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1.
Rose Morris-Wright 《Journal of Pure and Applied Algebra》2021,225(1):106468
Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic. 相似文献
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Rose Vogel Dr. 《ZDM》2005,37(5):445-449
Taking advantage of patterns is typical of our everyday experience as well as our mathematical thinking and learning. For example a working day or a morning at school displays a certain structure, which can be described in terms of patterns. On the one hand regular structures give us the feeling of permanence and enable us to make predictions. On the other hand they also provide a chance to be creative and to vary common procedures. School students usually encounter patterns in math classes either as number patterns or geometric patterns. There are also patterns that teachers can find in analyzing the errors students make during their calculations (error patterns) as well as patterns that are inherent to mathematical problems. One could even go so far as to say that identifying and describing patterns is elementary for mathematics (cf. Devlin 2003). Practising good interacting with patterns supports not only the active learning of mathematics but also a deeper understanding of the world in general. Patterns can be explored, identified, extended, reproduced, compared, varied, represented, described and created. This paper provides some examples of pattern utilization and detailed analyses thereof. These ideas serve as “hooks” to encourage the good use of patterns to facilitate active learning processes in mathematics. 相似文献
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Emily S. Tepe Ellen S. Deutsch MD Quiana Sampson Stephen Lawless James S. Reilly Robert Thayer Sataloff 《Journal of voice》2002,16(2):244-250
The objective of this study was to determine the incidence of vocal problems in young choir singers and to correlate vocal problems with demographic and behavioral information. A questionnaire addressing vocal habits and hygiene was offered to 571 young choir singers, up to 25 years of age, who sing at least weekly; 129 (22.6%) responded. More than one-half of the respondents had experienced vocal difficulty, particularly older adolescents. Detrimental behaviors and circumstances surveyed were not reflective of the incidence of vocal difficulty, except for morning hoarseness, chronic fatigue, insomnia, and female gender after puberty. Voice care professionals should be aware that self-reported voice difficulties are common among young choral singers, especially postpubescent girls, and children with symptoms consistent with reflux (morning hoarseness) and emotional stress (insomnia). Laryngologists should communicate with choral conductors and singing teachers to enhance early identification and treatment of children with voice complaints, and to develop choral educational strategies that help decrease their incidence. 相似文献
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Partially supported by NSF Grant DMS-9004123 and ARO through MSI Cornell (DAAG 29-85-C-0018) 相似文献
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We report the coexistence of γ(γ′) and θ alumina grown on the CoAl(1 0 0) surface. Both phases were observed after annealing of alumina at 1150 K by means of scanning tunnelling microscopy (STM). The crystal structures of γ(γ′) and θ alumina were indexed based on low energy electron diffraction (LEED) and STM experimental data. 相似文献
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