Extended higher Herglotz function II Gupta, Rajat; Kumar, Rahul
Journal of mathematical analysis and applications,
02/2023, Letnik:
518, Številka:
2
Journal Article
Recenzirano
Very recently, Radchenko and Zagier revived the theory of Herglotz functions. The main goal of the article is to show that one of the formulas on page 220 of Ramanujan's Lost Notebook actually lives ...in the realms of this theory. As a consequence of our general theorem, we derive an interesting identity analogous to Ramanujan's formula for ζ(2m+1). We also introduce a character analogue of the Herglotz function and initiate its theory by obtaining an elegant functional equation governed by it.
Satopanth Lake is a glacial lake, located at an altitude of 4600 m above sea level in Garhwal Himalaya of Uttarakhand state in India where an attempt was made to assess the water quality. A total of ...sixteen physico-chemical parameters including temperature, hardness, alkalinity, dissolved oxygen, conductivity, pH, calcium, magnesium, chlorides, nitrates, sulphates and phosphates were recorded during 2014 and 2015 between June and August in ice-free period. The mean values of pH ranged from 6.85 to 7.10; water temperature fluctuated from 0.1 to 0.3 °C; dissolved oxygen varied from 5.90 to 6.0 mg.L
−1
; free CO
2
varied from 8.40 to 8.60 mg.L
−1
; total dissolved solids varied from 88.0 to 89.5 mg.L
−1
; calcium from 7.88 to 7.95 mg.L
−1
; magnesium from 0.53 to 0.66 mg.L
−1
. All the physico-chemical values were within the prescribed WHO/BIS limit for drinking water. Water Quality Index (WQI) calculated based on these parameters also revealed the excellent quality of lake water.
Objective To report the results and oncological efficacy of laparoscopic radical nephrectomy (LRN) in patients with renal cell carcinoma with renal vein and inferior vena cava thrombus. Methods We ...performed retrospective record review of 41 patients who underwent LRN along with venous thrombectomy at 2 Canadian centers from 2002 to 2012 by dedicated laparoscopic surgeons. Results The mean age and body mass index of the 41 study patients (34 males and 7 female) were 64.4 years and 28.7 kg/m2 , respectively. Median tumor size was 9.3 cm; 39 patients had renal vein thrombus, and 2 had inferior vena cava thrombus. Nine patients (22%) had metastatic disease to begin with and underwent laparoscopic cytoreductive nephrectomy. Median estimated blood loss, operative time, and length of stay were 100 mL (range, 50-400 mL), 134.5 minutes (range, 99-183 minutes), and 4 days (range, 4-6 days), respectively. There were 4 (9.7%) grade 2 complications. There was no intraoperative death. Mean duration of follow-up was 42 months (range, 6-107 months). Of 32 patients with localized disease, 4 (12.5%) died of progressive disease, 3 (9.3%) died of unrelated causes, and 3 patients (9.3%) were lost to follow-up. Twenty-two patients (68.7%) were alive at a mean follow-up of 47 months. Conclusion LRN and venous thrombectomy for advanced renal tumors with venous thrombus are safe procedures in experienced hands with significant laparoscopic skills. The short-term oncological data are encouraging and advocate the efficacy of this procedure in this subset of patients, although longer follow-up is required in larger number of patients to further define its role.
We undertook the first study from India to evaluate the long-term health effects of coronavirus disease 2019 (COVID-19).
The patients enrolled in our post-COVID-19 clinic were followed up for ...assessment at 1, 3, 6 and 12 months after recovery from acute disease prospectively.
200 patients with mean age of 50.72 years and 57.5% males were analysed. 42.5% had severe and 17% had moderate disease at the time of diagnosis. The persistence of symptoms beyond 1 month of diagnosis was seen in 72.5% (145/200) patients. 8% (16/200) of the patients had post-COVID-19 complications that required rehospitalisation after discharge or recovery from acute COVID-19. The complications included respiratory failure (2%), lung cavities (3.5%), fungal infection, pericardial effusion, pneumothorax and death. The symptoms were persistent beyond 3 months in 51% (102/200) and beyond 6 months in 17.5% (35/200) of cases. The patients with persistent symptoms beyond 3 months and 6 months had significantly higher intensive care unit (ICU) admission during acute COVID-19, severe disease during acute COVID-19, and higher prevalence of comorbidities compared to the recovered patients. The clinical recovery was attained in 95.5% (91/200) patients, and the radiological recovery was attained in 97.92% patients at 1 year. The mean duration to clinical recovery was 174.2 days.
COVID-19 recovery takes longer time. However, clinico-radiological recovery is attained in >95% cases by one year.
Diesel degradation and bacterial growth were investigated in soil, marine water, and freshwater ecosystems using Acinetobacter baumannii IITG19, Providencia vermicola IITG20, and their mixed culture. ...Both bacteria were found to be effective in all three ecosystems, with the best degradation occurring in freshwater. Acinetobacter baumannii IITG19 showed higher degradation (59%, 62%, and 76%) than Providencia vermicola IITG20 (31%, 57%, and 67%) in soil, marine water, and freshwater, respectively. Alkanes showed higher degradation than naphthenes and aromatics for both strains. The mixed culture showed higher diesel degradation efficiency than individual strains in all ecosystems. The overall degradation was similar in soil and marine water (66%), while freshwater showed the highest degradation of 81%. In the presence of the mixed culture, the degradation of alkanes was more than 90%. Bacterial growth was highest in freshwater and lowest in soil for both bacteria and the mixed culture. Metabolite analysis confirmed alcoholic degradation for alkanes and cyclo-alcoholic degradation for naphthenes. The degradation rate for mixed culture was higher than that of both the individual strains. The mixed culture had highest degradation rate constant in freshwater at 0.11 day-1 followed by that in marine ecosystem at 0.078 day-1. The rate constant was lowest for soil ecosystem at 0.066 day-1. Thus the mixed culture showed effectiveness in all three ecosystems, with its highest effectiveness observed in the freshwater ecosystem.
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