4,741 research outputs found

    Expanding measures: Random walks and rigidity on homogeneous spaces

    Full text link
    Let GG be a real Lie group, Λ<G\Lambda<G a lattice and H<GH<G a connected semisimple subgroup without compact factors and with finite center. We define the notion of HH-expanding measures μ\mu on HH and, applying recent work of Eskin-Lindenstrauss, prove that μ\mu-stationary probability measures on G/ΛG/\Lambda are homogeneous. Transferring a construction by Benoist-Quint and drawing on ideas of Eskin-Mirzakhani-Mohammadi, we construct Lyapunov/Margulis functions to show that HH-expanding random walks on G/ΛG/\Lambda satisfy a recurrence condition and that homogeneous subspaces are repelling. Combined with a countability result, this allows us to prove equidistribution of trajectories in G/ΛG/\Lambda for HH-expanding random walks and to obtain orbit closure descriptions. Finally, elaborating on an idea of Simmons-Weiss, we deduce Birkhoff genericity of a class of measures with respect to some diagonal flows and extend their applications to Diophantine approximation on similarity fractals to a non-conformal and weighted setting.Comment: 63 pages; revised the presentation of the proof of Corollary 1.2 and made other small changes and corrections. Accepted for publication by Forum of Mathematics, Sigm

    Meso-scale FDM material layout design strategies under manufacturability constraints and fracture conditions

    Get PDF
    In the manufacturability-driven design (MDD) perspective, manufacturability of the product or system is the most important of the design requirements. In addition to being able to ensure that complex designs (e.g., topology optimization) are manufacturable with a given process or process family, MDD also helps mechanical designers to take advantage of unique process-material effects generated during manufacturing. One of the most recognizable examples of this comes from the scanning-type family of additive manufacturing (AM) processes; the most notable and familiar member of this family is the fused deposition modeling (FDM) or fused filament fabrication (FFF) process. This process works by selectively depositing uniform, approximately isotropic beads or elements of molten thermoplastic material (typically structural engineering plastics) in a series of pre-specified traces to build each layer of the part. There are many interesting 2-D and 3-D mechanical design problems that can be explored by designing the layout of these elements. The resulting structured, hierarchical material (which is both manufacturable and customized layer-by-layer within the limits of the process and material) can be defined as a manufacturing process-driven structured material (MPDSM). This dissertation explores several practical methods for designing these element layouts for 2-D and 3-D meso-scale mechanical problems, focusing ultimately on design-for-fracture. Three different fracture conditions are explored: (1) cases where a crack must be prevented or stopped, (2) cases where the crack must be encouraged or accelerated, and (3) cases where cracks must grow in a simple pre-determined pattern. Several new design tools, including a mapping method for the FDM manufacturability constraints, three major literature reviews, the collection, organization, and analysis of several large (qualitative and quantitative) multi-scale datasets on the fracture behavior of FDM-processed materials, some new experimental equipment, and the refinement of a fast and simple g-code generator based on commercially-available software, were developed and refined to support the design of MPDSMs under fracture conditions. The refined design method and rules were experimentally validated using a series of case studies (involving both design and physical testing of the designs) at the end of the dissertation. Finally, a simple design guide for practicing engineers who are not experts in advanced solid mechanics nor process-tailored materials was developed from the results of this project.U of I OnlyAuthor's request

    Operatic Pasticcios in 18th-Century Europe

    Get PDF
    In Early Modern times, techniques of assembling, compiling and arranging pre-existing material were part of the established working methods in many arts. In the world of 18th-century opera, such practices ensured that operas could become a commercial success because the substitution or compilation of arias fitting the singer's abilities proved the best recipe for fulfilling the expectations of audiences. Known as »pasticcios« since the 18th-century, these operas have long been considered inferior patchwork. The volume collects essays that reconsider the pasticcio, contextualize it, define its preconditions, look at its material aspects and uncover its aesthetical principles

    The cultural politics of anti-elitism between populism, pop culture and everyday life. An introduction

    Full text link
    The introductory chapter lays out a framework for conceptualising the recent wave of anti-elite rhetoric and sentiments in different arenas. It suggests analytical distinctions between a variety of forms of anti-elite articulations – which allows a better understanding of how they interacted and resonated – and also between egalitarian and non-egalitarian forms of anti-elitism. It situates the recent interest in these matters not only in responses to the populist wave of the mid-2010s but also in more general dynamics of societies structured in dominance, discussing the ways in which cultural politics in different fields have been shaped by anti-elitism at different conjunctures, including the spread of extreme conspiracy theories about hidden elites – and it poses the question how different forms of anti-elitism may have contributed to multiple and interconnected crises. Furthermore, particular attention is paid to anti-elitism as an argument in explanations of the populist wave, as well as the role and the epistemological status of diagnostic narratives of different types and the notion of conjunctural analysis and its purchase. Overall, the chapter discusses anti-elitism not only as an ambiguous pattern in cultural politics but also as an object of normative reflection from which academics – who are targeted by anti-elitism, but may hold egalitarian views themselves – should not refrain. In closing, the chapter asks what happened to anti-elite articulations and what their role might be after that specific historical “moment”

    A systematic review and meta-analysis of interventions based on metacognition and self-regulation in school-aged mathematics

    Get PDF
    Mathematics is an important gatekeeper for educational and professional opportunities and a useful tool for discovery and expression. Given previous research and theory demonstrating potential for metacognitive and self-regulated learning (MC/SRL) interventions to support mathematics achievement with diverse learners, a systematic review was conducted to evaluate their effectiveness within the years of general education, with pupils of ages three to 18. Appropriately-designed studies that were reported in English between 2005 and 2019 were included. Following a systematic search, with double-reviewing and expert consultation for consistency, 1,761 bibliographic items were screened, resulting in 60 included studies. Qualitative aspects of the designs, contexts, participants, and intervention activities were synthesised narratively. Posttest-only and adjusted, random effects meta-analyses were performed using a single mathematics achievement measure from each study. The results indicate a generally positive effect from the included interventions (combined Cohen’s d=0.46, SE=0.08, 95% CI=0.30 to 0.60). This represents a somewhat more modest effect compared with previous reviews in this area, possibly due to a greater range of included reports. No risk of publication bias was identified, reflecting the breadth and diversity of included studies, but efforts to mitigate heterogeneity were only partially successful. Interventions using structured problem-solving with metacognitive prompts were more effective than those not using it, while dissertations reported lower effects than journal articles. No differences were found based on participant age or intervention dose. Primary studies used a variety of assessments and differed on reporting of interventions and quality-related factors, and there remained substantial heterogeneity in the meta-analysis. Implications of this review for educational theory, research, and practice are discussed, with emphasis on reporting studies fully, using broad-scope, comparable assessments, and investing in comprehensive metacognitive and self-regulated learning interventions that can support lasting change in teaching and learning

    New dimensional estimates for subvarieties of linear algebraic groups

    Full text link
    For every connected, almost simple linear algebraic group GGLnG\leq\mathrm{GL}_{n} over a large enough field KK, every subvariety VGV\subseteq G, and every finite generating set AG(K)A\subseteq G(K), we prove a general {\em dimensional bound}, that is, a bound of the form AV(K)C1AC2dim(V)dim(G)|A\cap V(\overline{K})|\leq C_{1}|A^{C_{2}}|^{\frac{\dim(V)}{\dim(G)}} with C1,C2C_{1},C_{2} depending only on n,deg(V)n,\mathrm{deg}(V). The dependence of C1C_1 on nn (or rather on dimV\dim V) is doubly exponential, whereas C2C_2 (which is independent of deg(V)\mathrm{deg}(V)) depends simply exponentially on nn. Bounds of this form have proved useful in the study of growth in linear algebraic groups since 2005 (Helfgott) and, before then, in the study of subgroup structure (Larsen-Pink: AA a subgroup). In bounds for general VV and GG available before our work, the dependence of C1C_1 and C2C_2 on nn was of exponential-tower type. We draw immediate consequences regarding diameter bounds for classical Chevalley groups G(Fq)G(\mathbb{F}_{q}). (In a separate paper, we derive stronger diameter bounds from stronger dimensional bounds we prove for specific families of varieties VV.)Comment: 35 pages. Submitte

    Examples of works to practice staccato technique in clarinet instrument

    Get PDF
    Klarnetin staccato tekniğini güçlendirme aşamaları eser çalışmalarıyla uygulanmıştır. Staccato geçişlerini hızlandıracak ritim ve nüans çalışmalarına yer verilmiştir. Çalışmanın en önemli amacı sadece staccato çalışması değil parmak-dilin eş zamanlı uyumunun hassasiyeti üzerinde de durulmasıdır. Staccato çalışmalarını daha verimli hale getirmek için eser çalışmasının içinde etüt çalışmasına da yer verilmiştir. Çalışmaların üzerinde titizlikle durulması staccato çalışmasının ilham verici etkisi ile müzikal kimliğe yeni bir boyut kazandırmıştır. Sekiz özgün eser çalışmasının her aşaması anlatılmıştır. Her aşamanın bir sonraki performans ve tekniği güçlendirmesi esas alınmıştır. Bu çalışmada staccato tekniğinin hangi alanlarda kullanıldığı, nasıl sonuçlar elde edildiği bilgisine yer verilmiştir. Notaların parmak ve dil uyumu ile nasıl şekilleneceği ve nasıl bir çalışma disiplini içinde gerçekleşeceği planlanmıştır. Kamış-nota-diyafram-parmak-dil-nüans ve disiplin kavramlarının staccato tekniğinde ayrılmaz bir bütün olduğu saptanmıştır. Araştırmada literatür taraması yapılarak staccato ile ilgili çalışmalar taranmıştır. Tarama sonucunda klarnet tekniğin de kullanılan staccato eser çalışmasının az olduğu tespit edilmiştir. Metot taramasında da etüt çalışmasının daha çok olduğu saptanmıştır. Böylelikle klarnetin staccato tekniğini hızlandırma ve güçlendirme çalışmaları sunulmuştur. Staccato etüt çalışmaları yapılırken, araya eser çalışmasının girmesi beyni rahatlattığı ve istekliliği daha arttırdığı gözlemlenmiştir. Staccato çalışmasını yaparken doğru bir kamış seçimi üzerinde de durulmuştur. Staccato tekniğini doğru çalışmak için doğru bir kamışın dil hızını arttırdığı saptanmıştır. Doğru bir kamış seçimi kamıştan rahat ses çıkmasına bağlıdır. Kamış, dil atma gücünü vermiyorsa daha doğru bir kamış seçiminin yapılması gerekliliği vurgulanmıştır. Staccato çalışmalarında baştan sona bir eseri yorumlamak zor olabilir. Bu açıdan çalışma, verilen müzikal nüanslara uymanın, dil atış performansını rahatlattığını ortaya koymuştur. Gelecek nesillere edinilen bilgi ve birikimlerin aktarılması ve geliştirici olması teşvik edilmiştir. Çıkacak eserlerin nasıl çözüleceği, staccato tekniğinin nasıl üstesinden gelinebileceği anlatılmıştır. Staccato tekniğinin daha kısa sürede çözüme kavuşturulması amaç edinilmiştir. Parmakların yerlerini öğrettiğimiz kadar belleğimize de çalışmaların kaydedilmesi önemlidir. Gösterilen azmin ve sabrın sonucu olarak ortaya çıkan yapıt başarıyı daha da yukarı seviyelere çıkaracaktır

    On the Weisfeiler-Leman dimension of some polyhedral graphs

    Full text link
    Let mm be a positive integer, XX a graph with vertex set Ω\Omega, and WLm(X){\rm WL}_m(X) the coloring of the Cartesian mm-power Ωm\Omega^m, obtained by the mm-dimensional Weisfeiler-Leman algorithm. The WL{\rm WL}-dimension of the graph XX is defined to be the smallest mm for which the coloring WLm(X){\rm WL}_m(X) determines XX up to isomorphism. It is known that the WL{\rm WL}-dimension of any planar graph is 22 or 33, but no planar graph of WL{\rm WL}-dimension 33 is known. We prove that the WL{\rm WL}-dimension of a polyhedral (i.e., 33-connected planar) graph XX is at most 22 if the color classes of the coloring WL2(X){\rm WL}_2(X) are the orbits of the componentwise action of the group Aut(X){\rm Aut}(X) on Ω2\Omega^2

    Strategies for Early Learners

    Get PDF
    Welcome to learning about how to effectively plan curriculum for young children. This textbook will address: • Developing curriculum through the planning cycle • Theories that inform what we know about how children learn and the best ways for teachers to support learning • The three components of developmentally appropriate practice • Importance and value of play and intentional teaching • Different models of curriculum • Process of lesson planning (documenting planned experiences for children) • Physical, temporal, and social environments that set the stage for children’s learning • Appropriate guidance techniques to support children’s behaviors as the self-regulation abilities mature. • Planning for preschool-aged children in specific domains including o Physical development o Language and literacy o Math o Science o Creative (the visual and performing arts) o Diversity (social science and history) o Health and safety • Making children’s learning visible through documentation and assessmenthttps://scholar.utc.edu/open-textbooks/1001/thumbnail.jp

    Northern Powerhouses: the homes of the industrial elite, c.1780-1875

    Get PDF
    This thesis explores the world of the industrial elites of Manchester and Liverpool in the period c.1780-1875, through their houses. The homes of the industrial elites, namely merchants and manufacturers, were extremely important tangible communicators of wealth, taste, and comfort. Whilst status-building was closely connected to the house, this thesis argues that the industrial elites carved their own identities into their domestic spheres and that emulation was not solely linked with aspiration. The findings of this thesis are based around its three research aims regarding the changing location of houses in Manchester and Liverpool in the eighteenth and nineteenth centuries, the appearance and use of houses, and the daily routines and involvement of the industrial elite in their domestic routines. An analysis of elite residential patterns in Manchester and Liverpool across the eighteenth and nineteenth centuries has created a more nuanced look at urban geographies of the region in this period. Though some residential patterns differed because of economic and political structure, a key finding has been that the process of suburbanisation in and around Manchester and Liverpool commenced earlier than previous scholarship has suggested. Suburbanisation among the elites began in the latter decades of the eighteenth century and into the early decades of the nineteenth century, with elite suburban communities being firmly established by the 1820s. This thesis discovered that despite socio-economic and political differences, the industrial elites of Manchester and Liverpool used their houses, gardens, and landed estates in very similar ways. This was a result of conformity which arose from emulation at both a community-based level and the emulation and aspiration of elite, gentrified lifestyle. Also, the merchants and manufacturers analysed within this work were involved in their home at every level of domesticity, from the construction of the house to the financial management of the household, although this latter theme was often a cooperative effort between spouses and family members, adding more to our understanding of gender, domesticity, and familial relations. Through detailed case studies and a combination of sources, the private lives of the industrial elites have been revaluated and redefined, including showing how their houses functions metaphorically and in reality
    corecore