Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that conceptually introduce derivatives in four calculus textbooks. One widely used calculus textbook was selected for the study in each of the four categories: U.S. college, U.S. high school, China college, and China high school. Two qualified investigators and I conducted the study. We used a framework of five developmental levels for covariational reasoning. The conceptual analysis of four calculus textbooks found that the U.S. college and the U.S. high school textbooks emphasize the average and instantaneous rate of change. However, both lack development of the direction and magnitude of change. On the other hand, this study's Chinese high school calculus textbook has a greater degree of development in the direction and magnitude of change while having a deficit in the average rate of change. This study's Chinese college calculus textbook does not have any meaningful development regarding covariational reasoning pedagogy. The relational analysis of the concepts previously identified in the conceptual analysis phase revealed that this study's U.S. college calculus textbooks provide abundant examples and exercises to transition between the average and instantaneous rate of change. On the other hand, all other calculus textbooks in this study lack any significant transition among passages that stimulate covariational reasoning. The textbook analysis in this study provides insights into the current focus of calculus textbooks in both the U.S. and China. In addition, the study has implications for learning and teaching calculus at both high school and college, as well as future editions of calculus textbooks. Finally, limitations and recommendations are discussed.

Studien behandlar fenomenet personaliserad marknadsföring, som har avancerats i dess tillämpning på senare år och har kommit att bli en hyperanpassad upplevelse för mottagaren. Individens informationsutlämnande är centralt för företagens möjlighet att tillämpa marknadsföringsstrategin och därav har det konstaterats att det finns både fördelar och risker med personaliserad marknadsföring, vilket belyses av personalisering- och integritetsparadoxen. Studiens syfte är att undersöka vilken påverkan identifierade fördelar och risker med informationsutlämnande har på konsumentens upplevda värde av personaliserad marknadsföring samt hur en tidigare positiv respektive negativ varumärkesimage kan påverka det upplevda värdet. En enkätundersökning används som forskningsmetod och vid dataanalys tillämpas stegvis modellering samt multipel linjär regressionsanalys. Resultatet visar att preferensmatchning, söktid och positiv varumärkesimage har en positiv påverkan på upplevt värde medan personlig integritet har en negativ påverkan. Därav accepteras hälften av studiens hypoteser. Slutsatsen är att marknadsföring som är anpassad efter konsumentens intressen och preferenser har störst påverkan på konsumentens upplevda värde av personaliserad marknadsföring samt att en tidigare positiv varumärkesimage har en positiv påverkan på det upplevda värdet.

Archaeological dental calculus represents a depositional environment that entraps oral microbes, and debris of dietary, environmental, and cultural material that entered the mouth throughout the host’s life. Hence, they represent valuable archives of information about the host’s lifestyle, health, and environment. The aim of this study was to identify if the farming transition and its’ associated change in diet composition, may have influenced species composition in the oral cavity. To shed some light into the evolution of ancient oral microbiomes from Africa, 3 novel Iron Age dental calculus metagenomes together with a comparative dataset of 18 archaeological dental calculus metagenomes from North African Upper Palaeolithic, Later Stone Age, Iron Age, and 18th-19th century populations where analysed. Shotgun sequencing data was used to reconstruct 21 oral metagenomes from the past 15,000 years. This study found an oral microbiome that has been maintained from the Upper Palaeolithic (North Africa) to the 19th Century. However, closer examination to the relative abundance of three keystone species of the subgingival plaque, portray a chronological evolution that reflects that of its host during the major dietary and cultural transition that occurred during the farming revolution in the Iron Age.

This qualitative research project is a three publishable articles dissertation that centers on two counternarrative-based case studies on The Calculus Project, a school-based program that is a Counternarrative Generator — a program that has produced hundreds of living counternarratives since its conception. The focal population of living counternarratives within this research project is young men of African descent who have achieved high mathematical outcomes in secondary education. The research design for Article 1 is a standard literature review that serves as a Practitioners Guide for secondary educators focusing on school-based ideologies, systems, and methodologies that produce high academic outcomes for males of African descent. Article 2 is a single-instrument, narrative case study that tells the story of The Calculus Project from the vantage point of the founder, Dr. Adrian Mims, from vision to program implementation. Article 3 is a narrative, collective case study which tells the story of The Calculus Project from the vantage points of three tiers of young men of African descent — participants in their final year of the program (Tier 1) and program graduates who are either in college (Tier 2) or have graduated from college (Tier 3) — that reveal personal testimonies regarding the powerful impact The Calculus Project had on the young men. Through careful data analysis, there were three observed themes in Article 2, seven observed themes in Article 3, and an observed overlap between the desired aims of the founder and the actual impact the program had on the participants. / 2029-07-31T00:00:00Z

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<p>The rapid growth of fields such as metamaterials, composites, architected materials, porous solids, and micro/nano materials, along with the continuing advancements in design and fabrication procedures have led to the synthesis of complex structures having intricate material distributions and non-trivial geometries. These materials find important applications including biomedical implants and devices, aerospace and naval structures, and micro/nano-electromechanical devices. Theoretical and experimental evidences have shown that these structures exhibit size-dependent (or, nonlocal) effects. This implies that the response of a point within the solid is affected by a collection of points; ultimately a manifestation of the multiscale deformation process. Broadly speaking, at a continuum level, the mathematical description of these multiscale phenomena leads to integral constitutive models, that account for the long-range interactions via nonlocal kernels. </p> <p><br></p> <p>Despite receiving considerable attention, the existing class of approaches to nonlocal elasticity are predominantly phenomenological in nature, following from their definition of the material parameters of the nonlocal kernel based on 'representative volume element' (RVE)-based statistical homogenization of the heterogeneous microstructure. The size of the RVE required for practical simulation, does not achieve a full-resolution of the intricate heterogeneous microstructure, and also implicitly enforces the use of symmetric nonlocal kernels to achieve thermodynamic consistency and mathematically well-posedness. The latter restriction directly limits the application of existing approaches only to the linear deformation analysis of either periodic or isotropic nonlocal structures. Additionally, the lack of a consistent characterization of the nonlocal effects, often results in inconsistent (also labeled as 'paradoxical') predictions depending on the nature of the external loading. In order to address these fundamental theoretical gaps, this dissertation develops a fractional-order kinematic approach to nonlocal elasticity by leveraging cutting-edge mathematical operators derived from the field of fractional calculus.</p> <p><br></p> <p>In contrast to the class of existing class of approaches that adopt an integral stress-strain constitutive relation derived from the equilibrium of the RVE, the fractional-order approach is predicated on a differ-integral (fractional-order) strain-displacement relation. The latter relation is derived from a fractional-order deformation-gradient mapping between deformed and undeformed configurations, and this approach naturally localizes and captures the effect of nonlocality at the root of the deformation phenomena. The most remarkable consequence of this reformulation consists in its ability to achieve thermodynamic and mathematical consistency, irrespective of the nature of the nonlocal kernel. The convex and positive-definite nature of the formulation enabled the use of variational principles to formulate well-posed governing equations, the incorporation of nonlinear effects, and enabled the development of accurate finite element simulation methods. The aforementioned features, when combined with a variable-order extension of the fractional-order continuum theory, enabled the physically consistent application of the nonlocal formulation to general continua exhibiting asymmetric interactions; ultimately a manifestation of material heterogeneity. Indeed, a rigorous theoretical analysis was conducted to demonstrate the natural ability of the variable-order in capturing the role of microstructure in the deformation of heterogeneous porous solids. These advantages allowed the application of the fractional-order kinematic approach to accurately and efficiently model the response of porous beams and plates, with random microstructural descriptions. Results derived from multiphysical loading conditions, as well as nonlinear deformation regimes, are used to demonstrate the causal relation between the kinematics-based fractional-order characterization of nonlocal effects and the natural role of microstructure in determining the macroscopic response of heterogeneous solids. The potential implications of the developed formalism on scientific discovery of material laws are examined in-depth, and different areas for further research are identified.</p>

<p>This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady state heat conduction described by elliptic partial differential equations (PDEs) and involving a one dimensional cooling element represented by an open contour. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least square sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using the conjugate gradient algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus combined with adjoint analysis. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary integral formulation. A number of computational aspects of the proposed approach is discussed and optimization results obtained in several test problems are presented.</p> / Master of Science (MSc)

Golog programs allow to model complex behaviour of agents by combining primitive actions defined in a Situation Calculus theory using imperative and non-deterministic programming language constructs. In general, verifying temporal properties of Golog programs is undecidable. One way to establish decidability is to restrict the logic used by the program to a Description Logic (DL), for which recently some complexity upper bounds for verification problem have been established. However, so far it was open whether these results are tight, and lightweight DLs such as EL have not been studied at all. Furthermore, these results only apply to a setting where actions do not consume time, and the properties to be verified only refer to the timeline in a qualitative way. In a lot of applications, this is an unrealistic assumption. In this work, we study the verification problem for timed Golog programs, in which actions can be assigned differing durations, and temporal properties are specified in a metric branching time logic. This allows to annotate temporal properties with time intervals over which they are evaluated, to specify for example that some property should hold for at least n time units, or should become specified within some specified time window. We establish tight complexity bounds of the verification problem for both expressive and lightweight DLs. Our lower bounds already apply to a very limited fragment of the verification problem, and close open complexity bounds for the non-metrical cases studied before.