Monotonicity of Degrees of Generalized Alexander Polynomials of Groups and 3-Manifolds

We investigate the behavior of the higher-order degrees, db_n, of a finitely presented group G. These db_n are functions from H^1(G;Z) to Z whose values are the degrees certain higher-order Alexander polynomials. We show that if def(G) is at least 1 or G is the fundamental group of a compact, orientable 3-manifold then db_n is a monotonically increasing function of n for n at least 1. This is false for general groups. As a consequence, we show that if a 4 manifold of the form X times S^1 admits a symplectic structure then X ``looks algebraically like'' a 3-manifold that fibers over S^1, supporting a positive answer to a question of Taubes. This generalizes a theorem of S. Vidussi and is an improvement on the previous results of the author. We also find new conditions on a 3-manifold X which will guarantee that the Thurston norm of f*(psi), for psi in H^1(X;\Z) and f:Y -> X a surjective map on pi_1, will be at least as large the Thurston norm of psi. When X and Y are knot complements, this gives a partial answer to a question of J. Simon. More generally, we define Gamma-degrees, db_Gamma, corresponding to a surjective map G -> Gamma for which Gamma is poly-torsion-free-abelian. Under certain conditions, we show they satisfy a monotonicity condition if one varies the group. As a result, we show that these generalized degrees give obstructions to the deficiency of a group being positive and obstructions to a finitely presented group being the fundamental group of a compact, orientable 3-manifold.Comment: 19 page

Structure and dynamics in nanoionic materials

Nanomaterials, materials with particle dimensions less than 100 nm, show a range of unusual properties when compared with their bulk counterparts. Atomic transport is one of these properties and nanomaterials have been reported as having exceptionally high diffusion coefficients. In the case of ionic materials the atomic transport is important in a number of technological applications where they are used as solid electrolytes, for example in sensors, batteries and fuel cells. Hence ionic nanomaterials often referred to as nanoionics, can offer the means of producing electrolytes with improved performance. This contribution will examine the mechanisms of atomic transport in nanoionics in two model materials, zirconia and lithium niobate. Since an understanding of these mechanisms is dependent on knowledge of the microstructure of the materials consideration will also be given to the structural characterisation of the materials, with a focus on X-ray absorption spectroscopy. The use of this technique to characterise mesoporous a-Fe2O3 is also discussed

On the Cut Number of a 3-manifold

The question was raised as to whether the cut number of a 3-manifold X is bounded from below by 1/3 beta_1(X). We show that the answer to this question is `no.' For each m>0, we construct explicit examples of closed 3-manifolds X with beta_1(X)=m and cut number 1. That is, pi_1(X) cannot map onto any non-abelian free group. Moreover, we show that these examples can be assumed to be hyperbolic.Comment: Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper15.abs.htm

Scissors Modes and Spin Excitations in Light Nuclei including ΔN\Delta N=2 excitations: Behaviour of 8Be^8Be and 10Be^{10}Be

Shell model calculations are performed for magnetic dipole excitations in $^8{Be}$ and $^{10}{Be}$ in which all valence configurations plus $2\hbar\omega$ excitations are allowed (large space). We study both the orbital and spin excitations. The results are compared with the `valence space only' calculations (small space). The cumulative energy weighted sums are calculated and compared for the $J=0^+$ $T$=0 to $J=1^+$ $T$=1 excitations in $^8{Be}$ and for $J=0^+$ $T$=1 to both $J=1^+$ $T$=1 and $J$=$1^+$ $T$=2 excitations in $^{10}{Be}$. We find for the $J=0^+$ $T$=1 to $J=1^+$ $T$=1 isovector {\underline {spin}} transitions in $^{10}{Be}$ that the summed strength in the {\underline {large}} space is less than in the {\underline {small}} space. We find that the high energy energy-weighted isovector orbital strength is smaller than the low energy strength for transitions in which the isospin is changed, but for $J=0^+$ $T$=1 to $J=1^+$ $T$=1 in $^{10}{Be}$ the high energy strength is larger. We find that the low lying orbital strength in $^{10}{Be}$ is anomalously small, when an attempt is made to correlate it with the $B(E2)$ strength to the lowest $2^+$ states. On the other hand a sum rule of Zheng and Zamick which concerns the total $B(E2)$ strength is reasonably satisfied in both $^8{Be}$ and $^{10}{Be}$. The Wigner supermultiplet scheme is a useful guide in analyzing shell model results. In $^{10}Be$ and with a $Q \cdot Q$ interaction the T=1 and T=2 scissors modes are degenerate, with the latter carrying 5/3 of the T=1 strength.Comment: 51 pages, latex, 9 figures available upon reques

Getting In On the Act: How Arts Groups are Creating Opportunities for Active Participation

Arts participation is being redefined as people increasingly choose to engage with art in new, more active and expressive ways. This movement carries profound implications, and fresh opportunities, for the nonprofit arts sector.We are in the midst of a seismic shift in cultural production, moving from a "sit-back-and-be-told culture" to a "making-and-doing-culture." Active or participatory arts practices are emerging from the fringes of the Western cultural tradition to capture the collective imagination. Many forces have conspired to lead us to this point. The sustained economic downturn that began in 2008, rising ticket prices, the pervasiveness of social media, the roliferation of digital content and rising expectations for self-guided, on-demand, customized experiences have all contributed to a cultural environment primed for active arts practice. This shift calls for a new equilibrium in the arts ecology and a new generation of arts leaders ready to accept, integrate and celebrate all forms of cultural practice. This is, perhaps, the defining challenge of our time for artists, arts organizations and their supporters -- to embrace a more holistic view of the cultural ecology and identify new possibilities for Americans to engage with the arts.How can arts institutions adapt to this new environment?Is participatory practice contradictory to, or complementary to, a business model that relies on professional production and consumption?How can arts organizations enter this new territory without compromising their values r artistic ideals?This report aims to illuminate a growing body of practice around participatory engagement (with various illustrative case studies profiled at the end) and dispel some of the anxiety surrounding this sphere of activity

Plato and the notion of a dialectical rhetoric: pedagogical implications for composition studies

One of the most significant areas of debate within the Platonic dialogues has been Plato\u27s conception of rhetoric. This area of interpretation has been so vast and varied that it is hard to believe that everyone has been analyzing the same dialogues. However, one view has predominated, and that is the view that Plato, as seen primarily in the Gorgias and the Phaedrus, disapproved of rhetoric and writing and has historically been its fiercest opponent

Weaving the Braid of Culturally Responsive Leadership Within Policy and Governance to Improve Indigenous Student Success

This Organizational Improvement Plan (OIP) explores a Problem of Practice (PoP) that highlights the need for why the Board of Education and the Senior Administration team within the Raven Bay School Division (RBSD, pseudonym) would benefit from using a culturally responsive leadership approach when making decisions and how this may be achieved through policy and governance to guide their practice. The goal of this OIP is to examine why this leadership approach would be relevant for the Board of Education and the Senior Leadership team when they are making any policy and governance decisions, as it relates to Indigenous Education and how this leadership approach could positively support the improvement of educational outcomes and opportunities for Indigenous learners across the RBSD. The recommended solutions found within this OIP are intended to show how the RBSD can weave together a culturally responsive braid of policy and governance to address their goal of improving Indigenous learner outcomes found within their strategic. If this OIP is implemented, the solutions could be turned into strategies that work towards positively closing the current achievement gap that exists between Indigenous and non-Indigenous learners within the RBSD. Thus, beginning to shift the negative narrative of the culture of low expectations for Indigenous learners within the RBSD to a positive narrative of equity and success through the lens of culturally responsive leadership. Keywords: Aboriginal, Aboriginal Learning, Aboriginal Rights, Assimilation, Colonization, Culture, Decolonization, Educator, Emotional Intelligence, Ethical, Experiential Learning, First Nations, First Peoples, Holistic Education, Indigenizing Education, Lifelong Learning, Reconciliation, Social Emotional Learning, Transformative Change, Worldvie

What happens when veteran and beginner teachers\u27 life histories intersect with high-stakes testing and what does it mean for learners and teaching practice: The making of a culture of fear

This qualitative study explored the phenomenon of what happened as Florida\u27s high-stakes accountability system intersected with a beginning and veteran teachers\u27 life histories and different stocks of lifeworldly knowledge at demographically different lifeworld communities. Habermas\u27 (1987) theory of communicative action was used as the theoretical framework to explore what the teachers\u27 responses meant for learners and teaching practice. The research purpose of this study (emphasizing an interpretive approach) sought to gain insights and understandings regarding the phenomenon specifically. The practical purpose (according to critical theory) was to then use the insights gained (enlightenment) in order to contemplate the kinds of steering media and mechanisms needed to support teaching practice (emancipation) that can best satisfy the system (accountability) rationale to increase educational opportunities for all learners regardless of need. Three overarching themes central to learners and teaching practice emerged from the data obtained from interviews, classroom observations, and student products: (a) the greater the lifeworld needs of the school community (e.g., high mobility rate, low socio-economic status) the greater the response in terms of instructional and curricular accommodations designed to increase FCAT test scores; (b) the greater the colonization of the lifeworld perspective by Florida\u27s accountability system rationale, the greater the likelihood that various social actors experienced fear in relation to FCAT; and (c) school reform efforts both past and present (including Florida\u27s high-stakes accountability system) have consistently resulted in less educational opportunity for those learners who need it the most