Semistability and Hilbert-Kunz multiplicities for curves

We study Hilbert-Kunz multiplicity of non-singular curves in positive characteristic. We analyse the relationship between the Frobenius semistability of the kernel sheaf associated with the curve and its ample line bundle, and the HK multiplicity. This leads to a lower bound, achieved iff the kernel sheaf is Frobenius semistable, and otherwise to formulas for the HK multiplicity in terms of parameters measuring the failure of Frobenius semistability. As a byproduct, an explicit example of a vector bundle on a curve is given whose $n$-th iterated Frobenius pullback is not semistable, while its $(n-1)$-th such pullback is semistable, where $n>0$ is arbitrary.Comment: Latex2e, 12 pages, final version, revised as per the referee's suggestions, to appear in Journal of Algebr

Symmetry Constraints in Inflation, α\alpha-vacua, and the Three Point Function

The Ward identities for conformal symmetries in single field models of inflation are studied in more detail in momentum space. For a class of generalized single field models, where the inflaton action contains arbitrary powers of the scalar and its first derivative, we find that the Ward identities are valid. We also study a one-parameter family of vacua, called $\alpha$-vacua, which preserve conformal invariance in de Sitter space. We find that the Ward identities, upto contact terms, are met for the three point function of a scalar field in the probe approximation in these vacua. Interestingly, the corresponding non-Gaussian term in the wave function does not satisfy the operator product expansion. For scalar perturbations in inflation, in the $\alpha$-vacua, we find that the Ward identities are not satisfied. We argue that this is because the back-reaction on the metric of the full quantum stress tensor has not been self-consistently incorporated. We also present a calculation, drawing on techniques from the AdS/CFT correspondence, for the three point function of scalar perturbations in inflation in the Bunch-Davies vacuum.Comment: 51 pages, 3 figures, 6 appendices. v3: JHEP version. Minor typos correcte

IIMA in HealthCare Management: Abstract of Publications (2000-2010)

The Indian Institute of Management, Ahmedabad (IIMA), was established in 1961 as an autonomous institution by the Government of India in collaboration with the Government of Gujarat and Indian industry. IIMA’s involvement in the health sector started with the establishment of the Public Systems Group in 1975. In the initial period, our research focused on the management of primary healthcare services and family planning. We expanded our research activities to include the management of secondary healthcare services in the 80s and to tertiary healthcare services in the 90s. Currently our research interests focus on the governance and management issues in the areas on Rural Health, Urban Health, Public Health and Hospital Management. In June 2004, IIMA Board approved the setting up of a Centre for Management Health Services (CMHS) in recognition of IIMA’s contributions to the health sector in the past and the felt need to strengthen the management of health sector in the context of socio-economic developments of our country. The overall objectives of CMHS are to address the managerial challenges in the delivery of health services to respond to the needs of different segments of our population efficiently and effectively, build institutions of excellence in the health sector, and influence health policies and wider environments. All our research projects are externally funded and we have developed research collaborations with 15-20 international universities in USA, UK, Europe, and Asia. CMHS has also established strong linkages with the Ministry of Health and Family Welfare at the national and state government levels, particularly in the states of Gujarat, Maharashtra, Rajasthan, Madhya Pradesh, Chattisgarh, Orissa, and Bihar. This working paper is a compilation of the abstracts of all our publications in the last 10 years, which include 40 referred journal articles, 54 Working Papers, 19 Chapters in Books and 18 Case Studies.

A Note on the Effect of Wall Conduction on Heat Transfer in Couette Flow with and Without Injection

Problem of temperature distribution in transpiration cooled porous body and in hot gas stream have been solved in conjugation. The effect of wall conduction on heat transfer in Couette flow has been exhibited graphically and discussed

Enhancing Cross-Cultural Communication in Low-Resource Language Conversational Agents

Recent advancements in natural language processing (NLP) and large language models (LLMs) have facilitated the development of systems capable of generating human-like responses across a wide range of tasks. However, the majority of research has focused predominantly on English, overlooking the vast linguistic diversity globally. For true global inclusivity, extending research to other languages is crucial, particularly as it can significantly benefit various sectors such as business, healthcare, government, and education. A major challenge in this expansion is the scarcity of digital data available and the limited number of pre-trained models for low-resource languages. Our research specifically addresses these challenges by focusing on improving cross-cultural communication through the development of conversation agents for low-resource Indian languages, namely Hindi, Gujarati, Marathi, and Bengali. We propose an approach of integrating a translation model within the conversational model pipeline, aiming to enhance the conversational agent’s capabilities in these languages. Employing techniques such as transfer learning and zero-shot multilingual applications, we try to improve the translation quality of our conversational agent. Using a transfer learning approach, we achieved quantifiable enhancements in translation and improved language comprehension through the zero-shot multilingual method. Additionally, human evaluation of the system has yielded positive feedback, confirming the effectiveness of our models in facilitating more inclusive and accessible communication across different linguistic and cultural contexts