Cholathorn Chanoi, Apichaya Kauppamung, Panuwat Luangchaisri
et al.
Let Γ be a nonempty set. A nonempty set A is called a Γ-AG-groupoid if there is a function f of A × Γ × A into A, customary denoted aγb for f(a, γ, b), satisfying the identity (aγb)βc = (cγb)βa for any a, b, c ∈ A and γ, β ∈ Γ. For each γ ∈ Γ, an operation on A associated to γ is given by ab = aγb. Suppose further that A is finite, contains a left identity and a left zero a0. The objective of this paper is to provide sufficient conditions under which the set A \ {a0} is a commutative group under the operation on A determined by γ for all γ ∈ Γ.
We give necessary conditions for a category fibred in pseudo-abelian additive categories over the classifying topos of a profinite group to be a stack; these conditions are sufficient when the coefficients are $\mathbf{Q}$-linear. This applies to pure motives over a field in the sense of Grothendieck, Deligne-Milne and André, to mixed motives in the sense of Nori and to several motivic categories considered in arXiv:1506.08386 [math.AG]. We also give a simple proof of the exactness of a sequence of motivic Galois groups under a Galois extension of the base field, which applies to all the above (Tannakian) situations. Finally, we clarify the construction of the categories of Chow-Lefschetz motives given in arXiv:2302.08327 [math.AG] and simplify the computation of their motivic Galois group in the numerical case.
Youth workers are on the front line for supporting children and young people with the violence some of them face. However, education and training for this part of the role seemed lacking in our experience as a Youth and Community Worker and a Youth and Community Work Lecturer in the UK. An international project that sought to address this educational gap for ‘youth practitioners’ had a UK arm, which is the context for this article. This project created a three-day training course that sought to improve responses to gender-related violence (GRV) by increasing awareness, improving knowledge about providing support and making referrals, and also sought to prevent or reduce gender-related violence by challenging the inequalities on which it rests. The UK ‘youth practitioners’ who attended the training wrote almost 500 ‘action plans’—plans to act on the basis of the training, and analysis of these offers an indication of their concerns and priorities. Here, we present the concerns that UK-based teachers and youth workers had for the children and young people they worked with, and the forms of violence they were aware of when they began this training course. We then describe the interventions with young people or changes to their practice that these attendees said they would make in response to the training once they were back at work. This provides an agenda for action in youth, education and social services to address gender-related violence in the lives of children and young people in the UK. By the end of the training, the interventions they had committed to making included changes to their own practice, showing their reflexivity and their understanding that key tools for tackling gender-related violence included their own behaviour and reflexive practice in their service or team. They highlighted the need for culture change at an organisational level, and identified the problems of sexism and homophobia, even in their own workplaces. Their views about the value of the term gender-related violence (GRV) were mixed, with some practitioners finding it unnecessarily theoretical and others finding it a helpful link between areas of discrimination and of violence that they tended to tackle separately, such as between homophobia and violence against women and girls.
Paul Doesburg, Jürgen Fritz, Miriam Athmann
et al.
There is an increasing interest in a systemic approach to food quality. From this perspective, the copper chloride crystallization method is an interesting asset as it enables an estimation of a sample’s ‘resilience’ in response to controlled degradation. In previous studies, we showed that an ISO-standardized visual evaluation panel could correctly rank crystallization images of diverse agricultural products according to their degree of induced degradation. In this paper we examined the role of contextual sensitivity herein, with the aim to further improve the visual evaluation. To this end, we compared subjects’ performance in ranking tests, while primed according to two perceptional strategies (levels: analytical vs. kinesthetic engagement), according to a within-subject design. The ranking test consisted out of wheat and rocket lettuce crystallization images, exhibiting four levels of induced degradation. The perceptual strategy imbuing kinesthetic engagement improved the performance of the ranking test in both samples tested. To the best of our knowledge, this is the first report on the training and application of such a perceptual strategy in visual evaluation.
In this sequel to works D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we re-examine --- and reformulate when in need --- several basic notions in super $C^{\infty}$-algebraic geometry as guided by the mathematical formulation of Ramond-Neveu-Schwarz fermionic strings and of Green-Schwarz fermionic strings from the viewpoint of Grothendieck on Algebraic Geometry. Two theorems that are the super counterpart of Theorem~3.1.1 and Theorem~3.2.1 of D(11.3.1) are proved. They unify the notion of "smooth maps from an Azumaya/matrix super smooth manifold with a fundamental module to a super smooth manifold" introduced in D(11.2), making it a complete super parallel to the setting for D-branes in the realm of algebraic geometry in D(1) (arXiv:0709.1515 [math.AG]) and D(2) (arXiv:0809.2121 [math.AG]), and in the realm of differential or $C^{\infty}$-algebraic geometry in D(11.1) and D(11.3.1). A prototypical definition of dynamical fermionic stacked D-brane world-volume on a space-time in the same spirit of RNS fermionic strings or GS fermionic strings is thus laid down. Similar to D(11.3.1), which paved the path to the construction of non-Abelian Dirac-Born-Infeld action (D(13.1) (arXiv:1606.08529 [hep-th])) and the standard action (D(13.3) (arXiv:1704.03237 [hep-th])) for fundamental bosonic stacked D-branes, the current notes shall serve the same for the construction of supersymmetric action for fundamental fermionic stacked D-branes of various dimensions --- a theme of another subseries of the D-project. A notion of "noncommutative $C^{\infty}$-rings" and "morphism" between them is introduced at the end as a byproduct.
In earlier works, D(1) (arXiv:0709.1515 [math.AG]), D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we have explained why a D-brane in string theory, when treated as a fundamental dynamical object, can be described by a map $\varphi$ from an Azumaya/matrix manifold $X^{Az}$ (cf. D-brane world-volume) with a fundamental module with a connection $(E,\nabla)$ (cf. Chan-Paton bundle) to the target space-time $Y$. In this sequel, we construct a non-Abelian Dirac-Born-Infeld action functional $S_{DBI}^{(\Phi, g, B)}(\varphi,\nabla)$ for such pairs $(\varphi,\nabla)$. We next develop a technical tool needed to study variations of this action and apply it to derive the first variation $\delta S_{DBI}^{(\Phi,g,B)}/\delta(\varphi,\nabla)$ of $S_{DBI}^{(\Phi,g,B)}$ with respect to $(\varphi,\nabla)$. The equations of motion that govern the dynamics of D-branes then follow. A complete action for a D-brane world-volume must include also the Chern-Simons/Wess-Zumino term $S_{CS/WZ}^{(C)}(\varphi,\nabla)$ that governs how the D-brane world-volume couples with the Ramond-Ramond fields $C$ on $Y$. In the current notes, a version $S^{(C,B)}_{CS/WZ}(\varphi,\nabla)$ of non-Abelian Chern-Simons/Wess-Zumino action functional for $(\varphi,\nabla)$ that follows the same guide with which we construct $S^{(\Phi,g,B)}_{DBI}(\varphi,\nabla)$ is constructed for lower-dimensional D-branes (i.e. D(-1)-, D0-, D1-, D2-branes). Its first variation $\delta S^{(C,B)}_{CS/WZ}(\varphi,\nabla)/\delta(\varphi,\nabla)$ is derived and its contribution to the equations of motion for $(\varphi, \nabla)$ follows. The current notes lay down a foundation toward the dynamics of D-branes along the line of this D-project.
Hitchin pairs on Riemann surfaces are generalizations of Higgs bundles, allowing the Higgs field to be twisted by an arbitrary line bundle. We consider this generalization in the context of $G$-Higgs bundles for a real reductive Lie group $G$. We outline the basic theory and review some selected results, including recent results by Nozad and the author arXiv:1602.02712 [math.AG] on Hitchin pairs for the unitary group of indefinite signature $\mathrm{U}(p,q)$.
Nicole R. Fowler, Amber E. Barnato, Howard B. Degenholtz
et al.
Background. Dementia and cardiovascular disease (CVD) are frequently comorbid. The presence of dementia may have an effect on how CVD is treated.Objective. To examine the effect of dementia on the use of four medications recommended for secondary prevention of ischemic heart disease (IHD): angiotensin-converting enzyme inhibitors, beta-blockers, lipid-lowering medications, and antiplatelet medications.Design. Retrospective analysis of data from the Cardiovascular Health Study: Cognition Study.Setting and Subjects. 1,087 older adults in four US states who had or developed IHD between 1989 and 1998.Methods. Generalized estimating equations to explore the association between dementia and the use of guideline-recommended medications for the secondary prevention of IHD.Results. The length of follow-up for the cohort was 8.7 years and 265 (24%) had or developed dementia during the study. Use of medications for the secondary prevention of IHD for patients with and without dementia increased during the study period. In models, subjects with dementia were not less likely to use any one particular class of medication but were less likely to use two or more classes of medications as a group (OR, 0.60; 95% CI, 0.36–0.99).Conclusions. Subjects with dementia used fewer guideline-recommended medications for the secondary prevention of IHD than those without dementia.
We generalise a formula of Shou-Wu Zhang, which describes local arithmetic intersection numbers of three Cartier divisors with support in the special fibre on a a self-product of a semi-stable arithmetic surface using elementary analysis. By an approximation argument, Zhang extends his formula to a formula for local arithmetic intersection numbers of three adelic metrized line bundles on the self-product of a curve with trivial underlying line bundle. Using the results on intersection theory from arXiv:1404.1623 [math.AG] we generalize these results to d-fold self-products for arbitrary d. For the approximations to converge, we have to assume that d satisfies the vanishing condition 4.7 from arXiv:1404.1623 [math.AG], which is true at least for $d\in \{2,3,4,5\}$.
We prove that every simplicial complex is the dual complex of some simple normal crossing divisor in a smooth variety. As an application, we simplify and extend the results of Kapovich--Koll\'ar (math.AG:1109.4047) on the existence of singularities with given dual complex.
Paula Diehr, Stephen Thielke, Ellen O’Meara
et al.
Introduction. The traditional definitions of overweight and obesity are not age specific, even though the relationship of weight to mortality is different for older adults. Effects of adiposity on aspects of health beside mortality have not been well investigated.Methods. We calculated the number of years of healthy life (YHL) in the 10 years after baseline, for 5,747 older adults. YHL was defined in 16 different ways. We compared Normal and Overweight persons, classified either by body mass index (BMI) or by waist circumference (WC).Findings. YHL for Normal and Overweight persons differed significantly in 25% of the comparisons, of which half favored the Overweight. Measures of physical health favored Normal weight, while measures of mental health and quality of life favored Overweight. Overweight was less favorable when defined by WC than by BMI. Obese persons usually had worse outcomes.Discussion. Overweight older adults averaged as many years of life and years of healthy life as those of Normal weight. There may be no outcome based reason to distinguish Normal from Overweight for older adults.Conclusion. The “Overweight paradox” appears to hold for nonmortality outcomes. New adiposity standards are needed for older adults, possibly different by race and sex.
In this survey paper (which supersedes our earlier arXiv preprint math.AG/0507086) we give a relatively simple and coordinate free description of the WZW model as a local system whose base is a G_m-bundle on the moduli stack of pointed curves. We derive its main properties and show how it leads to a modular functor in the spirit of Graeme Segal (except for unitarity). The approach presented here is almost purely algebro-geometric in character; it avoids the Boson-Fermion correspondence, operator product expansions as well as Teichmueller theory.
In this continuation of [L-Y1], [L-L-S-Y], [L-Y2], and [L-Y3] (arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], arXiv:0901.0342 [math.AG], arXiv:0907.0268 [math.AG]), we study D-branes in a target-space with a fixed $B$-field background $(Y,α_B)$ along the line of the Polchinski-Grothendieck Ansatz, explained in [L-Y1] and further extended in the current work. We focus first on the gauge-field-twist effect of $B$-field to the Chan-Paton module on D-branes. Basic properties of the moduli space of D-branes, as morphisms from Azumaya schemes with a twisted fundamental module to $(Y,α_B)$, are given. For holomorphic D-strings, we prove a valuation-criterion property of this moduli space. The setting is then extended to take into account also the deformation-quantization-type noncommutative geometry effect of $B$-field to both the D-brane world-volume and the superstring target-space(-time) $Y$. This brings the notion of twisted ${\cal D}$-modules that are realizable as twisted locally-free coherent modules with a flat connection into the study. We use this to realize the notion of both the classical and the quantum spectral covers as morphisms from Azumaya schemes with a fundamental module (with a flat connection in the latter case) in a very special situation. The 3rd theme (subtitled "Sharp vs. Polchinski-Grothendieck") of Sec. 2.2 is to be read with the work [Sh3] (arXiv:hep-th/0102197) of Sharp while Sec. 5.2 (subtitled less appropriately "Dijkgraaf-Holland-Sułkowski-Vafa vs. Polchinski-Grothendieck") is to be read with the related sections in [D-H-S-V] (arXiv:0709.4446 [hep-th]) and [D-H-S] (arXiv:0810.4157 [hep-th]) of Dijkgraaf, Hollands, Sułkowski, and Vafa.
In math.AG/0207233, Okounkov and Pandharipande gave an operator formalism for computing the equivariant Gromov-Witten theory of the projective line. This thesis extends their result to orbifold lines. In the effective case the theory is again governed by the 2-Toda hierarchy. In the ineffective case the decomposition conjecture of hep-th/0606034 is verified.