This talk should be regarded as an elementary introduction to differential algebra. It culminates in a purely algebraic proof, due to M. Rosenlicht [Ros2], of an 1835 theorem of Liouville on the existence of “elementary” integrals of “elementary” functions. The precise meaning of elementary will be specified. As an application of that theorem we prove that the indefinite integral ∫ e 2 dx canno...

We develop a calculus of surgery data, called bridged links, which involves besides links also pairs of balls that describe one-handle attachements. As opposed to the usual link calculi of Kirby and others this description uses only elementary, local moves(namely modifications and isolated cancellations ), and it is valid also on non-simply connected and disconnected manifolds. In particular, i...

Purpose/Objectives Existing research has investigated the effects of using individual incentives and positive reinforcements to influence children to eat more fruits and vegetables for lunch and snack during school. This study explored using group-level incentives to motivate children in a Wisconsin elementary school to eat more fruits and vegetables. Methods This research examined the influenc...

Coalsack Bluff was the first discovery site in Antarctica for the latest Permian to earliest Triassic reptile Lystrosaurus. This together with discovery of Permian Glossopteris leaves during the heroic age of Antarctic exploration, indicated not only that Antarctica was part of Gondwanaland, but also that Antarctic rocks recorded faunas from the greatest of all mass extinctions at the Permian–T...

In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with n channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for inco...

This paper aims to extract a group-pair relation as a Problem-Solving relation, for example a DiseaseSymptom-Treatment relation and a CarProblem-Repair relation, between two event-explanation groups, a problem-concept group as a symptom/CarProblem-concept group and a solving-concept group as a treatment-concept/repair concept group from hospital-web-board and car-repair-guru-web-board documents...

In this note, we prove a theorem à la Fatou for the square root of Poisson Kernel in the context of quasi-convex cocompact discrete groups of isometries of δ-hyperbolic spaces. As a corollary we show that some matrix coefficients of boundary representations cannot satisfy the weak inequality of Harish-Chandra. Nevertheless, such matrix coefficients satisfy an inequality which can be viewed as a...

Most CAD or other spatial data models, in particular boundary representation models, are called “topological” and represent spatial data by a structured collection of “topological primitives” like edges, vertices, faces, and volumes. These then represent spatial objects in geo-information(GIS) or CAD systems or in building information models (BIM). Volume objects may then either be represented ...

Teacher mental health continues to be of concern in elementary and secondary schools; however, supporting teacher wellbeing is understudied (Parker et al., 2012; Roffey, 2012), particularly from a gender perspective (Bourgeault 2021). Among professionals, teachers exhibit one the highest levels job stress burnout on job. (Hakanen 2006; Stoeber & Rennert, 2008). This scoping review investiga...