Conics and Geometry is a report that focuses on the development of new approaches in mathematics by breaking from the accepted norm of the time. The conics themselves have their beginning in this manner. The author uses three ancient problems in geometry to illustrate this trend. Doubling the cube, squaring the circle, and trisecting an angle have intrigued mathematicians for centuries. The author shows various approaches at solving these three problems: Hippias’ Quadratrix to trisect an angle and square the circle, Pappus’ hyperbola to trisect an angle, and Little and Harris’ simultaneous solution to all three problems. After presenting these approaches, the focus turns to the conic sections in the non-Euclidean geometry known as Taxicab geometry. / text

Under consideration are two-point boundary value problems for a system of second order differential equations which contains a small parameter multiplying the highest dereivatives. We prove the existence of solutions exhibiting left and right boundary layers by constructing upper and lower solutions of the system. The behavior of the solutions as the parameter tends to zero is also established. Of special interest is the existence of a compound boundary layer (i.e., one involving two scales) at the left endpoint of the interval.

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No description available.

Spectral geometry is a mathematical discipline that studies the relationship between the geometry of Riemannian manifolds and the spectra of natural differential operators defined on them. The spectra of Laplacians are the ones most studied in this context. A sub-field of this discipline, called inverse spectral geometry, studies how much geometric information one can recover from such spectra. The motivation behind our study of inverse spectral geometry is a physical one. It has recently been proposed that inverse spectral geometry could be the missing mathematical link between quantum field theory and general relativity needed to unify those theories into a single theory of quantum gravity. Unfortunately, this proposed link is not well understood. Most of the efforts in inverse spectral geometry were historically concentrated on the generation of counterexamples to the most general formulation of inverse spectral geometry and the few positive results that exist are quite limited. In order to remedy to that, it has been proposed to linearize the problem, and study an infinitesimal version of inverse spectral geometry. In this thesis, I begin by reviewing the theory of pseudodifferential operators and using it to prove the spectral theorem for elliptic operators. I then define the commonly used Laplacians and survey positive and negative results in inverse spectral geometry. Afterwards, I briefly discuss a coordinate free reformulation of Riemannian geometry via the notion of spectral triple. Finally, I introduce a formulation of inverse spectral geometry adapted for numerical implementations and apply it to the inverse spectral geometry of a particular class of star-shaped domains in ℝ².

Lietuvos švietimo politikoje, moksliniuose darbuose vis didesnis demesys skiriamas vaikų adaptacijos problemoms mokykloje. Pedagoginėje spaudoje daug rašoma adaptacijos klausimais. Kur kas sunkiau mokiniams adaptuotis sanatorijos mokykloje. Kadangi jie patenka į visiškai naują aplinką. Atsižvelgiant į esamą situaciją, iškyla tyrimo problema, į gydymo įstaigos mokyklą atvykę mokiniai patiria adaptacijos sunkumų. Tyrimo objektas – Kačerginės vaikų sanatorijos „Žibutė“ mokykloje besimokančių mokinių adaptacija. Tyrimo tikslas – ištirti mokinių adaptacijos procesą lydinčius sunkumus ir priežastis. Tyrimo metu gauti rezultatai padės: - Kačerginės vaikų sanatorijos „Žibutė“ mokykloje mokinių adaptacijos sunkumams pašalinti. Tyrimas parodė, kad saugus mikroklimatas gydymo įstaigos mokykloje yra būtinas. Didžioji dalis respondentų nurodė, kad adaptacijos sunkumus palengvintų mokytojų teigiamas požiūris į kiekvieną vaiką, kaip į asmenybę, šiltesni mokinių tarpusavio santykiai, didesnis ir artimesnis bendravimas su vaiku, didesnis pačios sanatorijos medikų ir mokyklos bendradarbiavimas. / In Lithuanian education policy, scientific works more and more attention is paid to problems of adaptation of children at school. There are many articles on the issues of adaptation in pedagogical press. It is much more difficult for children to adapt in the school of sanatorium. As they find themselves in absolutely new surroundings. Taking into account the current situation research problems arise, the pupils who come to the school of the medical establishment face adaptation difficulties. The object of research is the adaptation of pupils of school “Zibute” of Kacergine children sanatorium. The objective of research is to analyze the difficulties and reasons of the adaptation process. The results obtained during the research will help to eliminate adaptation difficulties for pupils of school “Zibute” of Kacergine children sanatorium. The research showed that safe microclimate in the school of the medical establishment is obligatory. The majority of respondents indicated that positive attitude of teachers to every child as a personality, warmer relationships among the pupils, more and closer communication with the child, better cooperation of the medics of the sanatorium and the school would facilitate the difficulties of adaptation.

This thesis is an investigation of the needs and experiences of transition-aged youth with emotional and/or behavioural problems who accessed mental health services at a local child and adolescent clinic. Longitudinal studies have demonstrated that youth with mental health problems tend to have poor outcomes in adulthood. Moreover, many young adults do not make the transition from child- to adult-focused care even when they acknowledge their need for support. This study used a mixed methods approach, consisting of a survey design and phenomenological inquiry. In general, participants did not appear ready for an institutional transition, reporting only moderate levels of mental health self-efficacy. Youth disclosed their fears, underscoring the importance of supportive relationships, and stated the negative expectations they had concerning adult-focused care. The implementation of clinical supports to increase transition-aged youths’ mental health self-efficacy, by actively involving them in service-related decision-making processes, are likely to promote successful service transitions.

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No description available.

No description available.