A Characterization of the Two-weight Inequality for Riesz Potentials on Cones of Radially Decreasing Functions

We establish necessary and sufficient conditions on a weight pair $(v,w)$ governing the boundedness of the Riesz potential operator $I_{\alpha}$ defined on a homogeneous group $G$ from $L^p_{dec,r}(w, G)$ to $L^q(v, G)$, where $L^p_{dec,r}(w, G)$ is the Lebesgue space defined for non-negative radially decreasing functions on $G$. The same problem is also studied for the potential operator with product kernels $I_{\alpha_1, \alpha_2}$ defined on a product of two homogeneous groups $G_1\times G_2$. In the latter case weights, in general, are not of product type. The derived results are new even for Euclidean spaces

Market integration of wheat in Pakistan

Understanding market integration in developing countries is an important issue in current research. This study is an attempt to analyze wheat market integration in Pakistan. Previous research on the subject has attempted at analyzing market integration in Pakistan's south and north Punjab regions, mainly relying on co-integration only and not considering advanced dynamic models and transaction costs to analyze the degree of integration. Therefore, this study is a first attempt to analyze the extent of market integration in the whole country using a dynamic model. Monthly wholesale price data of five regional markets from January 1988 to April 2011 are used for this study. Price series were tested for stationarity with the Augmented Dickey Fuller (ADF) test and it was found that all prices are integrated of order one, commonly written as I(1). Co-integration was also identified in all price series pairs using Johansen's co-integration test. The Vector Error Correction Model (VECM) was then applied to the data to analyze the extent of market integration. As a result, it was found that the adjustment to shocks or disequilibrium was higher for the Lahore and Rawalpindi markets as compared to the Hyderabad and Peshawar markets. It might be because of the high consumption, low production and developed infrastructure in these regions. Adjustment coefficients were significant for most of the market pairs. The Threshold Vector Error Correction Model (TVECM) with a band of non-adjustment was applied to incorporate transaction costs, without relying on observations for these costs, which were not available for the study. It was found that linear ECMs or VECMs provide misleading results as compared to TVECMs. Short-run adjustments in the TVECM model provide mixed results depending on regimes as well as markets. Strong adjustments were found in the upper regime, which shows that when price differences are above the second threshold markets tend to adjust significantly

Wheat growth and phytoavailability of copper and zinc as affected by soil texture in saline-sodic conditions

Nutrient disorders in saline-sodic soils can adversely affect crop growth. In order to evaluate the growth response of wheat (Triticum aestivum L.) to Cu and Zn and the phytoavailability of these essential elements, a pot experiment was conducted in three different textured saline-sodic soils [sandy loam (SL), sandy clay loam (SCL) and clay (C)] having an ECe 8.63, 8.80, 8.98 dS m–1 and SAR 21.66, 23.48, 24.84 (mmol L–1)1/2 respectively. Seven treatments including levels of Cu (4, 6 and 8 mg kg–1) and levels of Zn (4, 6 and 8 mg kg–1) were separately applied together with a single control treatment. Dry matter yield (straw + grain) of wheat increased up to 35.2% with Cu and up to 31.2 % with Zn application relative to the control. As soil clay content increased, dry matter yield decreased up to 39.2% in SCL and up to 62.7% in C soil when compared to SL soil. Application of Cu increased the concentration in both wheat straw and grains up to 2.46 and 2.20 mg kg–1 DW respectively relative to the control. Zinc concentration in wheat straw and grains was also increased up to 29.97 and 29.40 mg kg–1 DW respectively relative to the controls. Copper application significantly increased Zn concentrations in wheat plants

Delayed surgical therapy reduces mortality in patients with acute necrotizing pancreatitis

Objective: To review the trends in management and analyze the factors influencing outcomes of acute necrotizing pancreatitis.Methods: It wa a retrospective analytical study. All adult patients with computed tomography with proven necrotizing pancreatitis managed at the department of surgery, Aga Khan University Hospital, Karachi were included in this study extending from January 1998 to January 2008. Outcome variables were hospital stay, complication rate and in-hospital mortality. Data analysis was carried out using SPSS version 16. For comparison, Pearson chi-square test, Fisher\u27s exact test, t-test and ANOVA were used, where applicable. A p-value less than 0.05 was considered statistically significant. Results: Of 1479 patients, 47 patients were included. Median age was 48 (range: 38-56) years with 31(66%) males and 16(34%) females. Overall out of 18(38%) that underwent necrosectomy, 16 had infected acute necrotizing pancreatitis while the rest were negative. Computed Tomography and/or FNAC identified 18 infective acute necrotizing pancreatitis patients, 16 underwent necrosectomy, one patient expired without surgery and the other was managed conservatively. Enteral nutrition was widely used with rising trend of oral feeding from 2006 onwards. Complication rate was 63%. Overall mortality remained 9/47(19.7%), where in infected ANP as well as in postoperative patients, mortality was 7/18 (38.9%). The patients with early pancreatic necrosectomy had prolonged hospital stay, more complications and statistically significant increase in in-hospital mortality. Conclusion: Better outcomes were achieved in infected acute necrotizing pancreatitis with delayed pancreatic necrosectomy and the other contributing factor could be early enteral nutritional therapy

Complications of total hip replacement

Objective: To determine the factors causing complications in unilateral total hip replacement. Study Design: Analytical study. Place and Duration of Study: The Aga Khan University Hospital, Karachi, between 2000 and 2010. Methodology: During the study period, 199 patients underwent elective unilateral total hip replacement at the Aga Khan University Hospital. Patients were divided into two groups on the basis of postoperative complications within 30 days of surgery. Significant factors at 5% significance level on univariate analysis were further analyzed by multivariate logistic regression. Results: Postoperative complications occurred in 39 patients (19.6%); dislocation being most common in 13 patients (6.5%), followed by wound infection in four (2%), all of these patients required intervention. Other minor complications which were managed conservatively included wound infection (2.5%), urinary tract infection (2.5%), dislocation (1%), pleural effusion and pneumonia (2%), deep venous thrombosis (0.5%) and myocardial infarction (0.5%). On univariate analysis, patients with ASA III and IV, peri-operative blood transfusion, pre-operative hip deformity and post-operative bisphosphonate use were significantly associated with complications. On multi-variate analysis, adjusted odd\u27s ratio for perioperative transfusion (3; 95% CI: 1.17-7.7) and hip deformity (3.2, 95% CI: 1.4-3.4) was found statistically significant. Conclusion: Pre-operative hip deformity and perioperative blood transfusion significantly influence the rates of complication after unilateral THR

Layer-By-Layer Microcapsules for the Delivery of Lipophilic Drugs

About 40% of new compounds have low water solubility, however they are therapeutically active. For such drugs, different methods of formulation development should be proposed. Layer by layer assembly has recently been studied to solve this problem in which lipophilic drugs have been encapsulated. In this layer by layer process, adsorption of different components is done which is facilitated by the electrostatic attraction resulting in the formation of multilayer shells of nanometer size. These drug delivery systems include nano- and micro-particles and emulsions. In this review article, the formulation methodology, advantages, and uses of layer-by-layer assembly approach have been discussed. Keywords: Lipophillic drugs, Layer-by-layer microcapsules, Drug deliver