Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.Comment: 25 page

Critical Life Experiences that Mold a Person into a Global Scholar

Global Scholar Toni Fuss Kirkwood Tucker shares her experiences in Nazi Germany. This column contains an excerpt of Toni's presentation her award luncheon

Some properties of the k-dimensional Lyness' map

This paper is devoted to study some properties of the k-dimensional Lyness' map. Our main result presentes a rational vector field that gives a Lie symmetry for F. This vector field is used, for k less or equal to 5 to give information about the nature of the invariant sets under F. When k is odd, we also present a new (as far as we know) first integral for F^2 which allows to deduce in a very simple way several properties of the dynamical system generated by F. In particular for this case we prove that, except on a given codimension one algebraic set, none of the positive initial conditions can be a periodic point of odd period.Comment: 22 pages; 3 figure

Enhancing Teamwork Skills Through an Interdisciplinary Engineering Service Learning Collaboration

The purpose of this research paper is to explore whether participation in an interdisciplinary collaboration program partnering Preservice Teachers (PST) and Undergraduate Engineering Students (UES) results in an increase in teamwork effectiveness. The interdisciplinary collaboration was designed as a service-learning project within existing undergraduate programs that included the development and delivery of engineering content to a K-12 audience. The collaborations were integrated into existing courses in two colleges, engineering and education. The Behaviorally Anchored Rating Scale (BARS) version of the Comprehensive Assessment of Team Member Effectiveness (CATME) was used midway and at the end of the project to evaluate teamwork effectiveness. Results of the analysis indicated that both PST and UES were rated significantly higher in team-member effectiveness at the end of the project across four of five factors: interacting with team members, keeping the team on track, expecting quality, and having relevant knowledge, skills and abilities. The gain in the teamwork effectiveness did not differ across majors, with both UES and PST showing similar gains. A noticeable positive increase in student attitudes towards the task was also observed between the midway and the end of the project. Findings from this study provide some preliminary evidence that an innovative interdisciplinary service learning experience partnering engineering and education students was conducive to the development of teamwork skills

The Influence of Participation in a Multi-Disciplinary Collaborative Service Learning Project on the Effectiveness of Team Members in a 100-level Mechanical Engineering Class

Engineers need to develop professional skills, including the ability to work successfully in teams and to communicate within and outside of their discipline, in addition to required technical skills. A collaborative multi-disciplinary service learning project referred to as Ed+gineering was implemented in a 100-level mechanical engineering course. In this collaboration, mechanical engineering students, primarily in the second semester of their freshman year or first semester of their second year, worked over the course of a semester with education students taking a foundations course to develop and deliver engineering lessons to fourth or fifth graders. Students in comparison engineering classes worked on a team project focused on experimental design for a small satellite system. The purpose of this study was to determine if participating in the Ed+gineering collaboration had a positive effect on teamwork effectiveness and satisfaction when compared to the comparison class. In both team projects, the five dimensions of the Comprehensive Assessment of Team Member Effectiveness (CATME) system were used as a quantitative assessment. The five dimensions of CATME Behaviorally Anchored Ratings Scale (BARS) (contribution to the team’s work, interacting with teammates, keeping the team on track, expecting quality, and having relevant Knowledge, Skills, and Abilities - KSAs) were measured. Additionally, within the CATME platform team satisfaction, team interdependence and team cohesiveness were measured. ANCOVA analysis was used to assess the quantitative data from CATME. Preliminary results suggest that students in the treatment classes had higher team member effectiveness and overall satisfaction scores than students in the comparison classes. Qualitative data from reflections written at the completion of the aforementioned projects were used to explore these results

Enhancing Preservice Teachers\u27 Intention to Integrate Engineering Through a Multi-Disciplinary Partnership (Evaluation)

Driven by the need to broaden participation and increase recruitment in STEM fields, considerable efforts are underway to promote the infusion of engineering into elementary and secondary grade levels. The benefits of engineering education and the strong support from professional and educational groups are well documented, yet the actual integration of engineering content in the K-12 setting remains a challenge. Pre-college educator programs that train future teachers are a natural target for the integration efforts. Although elementary educators recognize the importance of integrating engineering in their classrooms, they often lack the confidence to teach engineering content. The absence of effective engineering instruction in teacher preparation programs leaves future educators unprepared for this challenge. Ed+gineering is an NSF-funded partnership between education and engineering students and faculty aimed at increasing preservice teacher (PST) preparation, confidence, and intention to integrate engineering into their teaching. The project partners education and engineering students at three points in their professional preparation within the context of their respective university courses. As part of their coursework, small cross-disciplinary teams plan and deliver culturally responsive engineering lessons to elementary school students. This paper investigates the impact of Ed+gineering on PSTs’ knowledge of engineering practices, self-efficacy to integrate engineering, pedagogical knowledge, beliefs about engineering integration, and engineering pedagogy. ANCOVA analysis was used to assess the impact of Ed+gineering on participating PSTs. Data was collected from three collaborations involving students in engineering and education during Spring 2020. A validated survey was used to assess the variables of interest. Preliminary results suggest that the Ed+gineering partnership had a positive impact on engineering pedagogical knowledge, general pedagogical knowledge, knowledge of engineering practices, and self-efficacy for integrating engineering. The specific magnitude of the impact and its implications will be discussed in this paper

An implantable microdevice to perform high-throughput in vivo drug sensitivity testing in tumors

Current anticancer chemotherapy relies on a limited set of in vitro or indirect prognostic markers of tumor response to available drugs. A more accurate analysis of drug sensitivity would involve studying tumor response in vivo. To this end, we have developed an implantable device that can perform drug sensitivity testing of several anticancer agents simultaneously inside the living tumor. The device contained reservoirs that released microdoses of single agents or drug combinations into spatially distinct regions of the tumor. The local drug concentrations were chosen to be representative of concentrations achieved during systemic treatment. Local efficacy and drug concentration profiles were evaluated for each drug or drug combination on the device, and the local efficacy was confirmed to be a predictor of systemic efficacy in vivo for multiple drugs and tumor models. Currently, up to 16 individual drugs or combinations can be assessed independently, without systemic drug exposure, through minimally invasive biopsy of a small region of a single tumor. This assay takes into consideration physiologic effects that contribute to drug response by allowing drugs to interact with the living tumor in its native microenvironment. Because these effects are crucial to predicting drug response, we envision that these devices will help identify optimal drug therapy before systemic treatment is initiated and could improve drug response prediction beyond the biomarkers and in vitro and ex vivo studies used today. These devices may also be used in clinical drug development to safely gather efficacy data on new compounds before pharmacological optimization.National Cancer Institute (U.S.) (Innovative Molecular Analysis Technologies Program R21-CA177391)Kibur Medical, Inc

The Impact of a Multidisciplinary Service-Learning Project on Engineering Knowledge and Professional Skills in Engineering in Engineering and Education Students

A multidisciplinary service-learning project that involved teaching engineering to fourth and fifth graders was implemented in three sets of engineering and education classes to determine if there was an impact on engineering knowledge and teamwork skills in both the engineering and education students as well as persistence in the engineering students. Collaboration 1 paired a 100-level engineering Information Literacy class in Mechanical and Aerospace Engineering with a 300-level Educational Foundation class. Collaboration 2 combined a 300-level Electromechanical Systems class in Mechanical Engineering with a 400-level Educational Technology class. Collaboration 3 paired a 300-level Fluid Mechanics class in Mechanical Engineering Technology with a 400-level Elementary Science Methods class. Collaborations 1 and 3 interacted with fourth or fifth graders by developing and delivering lessons to the elementary students. Students in collaboration 2 worked with fifth graders in an after-school technology club. While each collaboration had its unique elements, all collaborations included the engineering design process both in classroom instruction and during the service learning project. Quantitative data were collected from both engineering and education students in a pretest/posttest design. Teamwork skills were measured in engineering students using a validated teamwork skills assessment based on peer evaluation. Each class had a comparison class taught by the same instructor that included a team project, and the same quantitative measures. Engineering students who participated in collaboration 1 were evaluated for retention, which was defined as students who were still enrolled in the college of engineering and technology two semesters after completion of the course. Engineering students also completed an evaluation of academic and professional persistence. For the engineering students, none of the assessments involving technical skills had significant differences, although the design process knowledge tests trended upward in the treatment classes. The preservice teachers in the treatment group scored significantly higher in the design process knowledge test, and preservice teachers in collaborations 1 and 3 had higher scores in the engineering knowledge test than the comparison group. Teamwork skills in the treatment group were significantly higher than in the comparison group for both engineering and education students. Thus, engineering and education students in the treatment groups saw gains in teamwork skills, while education students saw more gains in engineering knowledge. Finally, all engineering students had significantly higher professional persistence

How Does Working on an Interdisciplinary Service-Learning Project vs. a Disciplinary Design Project Affect Peer Evaluators\u27 Teamwork Skills

Over the course of several semesters, two different project-based learning approaches were used in two undergraduate engineering courses–a 100-level introductory course that covered a general education requirement on information literacy and a 300-level fluid mechanics course. One project (treatment) was an interdisciplinary service-learning project, implemented with undergraduate engineering and education students who collaborated to develop and deliver engineering lessons to fourth and fifth-grade students in a field trip model. The other projects (comparison) involved a team-based design project contained within each class. In the 100-level course, students selected their project based on personal interests and followed the engineering design process to develop, test, and redesign a prototype. In the fluid mechanics class, students designed a pumped pipeline system for a hypothetical plant. This study aimed to determine whether participating in the interdisciplinary project affected students’ evaluation of their own and their teammates’ teamwork effectiveness skills, measured using the Behaviorally Anchored Rating Scale (BARS) version of the Comprehensive Assessment of Team Member Effectiveness(CATME). The five dimensions of CATME measured in this study are (1) contribution to the team’s work, (2) interacting with teammates, (3) keeping the team on track, (4) expecting quality, and (5) having relevant knowledge, skills, and abilities (KSAs). The quantitative data from CATME were analyzed using ANCOVA analysis. Furthermore, since data were collected over three semesters and coincided with the pre, during, and post-phases of the COVID-19 pandemic, it was possible to examine the effects of the evolving classroom constraints over the course of the pandemic on the teamwork effectiveness skills of both the treatment and comparison classes. Preliminary results suggest that students in the treatment classes perceived that their teammates had greater relevant knowledge, skills, and abilities than the comparison cohort. Engineering students in the treatment group also believed their team members were more capable of quality work than the engineering students in the comparison group. Moreover, preliminary results showed a significant drop in scores for expecting quality and having relevant KSA during the peak of COVID during online instruction and performance of both projects, followed by a rise in mean scores during the return to in-person classes. Reflections from available qualitative data were paired to help understand the quantitative data results further

Non-autonomous 2-periodic Gumovski-Mira difference equations

We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones differ dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.Comment: 20 pages, 11 figure