A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.

De-DUFing the DUFs: Deciphering distant evolutionary relationships of Domains of Unknown Function using sensitive homology detection methods

Background: In the post-genomic era where sequences are being determined at a rapid rate, we are highly reliant on computational methods for their tentative biochemical characterization. The Pfam database currently contains 3,786 families corresponding to ``Domains of Unknown Function'' (DUF) or ``Uncharacterized Protein Family'' (UPF), of which 3,087 families have no reported three-dimensional structure, constituting almost one-fourth of the known protein families in search for both structure and function. Results: We applied a `computational structural genomics' approach using five state-of-the-art remote similarity detection methods to detect the relationship between uncharacterized DUFs and domain families of known structures. The association with a structural domain family could serve as a start point in elucidating the function of a DUF. Amongst these five methods, searches in SCOP-NrichD database have been applied for the first time. Predictions were classified into high, medium and low-confidence based on the consensus of results from various approaches and also annotated with enzyme and Gene ontology terms. 614 uncharacterized DUFs could be associated with a known structural domain, of which high confidence predictions, involving at least four methods, were made for 54 families. These structure-function relationships for the 614 DUF families can be accessed on-line at http://proline.biochem.iisc.ernet.in/RHD_DUFS/. For potential enzymes in this set, we assessed their compatibility with the associated fold and performed detailed structural and functional annotation by examining alignments and extent of conservation of functional residues. Detailed discussion is provided for interesting assignments for DUF3050, DUF1636, DUF1572, DUF2092 and DUF659. Conclusions: This study provides insights into the structure and potential function for nearly 20 % of the DUFs. Use of different computational approaches enables us to reliably recognize distant relationships, especially when they converge to a common assignment because the methods are often complementary. We observe that while pointers to the structural domain can offer the right clues to the function of a protein, recognition of its precise functional role is still `non-trivial' with many DUF domains conserving only some of the critical residues. It is not clear whether these are functional vestiges or instances involving alternate substrates and interacting partners. Reviewers: This article was reviewed by Drs Eugene Koonin, Frank Eisenhaber and Srikrishna Subramanian.

An organically modified exfoliated graphite electrode for the voltammetric determination of lead ions in contaminated water samples

This work presents a new electrode, 2-benzoylnaphtho 2,1-b]furan hydrazone exfoliated graphite paste electrode (B-EGPE) fabricated for the differential pulse anodic stripping voltammetric determination of lead (Pb). Under the optimal conditions, Pb2+ could be detected in the concentration range from 2.75 x 10(-7) to 1.5 x 10(-6) mol/L with the linear regression equation, y = 19.41 x 10(-6) x + 0.4249 x 10(-9) with R = 0.99. Interferences from other ions were investigated and the proposed method was further applied to the trace levels of Pb2+ detection in real samples with satisfactory results.

A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

A reliable and efficient a posteriori error estimator is derived for a class of discontinuous Galerkin (DG) methods for the Signorini problem. A common property shared by many DG methods leads to a unified error analysis with the help of a constraint preserving enriching map. The error estimator of DG methods is comparable with the error estimator of the conforming methods. Numerical experiments illustrate the performance of the error estimator. (C) 2015 Elsevier B.V. All rights reserved.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Voltammetric determination of paracetamol, tramadol and caffeine using poly(Nile blue) modified glassy carbon electrode

A poly(Nile blue) modified glassy carbon electrode (PNBMGCE) was fabricated by electropolymerisation of Nile blue (NB) monomer using cyclic voltammetry (CV) and was used for the determination of paracetamol (ACOP), tramadol (TRA) and caffeine (CAF). The electrochemical investigations showed that PNB - film formed on the surface of glassy carbon electrode (GCE) improved the electroactive surface area and displayed a remarkable increase in the peak current and a substantial decrease in over potential of ACOP, TRA and CAF when compared to bare GCE. The dependence of peak current and potential on pH, sweep rate and concentration were also investigated at the surface of PNBMGCE. It showed good sensitivity and selectivity in a wide linear range from 2.0 x 10(-7) to 1.62 x 10(-5) M, 1.0 x 10(-6) to 3.1 x 10(-4) M and 8.0 x 10(-7) to 2.0 x 10(-5) M, with detection limits of 0.08, 0.5 and 0.1 mu M, for ACOP, TRA and CAF, respectively. The PNBMGCE was also successfully applied for the determination of ACOP, TRA and CAF in pharmaceutical dosage forms. (C) 2016 Elsevier B.V. All rights reserved.