Search results for: algebraic identities

Authors: Amina Babou

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Gender and language is a moot and miscellaneous arena in the sphere of sociolinguistics, which has been proliferated so widely and rapidly in recent years. The dawn of research on gender and foreign language education was against the feminist researchers who allowed space for the bustling concourse of voices and perspectives in the arena of gender and language differences, in the early to the mid-1970. The objective of this scrutiny is to explore to what extent teaching gender and language in the English as a Foreign Language (EFL) classroom plays a pivotal role in learning language information and skills. And the gist of this paper is to investigate how EFL students in Algeria conflate their gender identities with the linguistic practices and scholastic expertise. To grapple with the full range of issues about the EFL students’ awareness about the negotiation of meanings in the classroom, we opt for observing, interviewing, and questioning later to check using ‘how-do-you do’ procedure. The analysis of the EFL classroom discourse, from five Algerian universities, reveals that speaking strategies such as the manners students make an abrupt topic shifts, respond spontaneously to the teacher, ask more questions, interrupt others to seize control of conversations and monopolize the speaking floor through denying what others have said, do not sit very lightly on 80.4% of female students’ shoulders. The data indicate that female students display the assertive style as a strategy of learning to subvert the norms of femininity, especially in the speaking module.

Keywords: gender identities, EFL students, classroom discourse, linguistics

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Authors: Dane Morace-Court

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This paper offers a reflective and reflexive examination of the lived experience of a group of young, white, working-class males engaging in secondary-education in England at a time when this population is widely recognised as the lowest attaining ethnic group within British schools. The focus of the paper is an exploration of the development of identities and aspirations, alongside contemporary demographic and ideological shifts in the British population, in their intersection with neoliberal education policies and the emerging ideological conflict between identity conservatism and liberalism. The construction and performance of intersecting social-class, gender, ethnic and national identities is considered as well as the process through which socially constructed narratives inform identities, values, and aspirations. Evocative autoethnography is then employed to offer reflections on working-class habitus and, in particular, classed and gendered codes that underpin expectations of manhood in post-industrial culture within an education system which seemingly requires the abandonment of aspects of a working-class background. Findings from the study identify the emergence of a culture of hyper-individualisation amongst white, working-class males in schools and a belief in the meritocratic ideologies of the New Right. In particular, the breakdown of the social contract, including notions of political and civic responsibility, coupled with the symbolic violence perpetrated against working-class culture and solidarity in British schools, have all informed the construction of a working-class masculinity which values the individual entrepreneur over the collective, and depoliticizes students to an extent where a focus on the spectacle and performance of success has replaced individual and collective investment in community.

Keywords: education, identity, masculinity, neoliberalism, working-class, intersectionality, autoethnography

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Authors: Samaneh Eshraghi Ivaria, Torkild Thellefsenb

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The article discusses the significance of understanding the semiotics of future cities and recognizing the signs of cultural identity in contributing to the preservation of citizens' memories. The identities of citizens are conveyed through memories in urban planning, and with the rapid advancements in technology, cities are constantly changing. Therefore, preserving memories in the design of future cities is essential in maintaining a quality environment that reflects the citizens' identities. The article focuses on the semiotics of the movement pattern morphology in Mashhad city's historical area, using the historical interpretation method. The practice of walking to the shrine of Imam Reza as a religious building has been a historical and religious custom among Shiites from the past until now. By recognizing the signs that result from this religious and cultural approach on the morphology of the city, the aim of the research is to preserve the place of memories in future cities. Overall, the article highlights the importance of recognizing the cultural and historical significance of cities in designing future urban spaces. By doing so, it is possible to preserve the memories and identities of citizens, ensuring that the urban environment reflects the unique cultural heritage of a place.

Keywords: memories, future cities, movement pattern, mashhad, semiotics

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Authors: Chih-Ping Chen

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Today, technology does not necessitate change; rather, social media has afforded a new arena and digital tools for users/individuals to be symbolized and marketed in meaningful exchanges of digital identities. We argue that these symbolic interactions may afford individuals the ability to create and present less restricted Line person-to-person (P2P) chats than would be possible in face-to-face communications. Individuals can select flexible influence strategies to market themselves, which enables them to create and present their digital identities and impressions in alternative ways within a dynamic sociocultural context. Therefore, this paper aims to explore the novel phenomenon of how individuals market themselves to manage their digital identities and impressions to connect with other users through the symbolic interactions created by new digital tools (e.g., stickers). A netnographic approach was developed by applying a triangulated methodology consisting of user self-diary reports, in-depth interviews, and observations. Totally, 20 participants (10 females and 10 males) were of Taiwanese origin, and their ages ranged from 20–47 years old. The findings of this research showed that individuals on Line P2P social media where traditional cultural gender norms have shifted. Both male and female participants market their modern digital identities by adopting a combination of flexible influence tactics/strategies when using digital stickers. Some findings showed that their influence tactics/strategies often flouted Taiwanese cultural gender norms or skirted traditional rules to fit individual or P2P needs. Finally, these findings potentially contributed to the literature regarding the consumer culture theory and symbolic interaction theory in digital marketing and social media fields.

Keywords: Consumer culture theory, Digital sticker, Self-marketing, Impression, Symbolic interaciton

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Authors: Eusebio Jr. Lina, Ederlina Nocon

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Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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Authors: Victoria G. Mountford-Brown

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The concept of the Entrepreneurial University and emphasis on higher education institutions as both hives of innovation and as producers of future innovators accord special significance to the role of academic researchers in future economic and social prosperity. Researcher development in the UK has embedded an emphasis or ‘enterprise lens’ on developing the capabilities of researchers to support a stable economy whilst providing solutions to societal challenges. However, the notion of the ‘entrepreneurial university’ and what that represents to many academics is met with tension and (dis)engagement in the premises of the ‘knowledge economy’ or ‘academic capitalism.’ Set in a landscape of UK higher education wherein the increasing emphasis on research impact, coupled with increasing competition for scarce funding, has created a ‘climate of performativity’. This research seeks to better understand the ways in which academic identities are (re)constructed in the everyday experiences of doctoral (PGR) and early career researchers (ECRs) as they navigate what is referred to by some as the ‘academic hunger games’. These daily pressures and high expectations of success are part of the identity work PGRs/ECRs undergo. This is often fraught with tension and struggles to adapt to the research environment suggesting a reason for imposter phenomenon to be rife in academia – particularly (but not exclusively) in the early stages of development. This pilot study involves qualitative semi-structured exploratory interviews with a mixed gendered sample of participants from a variety of subject disciplines who have taken part in an intensive 3-day innovation and enterprise program for PGR and ECRs premised on developing personal and research impact. The research seeks to better understand the processes of identity formation of becoming academic and offers a commentary on the notions of ‘imposter phenomenon’ and the exchange and development of resources or capital needed to ‘play the game’ in academia in the context of the ‘entrepreneurial university’. It explores ongoing (re)constructions of what it means to be an academic and the different ways in which social identities may embody and challenge the development of entrepreneurial academic identities. As such, it aims to contribute to our understanding of the innovation ecosystem of academia and the prosperity of academic researchers.

Keywords: entreprenruial development, higher education, identities, researcher development

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Authors: Anusmita Das

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In the post-industrial scenario, cities in India have become critical sites of negotiation and are expected to become some of the largest urban agglomeration of the twenty-first century. This has created a pluralist identity resulting in a new multifarious urbanism pervading throughout the entire urban landscape. There is an ambiguity regarding the character of present day Indian cities with new meanings emerging and no methodical study to understand them. More than an abstract diagram, the present day cities can be looked at as an ensemble of meanings. One of the ways in which the meaning is reflected is through events. Festivals such as Diwali, Dussera, Durga Puja, Ganesh Chaturthi, etc have transpired as the phenomenon of the city, and their presence in the everyday landscape weaves itself through the urban fabric dominating the popular visual culture of Indian cities. Festivals influence people’s idea of a city. Ritual, festival, celebrations are important in shaping of the urban environment and in their influence on the intangible aspect of the urban setting. These festivals pertaining to the city in motion have emerged as the symbolic image of the emerging urban Indian condition giving birth to new urban identities. The study undertaken to understand the present context of temporality of Indian cities is important in analyzing the process of its formation and transformation. This study aims to review the evolution of new dimensions of urbanism in India as well as its implication on the identity of cities.

Keywords: urban identities, urban design, festivals, rituals, celebrations, inter-disciplinary study

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Authors: Bharat Prasad Neupane

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Given the widespread concentration on beliefs, values, emotions, critical incidents, and practices in exploring teachers’ professional identities, this study presents the trajectories of identity construction of three English language teachers from Nepal, analyzing their storied lives from schoolteachers to university professors. For this purpose, the article considered the three-dimensional professional development model to explore the effective mediation by the state agencies, culture and the policies, appropriate support from the organizations, and the bottom-up initiatives taken by the teachers in their professional development. Besides, the professional development journey derived from the in-depth interview of the participants is analyzed by employing communities of practice theory, particularly engagement, alignment, and imagination, as theoretical categories to discover their professional identities. The analysis revealed that passion for language, creativity, and motivation to learn English during childhood initially encouraged them to study English. In addition, inspiration from their teachers during their schooling and later a competitive working environment motivated them to experiment with innovative teaching approaches and establish themselves in the profession. Furthermore, diversification in university teaching according to university requirements and resultant divergence from the professional root ultimately transformed their identity beyond English teachers. Finally, university policy, customization of teachers as per the university requirement, and their survival strategy as English teachers in a university where technical subjects are given more priority has impacted their professional identities.

Keywords: teachers’ professional development, English language teaching, professional identity, communities of practice

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Authors: Nuran Öze

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Communities and societies have been changing towards computer mediated communication. This paper explores online and offline identities and how relationships are formed and negotiated within internet environments which offer opportunities for people who know each other offline and move into relationships online. The expectations and norms of behavior within everyday life cause people to be embodied self. According to the age categories of Turkish Cypriots, their measurements of attitudes in Facebook will be investigated. Face-to-face field research and semi-structured interview methods are used in the study. Face-to-face interview has been done with Turkish Cypriots who are using Facebook already. According to the study, in constructing a linkage between real and virtual identities mostly affected from societal relations serves as a societal grooming tool for Turkish Cypriots.

Keywords: facebook, identity, social media, virtual reality

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Authors: Mike Seal

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This paper explores the traditions of critical and queer pedagogy, its intersections, tensions and paradoxes. Critical pedagogy, with a materialist realist ontology, and queer theory, which is often post-modern, post-structural and anti-essential, may not seem compatible. Similarly, there are tensions between activist orientations, often enacted through essential sexual identities, and a queer approach that questions such identities and subjectivities. It will argue that critical realism gives us a bridge between critical and queer pedagogy in preserving a realist materialist ontology, where economic forces are real, and independent of consciousness and hermeneutic constructions of them. At the same time, it offers an epistemology that does not necessitate a binary view of the roles of the oppressed, liberator, or even oppressor. It accepts that our knowledge is contingent, partial and contestable, but has the potential, and enough validity, to demand action and potentially inform the actions of others.

Keywords: critical pedagogy, queer pedagogy, critical realsim, heteronormativity

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Authors: Sharapat Sharapat

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English language is perceived as cultural capital in many non-native English-speaking countries, and minority groups in these social contexts seem to invest in the language to be empowered and reposition themselves from the imbalanced power relation with the dominant group. This study is devoted to explore how English learning influence minority Kazakh students’ identity (re)construction at Chinese universities from the scope of ‘imagined community, investment, and identity’ theory of Norton (2013). To this end the three research questions were designed as follows: 1) Kazakh minority students’ English learning experiences at Chinese universities; 2) Kazakh minority students’ views about benefits and opportunities of English learning; 3) the influence of English learning on Kazakh minority students’ identity (re)construction. The study employs an interview-based qualitative research method by interviewing nine Kazakh minority students in universities in Xinjiang and other inland cities in China. The findings suggest that through English learning, some students have reconstructed multiple identities as multicultural and global identities, which created ‘a third space’ to break limits of their ethnic and national identities and confused identity as someone in-between. Meanwhile, most minority students were empowered by the English language to resist inferior or marginalized positions and reconstruct imagined elite identity. However, English learning disempowered students who have little previous English education in school and placed them on unequal footing with other students, which further escalated the educational inequities.

Keywords: minority in China, identity construction, multilingual education, language empowerment

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Authors: Renee Monchalin

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Métis peoples, while comprising over a third of the total Indigenous population in Canada, experience major gaps in health services that accommodate their cultural identities. This is problematic given Métis peoples experience severe disparities in health determinants and outcomes compared to the non-Indigenous Canadian population. At the same time, Métis are unlikely to engage in health services that do not value their cultural identities, often utilizing mainstream options. Given these contexts, this research aims to fill the culturally-safe health care gap for Métis peoples in Canada. It does this by engaging 56 urban Métis women who participated in a longitudinal cohort study, Our Health Counts (OHC) Toronto. Traditionally, Métis women were central to the health and well-being of their communities. However, due to decades of colonial legislation and forced land displacement, female narratives have been silenced, and Métis identities have been fractured. This has resulted in having direct implications on Métis people’s current health and access to health services. Solutions to filling the Métis health service gap may lie in the all too often unacknowledged or missing voices of Métis women. Through a conversational method, this research will explore urban Métis women’s perspectives on identity and their experiences with health services in Toronto. The goal of this research is to learn from urban Métis women on steps towards filling the health service gap. This research is currently in the data collection stage. Preliminary findings from the conversations will be disseminated. Policy recommendations for health service providers will be provided to better accommodate Métis people.

Keywords: indigenous health, Metis health, urban, health service access, identity

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Yuan-Yu Chiang, Yu-Han Tseng, Chin-Chen Wen

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Many southeast-Asia women migrate to Taiwan by marriage, and it usually takes 4 to 8 years for them to acquire Taiwanese citizenship. This study investigates the relationships between their citizenship acquisition and whether they develop Taiwanese identities. One hundred and ninety-two immigrant women were measured using Multigroup Ethnic Identity Measure-Revised and a global 10-point ethnic identity question. Correlation tests and hierarchical regression were performed to explore whether acquiring citizenship would help immigrant women to develop Taiwanese identities. The results revealed that citizenship acquisition does help immigrant women to identify with Taiwanese society symbolically. However, the results also indicated that acquiring citizenship would not help these immigrant women become involved in deeper cultural exploration of Taiwan nor would it encourage them to make commitments to the host society.

Keywords: immigrants, international marriage, ethnic identity, Taiwan

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Authors: Rachel Turney

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American Woman is a discussion of being a woman in American through the lens of intersectionality, critical race theory, Muslim American identities, and social citizenship. The survey design and resulting paper are based on the researcher’s personal experience studying intersectionality and Muslim American identities through National Endowment for the Humanities. The researcher poses three questions to White, African American, and Muslim American women about female identify in America. Results are coded and analyzed in their meaning in the context of American society. Results show the similarities, primarily the idea of motherhood and fighting in society. Results also examine differences like those related to faith and family identifies in responses. The researcher examines the specific overlap in responses in the context of social citizenship.

Keywords: women, Muslim women, intersectionality, feminism

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Authors: Shirin Zubair

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Keeping in view the segregation of space(s) experienced by young women and men at puberty in Pakistan and the socially constructed and performative aspect of gender identity by Western theorists of gender and self, this paper will explore Pakistani youth’s differential, gendered performances. Specifically focused on Pakistani youth’s perceptions and experiences of sexuality, extramarital and same-sex relationships in constructing and performing gendered identities as manifested through their talk, the research will also draw upon recent theories of space in cultural studies and postcolonial discourses. The data cited has been culled from two different studies conducted at universities in the city of Multan. Informal, unstructured group discussions of women and men aged between twenty and twenty nine years of age were recorded separately among groups of friends and cohorts studying at two different universities. The findings clearly show both young women and men doing the boundary work in identity construction in private and public spaces: talking of sexuality, sexual desire and sexual relationships, women tend to safely couch their articulations in euphemisms: distance themselves from the Western concepts of sexual liberation ; while young men’s exhibitionism in boasting of their sexual prowess and sexual encounters as well as the use of sexually explicit and tabooed words frequently in their intimate conversations shows a clear departure from and a contestation of the normative public discourses. Further the findings illustrate that young men conform to the patriarchal ideologies by constructing heterosexual identities whereas young women initiate discourse on same-sex relationships. The data also reveals that the private identities of these young Pakistanis are different from their public identities, as it is in their intimate conversations and private (or safe) spaces that they talk about their pre-marital sexual activities and love affairs. These intimate and safe spaces thus emerge as subversion and contestation of their public identity, as sex and sexuality are tabooed subjects in public discourses.

Keywords: sexuality, gender, identity, performance

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Authors: Malika Yaici, Kamel Hariche, Tim Clarke

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The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: eigenvalues/eigenvectors, latent values/vectors, matrix fraction description, state space description

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Authors: Olteanu Constanta, Olteanu Lucian

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Researchers note that algebraic reasoning and sense making is essential for building conceptual knowledge in school mathematics. Consequently, pre-service teachers’ own reasoning and sense making are useful in fostering and developing students’ algebraic reasoning and sense making. This article explores the forms of reasoning and sense making that pre-service mathematics teachers exhibit and use in the process of analysing problem-posing tasks with a focus on first-degree equations. Our research question concerns the characteristics of the problem-posing tasks used for reasoning and sense making of first-degree equations as well as the characteristics of pre-service teachers’ reasoning and sense making in problem-posing tasks. The analyses are grounded in a post-structuralist philosophical perspective and variation theory. Sixty-six pre-service primary teachers participated in the study. The results show that the characteristics of reasoning in problem-posing tasks and of pre-service teachers are selecting, exploring, reconfiguring, encoding, abstracting and connecting. The characteristics of sense making in problem-posing tasks and of pre-service teachers are recognition, relationships, profiling, comparing, laddering and verifying. Beside this, the connection between reasoning and sense making is rich in line of flight in problem-posing tasks, while the connection is rich in line of rupture for pre-service teachers.

Keywords: first-degree equations, problem posing, reasoning, rhizomatic assemblage, sense-making, variation theory

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Authors: Shomaila Sadaf, Margarethe Olbertz-Siitonen

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This study looks at identity and othering in discourses around sensitive issues in social media. More specifically, the study explores the multimodal resources and narratives through which the other is formed, and identities are ascribed in online spaces. As an integral part of social life, media spaces have become an important site for negotiating and ascribing identities. In line with recent research, identity is seen hereas constructions of belonging which go hand in hand with processes of in- and out-group formations that in some cases may lead to othering. Previous findings underline that identities are neither fixed nor limited but rather contextual, intersectional, and interactively achieved. The goal of this study is to explore and develop an understanding of how people co-construct the ‘other’ and ascribe certain identities in social media using multiple modes. In the beginning of the year 2018, the British government decided to include relationships, sexual orientation, and sex education into the curriculum of state funded primary schools. However, the addition of information related to LGBTQ+in the curriculum has been met with resistance, particularly from religious parents.For example, the British Muslim community has voiced their concerns and protested against the actions taken by the British government. YouTube has been used by news companies to air video stories covering the protest and narratives of the protestors along with the position ofschool officials. The analysis centers on a YouTube video dealing with the protest ofa local group of parents against the addition of information about LGBTQ+ in the curriculum in the UK. The video was posted in 2019. By the time of this study, the videos had approximately 169,000 views andaround 6000 comments. In deference to multimodal nature of YouTube videos, this study utilizes multimodal discourse analysis as a method of choice. The study is still ongoing and therefore has not yet yielded any final results. However, the initial analysis indicates a hierarchy of ascribing identities in the data. Drawing on multimodal resources, the media works with social categorizations throughout the documentary, presenting and classifying involved conflicting parties in the light of their own visible and audible identifications. The protesters can be seen to construct a strong group identity as Muslim parents (e.g., clothing and reference to shared values). While the video appears to be designed as a documentary that puts forward facts, the media does not seem to succeed in taking a neutral position consistently throughout the video. At times, the use of images, soundsand language contributes to the formation of “us” vs. “them”, where the audience is implicitly encouraged to pick a side. Only towards the end of the documentary this problematic opposition is addressed and critically reflected through an expert interview that is – interestingly – visually located outside the previously presented ‘battlefield’. This study contributes to the growing understanding of the discursive construction of the ‘other’ in social media. Videos available online are a rich source for examining how the different social actors ascribe multiple identities and form the other.

Keywords: identity, multimodal discourse analysis, othering, youtube

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Authors: Panayiota Romios

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As the use of 'diaspora' has proliferated in the last decade, its meaning has been stretched in various directions. Current diaspora frames of identity representation do not adequately capture the complexities of everyday lived experiences of transnational individuals and groups. This paper presents the findings of a qualitative research project conducted in Melbourne, Australia with second generation Greek Australians. It analyses the forms of intercultural identities of the second generation Greek Australians returning to Australia post-2008, after living in Greece for an extended period of time. The discussion highlights key characteristics in relation to diaspora-homeland ties, seeking to denaturalise the commonplace assumptions and imaginations about the cultures and identities of Greek Australian diaspora communities and probe the relevance of identity markers such a country of origin, nationality, ethnicity, ethnic origin, language and mother tongue. The definition of diaspora experienced in this transnational lexicon is interestingly quite distinct from original articulations and also from others returning ‘home’.

Keywords: diaspora, identity, migration, displacement

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Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: R. Chinnaiyaprabhu, S. Bharanidharan, V. Dharsana, Rajalavanya

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The concept of the Metaverse represents a potential evolution in the realm of cyberspace. In the early stages of Web 2.0, we observed a proliferation of online pseudonyms or 'nyms,' which increased the prevalence of fake accounts and made it challenging to establish unique online identities for various roles. However, in the era of Web 3.0, particularly in the context of the Metaverse, an individual's digital identity is intrinsically linked to their real-world identity. Consequently, actions taken in the Metaverse can carry significant consequences in the physical world. In light of these considerations, we propose the development of an innovative authentication system known as 'Metasec.' This system is designed to enhance security for digital assets, online identities, avatars, and user accounts within the Metaverse. Notably, Metasec operates as a password less authentication solution, relying on a multifaceted approach to security, encompassing device attestation, facial recognition, and pattern-based security keys.

Keywords: metaverse, multifactor authentication, security, facial recognition, patten password

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Authors: Wang, Kuei-Ing, Jou-Fan Shih

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This study adopts deterrence theory as well as social identities as moderators, and explores their moderating affects on online toxic disinhibition. Survey and Experimental methodologies are applied to test the research model and four hypotheses are developed in this study. The controllability of identity positively influenced the behavior of toxic disinhibition both in experimental and control groups while the fluidity of the identity did not have significant influences on online disinhibition. Punishment certainty, punishment severity as well as social identity negatively moderated the relation between the controllability of the identity and the toxic disinhibition. The result of this study shows that internet users hide their real identities when they behave inappropriately on internet, but once they acknowledge that the inappropriate behavior will be found and punished severely, the inappropriate behavior then will be weakened.

Keywords: seductive properties of internet, online disinhibition, punishment certainty, punishment severity, social identity

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Authors: Rosy Joseph

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From an algebraic point of view, Semirings provide the most natural generalization of group theory and ring theory. In the absence of additive inverse in a semiring, one had to impose a weaker condition on the semiring, i.e., the additive cancellative law to study interesting structural properties. In many practical situations, fuzzy numbers are used to model imprecise observations derived from uncertain measurements or linguistic assessments. In this connection, a special class of fuzzy numbers whose shape is symmetric with respect to a vertical line called the symmetric fuzzy numbers i.e., for α ∈ (0, 1] the α − cuts will have a constant mid-point and the upper end of the interval will be a non-increasing function of α, the lower end will be the image of this function, is suitable. Based on this description, arithmetic operations and a ranking technique to order the symmetric fuzzy numbers were dealt with in detail. Wherein it was observed that the structure of the class of symmetric fuzzy numbers forms a commutative semigroup with cancellative property. Also, it forms a multiplicative monoid satisfying sub-distributive property.In this paper, we introduce the algebraic structure, sub-distributive semiring and discuss its various properties viz., ideals and prime ideals of sub-distributive semiring, sub-distributive ring of difference etc. in detail. Symmetric fuzzy numbers are visualized as an illustration.

Keywords: semirings, subdistributive ring of difference, subdistributive semiring, symmetric fuzzy numbers

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Authors: Peter Jean-Paul, Shanaz Wahid

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The problem of division by zero can be stated as: “what is the value of 0 x 1/0?” This expression has been considered undefined by mathematicians because it can have two equally valid solutions either 0 or 1. Recently semi-structured complex number set was invented to solve “division by zero”. However, whilst the number set had some merits it was considered to have a poor theoretical foundation and did not provide a quality solution to “division by zero”. Moreover, the set lacked consistency in simple algebraic calculations producing contradictory results when dividing by zero. To overcome these issues this research starts by treating the expression " 0 x 1/0" as a quantum mechanical system that produces two tangled results 0 and 1. Dirac Notation (a tool from quantum mechanics) was then used to redefine the unstructured unit p in semi-structured complex numbers so that p represents the superposition of two results (0 and 1) and collapses into a single value when used in algebraic expressions. In the process, this paper describes a new number set called Quantum Semi-structured Complex Numbers that provides a valid solution to the problem of “division by zero”. This research shows that this new set (1) forms a “Field”, (2) can produce consistent results when solving division by zero problems, (3) can be used to accurately describe systems whose mathematical descriptions involve division by zero. This research served to provide a firm foundation for Quantum Semi-structured Complex Numbers and support their practical use.

Keywords: division by zero, semi-structured complex numbers, quantum mechanics, Hilbert space, Euclidean space

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Authors: Sitong. Chen, Bing Wei

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As a sociocultural concept, identity has increasingly gained attention in educational research, and the notion of students’ science identity has been widely discussed in the field of science education. Science identity was proved to be a key indicator of students’ learning engagement, persistence, and career intentions in science-related and STEM fields. Thus, a great deal of educational effort has been made to promote students’ science identity in former studies. However, most of this research was focused on students’ identity development during undergraduate and graduate periods, except for a few studies exploring high school students’ identity formation. High school has been argued as a crucial period for promoting science identity. This study applied a qualitative method to explore how high school students have come to form their science identities in previous learning and living experiences. Semi-structured interviews were conducted with 8 newly enrolled undergraduate students majoring in science-related fields. As suggested by the narrative data from interviews, students’ formation of science identities was driven by their five interrelated experiences: growing self-recognition as a science person, achieving success in learning science, getting recognized by influential others, being interested in science subjects, and informal science experiences in various contexts. Specifically, students’ success and achievement in science learning could facilitate their interest in science subjects and others’ recognition. And their informal experiences could enhance their interest and performance in formal science learning. Furthermore, students’ success and interest in science, as well as recognition from others together, contribute to their self-recognition. Based on the results of this study, some practical implications were provided for science teachers and researchers in enhancing high school students’ science identities.

Keywords: high school students, identity formation, learning experiences, living experiences, science identity

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Authors: Yanni Chang, Dezhi Dai, Albert Y. Tong

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Piecewise linear interface calculation (PLIC) schemes are widely used in the volume-of-fluid (VOF) method to capture interfaces in numerical simulations of multiphase flows. Dynamic overset meshes can be especially useful in applications involving component motions and complex geometric shapes. In the present study, the VOF value of an acceptor cell is evaluated in a geometric way that transfers the fraction field between the meshes precisely with reconstructed interfaces from the corresponding donor elements. The acceptor cell value is evaluated by using a weighted average of its donors for most of the overset interpolation schemes for continuous flow variables. The weighting factors are obtained by different algebraic methods. Unlike the continuous flow variables, the VOF equation is a step function near the interfaces, which ranges from zero to unity rapidly. A geometric interpolation scheme of the VOF field in overset meshes for the PLIC-VOF method has been proposed in the paper. It has been tested successfully in quadrilateral/hexahedral overset meshes by employing several VOF advection tests with imposed solenoidal velocity fields. The proposed algorithm has been shown to yield higher accuracy in mass conservation and interface reconstruction compared with three other algebraic ones.

Keywords: interpolation scheme, multiphase flows, overset meshes, PLIC-VOF method

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Authors: Thi Thi Zin, Pyke Tin, Ikuo Kobayashi, Yoichiro Horii

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Today dairy farm experts and farmers have well recognized the importance of dairy cow Body Condition Score (BCS) since these scores can be used to optimize milk production, managing feeding system and as an indicator for abnormality in health even can be utilized to manage for having healthy calving times and process. In tradition, BCS measures are done by animal experts or trained technicians based on visual observations focusing on pin bones, pin, thurl and hook area, tail heads shapes, hook angles and short and long ribs. Since the traditional technique is very manual and subjective, the results can lead to different scores as well as not cost effective. Thus this paper proposes an algebraic geometric imaging approach for an automatic dairy cow BCS system. The proposed system consists of three functional modules. In the first module, significant landmarks or anatomical points from the cow image region are automatically extracted by using image processing techniques. To be specific, there are 23 anatomical points in the regions of ribs, hook bones, pin bone, thurl and tail head. These points are extracted by using block region based vertical and horizontal histogram methods. According to animal experts, the body condition scores depend mainly on the shape structure these regions. Therefore the second module will investigate some algebraic and geometric properties of the extracted anatomical points. Specifically, the second order polynomial regression is employed to a subset of anatomical points to produce the regression coefficients which are to be utilized as a part of feature vector in scoring process. In addition, the angles at thurl, pin, tail head and hook bone area are computed to extend the feature vector. Finally, in the third module, the extracted feature vectors are trained by using Markov Classification process to assign BCS for individual cows. Then the assigned BCS are revised by using multiple regression method to produce the final BCS score for dairy cows. In order to confirm the validity of proposed method, a monitoring video camera is set up at the milk rotary parlor to take top view images of cows. The proposed method extracts the key anatomical points and the corresponding feature vectors for each individual cows. Then the multiple regression calculator and Markov Chain Classification process are utilized to produce the estimated body condition score for each cow. The experimental results tested on 100 dairy cows from self-collected dataset and public bench mark dataset show very promising with accuracy of 98%.

Keywords: algebraic geometric imaging approach, body condition score, Markov classification, polynomial regression

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Authors: Yolanda Havenga

Abstract:

Being a competent nurse requires clinical, general, and moral competencies. Moral competence is a culmination of moral perceptions, moral judgment, moral behaviour, and moral identity. Moral identity is the values, images, and fundamental principles held in the collective minds and memories of nurses about what it means to be a ‘good nurse’. It is important to explore and describe South African nurses’ moral identities and excavate the post-colonial counter-narrative to nurses moral identities as a better understanding of these identities will enable means to positively address nurses’ moral behaviours. This study explored the moral identity of nurses within the South African context. A qualitative approach was followed triangulating with phenomenological and narrative designs with the same purposively sampled group of professional nurses. In-depth interviews were conducted until saturation of data occurred about the sampled nurses lived experiences of being a nurse in South Africa. They were probed about their core personal-, social-, and professional values. Data were analysed based on the steps used by Colaizzi. These nurses were then asked to write a narrative telling a personal story that portrayed a significant time in their professional career that defines their identity as a nurse. This data were analysed using a critical narrative approach and findings of the two sets of data were merged. Ethical approval was obtained and approval from all relevant gate keepers. In the findings, themes emerged related to personal, social and professional values, images and fundamental principles of being a nurse within the South African context. The findings of this study will inform a future national study including a representative sample of South African nurses.

Keywords: moral behaviour, moral identity, nurses, qualitative research

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Authors: Zhou Congling

Abstract:

The integration of private tutoring has emerged as an indispensable facet in the acquisition of language proficiency beyond formal educational settings. Notably, there has been a discernible surge in the demand for private English tutoring, specifically geared towards the preparation for internationally recognized gatekeeping examinations, such as IELTS, TOEFL, GMAT, and GRE. This trajectory has engendered an escalating need for English Language Teaching Assistants (ELTAs) operating within the realm of Private Tutoring Schools (PTSs). The objective of this study is to unravel the intricate process by which these ELTAs formulate their professional identities in the nascent stages of their careers as English educators, as well as to delineate their perceptions regarding their professional trajectories. The construct of language teacher identity is inherently multifaceted, shaped by an amalgamation of individual, societal, and cultural determinants, exerting a profound influence on how language educators navigate their professional responsibilities. This investigation seeks to scrutinize the experiential and influential factors that mold the identities of ELTAs in PTSs, particularly post the culmination of their language-oriented academic programs. Employing a qualitative narrative inquiry approach, this study aims to delve into the nuanced understanding of how ELTAs conceptualize their professional identities and envision their future roles. The research methodology involves purposeful sampling and the conduct of in-depth, semi-structured interviews with ten participants. Data analysis will be conducted utilizing Barkhuizen’s Short Story Analysis, a method designed to explore a three-dimensional narrative space, elucidating the intricate interplay of personal experiences and societal contexts in shaping the identities of ELTAs. The anticipated outcomes of this study are poised to contribute substantively to a holistic comprehension of ELTA identity formation, holding practical implications for diverse stakeholders within the private tutoring sector. This research endeavors to furnish insights into strategies for the retention of ELTAs and the enhancement of overall service quality within PTSs.

Keywords: China, English language teacher, narrative inquiry, private tutoring school, teacher identity

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