On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms

AbstractIn this paper we introduce decomposition functions CΓ(α,x;ω), SΓ(α,x;ω), Cγ(α,x;ω) and Sγ(α,x;ω) of the generalized gamma functions. These functions are found useful in the analytic study of the temperature distribution of a semi-infinite solid with periodic boundary conditions and to the theory of Fourier transforms. Several new identities involving the Fourier transforms are investigated and some of the classical ones are recovered as special cases. For numerical and scientific computations, tabular and graphical representations of the functions CΓ(α,x;ω) and SΓ(α,x;ω) are also given

The relationship between money stock and economic growth of Sri Lanka: an aeg testing approach

In modern economy, money stocky is identified as a mechanism of economic growth of all nations. The purpose of this study was to test the relationship among the money stocky and economic growth of Sri Lanka. The time series data of the gross domestic product and the money stockused in this study were collected from the sample period from 1959 to 2013. The Augmented Dickey Fuller (ADF) and Philips Perron tests were used to test the stationarity of the time series variables, and then the Augmented Engel – Granger (AEG) testing approach was employed to test the relationship between the variables. Based on the Augmented Engel – Granger (AEG) testingresults, this study found that the money stock was positively impacting on economic growth of Sri Lanka. The partial p – Value of the money stock was less than 1% and the value of R- squared of this testing model was 0.85, which was higher than Durbin Watson statistic. In the meantime, the absolute value of the Augmented Dickey Fuller (ADF) test of the residual of the estimated model was stationary at 5% critical value. So, the conclusion was that the money stock and economic growth of Sri Lanka were maintained the relationship between them at I(0) level form

Inflation and economic growth in Sri Lanka: an ARDL bound testing approach

Nowadays, number of researchers empirically confirmed that the inflation and economic growth equally move together in negative liaison. But, in Sri Lankan context, this relationship was inferentially not proofed. Therefore, this study was empirically going to test this relationship. The objective of this study was to test the long run nexus between the inflation and economic growth in Sri Lanka. To test this objective, this study used the annual time series data during the periods of 1970 to 2014. And, the multiple regressions model was employed with support of the Auto Regressive Distributed Lag (ARDL) technique which was newly introduced by Pesaran et al., (2001). In this study, the economic growth was used as dependent variable and the inflation rate, exchange rate, and money supply were considered as independent variables. In these independent variables, the inflation rate was considered as key variable and others were exercised as control variables. Based on the ARDL technique, this study selected the lag- 2 model for interpreting the findings which was selected by Akaike Info Criterion (AIC) and Schwarz Bayesian Criterion (SBC). Furthermore, this study fitted a long run nexus model using ordinary least square method with support of ARDL technique. Based on this model, this study confirmed that both the inflation and the economic growth maintain the long run nexus between them with appearing of negative sign. Therefore, this study recommends that, when the development policy makers frame the development policy they should consider this nexus

Impact of fiscal deficit on inflation in Sri Lanka: an econometric time series analysis

There is a relationship between the fiscal deficit and inflation, which was confirmed empirically in several studies conducted in many countries. Sri Lanka has been encountering the problem of inflation for the recent years. But in Sri Lanka, this proposition has not yet been studied scientifically. Therefore, this study was going to fill this gap. The objective of this study was to test the impact of fiscal deficit on inflation in Sri Lanka. For this study, the annual time series data were used during the period of 1959 to 2013. The fiscal deficit, exchange rate, government expenditures and import outflow were used as independent variables while the Colombo consumer price index was considered as dependent variable. In addition, the multiple regressions model was used to test the impact of fiscal deficit on inflation. Based on the regression results, the fiscal deficit preserved the positive relationship with inflation in Sri Lanka at one percent significant level. Therefore, this study confirmed that the fiscal deficit accelerates the inflation in Sri Lanka

Salt stress induces genotype-specific DNA hypomethylation in ZmEXPB2 and ZmXET1 genes in maize

Maize, a moderately salt sensitive crop, first experiences osmotic stress that cause reduction in plant growth under salt stress. Fluctuation in cell wall elongation is one of the reasons of this reduction. Along with others, two important proteins expansins and xyloglucan endotransglucosylase are involved in regulation of cell wall elasticity, but the role of epigenetic mechanisms in regulating the cell wall related genes is still elusive. The present study was conducted with the aim of understanding the role of DNA methylation in regulating ZmEXPB2 and ZmXET1 genes. One salt sensitive and one salt tolerant maize cultivar was grown under hydroponic conditions at different levels of salt stress: T1 = 1 mM (control), T2 = 100 mM and T3 = 200 mM in three replicates. DNA and RNA were extracted from roots. After bisulfite treatment, Methyl Sensitive PCR was used for the DNA methylation analysis. It was revealed that fragment in promoter of ZmEXPB2 gene showed high level of DNA methylation under T1 in both varieties. Comparison of different stress treatments revealed decrease in DNA methylation with the increase in salt stress, significantly lower methylation appearing in T3. Similarly, the fragment in promoter of ZmXET1 gene also showed high levels of DNA methylation in T1. When different treatments were analysed, this gene significantly hypomethylated at T2 which continued to decrease in T3 in sensitive variety but remain stable in tolerant variety. Although, further in-depth analysis is required, our results demonstrate region-specific and genotype-specific methylation shift in the promoter of the ZmEXPB2 and ZmXET1 genes when subjected to the salt stress confirming the epigenetic regulation of these genes under stress conditions

Kinematic measurements of novel chaotic micromixers to enhance mixing performances at low reynolds numbers : Comparative study

Funding Information: Funding: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2019R1A2C1007657). The authors gratefully acknowledge this support.Peer reviewedPublisher PD

Tocilizumab in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Background: In this study, we aimed to evaluate the effects of tocilizumab in adult patients admitted to hospital with COVID-19 with both hypoxia and systemic inflammation. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. Those trial participants with hypoxia (oxygen saturation <92% on air or requiring oxygen therapy) and evidence of systemic inflammation (C-reactive protein ≥75 mg/L) were eligible for random assignment in a 1:1 ratio to usual standard of care alone versus usual standard of care plus tocilizumab at a dose of 400 mg–800 mg (depending on weight) given intravenously. A second dose could be given 12–24 h later if the patient's condition had not improved. The primary outcome was 28-day mortality, assessed in the intention-to-treat population. The trial is registered with ISRCTN (50189673) and ClinicalTrials.gov (NCT04381936). Findings: Between April 23, 2020, and Jan 24, 2021, 4116 adults of 21 550 patients enrolled into the RECOVERY trial were included in the assessment of tocilizumab, including 3385 (82%) patients receiving systemic corticosteroids. Overall, 621 (31%) of the 2022 patients allocated tocilizumab and 729 (35%) of the 2094 patients allocated to usual care died within 28 days (rate ratio 0·85; 95% CI 0·76–0·94; p=0·0028). Consistent results were seen in all prespecified subgroups of patients, including those receiving systemic corticosteroids. Patients allocated to tocilizumab were more likely to be discharged from hospital within 28 days (57% vs 50%; rate ratio 1·22; 1·12–1·33; p<0·0001). Among those not receiving invasive mechanical ventilation at baseline, patients allocated tocilizumab were less likely to reach the composite endpoint of invasive mechanical ventilation or death (35% vs 42%; risk ratio 0·84; 95% CI 0·77–0·92; p<0·0001). Interpretation: In hospitalised COVID-19 patients with hypoxia and systemic inflammation, tocilizumab improved survival and other clinical outcomes. These benefits were seen regardless of the amount of respiratory support and were additional to the benefits of systemic corticosteroids. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research

Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial

Background: Many patients with COVID-19 have been treated with plasma containing anti-SARS-CoV-2 antibodies. We aimed to evaluate the safety and efficacy of convalescent plasma therapy in patients admitted to hospital with COVID-19. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]) is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. The trial is underway at 177 NHS hospitals from across the UK. Eligible and consenting patients were randomly assigned (1:1) to receive either usual care alone (usual care group) or usual care plus high-titre convalescent plasma (convalescent plasma group). The primary outcome was 28-day mortality, analysed on an intention-to-treat basis. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936. Findings: Between May 28, 2020, and Jan 15, 2021, 11558 (71%) of 16287 patients enrolled in RECOVERY were eligible to receive convalescent plasma and were assigned to either the convalescent plasma group or the usual care group. There was no significant difference in 28-day mortality between the two groups: 1399 (24%) of 5795 patients in the convalescent plasma group and 1408 (24%) of 5763 patients in the usual care group died within 28 days (rate ratio 1·00, 95% CI 0·93–1·07; p=0·95). The 28-day mortality rate ratio was similar in all prespecified subgroups of patients, including in those patients without detectable SARS-CoV-2 antibodies at randomisation. Allocation to convalescent plasma had no significant effect on the proportion of patients discharged from hospital within 28 days (3832 [66%] patients in the convalescent plasma group vs 3822 [66%] patients in the usual care group; rate ratio 0·99, 95% CI 0·94–1·03; p=0·57). Among those not on invasive mechanical ventilation at randomisation, there was no significant difference in the proportion of patients meeting the composite endpoint of progression to invasive mechanical ventilation or death (1568 [29%] of 5493 patients in the convalescent plasma group vs 1568 [29%] of 5448 patients in the usual care group; rate ratio 0·99, 95% CI 0·93–1·05; p=0·79). Interpretation: In patients hospitalised with COVID-19, high-titre convalescent plasma did not improve survival or other prespecified clinical outcomes. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research