Existence of positive solutions for a nonlinear semipositone boundary value problems on a time scale

In this paper, we are concerned with the existence of positive solution of the following semipositone boundary value problem on time scales: \begin{align*} (\psi(t)y^\Delta (t))^\nabla + \lambda_1 g(t, \,y(t)) + \lambda_2 h(t,\,y(t)) = 0, \,t \in [\rho(c), \,\sigma(d)]_\mathbb{T}, \end{align*} with mixed boundary conditions \begin{align*} \alpha y(\rho(c))-\beta \psi(\rho(c)) y^\Delta(\rho(c))=0,\\ \gamma y(\sigma(d))+\delta \psi(d) y^\Delta(d)=0, \end{align*} where $\psi:C[\rho(c),\, \sigma(d)]_\mathbb{T}$, $\psi(t)>0$ for all $t \in [\rho(c),\,\sigma(d)]_\mathbb{T}$; both $g$ and $h : [\rho(c),\,\sigma(d)]_\mathbb{T} \times [0,\,\infty) \to \mathbb{R}$ are continuous and semipositone. We have established the existence of  at least one positive solution or multiple positive solutions of the above boundary value problem by using fixed point theorem on a cone in a Banach space, when $g$ and $h$ are both superlinear or sublinear or one is superlinear and the other is sublinear for $\lambda_i>0;\,i=1,\,2$ are sufficiently small

Prediction of outcome in adults with severe falciparum malaria: a new scoring system

BACKGROUND: Mortality of falciparum malaria is related to the presence of severe complications. However, no scoring system is available to predict outcome of these patients. The aim of this paper was to devise a simple and reliable malaria prognosis score (MPS) to predict the outcome of adults with severe malaria. METHODS: All slide-positive severe falciparum malaria patients admitted to Ispat General Hospital were studied. Eight clinical parameters that may potentially differentiate or influence the outcome were identified to predict recovery or death RESULTS: Of 248 severe malaria cases, 35 died. There were 212 adults (34 deaths) and 36 children (one death). The malaria score for adults was (MSA) = 1(severe anaemia) + 2 (acute renal failure) + 3(Respiratory distress) +4 (cerebral malaria). The MSA ranges from 0 to 10. The mortality was 2% for MSA 0 – 2; 10% for MSA 3–4, 40% for MSA 5–6 and 90% for MSA 7 or more. The sensitivity is 89.9% and positive predictive value is 94.1% when 5 is taken as the cut off value. CONCLUSION: MSA is a simple and sensitive predictor. It can be administered rapidly and repeatedly to prognosticate the outcome of severe malaria in adults. It can help the treating doctor to assess the patient as well as to communicate to the relatives of the patients about prognosis. The score needs revalidation in other geographical areas

Effect of sodium lauryl sulphate micelle in the oxidation of <i>dl-</i>mandelicacid by Cr(VI)

660-666dl-Mandelicacid on oxidation by Cr(VI) in the absence and presence of sodium lauryl sulphate (NaLS) follows a route conforming to Michaelis-Menten kinetics. Rate data in the presence of [H+] show an acid dependent and acid independent path. Entropy of activation is found to be negative. Rate of oxidation is mildly enhanced in the presence of increasing concentration of NaLS upto the CMC value of NaLS beyond which rate decreases. An attempt has been made to rationalise the observations

Expression of CD68+ Tumor associated macrophages in relation to β-catenin in carcinoma stomach

Background: With no unified system for tumor associated macrophages (TAMs) density assessment, limited information is available on their relationship with β-catenin expression. Aim: To evaluate the density of CD68+ TAMs in gastric adenocarcinoma samples by immunohistochemistry and correlate it with grade, stage, invasion, and beta-catenin. Designs and Settings: Formalin fixed paraffin embedded (FFPE) blocks from gastrectomy specimens of proven gastric adenocarcinoma were prospectively and retrospectively were studied over a period of two years. Materials and Methods: Immunohistochemistry with CD68 and β-catenin was performed. TAM density was qualitatively compared in “tumor” versus “stroma” and “tumor” versus “non-tumor” regions. Quantitative CD68+ TAM density was assessed using different methods and compared. Cases were classified as high and low TAM based on the median value and correlated with histologic type, location, grade, stage and β-catenin expression pattern. Statistical Analysis: Spearman's rank correlation test was used to compare the different methods of TAM density evaluation. The categorical variables were studied using Pearson's Chi-square or Fisher's exact test. CD68+ TAM density and β-catenin expression were correlated by analysis of variance. A P value ≤ 0.05 was taken as statistically significant. Results: The CD68+ TAMs in the “tumor” versus “non-tumor” area (p = 0.34) and “tumor” versus “stroma distribution” (p = 0.81) did not show any statistical significance. All methods of TAM density were found to be comparable. High TAM group is significantly associated with lymphovascular invasion, tumor depth, lymph node metastasis, and abnormal β-catenin expression. Conclusion: TAMs density plays an important role in the tumor stage. Macrophages may possibly induce gastric cancer invasiveness by activating β-catenin pathway