In this paper we will study the 1p spaces. We will begin with definitions and different examples of 1p spaces. In particular, we will prove Holder's and Minkowski's inequalities for 1p sequence.

Orientador: Maria Aparecida Viggiani Bicudo / Resumo: A continuidade é um tema que sempre trouxe desafios aos filósofos e matemáticos, desde a Grécia antiga com os paradoxos sobre o movimento, que persistem até os dias atuais, quando nos encontramos discutindo a continuidade da consciência e do tempo. Com o advento da tecnologia digital uma perspectiva se abre nessa discussão, pois modelos matemáticos contínuos estão sendo aplicados a problemas numéricos computacionais, que são caracteristicamente discretos. Essa possível discretização do contínuo mostra-se de modo claro, levando-nos a investigar a presença do contínuo ao se produzir Matemática junto ao computador. Investigaremos esse assunto realizando um movimento característico do pensar filosófico, tomando o tema como uma lectio, entendida como momento de discussão sobre textos numa dimensão argumentativa filosófica sobre nossa interrogação de pesquisa, ou seja, nossa quaestio. Nossa compreensão dos textos é exposta de maneira articulada e dividida em três seções, que versam sobre os estudos realizados no âmbito das Ciências Matemática, Filosofia e Computação. Finalizaremos trazendo uma meta-compreensão dos estudos realizados, tomando como centro articulador da reflexão a interrogação formulada. Nosso objetivo com esse exercício filosófico é compreender o fenômeno “contínuo-discreto” na região de inquérito das Ciências Ocidentais e sua presença na computação / Abstract: Continuity has been a challenging topic to philosophers and mathematicians, since the ancient Greece, with paradoxes of movement, until present days when continuity of consciousness and of time are discussed. With the advent of digital technology another perspective has brought into the discussion, because continuous mathematical models are being applied in numerical computational problems, which are characteristically discrete. This possibility of continuos’ discretization is drawing our attention. Therefore, this research aims to understand the presentification of continuous when we are producing Mathematics with computers. We will investigate this subject via a philosophical approach. This thesis is constituted as a lectio, understood as a moment of discussion about texts in a philosophical argumentative dimension about our research question, that is, our quaestio. Our understanding of the texts is articulated and divided into three sections, which deal with the studies carried out in Mathematics, Philosophy and Computer Science. Our goal with this philosophical exercise is to explore the "continuous-discrete" phenomenon under Western Sciences influence and its presence in computation. / Doutor

Continuum manipulators which are robot limbs inspired by trunks, snakes, and tentacles, represent a promising field in robotic manipulation research. They are well known for their compliance, as they can conform to the shape of objects they interact with. Furthermore, they also benefit from improved dexterity and reduced weight compared to traditional rigid manipulators. The current state of the art continuum robots typically consists of a bulky pneumatic or tendon-driven actuation system at the base, hindering their scalability. Additionally, they tend to sag due to their own weight and are weak in the torsional direction, limiting their performance under external load. This work presents an origami-inspired cable-driven continuum manipulator module that offers low-cost, light-weight, and is inherently safe for human-robot interaction. This dissertation includes contributions in the design of the modular and torsionally strong continuum robot, the motion planning and control of the system, and finally the embedded sensing to close the loop providing robust feedback.

The oratorio August 4, 1964 is a twelve-movement work for orchestra, chorus, and four soloists written by Steven Stucky. The premise for the libretto, adapted by Gene Scheer, is the confluence of two events during one day (August 4, 1964) in the life of Lyndon B. Johnson. Although the main idea of the libretto focuses on these two events of this one day, many cultural references of the 1960's in general can be found as well, such as quotations from the well-known song "We Shall Overcome." Stucky borrows from a motet he wrote in 2005 for another quotation source utilized in this oratorio, "O Vos Omnes." My goal in this thesis is to reveal and analyze the many different levels of quotations that exist within August 4, 1964, to explore each quotation's individual function within the oratorio (as a cultural gesture, commentary or remembrance), and to examine the structural coherence that emerges as a result of their use within the oratorio.

Recent advances in non-local continuum models, notably peridynamics, have spurred a paradigm shift in solid mechanics simulation by allowing accurate mathematical representation of singularities and discontinuities. This doctoral work attempts to extend the use of this theory to a community more familiar with local continuum models. In this communication, a coupling strategy - the morphing method -, which bridges local and non-local models, is presented. This thesis employs the morphing method to ease use of the non-local model to represent problems with failure-induced discontinuities. First, we give a quick review of strategies for the simulation of discrete degradation, and suggest a hybrid local/non-local alternative. Second, we present the technical concepts involved in the morphing method and evaluate the quality of the coupling. Third, we develop a numerical tool for the simulation of the hybrid model for fracture and damage and demonstrate its capabilities on numerical model examples

abstract: The term Poly-Limb stems from the rare birth defect syndrome, called Polymelia. Although Poly-Limbs in nature have often been nonfunctional, humans have had the fascination of functional Poly-Limbs. Science fiction has led us to believe that having Poly-Limbs leads to augmented manipulation abilities and higher work efficiency. To bring this to life however, requires a synergistic combination between robot manipulation and wearable robotics. Where traditional robots feature precision and speed in constrained environments, the emerging field of soft robotics feature robots that are inherently compliant, lightweight, and cost effective. These features highlight the applicability of soft robotic systems to design personal, collaborative, and wearable systems such as the Soft Poly-Limb. This dissertation presents the design and development of three actuator classes, made from various soft materials, such as elastomers and fabrics. These materials are initially studied and characterized, leading to actuators capable of various motion capabilities, like bending, twisting, extending, and contracting. These actuators are modeled and optimized, using computational models, in order to achieve the desired articulation and payload capabilities. Using these soft actuators, modular integrated designs are created for functional tasks that require larger degrees of freedom. This work focuses on the development, modeling, and evaluation of these soft robot prototypes. In the first steps to understand whether humans have the capability of collaborating with a wearable Soft Poly-Limb, multiple versions of the Soft Poly-Limb are developed for assisting daily living tasks. The system is evaluated not only for performance, but also for safety, customizability, and modularity. Efforts were also made to monitor the position and orientation of the Soft Poly-Limbs components through embedded soft sensors and first steps were taken in developing self-powered compo-nents to bring the system out into the world. This work has pushed the boundaries of developing high powered-to-weight soft manipulators that can interact side-by-side with a human user and builds the foundation upon which researchers can investigate whether the brain can support additional limbs and whether these systems can truly allow users to augment their manipulation capabilities to improve their daily lives. / Dissertation/Thesis / Doctoral Dissertation Systems Engineering 2020

Syfte: I denna studie undersöktes bildterapeuters berättelser om hur de arbetar med affektmedvetenhet i bildterapi. Metod: En kvalitativ studiedesign användes genom semistrukturerade intervjuer med fyra bildterapeuter. För att utvinna data valdes tematisk analys. Bearbetning av intervjuerna utgick ifrån fyra dimensioner av affektmedvetenhet enligt Monsen, Eilertsen, Melgård och Ødegård (1996): Uppmärksamma, Tolerera, Icke-verbalt uttryck samt Verbalt uttryck av känslor. Resultat: Analysen av intervjuerna resulterade i nio teman/bildterapeutiska arbetssätt för ökad affektmedvetenhet hos klienten: Lägga märke till känslor, Synliggöra omedvetna känslor, Synliggöra mer medvetna känslor, Växla mellan tanke och känsla, Reglera överväldigande känslor, Omstrukturera, Kroppsfokus, Öppna bilden och Låna bilden. Slutsats: Genom om att belysa bildterapimetoder med fokus på affektmedvetenhet tydliggörs viktiga tekniker och aspekter, såväl icke-verbala som verbala. Resultatet kan generera idéer till interventionsforskning kring bildterapeutiskt arbete med affekter. / Aims: In this study, art therapists' stories of how they work with affect awareness in art therapy were examined. Methods: A qualitative study design was used with semi-structured interviews with four art therapists. The thematic analysis was based on four dimensions of affect awareness: Affect awareness, Affect tolerance, Nonverbal and Conceptual expression of affect (Monsen, Eilertsen, Melgård & Ødegård 1996). Results: Analysis of the interviews resulted in nine themes/art therapy methods for increased affect awareness: Paying attention to affect, Highlighting unconsiousnes affects, Highlighting more aware affects, Switching between thought and affect, Regulate overwhelming affects, Restructure, Body focus, Opening the image and Borrowing the image. Conclusion: By highlighting art therapy methods focusing on affect awareness, important techniques and aspects, both non-verbal and verbal, are clarified. The result can generate ideas for intervention research on art therapy with affects.

<p>In today’s evolving classrooms, educators are tasked with going beyond providing the necessary content knowledge to reach the needs of their students. In addition to effectively differentiating instruction, global competency skills have become an increasingly pressing concern as the American society gradually becomes more diverse. In response, recent programs and supports have been created to allow prospective teacher candidates to develop their global competence to better meet the needs of an increasingly diverse and globally connected society.</p><p>An explanatory sequential mixed methods research design examined how participation in a short-term study abroad can impact teachers’ empathetic dispositions related to globally competent teaching practices. Quantitative data was first collected through an online Qualtrics questionnaire from pre-service, in-service, and other agricultural educators (n=36) who participated in a short-term study abroad experience in Jamaica from 2015-2019. Following the online questionnaire, four virtual follow-up focus groups were conducted via Zoom to further explore the collection and analysis of study participants’ self-rated stage of empathy development along the Globally Complement Teaching and Learning Continuum. Inductive coding revealed themes for both internal and external factors influencing study participants’ rationale and desired movement along the continuum.</p><p>Overall, participants acknowledged the transformative experience during the short-term study abroad to Jamaica as an external factor for building competence in the dispositions element of empathy and valuing multiple perspectives. Implications for practice and suggestions for future research were provided to help agricultural educators develop globally competent teaching practices.</p>

The purpose of this qualitative study was to determine the cultural competence of district leaders and their potential resulting influence on campus leaders in the face of a rapidly changing educational and community landscape. A secondary purpose was to ascertain district and school leaders' placement on the cultural proficiency continuum to gain a greater understanding of (a) the potential effect, if any, that district leaders' level of cultural competency had on the cultural competency of campus leaders, and (b) how the cultural competency level of both district and campus leaders influenced district policies, practices, and school climate. The analysis and interpretation of findings of this research study were based on a conceptual framework, informed by the six constructs of the cultural proficiency continuum as developed by R. Lindsey, Nuri-Robins, D. Lindsey and Terrell. Four district office leaders and three campus principals, from the same district, were selected as participants. The campus principals represented elementary, middle, and high schools. Data were gathered from semi-structured face-to-face interviews with each participant, three meeting observations, and document analysis. Findings revealed evidence of a strong relationship between district leaders' cultural competence, campus principals' cultural competence, and district policies and procedures. There was also a direct relationship between the district leaders' cultural competence levels and their direct reports' level of cultural competence. This study can afford school districts an opportunity to recognize the value and implications of culturally proficient leaders, as they serve all students.

Sedimentation is a fundamental operation in wastewater treatment works. A rational design of sedimentation tanks is currently achieved by plotting iso-percentile (iso-percentage) concentration removal profiles from flocculent settling data. A major drawback of the graphical iso-percentage method is that the iso-percentile lines are often manually interpolated and are mere hand drawn estimations. This is because the settling behaviour of sludge particles is highly non-linear. The manual analytical process is therefore very tedious, inaccurate and subjective. Hence, an optimised design of sedimentation tanks is necessary in order to eliminate the errors incurred during data analysis. In this study, a mechanistic iso-percentile flocculent model (referred to as the velocity flocculation model) is developed to simulate the behaviour of flocculating colloidal particles in turbid water. This model is based on the physical meanings of flocculent settling particles and on fractal theory. It is formulated to produce automated iso-percentile curves which are fundamental in the design of sedimentation tanks. The iso-percentile model was vertically integrated into a velocity model to produce a model expressing the velocity of particles as a function of removal rate. The velocity model has an obvious advantage over the iso-percentile model in that it is easy to contextualize. It can be reverted back to the iso-percentile trajectory analysis eliminating the need for extensive data interpolation and may in future eliminate the need for settling column analysis altogether. In the current study, the integrated velocity form is used to predict instantaneous flocculent settling velocity of fine suspended particles under near quiescent conditions. This is vital since it is difficult to obtain velocity values in-situ or directly from sedimentation tanks. Model validity and competency was tested by a direct comparison with existing literature models, such as Ozer’s model and Ramatsoma and Chirwa’s model. Model comparison was based on the goodness of fit, the least sum of square errors and mathematical consistency with known flocculent settling behaviour. The newly developed iso-percentile model achieved a more accurate simulation of physical experimental data, did not violate any of the mathematical constraints and yielded lower sum of square errors than originally achieved by Ozer and Ramatsoma and Chirwa. Notably, the proposed velocity model offers a distinctive advantage over conventional interpolated-iso-percentile based models which are prone to numerical errors during interpolation. Its performance (velocity model) was compared against Je and Chang’s velocity model. Higher velocity values were observed for the new model than for Je and Chang’s model implying that empirically based models would tend to under-predict the velocity values. The model developed in this study brings us one step closer to achieving full automation of the settling tank and clarifier design. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Chemical Engineering / unrestricted