The thesis describes the theory and design of a general problem-solving system. The system uses a single general heuristic based on a formal definition of differences within the framework of means/ends analysis and employs tree search during problem solution. A comparison is made with two other systems using means/ends analysis. The conditions under which the system is capable of solving problems are investigated and the efficiency of the system is considered. The system has solved a variety of problems of varying complexity and the difference heuristic appears comparatively accurate for goal-directed search within certain limits.

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In this paper we study the uniqueness of positive solutions as well as the non existence of sign changing solutions for Dirichlet problems of the form $$\eqalign{\Delta u + g(\lambda,\ u) &= 0\quad\rm in\ \Omega,\cr u &= 0\quad\rm on\ \partial\Omega,}$$where $\Delta$ is the Laplace operator, $\Omega$ is a region in $\IR\sp{N}$, and $\lambda>0$ is a real parameter. For the particular function $g(\lambda,\ u)=\vert u\vert\sp{p}u+\lambda$, where $p={4\over N-2}$, and $\Omega$ is the unit ball in $\IR\sp{N}$ for $N\ge3$, we show that there are no sign changing solutions for small $\lambda$ and also we show that there are no large sign changing solutions for $\lambda$ in a compact set. We also prove uniqueness of positive solutions for $\lambda$ large when $g(\lambda,\ u)=\lambda f(u)$, where f is an increasing, sublinear, concave function with f(0) $<$ 0, and the exterior boundary of $\Omega$ is convex. In establishing our results we use a number of methods from non-linear functional analysis such as rescaling arguments, methods of order, estimation near the boundary, and moving plane arguments.

Thesis (Ph. D.)--University of Oregon, 2004. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 130-136). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (M.S.)--University of Wisconsin--Madison, 1969. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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Bakgrund Sömn och matproblem är vanliga hos små barn. Bekymren kan vara stora och föräldrarna i behov av professionell hjälp. Barnavårdscentralerna har stor stöd- och hjälpfunktion men inte alltid resurser för detta. I Uppsala län finns en specialbarnavårdscentral som erbjuder råd och stöd vid dessa problem. Syfte med studien var att studera föräldrarnas bedömning av barnets sömn- eller matproblem före och efter kontakt med Special-BVC, samt om det fanns ett samband mellan antal kontakter och föräldrarnas bedömning av barnets situation efter avslutat kontakt. Metod Designen var en deskriptiv, komparativ studie där 67 av 102 (66 %) föräldrar besvarade frågor om förhållanden före och efter kontakt med Special-BVC. Resultat Inom flera områden minskade barnens sömn- eller matproblem efter kontakten med enheten. Emellertid bedömde föräldrar till barn med matproblem att dessa fortfarande var ett problem för barnet men inte för familjen medan barns problem gällande sömn minskat både för barnet och familjen. Diskussion Kvalitetssäkring av vårdverksamheters resultat är viktigt. Studien visade att Special-BVCs arbete ledde till en förbättrad situation för familjerna. Barnen hade haft sina problem länge, i genomsnitt tio månader. Många familjer borde kunna få hjälp på sin ordinarie BVC genom primärprevention eller genom tidiga sekundärpreventiva åtgärder. Special-BVCs arbetsmetodik borde därför spridas till den ordinarie BVC-verksamheten. / Background Sleeping and feeding problems are common in young children. The problem can be large and the parents need professional help. The Child Health Clinics aim to give help but hasn’t always enough resources. In Uppsala, a Specialist Child Health Team (Special-BVC) provides help to families with special needs. Aim was to study parents’ assessment of their child’s sleep or feeding problems before and after contact with "Special-BVC" and the relation between number of contacts and the child’s situation after the contact. Method The design was a descriptive, comparative study where 67 of 102 (66%) parents answered two questionnaires measuring the situation before and after contact with Special-BVC. Results In many areas the children's sleep or feeding problems decreased after the contact. Parents to children with food problems thought the child’s situation still was a problem for the child but not for the family, whereas parents to children with sleeping problems thought the problematic situation hade improved both for the child and the family. Discussion Quality assurance of care is important. The study showed the work done by Special-BVC improved the situation for the families. The children had had their problems a long time, an average of ten months. Many families should be help from their regular child health clinics through primary prevention or earlier secondary prevention. The working methods used at the Special-BVC should be disseminated to the regular child health clinics.

In this thesis, we study the inverse nodal problem and inverse spectral problem for various Sturm-Liouville operators, in particular, Hill's operators. We first show that the space of Schr"odinger operators under separated boundary conditions characterized by ${H=(q,al, e)in L^{1}(0,1) imes [0,pi)^{2} : int_{0}^{1}q=0}$ is homeomorphic to the partition set of the space of all admissible sequences $X={X_{k}^{(n)}}$ which form sequences that converge to $q, al$ and $ e$ individually. The definition of $Gamma$, the space of quasinodal sequences, relies on the $L^{1}$ convergence of the reconstruction formula for $q$ by the exactly nodal sequence. Then we study the inverse nodal problem for Hill's equation, and solve the uniqueness, reconstruction and stability problem. We do this by making a translation of Hill's equation and turning it into a Dirichlet Schr"odinger problem. Then the estimates of corresponding nodal length and eigenvalues can be deduced. Furthermore, the reconstruction formula of the potential function and the uniqueness can be shown. We also show the quotient space $Lambda/sim$ is homeomorphic to the space $Omega={qin L^{1}(0,1) : int_{0}^{1}q = 0, q(x)=q(x+1) mbox{on} mathbb{R}}$. Here the space $Lambda$ is a collection of all admissible sequences $X={X_{k}^{(n)}}$ which form sequences that converge to $q$. Finally we show that if the periodic potential function $q$ of Hill's equation is single-well on $[0,1]$, then $q$ is constant if and only if the first instability interval is absent. The same is also valid for convex potentials. Then we show that similar statements are valid for single-barrier and concave density functions for periodic string equation. Our result extends that of M. J. Huang and supplements the works of Borg and Hochstadt.

This study employed thinking aloud and semi-structured interviews to explore problem-solving representations, problem-solving processes, and problem-solving strategies of six grade seven students on word problems of linear equation in one variable. The instrument of the study was a researcher-designed test with literal, graphics and/or symbolic descriptions and was examined and revised by three senior secondary mathematics teachers. According to their mathematics scores of 3rd midterm exam last semester, students were divided into three achievement groups¡Ð¡Ðlow achievement group (the lowest 27%)¡Amiddle achievement group (46%) and high achievement group (the highest 27%). One subject was selected from each of middle and high achievement groups of three grade seven classes. Six subjects, in total, had taken thinking aloud training for three weeks, and then they took the paper and pencil test individually with a follow-up interview. All the processes of individual tests and interviews were video recorded. The videotapes were transcribed and provided the major evidence of the analyses of participants¡¦ performances of problem-solving processes, their problem-solving representations, and their problem-solving strategies. The results of problem-solving representation, problem-solving process, and problem-solving strategy were reported separately as follows: (1)Problem-solving representation. Participants applied literal, algebraic and numeral representations to solve one-variable leaner equation problems more often than used graphic one. (2)Problem-solving process. (a)When graphic representation was applied in this test, the time of problem solving could be shortened effectively. (b)The times that Participants repeat to read and analyze the topic increased relatively in the topics with more writing narration. (c)In more than one half of the fault problem-solving cases, the three stages of exploration, implementation, and planning were administered simultaneously. (d)The more verification was applied during participant¡¦s problem-solving process, his/her opportunity of success was higher. (e)Verification was often administered in problems with complex computations or questionable topics. (f)The relevance was higher between problem content and daily life, the opportunity of success was higher. (g)The time that the high achievement group used to solve problems was shorter than the middle achievement group used, and the opportunity of success was also higher than the middle achievement group. (3)Problem-solving strategy. (a)The problem-solving strategies applied by participants of high achievement group were more consistent, and the problem-solving strategies among participants of middle achievement group were more diverse. (b)The problem-solving strategies that participants often used to solve word problems of linear equations in one variable were translating the word problem into an equation, simplification of equation by collecting terms, using inverse operations, and properties of equality.

Thesis (Ph. D.)--University of Oregon, 2001. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 133-139). Also available for download via the World Wide Web; free to University of Oregon users.