Srikishan Sarda College

The U(2)-Lie algebraic formalism can be used to systematically describe the vibrational spectral analysis of aromatic compounds like benzene, toluene, m-xylene, and mesitylene. Instead of using traditional force-constant methods to model vibrational dynamics,U(2) algebra offers a compact and symmetry-adapted framework by treating molecular vibrations as excitations within an algebraic space. Despite having a common aromatic benzene ring, each molecule in this study has unique point-group symmetries (D6h for benzene,CSfor toluene,C2v for m-xylene, and D3h for mesitylene). These symmetries are used to assign vibrational modes and determine their Raman and infrared activity. The permitted vibrational transitions are obtained by applying symmetry constraints from the corresponding point groups and buildingU(2) Hamiltonians for pertinent stretching and bending co-ordinates. By determining the transformation properties of the normal modes under the U(2) generators and connecting them with irreducible representations of individually molecules' point group, the resulting algebraic model reliably predicts the Raman-active modes that necessitate a variation in the polarizability of the molecule during its vibration, along with the IR-active modes that demand a change in the molecule's dipole moment. This method offers a sophisticated, group-theoretical method for examining the vibrational spectra of substituted aromatic systems in addition to making the assignment of spectral features simpler.

This paper undertakes a comprehensive examination of Dhritarashtra, the blind king of Hastinapura in the Mahabharata, through the interdisciplinary lenses of disability studies, political philosophy, and literary theory. It interrogates how Dhritarashtra’s physical impairment—his congenital blindness—is politicized and construed as a fundamental disqualification from leadership. By analysing the narrative structure of the Mahabharata, the symbolic functions of blindness, and the sociopolitical context of ancient Indian kingship, the study explores how perception—both literal (sensory) and metaphorical (cognitive, ethical)—is deeply enmeshed with the construction of political legitimacy. This paper further investigates how the notion of ‘vision’ is central to leadership paradigms and how the absence of this faculty is framed as epistemic and moral failure. Drawing on modern theories of ableism and critical disability studies, the research critiques the normative assumptions embedded within the epic, revealing how Dhritarashtra’s blindness is not just a physical trait but a narrative device that delegitimizes his political agency. The paper argues that such portrayals are symptomatic of a broader cultural discomfort with non-normative bodies in positions of authority. Ultimately, the study reflects on the enduring impact of mythological archetypes on contemporary discourses around disability and leadership, urging a re-evaluation of how societies define competence, authority, and moral insight.

Linear carbon clusters Cn represent one-dimensional, highly reactive assemblies of carbon atoms that serve as fundamental structural units for a wide range of carbon nanomaterials, including graphene and carbon nanotubes. Owing to their unique structural and electronic properties, the investigation of their vibrational characteristics—particularly the fundamental vibrational frequencies—plays a crucial role in understanding their stability, bonding, and chemical reactivity. These vibrational properties are commonly explored through experimental techniques such as Raman and infrared (IR) spectroscopy, as well as through theoretical frameworks. In the present study, the Lie Algebraic Model (LAM) is employed to investigate the stretching and bending vibrational modes of linear carbon clusters C3, C4, C5, C6, C7, and C8. Within this algebraic framework, a model Hamiltonian is constructed that explicitly incorporates the pseudo-Cnv ​dynamical symmetry associated with these molecular systems. The formulation utilizes a compact set of algebraic parameters capable of effectively describing the C–C stretching and bending dynamics. Furthermore, the invariant Majorana and Casimir operators are systematically derived to characterize the vibrational structure of the clusters. The results obtained from the algebraic treatment exhibit a high degree of consistency with available experimental observations and other theoretical calculations, demonstrating the reliability and effectiveness of the Lie algebraic approach in describing the vibrational behaviour of linear carbon clusters.

India’s extraordinary linguistic diversity forms a vital part of its cultural, intellectual, and civilisational heritage. Indigenous and minority languages are repositories of collective memory, oral traditions, ecological knowledge, cultural values, and community identity. However, unequal educational, economic, administrative, and technological structures often enable dominant languages to displace indigenous languages from important domains, weakening intergenerational transmission of language and culture. The National Education Policy (NEP) 2020 provides an important framework for addressing these challenges through its emphasis on multilingualism, mother-tongue or home-language education, Indian languages, bilingual learning materials, local cultural contexts, and Indian Knowledge Systems. It recommends the use of the home, mother, local, or regional language as the medium of instruction, wherever possible, at least until Grade 5 and preferably beyond Grade 8 (Ministry of Education, 2020). The National Curriculum Framework for School Education (NCF-SE) 2023 further stresses local language, culture, heritage, indigenous knowledge, and traditional learning practices (National Steering Committee for National Curriculum Frameworks, 2023). UNESCO’s Bhasha Matters: State of the Education Report for India 2025 likewise highlights mother-tongue-based multilingual education as essential to inclusion and linguistic diversity (UNESCO, 2025). Focusing particularly on Assam and North-East India, this paper critically examines NEP 2020 through Language Ecology, Linguistic Human Rights, Additive Multilingualism, Indigenous Knowledge Systems, and Cultural Sustainability. It proposes the DECDI framework—Documentation, Educational Inclusion, Community Participation, Digital Revitalisation, and Intergenerational Transmission—to translate policy vision into sustainable practice. The paper argues that preservation requires not merely symbolic recognition but meaningful contemporary domains for indigenous languages in education, research, digital spaces, and everyday life.

This paper examines the relationship between oral traditions, linguistic continuity, and cultural identity among the Chakmas of Assam, a Particularly Vulnerable Tribal Group (PVTG) with a long history of migration and displacement. Drawing upon borderland theory, ethnolinguistics, and oral narrative studies, the study investigates how migration memories, Theravada Buddhist institutions, bilingual practices, and ritual performances contribute to the preservation of collective identity. The research adopts a qualitative ethnographic methodology involving participant observation, semi-structured interviews, oral history collection, and linguistic documentation in Chakma settlements of Hailakandi and Karbi Anglong districts. The paper argues that oral narratives function as alternative archives of historical memory while bilingualism produces adaptive and hybrid forms of belonging rather than simple cultural erosion. Buddhist monasteries, ritual festivals, and oral storytelling continue to sustain intergenerational continuity despite the pressures of modernization, migration, and linguistic assimilation. The study contributes to broader discussions on indigenous resilience, borderland identity, endangered languages, and cultural preservation in Northeast India. It also recommends community-based language documentation, mother-tongue education, and digital archival initiatives for safeguarding indigenous knowledge systems.