Decomposable polynomials in second order linear recurrence sequences

We study elements of second order linear recurrence sequences $(G_n)_{n= 0}^{\infty}$ of polynomials in $\mathbb{C}[x]$ which are decomposable, i.e. representable as $G_n=g\circ h$ for some $g, h\in \mathbb{C}[x]$ satisfying $\operatorname{deg}g,\operatorname{deg}h>1$. Under certain assumptions, and provided that $h$ is not of particular type, we show that $\operatorname{deg}g$ may be bounded by a constant independent of $n$, depending only on the sequence.Comment: 26 page

Music Appreciation (Clayton State)

This Grants Collection for Music Appreciation was created under a Round Four ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/arts-collections/1002/thumbnail.jp

Game of Clones: Students Model the Dispersal and Fighting of Japanese Knotweed (<em>Fallopia japonica</em>)

Fallopia japonica as an invasive alien species in Europe and North America presents a significant problem to the existing flora as well as to infrastructures and agricultural land. That is why measures and attempts to control the plant are increasing rapidly. However, conservationists are not yet able to agree on the most suitable method. In the research project ‘Game of Clones’, a team of scientists together with the help of high school students is spatially modeling the spreading behavior of knotweed under different circumstances and is creating and providing a board game as well as a computer simulation as an experimental platform. To develop sustainable assumptions to be able to model the responses of knotweed to each control measure, a vast understanding of the plant is necessary. The chapter covers the results of research activities and experiments within the project and gives a comprehensive review about Japanese knotweed

Phospholipases and Reactive Oxygen Species Derived Lipid Biomarkers in Healthy and Diseased Humans and Animals – A Focus on Lysophosphatidylcholine

Phospholipids (PL) are converted into lipid biomarkers by the action of phospholipases and reactive oxygen species (ROS), which are activated or released under certain physiological and pathophysiological conditions. Therefore, the in vivo concentration of such lipid biomarkers [e.g., lysophospholipids (LPLs)] is altered in humans and animals under different conditions such as inflammation, stress, medication, and nutrition. LPLs are particularly interesting because they are known to possess proand anti-inflammatory properties and may be generated by two different pathways: either by the influence of phospholipase A2 or by different reactive oxygen species that are generated in significant amounts under inflammatory conditions. Both lead to the cleavage of unsaturated acyl residues. This review provides a short summary of the mechanisms by which lipid biomarkers are generated under in vitro and in vivo conditions. The focus will be on lysophosphatidylcholine (LPC) because usually, this is the LPL species which occurs in the highest concentration and is, thus, easily detectable by chromatographic and spectroscopic methods. Finally, the effects of lipid biomarkers as signaling molecules and their roles in different human and animal pathologies such as infertility, cancer, atherosclerosis, and aging will be shortly discussed