Stability and Convergence analysis of a Crank-Nicolson Galerkin scheme for the fractional Korteweg-de Vries equation

In this paper we study the convergence of a fully discrete Crank-Nicolson Galerkin scheme for the initial value problem associated with the fractional Korteweg-de Vries (KdV) equation, which involves the fractional Laplacian and non-linear convection terms. Our proof relies on the Kato type local smoothing effect to estimate the localized $H^{\alpha/2}$-norm of the approximated solution, where $\alpha \in [1,2)$. We demonstrate that the scheme converges strongly in $L^2(0,T;L^2_{loc}(\mathbb{R}))$ to a weak solution of the fractional KdV equation provided the initial data in $L^2(\mathbb{R})$. Assuming the initial data is sufficiently regular, we obtain the rate of convergence for the numerical scheme. Finally, the theoretical convergence rates are justified numerically through various numerical illustrations

MONITORING OXIDATIVE STRESS ACROSS WORSENING CHILD PUGH CLASS OF CIRRHOSIS

, , ) nmol/l} and a significant decrease in levels of , ) U/gm Hb}, , ) U/ gm , ) mmol/ gm Hb}. CONCLUSIONS: Oxidative stress is associated with the development and progression of cirrhosis

Monitoring Oxidative Stress Across Worsening Child Pugh Class of Cirrhosis

Context :Oxidative stress has been increasingly implicated in the pathogenesis and progression of cirrhosis. Aims :We studied oxidative stress in patients with cirrhosis by measuring markers reflecting pro-oxidant (serum malondialdehyde-MDA) and antioxidant factors (RBC catalase-CAT, superoxide dismutase-SOD and blood reduced glutathione-GSH) factors. The level of oxidative stress was also assessed with respect to functional compromise of liver, as determined by Child Turcotte Pugh (CTP) scoring. Design :Case-controlled retrospective study. Materials and Methods :Twenty-three patients of cirrhosis along with 23 age and sex matched healthy controls were studied. Exclusion criteria were concurrent use of anti-oxidant drugs; co-existing diseases like DM, CKD; alcohol use, gastrointestinal bleed or blood transfusion within previous 2 weeks. Besides routine investigations, MDA, CAT, SOD and GSH levels were measured and compared with controls. Statistical Analysis :Continuous variables were recorded as mean ± SD; ANOVA-f test, followed by Tukey′s test, was used to evaluate the significance of difference (P < 0.05) among groups. Results :Mean age of patients was 41.04 ± 12.3 yrs. Patients showed a significant increase in MDA {control 3.31 ± 0.25 (95% CI 3.21-3.41), Child B 6.30 ± 0.4 (95% CI 6.03-6.53), Child C 8.05 ± 0.66 (95% CI 7.29-8.81) nmol/l} and a significant decrease in levels of SOD {control 845.13 ± 36.44 (95% CI 829.92-860.34), Child B 582.91 ± 42.12 (95% CI 557.45-608.32), Child C 489.5 ± 17.66 (95% CI 479.3-499.7) U/gm Hb}, CAT {controls 2.54 ± 0.22 (95% CI 2.45-2.63), Child B 1.93 ± 0.23 (95% CI 1.72-2.14), Child C 1.46 ± 0.10 (95% CI 1.40-1.52) U/ gm Hb} and GSH {controls 6.52 ± 0.25 (95% CI 6.42-6.52), Child B 3.85 ± 0.18 (95%CI 3.74-3.96), Child C 2.99 ± 0.30 (95% CI 2.82-3.16) mmol/ gm Hb}. Conclusions : Oxidative stress is associated with the development and progression of cirrhosis

Studies on character association and path coefficient for quantitative traits to yield and its attributes in garlic: Character association for quantitative traits to yield in garlic

Association between characters and path analysis in seventeen genotypes/lines of garlic (Allium sativum L.) was studied at the Vegetable Research Farm, BUAT, Banda during 2019 and 2020. The pooled data of correlation studies, revealed that gross yield plot-1 had positive and significant correlation with equatorial bulb diameter, weight of 20 bulbs and weight of 50 cloves at genotypic and phenotypic level respectively. This showed that improving these features could improve the crop’s physiological capacity to mobilise and translocate photosynthates to economically valuable organs (the bulb), perhaps increasing bulb yield as seen in the study. Yield was significantly and negatively correlated with bulb shape index, number of cloves bulb-1, and thrips plant-1 at genotypic level. The genotypic path coefficient analysis showed that equatorial bulb diameter and plant height had the highest positive direct effect on bulb yield. Weight of 20 bulbs and collar thickness had negative direct effect on bulb yield. Positive direct effect of equatorial bulb diameter and plant height indicated good scope for improvement in bulb yield by selecting genotypes having bigger bulb along with increased plant height

Structure and thermal stability of amorphous Co23Fe60B17 film on Si substrate

Structural evolution with thermal annealing of the thin film of amorphous Co23Fe60B17 depositors on Si/SiO2 substrate has been studied using grazing incidence x-ray diffraction, soft x-ray absorption spectroscopy (SXAS), and secondary ion mass spectrometry (SIMS). Amorphous to crystalline transformation starts occurring in the film at a temperature between 200 and 300 °C, which is significantly below the crystallization temperature of amorphous ribbon of similar composition. In the process, the body centered cubic CoFe is the primary phase to precipitate out. Combined SIMS and SXAS measurements show that at the surface iron gets preferentially oxidized as compared to cobalt. Surface oxidation is found to decreases with thermal annealing in vacuum. Boron is found to gradually migrate to the surface and get sublimated. Higher surface and interface energies and depletion of B with thermal annealing are expected to be the cause of lower thermal stability of the film. Magneto-optical Kerr effect measurements show that the as-deposited film possesses a well-defined uniaxial magnetic anisotropy. The anisotropy does not disappear even after the partial crystallization of the film. This suggests that the origin of the observed anisotropy is a combined effect of long-range internal stresses and possible chemical short range order in the film

Anomalous Behavior of Magnetic Anisotropy of Amorphous Co40_{40}Fe43_{43}B17_{17} Thin Film Sandwiched Between Mo Layers

Anomalous behavior of magnetic anisotropy in Co$_{40}$Fe$_{43}$B$_{17}$ film sandwiched between Mo layers has been observed as a function of thermal annealing at different temperatures. The as-deposited amorphous film exhibits a uniaxial magnetic anisotropy, the origin of which can be traced to quenched-in stresses. With thermal annealing up to 300 °C, anisotropy remains unchanged. We observe an anomalous magnetic reversal near the hard axis (HA) in the samples annealed at 350 °C and above. The anomaly of the occurrence of nonuniform magnetization near HA can be explained in terms of distribution of easy magnetization direction, as evidenced by the ripple domain structure in Kerr microscopy images

Simple Extraction Cum RP-HPLC Method for Estimation of Nanotized Quercetin in Serum and Tissues of Mice

In recent years, several studies have focused on antioxidant, anti-inflammatory, and anti-cancer activities of quercetin (3,3',4',5, -pentahydroxyflavone). The nanotization of quercetin was shown to enhance its therapeutic efficacy due to smaller particle size. In the present study, an additional step was added to simple extraction cum RP-HPLC method for the quantification of nanotized quercetin (nQ) in biological samples to understand the pharmacokinetics and biodistribution of nQ following intravenous administration. The proposed method involves extraction of nQ from blood serum and tissues of mice with 2N HCl in comparison to well-known DMSO:MeOH mix method. The HCl extraction was found to be 2 - 3 times more efficient than DMSO:MeOH mix method. Results showed that the amount of nQ at various time intervals in the serum and tissues was 2 - 3 fold greater for HCl extraction than for DMSO:MeOH mix method, suggesting that HCl extraction must take into account nQ bound with protein. The reversed-phase HPLC was used for nQ detection, which showed the nQ retention time of 3.2 min. The limit of detection of nQ in blood serum was found to be 0.1 mu g/mL. The proposed method was also validated in terms of linearity, precision, and accurac