The Merrifield-Simmons conjecture holds for bipartite graphs

Let $G = (V, E)$ be a graph and $\sigma(G)$ the number of independent (vertex) sets in $G$. Then the Merrifield-Simmons conjecture states that the sign of the term $\sigma(G_{-u}) \cdot \sigma(G_{-v}) - \sigma(G) \cdot \sigma(G_{-u-v})$ only depends on the parity of the distance of the vertices $u, v \in V$ in $G$. We prove that the conjecture holds for bipartite graphs by considering a generalization of the term, where vertex subsets instead of vertices are deleted.Comment: 8 page

Ethical dilemmas in senior teacher educators’ administrative work

The current study presents the professional experiences of senior teacher educators (‘Associate Professors’), with an emphasis placed on ethical dilemmas they face during their administrative work. The main purpose is to characterize the critical incidents underlying these dilemmas, their interpretation, and the ways of balancing the different considerations in their resolution. A qualitative analysis of twelve narrative interviews pointed to four core values which underpinned the approaches taken by teacher educators in their handling of critical situations: perception of integrity, empathy and care, commitment to the institution, and the need to promote initiatives. Findings indicate that the concept of integrity is central to the decision making processes, but that this concept is interpreted differently according to the personality characteristics, experience, and educational vision of the interviewees. It is proposed to conduct further studies that examine the interpretation of ‘integrity’ as a concept among senior teacher educators

Occupational therapy\u27s link to vocational reeducation, 1910-1925.

The development of occupational therapy is rooted in early 20th century medical reform. During the early 1910s, several members of the medical profession, human service workers, and the larger American society were increasingly disturbed by medical practices that did not consider the individual\u27s personal experience of disability. Occupational therapy was developed, in part, out of this desire to provide persons with treatment that helped them to function in their communities despite their disability. Early occupational therapy leaders envisioned the fledgling profession as a societal service capable of assisting persons with disabilities to return to both work and community life. Vocational reeducation was initially considered to be an integral component of occupational therapy in the years from 1910 to 1920. However, the profession\u27s early link to vocational reduction was challenged by vocational technical trainers during World War I. To prevent occupational therapy from being subsumed by vocational technical training, the early occupational therapy leaders implemented several strategies: adoption of physician prescription for all occupational therapy services, delivery of occupational therapy services primarily within hospital settings, and dissociation from vocational reeducation services. Reasons accounting for why the early occupational therapy leaders abandoned their initial commitment to vocational reeducation are explored. Suggestions about how this decision has affected present-day practice are also offered

Uncertain dynamical systems: A differential game approach

A class of dynamical systems in a conflict situation is formulated and discussed, and the formulation is applied to the study of an important class of systems in the presence of uncertainty. The uncertainty is deterministic and the only assumption is that its value belongs to a known compact set. Asymptotic stability is fully discussed with application to variable structure and model reference control systems