On nonparametric classification with missing covariates

General procedures are proposed for nonparametric classification in the presence of missing covariates. Both kernel-based imputation as well as Horvitz-Thompson-type inverse weighting approaches are employed to handle the presence of missing covariates. In the case of imputation, it is a certain regression function which is being imputed (and not the missing values). Using the theory of empirical processes, the performance of the resulting classifiers is assessed by obtaining exponential bounds on the deviations of their conditional errors from that of the Bayes classifier. These bounds, in conjunction with the Borel-Cantelli lemma, immediately provide various strong consistency results.     

Anyonic FRT construction

The Faddeev-Reshetikhin-Takhtajan method to construct matrix bialgebras from nonsingular solutions of the quantum Yang-Baxter equation is extended to the anyonic or ? _n -graded case. The resulting anyonic quantum matrices are braided groups in which the braiding is given by a phase factor.     

Study of the oxidation of some catechols in the presence of 4‐amino‐3‐thio‐1,2,4‐triazole by digital simulation of cyclic voltammograms

Electrochemical oxidation of catechol and its derivatives ( 1a–d ) has been studied in the presence of 4‐amino‐3‐thio‐1,2,4‐triazole ( 3 ) at various pHs. Some electrochemical techniques such as cyclic voltammetry using the diagnostic criteria derived by Nicholson and Shain for various electrode mechanisms and controlled‐potential coulometry were used. Results indicate the participation of catechols ( 1a–d ) with 3 in an intramolecular cyclization reaction to form the corresponding 1,2,4‐triazino[5,4‐b]‐1,3,4‐thiadiazine derivatives. In various scan rates, based on an electron transfer–chemical reaction–electron transfer–chemical reaction mechanism, the observed homogeneous rate constants (k_obs) for Michael addition reaction were estimated by comparing the experimental cyclic voltammetric responses with the digital simulated results. The oxidation reaction mechanism of catechols ( 1a–d ) in the presence of 4‐amino‐3‐thio‐1,2,4‐triazole ( 3 ) was also studied. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 340–345, 2007     

More examples of bicrossproduct and double cross product Hopf algebras

We construct examples of bicrossproducts and double cross products of quantum groupsă(R) associated to general matrix solutionsR of the Quantum Yang-Baxter Equations. We also describe iterated double cross products of quantum groups. In the course of constructingă(R) we are led to introduce a suitable notion of mutually dual Hopf algebras and a dual quantum groupŬ(R). Work supported by SERC Research Assistantship.     

Riemannian Geometry of Quantum Groups¶and Finite Groups with Nonuniversal Differentials

We construct noncommutative “Riemannian manifold” structures on dual quasitriangular Hopf algebras such as ℂ _q [SU ₂] with its standard bicovariant differential calculus, using the quantum frame bundle approach introduced previously. The metric is provided by the braided-Killing form on the braided-Lie algebra on the tangent space and the n-bein by the Maurer–Cartan form. We also apply the theory to finite sets and in particular to finite group function algebras ℂ[G] with differential calculi and Killing forms determined by a conjugacy class. The case of the permutation group ℂ[S ₃] is worked out in full detail and a unique torsion free and cotorsion free or “Levi–Civita” connection is obtained with noncommutative Ricci curvature essentially proportional to the metric (an Einstein space). We also construct Dirac operators in the metric background, including on finite groups such as S ₃. In the process we clarify the construction of connections from gauge fields with nonuniversal calculi on quantum principal bundles of tensor product form. Received: 22 June 2000 / Accepted: 26 August 2001     

Formulation of a Hysteretic Restoring Force Model. Application to Vibration Isolation

This article focuses on the formulation of a hysteretic model used as anisolator restoring force model. The proposed model is based on operatorgoverning input and output functions that depend on the deflection andthe restoring force of the isolator. First, the mathematical formulationis demonstrated, then the hysteretic model proposed is applied toisolators having different types of behavior. The model parameters aresought using the experimental force-deflection loop of each of theisolators studied. Next, the transient response of a flexible structuremounted on an all-metal isolator is predicted by coupling the firstorder differential equation of the restoring force and the second orderdifferential equations of the structure's motion. The experimentalinvestigation validates the proposed hysteretic model applied to theall-metal mount.     

Lithium‐Salt‐Containing High‐Molecular‐Weight Polystyrene‐block‐Polyethylene Oxide Block Copolymer Films

Ionic conductivity in relation to the morphology of lithium‐doped high‐molecular‐weight polystyrene‐block‐polyethylene oxide (PS‐b‐PEO) diblock copolymer films was investigated as solid‐state membranes for lithium‐ion batteries. The tendency of the polyethylene (PEO) block to crystallize was highly suppressed by increasing both the salt‐doping level and the temperature. The PEO crystallites completely vanished at a salt‐doping ratio of Li/EO>0.08, at which the PEO segments were hindered from entering the crystalline unit of the PEO chain. A kinetically trapped lamella morphology of PS‐b‐PEO was observed, due to PEO crystallization. The increase in the lamella spacing with increasing salt concentration was attributed to the conformation of the PEO chain rather than the volume contribution of the salt or the previously reported increase in the effective interaction parameter. Upon loading the salt, the PEO chains changed from a compact/highly folded conformation to an amorphous/expanded‐like conformation. The ionic conductivity was enhanced by amorphization of PEO and thereby the mobility of the PEO blocks increased upon increasing the salt‐doping level.     

Ion-pair-based surfactant-assisted dispersive liquid–liquid microextraction for the determination of cadmium in water samples: Optimization using response surface methodology

A sensitive, simple, and rapid method is developed for ion-pair-based surfactant-assisted dispersive liquid–liquid microextraction (IPSA-DLLME) and flame atomic absorption spectrometric determination of cadmium in water samples. In this procedure, trace amounts of Cd²⁺ were converted to CdI ₄ ^2– , and after addition of a tetrabutylammonium bromide (TBAB) solution as cationic surfactant the analyte was transformed to the ion-pair state. This cadmium species was extracted by fast injection of a solution containing 200 μL of chloroform and 800 μL of methanol as extraction and disperser solvents, respectively. The pH of the sample solution, concentration of iodide, TBAB amount, and the extractant volume were optimized using a 27-run Box–Behnken design with a triplicate central point. Under the optimized conditions, the calibration curve was linear in the range 1–200 μg L^–1 (R ² = 0.9959); with the detection limit (signal/noise = 3) of 0.28 μg L^–1. The relative standard deviations (RSD) for eight runs (Cd²⁺ = 10 μg L^–1) and enrichment factor were found to be 3.04 % and 50, respectively.     

Identification,control strategies,and analytical approaches for the determination of potential genotoxic impurities in pharmaceuticals: A comprehensive review

Potential genotoxic impurities in pharmaceuticals at trace levels are of increasing concern to both pharmaceutical industries and regulatory agencies due to their possibility for human carcinogenesis. Molecular functional groups that render starting materials and synthetic intermediates as reactive building blocks for small molecules may also be responsible for their genotoxicity. Determination of these genotoxic impurities at trace levels requires highly sensitive and selective analytical methodologies, which poses tremendous challenges on analytical communities in pharmaceutical research and development. Experimental guidance for the analytical determination of some important classes of genotoxic impurities is still unavailable in the literature. Therefore, the present review explores the structural alerts of commonly encountered potential genotoxic impurities, draft guidance of various regulatory authorities in order to control the level of impurities in drug substances and to assess their toxicity. This review also describes the analytical considerations for the determination of potential genotoxic impurities at trace levels and finally few case studies are also discussed for the determination of some important classes of potential genotoxic impurities. It is the authors’ intention to provide a complete strategy that helps analytical scientists for the analysis of such potential genotoxic impurities in pharmaceuticals.