.2. There were no significant differences between the two groups based on teacher perceptions.3. There were no significant differences between the two groups based on peer perceptions.4. In regard to the six factors from the standardized instruments significant differences were found in two instances, at the .05 and .01 levels, both favoring the relationship approach.5. The relationship approach was better than the behavioristic approach in fostering overt, adaptive behavior in the experimental setting.6. In regards to arithmetic achievement within each group, the behavioristic group made an average gain of 1.2 years and the relationship group 0.8 years in grade levels.7. With respect to peer perceptions in each group, the change from pre-test to post-test was very marginal for both groups.8. On all six factors studied on the standardized inventory, pre-test performance of the behavioristic and relationship groups were below average. On the post-test the behavioristic groupperformed average or better on 3 of the 6 factors. The relationship group performed average or better on 4 of the 6 factors.The findings suggest a behavioristic approach is better in fostering arithmetic achievement in withdrawn children. In regard to personality adjustment and overt, adaptive behavior a relationship approach was suggested as being superior by the study.

This dissertation describes research conducted on the development and improvement of microwave tomography algorithms for imaging the bulk-electrical parameters of unknown objects. The full derivation of a new inversion algorithm based on the state-of-the-art contrast source inversion (CSI) algorithm coupled to a finite-element method (FEM) discretization of the Helmholtz differential operator formulation for the scattered electromagnetic field is presented. The algorithm is applied to two-dimensional (2D) scalar and vectorial configurations, as well as three-dimensional (3D) full-vectorial problems. The unknown electrical properties of the object are distributed on the elements of arbitrary meshes with varying densities. The use of FEM to represent the Helmholtz operator allows for the flexibility of having an inhomogeneous background medium, as well as the ability to accurately model any boundary shape or type: both conducting and absorbing. The CSI algorithm is used in conjunction with multiplicative regularization (MR), as it is typical in most implementations of CSI. Due to the use of arbitrary meshes in the present implementation, new techniques are introduced to perform the necessary spatial gradient and divergence operators of MR. The approach is different from other MR-CSI implementations where the unknown variables are located on a uniform grid of rectangular cells and represented using pulse basis functions; with rectangular cells finite-difference operators can be used, but this becomes unwieldy in FEM-CSI. Furthermore, an improvement for MR is proposed that accounts for the imbalance between the real and imaginary parts of the electrical properties of the unknown objects. The proposed method is not restricted to any particular formulation of the contrast source inversion. The functionality of the new inversion algorithm with the different enhancements is tested using a wide range of synthetic datasets, as well as experimental data collected by the University of Manitoba electromagnetic imaging group and research centers in Spain and France.

We introduce two online models for the vertex k-center and the vertex k-median problems. Clients (i.e., graph vertices) and their corresponding links (i.e., graph edges) are revealed sequentially, determining the topology of a graph over time. Clients are revealed by an adversary to an online algorithm that selects existing graph vertices on which to open facilities; once open, a facility cannot be removed or relocated. We define two models: an online algorithm may be restricted to open a facility only at the location of the most recent client or at the location of any existing client. We examine these models on three classes of graphs under two types of adversaries. We establish lower bounds on the respective competitive ratios attainable by any online algorithm for each combination of model, adversary, and graph class. Finally, we describe algorithms whose competitive ratios provide corresponding upper bounds on the best competitive ratios achievable.

The solution of convection-diffusion problems is a challenging task for numerical methods because of the nature of the governing equation, which includes a non-dissipative component and a dissipative component. Once the convection-diffusion equation is discretised, it is usual to observe oscillations in the computed solution regardless of whether these might be expected in the original physical situation. Mostly these oscillations are the result of numerical instability. This thesis centres on this fundamental difficulty: the numerical stability of finite difference discretisation of a convection-diffusion equation. The existence of an exact evolution operator for the constant coefficient convection diffusion problem is the framework we use to derive new finite difference schemes in one and two dimensions and also, when a high-order scheme is considered, to derive numerical boundary conditions. The influence of numerical boundary conditions on the stability of a general scheme is one of the main themes. The stability analysis is done mostly by using the von Neumann method and the matrix method. The Godunov-Ryabenkii theory is also applied to the one dimensional case. In two dimensions we deduce different forms of second-order (Lax-Wendroff) schemes and third-order (Quickest) schemes. We apply some of those schemes to a Navier-Stokes problem by running experiments to illustrate the practical stability region, showing how results from a simpler case presented in previous chapters carry over to the more complex case.

I dagens samhälle finns det ett stort antal elever som har språksvårigheter i matematikämnet, vilket påverkar elevernas prestationer vid lösningar av matematiska textuppgifter. Denna fallstudie syftar till att undersöka pedagogers och elevers perspektiv när det gäller språksvårigheter inom matematiska textuppgifter. Vi belyser även hur pedagogerna tar hänsyn till elever som har språksvårigheter och hur de agerar för att hjälpa och stötta dem i textuppgifter. Vi blev intresserade av att lyfta fram elevers affektiva och kognitiva hantering av matematiska textuppgifter eftersom vi har personliga erfarenheter om detta sedan tidigare. Fallstudien är uppbyggd kring kvalitativa intervjuer och observationer. I studien deltog 2 klasslärare, en specialpedagog och 24 elever. Resultatet visar att det finns elever som har språksvårigheter inom matematiska textuppgifter på grund av olika påverkande faktorer. Alla pedagoger i intervjuerna är överens om att elevers prestationsförmåga inom matematikförståelse kan bli påverkade av olika faktorer. Pedagoger samarbetar för att hjälpa och stötta dessa elever genom att använda olika metoder och arbetssätt. Språkförståelsen och svåra matematiska begrepp i textuppgifter kan leda till att olika kognitiva och affektiva svårigheter kan dyka upp vid hanteringen av matematiska textuppgifter. Vissa elever var väldigt motiverade i att klara av textuppgifterna, medan andra med svårigheter i språkförståelse fann uppgifternas nivå och struktur alldeles för krävande.

No description available.