Class Group Research Articles

Mapping class group representations and Morita classes of algebras

A modular fusion category \mathcal{C} allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then \mathcal{C} has a unique Morita class of simple non-degenerate algebras, namely, that of the tensor unit. This improves on a result by Andersen and Fjelstad, albeit under stronger assumptions. One motivation to look at this problem comes from questions in three-dimensional quantum gravity.

Extrafamilial stressors in families of transgender adolescents referred for gender-affirming medical care: a mixed-methods analysis

Transgender and nonbinary (TNB) adolescents and their families often experience trans-specific, extrafamilial stressors, which may increase when adolescents come out and try to access gender-affirming medical care. While studies have described such stressors, it is unclear whether distinct underlying patterns of stressor experiences exist, shaping family experience. 159 adolescent–parent dyads attending an initial hormone appointment for gender-affirming medical care at any of 10 clinics in Canada reported on trans-specific, extrafamilial stressor experiences in Trans Youth CAN! Latent class analysis (LCA) assessed underlying patterns; parent and family characteristics were then described for each stressor class in the final model. LCA interpretation was supplemented with thematic analysis of qualitative interviews with 36 parents at 3 of the clinics from the Stories of Care study. The optimal model had four stressor classes: “Low Disruption, Some Advocacy” (estimated 30.4%); “Some Disruption, Some Advocacy” (9.8%); “Low Disruption, Low Advocacy” (55.7%); and “Major Disruption, High Advocacy” (4.1%). Family characteristics suggested a heterogeneous sample, with differing proportions of sociodemographic and family characteristics across stressor classes. Quotations from parent interviews in Stories of Care supported the four-class stressor model. Families of TNB adolescents accessing gender-affirming medical care may experience trans-specific, extrafamilial stressors according to four latent class groupings.

On the p-Rank of Class Groups of p-Extensions

Abstract We prove a local–global principle for the embedding problems of global fields with restricted ramification. By this local–global principle, for a global field $k$, we use only the local information to give a presentation of the maximal pro-$p$ Galois group of $k$ with restricted ramification, when some Galois cohomological conditions are satisfied. For a Galois $p$-extension $K/k$, we use our presentation result for $k$ to study the structure of pro-$p$ Galois groups of $K$. Then for $k={{\mathbb{Q}}}$ and $k={{\mathbb{F}}}_{q}(t)$ with $p\nmid q$, we give upper and lower bounds for the rank of $p$-torsion subgroup of the class group of $K$, and these bounds depend on the structure of the Galois group and the inertia subgroups of $K/k$. Finally, we study the $p$-rank of class groups of cyclic $p$-extensions of ${{\mathbb{Q}}}$ and the $2$-rank of class groups of multiquadratic extensions of ${{\mathbb{Q}}}$, for a fixed ramification type.

ABOUT GROUP OF POINTWISE INNER AUTOMORPHISMS FOR NILPOTENCY CLASS FOUR

Let $L_{m,c}$ stand for the free metabelian nilpotent Lie algebra of class $c$ of rank $m$ over a field $K$ of characteristic zero.
 Automorphisms of the form $\varphi(x_i)=e^{adu_i}(x_i)$ are called pointwise inner, where $e^{adu_i}$, is the inner automorphism
 induced by the element $u_i\in L_{m,c}$ for each $i=1,\ldots,m$. In the present study, we investigate the group structure of
 the group $\text{\rm PInn}(L_{m,4})$ of pointwise inner automorphisms of $L_{m,4}$ for nilpotency class four.

Is There a Relationship Between Vertical Facial Development And Nasal Cavity?

There are no studies investigating the relationship between cone beam computed tomography (CBCT) and nasal passage findings and vertical facial development. The aim of this study is to determine the relationship between nasal cavity anatomy and vertical development of patients. A total of 60 CBCTs were examined, and Class I malocclusion individuals were divided into two groups (30 each) according to vertical facial development. All nasal cavity findings were recorded in the study. Vertical facial development, nasal septum, nasal cavity width, thickness and angle were evaluated. Mann-Whitney U Test was used, and Student's t test was used for the comparison of two groups with normal distribution. Significance was evaluated at p<0.01 and p<0.05 levels. Statistical analysis showed a relationship between vertical facial development and nasal cavity findings. Nasal septum deviation was mild to moderate in the hyperdivergent group, while septal deviation was absent in the hypodivergent group. A statistically significant difference was found in the width, distance (x-y) and angle of the nasal cavity from the hyperdivergent group in Class I vertical subgroups (p<0.05). When compared between low-angle and high-angle groups, statistically significant differences were observed in anterior face height, nasal passage angle, and distance between the outermost points of the nasal cavity.

Design and evaluation of blended teaching in the smart classroom combined with virtual simulation training in basic nursing courses

ObjectiveThis study explored the application effect of smart classrooms combined with virtual simulation training in basic nursing courses for nursing undergraduates.MethodsIn this quasi-experimental study, a total of 135 undergraduate nursing students in the 2021 matriculating cohort were selected as the research subjects. The experimental group of Class 1 had 71 students, and a blended teaching design utilizing a smart classroom and virtual simulation training was adopted. The control group of Class 2 had 64 students, and traditional lecture-based teaching design was adopted. After the course, the independent learning ability scale, test scores and teaching effectiveness questionnaire were used to evaluate the teaching effect. All tests had a maximum score of 100.ResultsNursing undergraduates in the experimental group had scores of 86.32 ± 8.25 for virtual simulation training and 84.82 ± 9.04 for peer-assisted learning. The scores of the theoretical examination, experimental examination, and subjective questions in the experimental group were significantly higher than those in the control group (P < 0.05). The approval rate of nursing undergraduates in the experimental group was significantly higher than that of the control group for four items (Ps < 0.05). Among the 71 students, most students (91.55%) claimed that the use of instructional designs increased the fun of the classroom. In addition to the dimension of information literacy, the total score of independent learning ability and the other three dimensions of the experimental group were significantly higher than those of the control group (P < 0.05).ConclusionThe teaching design combining smart classrooms and virtual simulation training can be applied to realize online blended teaching and classroom informatization, improving the academic performance and independent learning ability of nursing undergraduates, and thus achieving good teaching effects.

Crossed homomorphisms and low dimensional representations of mapping class groups of surfaces

We continue the study of low dimensional linear representations of mapping class groups of surfaces initiated by Franks–Handel [Proc. Amer. Math. So. 141 (2013), pp. 2951–2962] and Korkmaz [Low-dimensional linear representations of mapping class groups, preprint, arXiv:1104.4816v2 (2011)]. We consider ( 2 g + 1 ) (2g+1) -dimensional complex linear representations of the pure mapping class groups of compact orientable surfaces of genus g g . We give a complete classification of such representations for g ≥ 7 g \geq 7 up to conjugation, in terms of certain twisted 1 1 -cohomology groups of the mapping class groups. A new ingredient is to use the computation of a related twisted 1 1 -cohomology group by Morita [Ann. Inst. Fourier (Grenoble) 39 (1989), pp. 777–810]. The classification result implies in particular that there are no irreducible linear representations of dimension 2 g + 1 2g+1 for g ≥ 7 g \geq 7 , which marks a contrast with the case g = 2 g=2 .

Asymptotic behavior of class groups and cyclotomic Iwasawa theory of elliptic curves

Asymptotic behavior of class groups and cyclotomic Iwasawa theory of elliptic curves

How to construct CSIDH on Edwards curves

CSIDH is an isogeny-based key exchange protocol proposed by Castryck et al. in 2018. It is based on the ideal class group action on Fp-isomorphism classes of Montgomery curves. The original CSIDH algorithm requires a calculation over Fp by representing points as x-coordinate over Montgomery curves. There is a special coordinate on Edwards curves (the w-coordinate) to calculate group operations and isogenies. If we try to calculate the class group action on Edwards curves by using the w-coordinate in a similar way on Montgomery curves, we have to consider points defined over Fp4. Therefore, calculating the class group action on Edwards curves with w-coordinates over only Fp is not a trivial task.In this paper, we prove some theorems about the properties of Edwards curves. We construct the new CSIDH algorithm using these theorems on Edwards curves with w-coordinates over Fp. This algorithm is as fast as (or a little bit faster than) the algorithm proposed by Meyer and Reith.This paper is an extended version of [29]. We added the construction of a technique similar to Elligator on Edwards curves. This technique contributes to the efficiency of the constant-time CSIDH algorithm. We also added the construction of new formulas to compute isogenies in O˜(ℓ) time on Edwards curves. It is based on formulas on Montgomery curves proposed by Bernstein et al. (élu's formulas). In our analysis, these formulas on Edwards curves are a little bit faster than those on Montgomery curves.We finally implemented CSIDH, élu's formulas, and CTIDH [3] (faster constant-time CSIDH) on Edwards curves. Each result shows the efficiency of algorithms on Edwards curves.

Convex-compact subgroups of the Goeritz group

Let G &gt; Mod 2 G&gt;\operatorname {Mod}_2 be the Goeritz subgroup of the genus-2 mapping class group. We show that finitely-generated, purely pseudo-Anosov subgroups of G G are convex cocompact in Mod 2 \operatorname {Mod}_2 , addressing a case of a general question of Farb–Mosher. We also give a simple criterion to determine if a Goeritz mapping class is pseudo-Anosov, which we use to give very explicit convex-cocompact subgroups. In our analysis, a central role is played by the primitive disk complex P \mathcal {P} . In particular, we (1) establish a version of the Masur–Minksy distance-formula for P \mathcal {P} , (2) classify subsurfaces X ⊂ S X\subset S that are infinite-diameter holes of P \mathcal {P} , and (3) show that P \mathcal {P} is quasi-isometric to a coned-off Cayley graph for G G .

Problem-based learning method in the context of a flipped classroom: Outcomes on pain management course acquisition

Introduction: A deep understanding of physiology, physiopathology, pharmacology, and the management of pain is crucial for nurse anaesthetists to ensure the well-being of their patients. Thus, the teaching strategies should enhance the transition from acquiring the fundamental pain phenomena, to developing translational and critical thinking. The aim of the study is to determine if the flipped classroom that is considered an active learning approach is most effective compared to the traditional method in teaching pain management and if it improves students' academic performance. Methods: This study was quasi experimental, at a higher institute of nursing professions, among third-year anaesthesia resuscitation nursing students. participants were randomly allocated into either: the flipped classroom group where PBL was used (FG, n = 19), or the traditional lecture-based classroom group (TG, n = 19). The results and impact of the above approach were appreciated via the analysis of the summative assessment of the class group and from the questionnaire submitted to students. Results: The present study revealed that in the midterm exam, the mean score of the flipped classroom group (14.0) which is significantly higher (p&lt;0.01) than the traditional lecture group (11.9). Moreover, the standard deviation of this latter is slightly higher (2.41) which indicates scores far from the average. Also, a significant difference between the averages of the two approaches in favor of flipped classroom Group was revealed (p&lt;0.01). Conclusion: The assessment of student’s grades and their appreciation of both teaching approaches showed a preference for the PBL. Keywords: Flipped Classroom, Nursing Education, Pain Management, Problem-Based Learning

Fitting ideals of class groups for CM abelian extensions

Fitting ideals of class groups for CM abelian extensions

Place, Class, and the Destruction of the American Dream in The Great Gatsby From the Perspective of Space

This study is a spatial analysis of The Great Gatsby (1925). This novel presents the power game among various white classes in American society in the context of the Roaring Twenties, with obvious spatial characteristics. The geographical distribution between East Egg, West Egg, and the Valley of Ashes presents the high-and-low-class distinction of different classes in social space. The upper classes practice class oppression and exploitation through space, while the lower classes also use space to resist oppression and climb the class ladder. This paper draws on French philosopher Henri Lefebvre’s spatial ideas, especially the spatial triad, to explore the close connection between space and class in the novel. The Great Gatsby encompasses various class groups in white society, including the hereditary aristocracy like the Buchanans, the new money represented by Gatsby, and the lower class represented by the Wilsons. To modify the spatial order, different classes use space as a medium to preserve their class identity and seek their social presence, which reproduces the illusion of the American Dream of the Jazz Age and reveals Fitzgerald’s humanistic concern for people in spatial relations.

The Implementation of Word Find Game to Improve Students’ English Vocabulary

This research is Quasi Experimental Research. The objective of this research is to investigate the process of improving students’ English vocabulary by using word find game. The respondents in this research are the eleventh grade students of MAN Bantaeng, consist of 30 students which divided into two group of class where 15 students from MIA 2 as experiment class and 15 students from MIA 1 as a control class. In collecting data, this research used pre-test and post-test. Data calculation using SPSS v.20. The independent variable of this research is word find game and the dependent variable of this research is students’ english vocabulary. This research used random sampling technique. The results of the research showed that score test on pre-test in experiment class was 74.33 and score test pre-test in control class was 65.00. The score post-test in experiment class was 92.67 and score post-test in control class was 76.73. The results of the research showed that the implementation of word find game can increase students' English vocabulary.

Association between antibiotics and asthma risk among adults aged over 40 years: a nationally representative retrospective cohort study

IntroductionSeveral studies have reported that exposure to antibiotics can lead to asthma during early childhood. However, the association between antibiotic use and risk of asthma in the adult population remains...

The issues of design of a Petri net-based software component for modelling holistic and coordinated curriculum for potential specialists’ training

This paper proposes a Petri nets-based software component for automating the holistic and coordinated curriculum building process for pre-service IT specialists. The design of the software module is based on the holistic educational paradigm and the authors’ approach to Petri nets-based curriculum modeling. The core components of the software module are identified and their requirements are formulated. The groups of software classes are specified and described. The benefits of the software module for pre-service IT specialists are highlighted. The prospects for further research include implementing the software module and testing it on specially prepared cases.

Proper proximality in non-positive curvature

abstract: Proper proximality of a countable group is a notion that was introduced by Boutonnet, Ioana and Peterson as a tool to study rigidity properties of certain von Neumann algebras associated to groups or ergodic group actions. In the present paper, we establish the proper proximality of many groups acting on nonpositively curved spaces. First, these include many countable groups $G$ acting properly nonelementarily by isometries on a proper ${\rm CAT}(0)$ space $X$. More precisely, proper proximality holds in the presence of rank one isometries or when $X$ is a locally thick affine building with a minimal $G$-action. As a consequence of Rank Rigidity, we derive the proper proximality of all countable nonelementary ${\rm CAT}(0)$ cubical groups, and of all countable groups acting properly cocompactly nonelementarily by isometries on either a Hadamard manifold with no Euclidean factor, or on a $2$-dimensional piecewise Euclidean ${\rm CAT}(0)$ simplicial complex. Second, we establish the proper proximality of many hierarchically hyperbolic groups. These include the mapping class groups of connected orientable finite-type boundaryless surfaces (apart from a few low-complexity cases), thus answering a question raised by Boutonnet, Ioana, and Peterson. We also prove the proper proximality of all subgroups acting nonelementarily on the curve graph. In view of work of Boutonnet, Ioana and Peterson, our results have applications to structural and rigidity results for von Neumann algebras associated to all the above groups and their ergodic actions.

ANALISIS PENGGUNAAN WHATSAPP TERHADAP MOTIVASI BELAJAR PADA TIK SISWA SEKOLAH MENENGAH ATAS

This study aims to analyze the use of Whatsapp on learning motivation in ICT subjects of grade XI students at SMAN 5 Serang City.The type of research used is qualitative research. This interview was conducted by 5 grade XI students, where the analysis was carried out in three steps, namely data reduction, data presentation, and conclusion pulling.The result of this study is that students use Whatsapp to discuss and communicate, as well as exchange information on material discussed at school. And the use of Whatsapp can affect their focus at school, but it depends on how the person uses it, and students during subjects also students do not play mobile phones because the mobile phones are taro or stored by the teacher. The conclusion of this study is that by providing motivation before holding tests in the class group, students will be more enthusiastic in doing assignments or related to learning. And teachers must also give rules for using mobile phones while studying and when in their spare time. This is so that students focus on following the lesson and the lesson can also enter their brain

Pengaruh Model Pembelajaran Kooperatif Tipe STAD Berbantuan Media Puzzle Terhadap Hasil Belajar Siswa Pada Pembelajaran Matematika Kelas 2 SD

Classical lecture and question and answer methods are mostly chosen by teachers. As a result, students are less enthusiastic in following the lesson and the classroom atmosphere looks inactive. To improve students' learning outcomes, a learning innovation based on the STAD type cooperative learning model is needed. The purpose of this study was to analyze the effect of the STAD type cooperative learning model assisted by Puzzle Media on student learning outcomes in Grade 2 mathematics learning. This research uses quantitative research using experimental methods. The design form used in this research is true experimental. In this study the research subjects were divided into two groups, namely the control class group and the experimental class group. Of the two classes, the control class and the experimental class were determined, class II A was selected as the experimental class and class II B was selected as the control class. The technique used in collecting data in this study used a test instrument. The results of this study are the average of the experimental class which is 70, 17 and the control class is 57, 00, from these results there is a significant difference in learning outcomes which indicates the effect of the STAD type cooperative learning model as an effective learning innovation that can be applied so that learning is fun for students.

The impact of integrating playful activities in the teaching / learning of oral production in FLE class.

This research aims to solve a complex and persistent problem which is represented by the fear of our learner to produce orally in FLE class, namely: glossophobia and the blocking of the FLE learner in class. This is the reason why we are studying, as a solution, the impact of integrating playful activities in the teaching / learning of oral production in FLE class and aim, in this integration, to help our learner to feel confident in groups in FLE class and to unlock orally. So, first of all, we started with the definition of the word ʺplayful‶ to find out its exact meaning. Then, we indicated the types of playful activities in FLE class. Afterwards, we proposed ten essential criteria for the selection of playful activities in FLE class to make our learner speak in FLE class. In addition, we have written twenty important points of advantages and disadvantages of playful activities in FLE class. On the other hand, we have prepared a detailed questionnaire of twenty seven questions addressed to the learner. Finally, we have proposed recommendations as a solution favorable to the problem of blocking our learner orally. Finally, we put an exhaustive conclusion as a final point to this study.