62 research outputs found
Some theorems on the explicit evaluations of singular moduli
No full textAt scattered places in his notebooks, Ramanujan recorded some theorems for calculating singular moduli and also recorded several values of singular moduli. In this paper, we establish several general theorems for the explicit evaluations of singular moduli. we also
obtain some values of class invariants and singular moduli
The Genome Database for Rosaceae (GDR): year 10 update
No full textThe Genome Database for Rosaceae (GDR
On some new Schläfli-type mixed modular equations
No full textOn pages 86 and 88 of his first notebook, Ramanujan recorded eleven Schl\"{a}fli-type modular equations for composite degrees. Out of eleven, ten have been proved by Berndt using theory of modular forms. In this paper, we establish several new Schl\"{a}fli-type mixed modular equations
Sustainable Reporting Practices of Indian Listed Companies: A Comprehensive Comparison with Global Standards
No full text As the world\u27s attention shifts to sustainable development, companies everywhere are implementing open and accountable reporting practices, with a focus on environmental, social, and governance (ESG) issues. This study looks at the extent to which Indian listed companies integrate environmental, social, and governance (ESG) aspects into their reporting practices and how they report sustainably. Through an examination of annual reports, sustainability reports, and other relevant documents, this study aims to identify the prevailing patterns, challenges, and factors impacting sustainable reporting in the Indian business sector. The study assesses the impact of legislative frameworks and international reporting standards on the adoption of sustainable reporting practices by Indian listed enterprises. Through a thorough examination of multiple approaches, the research enhances our understanding of the dynamic environment. The study was conducted for a period of five years. The study is empirical in nature. The major sources of data were collected from secondary sources. For analysis, the proper statistical techniques are employe
Multivariate analysis methods improve the selection of strawberry genotypes with low cold requirement
No full textMethods of multivariate analysis is a powerful approach to assist the initial stages of crops genetic improvement, particularly, because it allows many traits to be evaluated simultaneously. In this study, heat-tolerant genotypes have been selected by analyzing phenotypic diversity, direct and indirect relationships among traits were identified, and four selection indices compared. Diversity was estimated using K-means clustering with the number of clusters determined by the Elbow method, and the relationship among traits was quantified by path analysis. Parametric and non-parametric indices were applied to selected genotypes using the magnitude of genotypic variance, heritability, genotypic coefficient of variance, and assigned economic weight as selection criteria. The variability among materials led to the formation of two non-overlapping clusters containing 40 and 154 genotypes. Strong to moderate correlations were found between traits with direct effect of the number of commercial fruit on the mass of commercial fruit. The Smith and Hazel index showed the greatest total gains for all criteria; however, concerning the biochemical traits, the Mulamba and Mock index showed the highest magnitudes of predicted gains. Overall, the K-means clustering, correlation analysis, and path analysis complement the use of selection indices, allowing for selection of genotypes with better balance among the assessed traits
Functional outcome of peritrochanteric fractures femur treated with proximal femoral nail
No full textBackground: Peritrochanteric fractures are common injuries, especially in the elderly, with significant impact on health care. The aim of treatment should be prevention of malunion and early mobilization. Taking all the factors into consideration, surgery by internal fixation of the fracture is an ideal choice.
Methods: This study included 40 adult patients with peritrochanteric fractures of the femur who met the inclusion criteria and were treated with a Proximal Femoral Nail at BGS Global Institute of Medical Sciences, Bangalore, from November 2022 to November 2024.
Results: The study included 40 cases, 31 males and 9 females, aged 22–94. The majority of patients (45%) were admitted for slip-and-fall injuries, mostly right-sided fractures. 25 of 40 cases were trochanteric, 15 subtrochanteric. The trochanteric fracture group had 40% Boyd and Griffin type 2, while the subtrochanteric group had 33.3% Seinsheimer type IIIa and 20% type IIb. The average hospital stay was 20.67 days and weight-bearing took 16.5 weeks. Two patients died before the 6-week follow-up and three were lost to follow-up. The remaining 35 fractures were 22 trochanteric and 13 subtrochanteric. 90.9% of trochanteric fractures and 88.57% of subtrochanteric fractures had good to excellent results.
Conclusions: The study concludes that the PFN is an excellent implant for the treatment of peritrochanteric fractures. The terms of a successful outcome include a thorough understanding of fracture biomechanics, proper patient selection, good preoperative planning, accurate reduction of the fracture, instrumentation and a good image intensifier
Some new identities for a continued fraction of order 12.
No full textIn this paper, we establish some new modular equations of degree three. We establish some new relations for continued fraction of order 12 and also for a parameter µ(q) = 2V (q)V (q 2 ) connecting Ramanujan’s cubic continued fraction
Certain identities for a continued fraction of Ramanujan.
No full textRamanujan has recorded several continued fractions in his notebooks. In this paper, we establish several identities of a continued fraction of Ramanujan . We also establish several relations between and and several explicit evaluations of
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