On It\^o-Taylor expansion for stochastic differential equations with Markovian switching and its application in γ∈{n/2:n∈N}\gamma\in\{n/2:n \in\mathbb{N}\}-order scheme

The coefficients of the stochastic differential equations with Markovian switching (SDEwMS) additionally depend on a Markov chain and there is no notion of differentiating such functions with respect to the Markov chain. In particular, this implies that the It\^o-Taylor expansion for SDEwMS is not a straightforward extension of the It\^o-Taylor expansion for stochastic differential equations (SDEs). Further, higher-order numerical schemes for SDEwMS are not available in the literature, perhaps because of the absence of the It\^o-Taylor expansion. In this article, first, we overcome these challenges and derive the It\^o-Taylor expansion for SDEwMS, under some suitable regularity assumptions on the coefficients, by developing new techniques. Secondly, we demonstrate an application of our first result on the It\^o-Taylor expansion in the numerical approximations of SDEwMS. We derive an explicit scheme for SDEwMS using the It\^o-Taylor expansion and show that the strong rate of convergence of our scheme is equal to $\gamma\in\{n/2:n\in\mathbb{N}\}$ under some suitable Lipschitz-type conditions on the coefficients and their derivatives. It is worth mentioning that designing and analysis of the It\^o-Taylor expansion and the $\gamma\in\{n/2:n\in\mathbb{N}\}$-order scheme for SDEwMS become much more complex and involved due to the entangling of continuous dynamics and discrete events. Finally, our results coincide with the corresponding results on SDEs when the state of the Markov chain is a singleton set.Comment: 5

Stripping Voltammetric Determination Of Zinc, Cadmium, Lead And Copper In Blood Samples Of Children Aged Between 3 Months And 6 years

Blood samples of 160 children, ranging age between 3 months and 6 years were selected from five different parts of Amritsar district of Punjab (India) and were analyzed for Zn, Cd, Pb and Cu using anodic stripping voltammetry. Large variations in the results have been correlated to the area inhabited, age differences and other factors. It was found that the areas, more prone to environmental stress, had shown more quantities of these metals in blood samples in comparison to those which were taken from safer sites. Similarly the younger children lesser exposed to environmental pollution had shown comparatively lesser quantity of these metals in comparison to older objects

Hypocellular acute myeloid leukemia with bone marrow necrosis in young patients: two case reports

<p>Abstract</p> <p>Introduction</p> <p>Hypocellular variants of acute myeloid leukemia are very rare and almost always occur in old aged patients. In contrast, hypocellular acute lymphoblastic leukemia usually occurs in children.</p> <p>Case presentation</p> <p>We report two Indian patients with hypocellular acute myeloid leukemia, a 32-year-old woman and a 13-year-old boy. Interestingly, one of the patients also showed bone marrow necrosis.</p> <p>Conclusion</p> <p>Hypocellular acute myeloid leukemia is a rare entity and can affect young individuals. It can be considered as a rare cause of bone marrow necrosis.</p

Clinical profile and epidemiological characteristics of COVID-19 patients admitted in the district hospital of North India- a retrospective study

Background: During COVID-19 all the tertiary institutes were overburdened so all the peripheral institutes, mostly district hospitals were made functional to provide management to COVID-19 patients in moderate and severe cases. The study attempts to find out the clinical profile of admitted patients in one of the district hospital. Methods: Retrospective data was studied from records of district hospital Samba when it was chosen as COVID-19 dedicated hospital. Results: Record of 77 patients was studied and data was analyzed with the help of descriptive statistics. Chi square test was done to find out the association. Mean age was 56.8±16.19 years with male female ratio of 1.33:1. 50% males and 42.4% of females did not have any associated co-morbidities. Half of the studied participants were anemic. Conclusions: Study showed that patients admitted in hospital presented with variable presentation and associated co morbidities were significantly associated with mortality. Peripheral institutions should be equipped with all the facilities to cope with such public health emergencies

Hepatitis B vaccination in human immunodeficiency virus-infected adults receiving hemodialysis

Hepatitis B vaccination in human immunodeficiency virus-infected adults receiving hemodialysis.BackgroundThe Centers for Disease Control and Prevention (CDC) recommends hepatitis B virus (HBV) immunization for all hemodialysis (HD) patients because they are at high risk of infection. Several studies have shown that the development of protective antibody titers after HBV vaccination is much lower in HD patients. We hypothesized that human immunodeficiency virus (HIV) infection in patients with end-stage renal disease (ESRD) would further impair the immune response to hepatitis B vaccination.MethodsWe performed a retrospective cohort study of patients undergoing long-term hemodialysis from 1990 to 2002 at the United States-based dialysis facilities of Gambro Corporation, North America. The response rate defined as an increase in anti-HBs levels ≥10 mIU/L after a month of the third dose of HBV vaccination was determined in HIV-infected and a randomly selected group of ESRD patients. The demographic information, laboratory data, and hepatitis B surface antibody (anti-HBs) titers were recorded from the Gambro Corporation database on these patients.ResultsOf the 347 adult HIV ESRD patients, 116 received three doses of recombinant hepatitis B vaccination. Seventy percent were male, and the majority (86%) were black. Of the 116 patients who received three doses of HBV vaccination, 62 (53.4%) developed protective antibody titers. This was comparable to the response rate of 50.4% in the randomly selected 220 non-HIV hemodialysis patients. Among HIV ESRD patients, the mean hemoglobin (Hgb) was higher in patients who developed protective antibody titers (Hgb 11.61 ± 2 vs. 10.55 ± 1.86,P value <0.01). On multivariate logistic regression analysis, higher Hgb was associated with protective antibody titers (odds ratio: 1.34, 95% CI 0.99–1.72). Seventy percent of the HIV-infected responders maintained protective antibody titers 6 months after vaccination.ConclusionHepatitis B vaccination should be offered to all HIV-infected ESRD patients because over half of the patients with HIV and ESRD can develop protective antibodies

A comparative study based on control system for a pulse detonation engine

Pulse Detonation Engine has been a point of interest in the propulsion industry for some time and the interest has been rising due to its better output and results. But any system can perform its task efficiently based on the efficiency of its control system. In this paper we have presented a comparative study between multiple control systems- one based on Bluetooth technology, the other based on infrared sensor technology and one based on wired electrical system. For the wireless system, the signal received from either of the media is passed to the various sensors and systems connected through an Arduino board that further controls the solenoid valves and ignition system. Primarily, a control system circuit is developed using Arduino board and different sensors to connect the fuel supply and ignition system. In the next stage, Bluetooth sensors are connected using an android app and then an infrared sensor based system is integrated with the Arduino to control the engine and the performance of the two systems are compared. Whereas for wired system, every sub system is controlled through optical wires including the solenoid valves, the injection system and the sensors