Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

In this paper, we first split the biharmonic equation Δ² u=f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v=Δu and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation v _h of v can easily be eliminated to reduce the discrete problem to a Schur complement system in u _h , which is an approximation of u. A direct approximation v _h of v can be obtained from the approximation u _h of u. Using piecewise polynomials of degree p≥3, a priori error estimates of u−u _h in the broken H ¹ norm as well as in L ² norm which are optimal in h and suboptimal in p are derived. Moreover, a priori error bound for v−v _h in L ² norm which is suboptimal in h and p is also discussed. When p=2, the preset method also converges, but with suboptimal convergence rate. Finally, numerical experiments are presented to illustrate the theoretical results. Supported by DST-DAAD (PPP-05) project.     

Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C ⁰ interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H ², H ¹ and L ₂ norms. L _?? norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.     

Superconvergent Discontinuous Galerkin Methods for Linear Non-selfadjoint and Indefinite Elliptic Problems

Based on Cockburn et al. (Math. Comp. 78:1?C24, 2009), superconvergent discontinuous Galerkin methods are identified for linear non-selfadjoint and indefinite elliptic problems. With the help of an auxiliary problem which is the discrete version of a linear non-selfadjoint elliptic problem in divergence form, optimal error estimates of order k+1 in L ²-norm for the potential and the flux are derived, when piecewise polynomials of degree k??1 are used to approximate both potential and flux variables. Using a suitable post-processing of the discrete potential, it is then shown that the resulting post-processed potential converges with order k+2 in L ²-norm. The article is concluded with a numerical experiment which confirms the theoretical results.     

Automatic image semantic interpretation using social action and tagging data

The plethora of social actions and annotations (tags, comments, ratings) from online media sharing Websites and collaborative games have induced a paradigm shift in the research on image semantic interpretation. Social inputs with their added context represent a strong substitute for expert annotations. Novel algorithms have been designed to fuse visual features with noisy social labels and behavioral signals. In this survey, we review nearly 200 representative papers to identify the current trends, challenges as well as opportunities presented by social inputs for research on image semantics. Our study builds on an interdisciplinary confluence of insights from image processing, data mining, human computer interaction, and sociology to describe the folksonomic features of users, annotations and images. Applications are categorized into four types: concept semantics, person identification, location semantics and event semantics. The survey concludes with a summary of principle research directions for the present and the future.     

Physicochemical and sensory quality of wines from red sorrel/roselle (Hibiscus sabdariffa L.) calyces: effects of pretreatments of pectolase and temperature/time

The effects of pretreating red sorrel (Hibiscus sabdariffa L.) calyces on the physicochemical and sensory quality of wines were investigated. Sorrel calyces were processed at 60 °C for 3.5 h or 90 °C for 30 min at 0%, 0.5% and 1.0% w/w pectolase addition in fermentation of wines. Significant changes (P < 0.01) in all physicochemical parameters of sorrel wines were found during fermentation, but not (P > 0.05) because of temperature/time effects. Colour (P < 0.01) became redder with pectolase and on storage at 23 °C for 2 months. Significant differences (P < 0.01) were noted in sensory quality for taste and flavour, balance, duration and overall quality. Higher (P < 0.01) overall sensory quality scores were obtained for wines by pretreatment at 90 °C for 30 min (10.44–11.06/20) when compared with wines at 60 °C for 3.5 h (6.88–9.06/20). Colour of wines from 90 °C/30 min was most saturated and red than all wines and had pH 2.57 ± 0.01, 0.43 ± 0.07% citric acid, 10.53 ± 0.53 °Bx and 15.29 ± 0.71% alcohol.     

Right atrial thrombus due to internal jugular vein catheter

Right atrial thrombus is rare complication of hemodialysis central venous catheter. Literature survey revealed 49 documentations of right atrial thrombus due to a central venous catheter. We report a 58-year-old type 2 diabetic, hypertensive, end-stage renal disease patient, who 2 months after initiation of hemodialysis through a right internal jugular vein catheter, developed clinical features suggestive of pulmonary thromboembolism. An echocardiography revealed presence of a serpentine thrombus in right atrium. The internal jugular vein catheter was removed and unfractionated heparin was initiated. At the end of 6 weeks he was symptom free. We compared conservative treatment with surgery for RAT. Conservative management with central venous catheter removal and anticoagulation therapy is not inferior to the surgery.     

Binding of water and solute to protein-mixture and protein-coated alumina

Extent of water vapour adsorption (n1) of gelatin and bovine serum albumin and their mixtures in different proportion respectively has been measured by isopiestic vapour pressure methods at various values of water activity (a1) ranging between zero and unity. Similar measurements have also been carried out with gelatin and BSA coated alumina powder. At a given value of a1, n1 for the protein mixture is found to be significantly less than their ideal value obtained from the additivity rule. Such decrease is probably due to the protein-protein interaction as a result of which some of the water binding sites become unavailable for water vapour adsorption. On the other hand when a protein is mixed with alumina powder, the water vapour adsorption of the protein coated alumina surface at a given water activity is found to be 2 to 3 times larger than its ideal value obtained from the additivity rule. The standard free energy changes for hydration of protein mixtures and protein-coated alumina have been evaluated using Bull equation. The extent of excess hydration of these proteins and their mixtures as well as protein-coated alumina in the presence of excess neutral salts and urea respectively have been evaluated using the isopiestic method. In all cases, the moles of water and solute respectively bound in absolute amount to biopolymers, biopolymer mixtures and protein-coated alumina have been evaluated in the limited range of solute concentrations in the medium. Based on the Gibbs-Duhem equations, a rigorous expression for the standard free energy change for binding of excess solute and solvent to biopolymer have been evaluated with reference to unit solute mole fraction as standard state. Free energies of excess hydration of different biopolymer systems have been evaluated using this equation.