12 research outputs found
On Schur's irreducibility results and generalised -Hermite polynomials
Let be a fixed integer such that Let be a positive
integer such that either or for any integer
according as or not. Let belonging to be a
monic polynomial which is irreducible modulo all primes less than . Let
with belonging to be polynomials
having degree less than . Let and the content
of is not divisible by any prime less than . For a positive
integer , if denotes the product of the odd numbers , then we
show that the polynomial
is irreducible over the field of rational numbers. This
generalises a well-known result of Schur which states that the polynomial
with and
is irreducible over . We illustrate our result
through examples
A short note on number fields defined by exponential Taylor polynomials
Let be a positive integer and denote the -th Taylor polynomial of the exponential
function. Let be an algebraic number field where
is a root of and denote the ring of algebraic
integers of . In this paper, we prove that for any prime , does not
divide the index of the subgroup in if and
only if
Correlation of non-stress test with fetal outcome in term of apgar score: a prospective observation study
Background: The objectives of antepartum fetal surveillance are to prevent fetal death and avoidance of unnecessary intervention. This study using NST as a tool for routine antepartum fetal surveillance is we will be trying to catch up those fetuses who might be at risk in womb and provide prompt intervention in otherwise considered normal pregnancies without any obvious high-risk factor thus giving the best outcome in mothers.Methods: The objective of this study was to evaluate the correlation of the non-stress test with fetal outcome in pregnancies from 37-42 weeks of gestation. This was a prospective observational study at RNT Medical college Udaipur (Rajasthan) from November 2021 to March 2022. This study included 100 normal pregnant mothers from 37 weeks to 42 weeks who were subjected to NST.Results: The parameters of poor fetal outcome like apgar score <7 at 5 minutes had increased incidences in the non-reactive group.Conclusions: This study suggests that the NST was found to be a good predictor of the healthy foetus even in normal pregnancies between 37-42 weeks of gestation and the probability of an adverse outcome such as poor Apgar score increases with a non-reactive strip
Using the new ICD-MM classification system for attribution of cause of maternal death: a retrospective study from a tertiary care hospital of Rajasthan
Background: Sustainable development goal 3 includes an ambitious target of reducing the global maternal mortality rate (MMR) to less than 70 per 100,000 births by 2030. Understanding the causes of and factors contributing to maternal deaths is critically important for development of interventions that reduce the global burden of maternal mortality and morbidity. The International classification of diseases-maternal mortality has proven to be easily applicable and helps clarify the cause of maternal death. Methods: Retrospective study of 100 maternal death cases was done in a tertiary medical centre of Rajasthan from December 2020 to November 2021 for determining the causes of maternal death and their classification according to ICD-MM. Results: A total of 100 maternal mortality cases were analyzed in this study for causes of death. Classification of causes of death according to WHO ICD-MM is represented in study results. Direct causes of maternal deaths were observed in 82 % cases whereas indirect causes were present in remaining 18%. Hypertensive disorders (29%), obstetric haemorrhage (27%) and pregnancy related infection (12%) constituted the major groups of direct cause of maternal deaths whereas systemic infections were the most common indirect cause (15%). During the study period, COVID-19 was attributable to 12 cases of maternal death.Conclusions: Hypertensive disorders (29%), obstetric haemorrhage (27%) and pregnancy related infection (12%) were the major causes of direct obstetric death and systemic infections (15%) was the most common cause of indirect obstetric death. All of these causes are preventable with targeted interventions
On prime divisors of the index of an algebraic integer
Let A<sub>K</sub> denote the ring of algebraic integers of an algebraic number field K = Q(θ) where the algebraic integer θ has minimal polynomial F(x) = x<sup>n</sup> + ax<sup>m</sup> + b over the field Q of rational numbers with n = mt + u, t ∊ N, 0 ≤ u ≤ m - 1. In this paper, we characterize those primes which divide the discriminant of F(x) but do not divide [A<sub>K</sub> : Z[θ]] when u = 0 or u divides m; such primes p are important for explicitly determining the decomposition of pA<sub>K</sub> into a product of prime ideals of A<sub>K</sub> in view of the well known Dedekind theorem. As a consequence, we obtain some necessary and sufficient conditions involving only a, b, m, n for A<sub>K</sub> to be equal to Z[θ]