A Classification of Homogeneous Operators in the Cowen-Douglas Class

A complete list of homogeneous operators in the Cowen-Douglas class is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc. This research was supported in part by a DST - NSF S&T Cooperation Programme and a PSC-CUNY grant.     

Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation

Use of prior information in the consistent estimation of regression coefficients in measurement error models

A multivariate ultrastructural measurement error model is considered and it is assumed that some prior information is available in the form of exact linear restrictions on regression coefficients. Using the prior information along with the additional knowledge of covariance matrix of measurement errors associated with explanatory vector and reliability matrix, we have proposed three methodologies to construct the consistent estimators which also satisfy the given linear restrictions. Asymptotic distribution of these estimators is derived when measurement errors and random error component are not necessarily normally distributed. Dominance conditions for the superiority of one estimator over the other under the criterion of Löwner ordering are obtained for each case of the additional information. Some conditions are also proposed under which the use of a particular type of information will give a more efficient estimator.     

A total reflection X‐ray fluorescence method for the determination of chlorine at trace levels in nuclear materials without sample dissolution

A total reflection X‐ray fluorescence (TXRF) method for the determination of chlorine at trace levels in nuclear fuel samples is described. Chlorine present in trace concentrations in nuclear fuel materials such as U₃O₈, (U,Pu)C, PuO₂ and Pu‐alloys was first separated from the solid matrix by pyrohydrolysis as HCl and was collected in 5 mM NaOH solution. This solution was analyzed for chlorine by TXRF spectrometry using Cl Kα analytical line excited by W Lα. Cobalt was used as internal standard. The precision for such chlorine determination was found to be within 27% (n = 4) when the analysis was carried out in air atmosphere. This could be improved to 8% by making TXRF measurement in flowing helium atmosphere. The results obtained from TXRF determinations were also compared with those obtained from ion chromatography (IC) and were in good agreement. The collection of distillate during pyrohydrolysis in NaOH helped in counterchecking loss of chlorine during TXRF sample preparation. The average deviation of TXRF‐determined values in helium‐purged TXRF measurements with IC determined values (as chloride) was 15% at a chlorine concentration level in the range of 1–70 µg/mL. Copyright © 2012 John Wiley & Sons, Ltd.     

A Pro-Fluorescent Ubiquitin-Based Probe to Monitor Cysteine-Based E3 Ligase Activity

Protein post-translational modification with ubiquitin (Ub) is a versatile signal regulating almost all aspects of cell biology, and an increasing range of diseases is associated with impaired Ub modification. In this light, the Ub system offers an attractive, yet underexplored route to the development of novel targeted treatments. A promising strategy for small molecule intervention is posed by the final components of the enzymatic ubiquitination cascade, E3 ligases, as they determine the specificity of the protein ubiquitination pathway. Here, we present UbSRhodol, an autoimmolative Ub-based probe, which upon E3 processing liberates the pro-fluorescent dye, amenable to profile the E3 transthiolation activity for recombinant and in cell-extract E3 ligases. UbSRhodol enabled detection of changes in transthiolation efficacy evoked by enzyme key point mutations or conformational changes, and offers an excellent assay reagent amenable to a high-throughput screening setup allowing the identification of small molecules modulating E3 activity.     

A Magnetic Bio-Inspired Soft Carrier as a Temperature-Controlled Gastrointestinal Drug Delivery System

Currently, gastrointestinal bleeding in the colon wall and the small bowel is diagnosed and treated with endoscopes. However, the locations of this condition are often problematic to treat using traditional flexible and tethered tools. New studies commonly consider untethered devices for solving this problem. However, there still exists a gap in the extant literature, and more research is needed to diagnose and deliver drugs in the lower gastrointestinal tract using soft robotic carriers. This paper discusses the development of an untethered, magnetically-responsive bio-inspired soft carrier. A molding process is utilized to produce prototypes from Diisopropylidene-1,6-diphenyl-1,6-hexanediol-based Polymer with Ethylene Glycol Dimethacrylate (DiAPLEX) MP-3510 - a shape memory polymer with a low transition temperature to enable the fabrication of these carriers. The soft carrier design is validated through simulation results of deformation caused by magnetic elements embedded in the carrier in response to an external field. The thermal responsiveness of the fabricated prototype carriers is assessed ex vivo and in a phantom. The results indicate a feasible design capable of administering drugs to a target inside a phantom of a large intestine. The soft carrier introduces a method for the controlled release of drugs by utilizing the rubbery modulus of the polymer and increasing the recovery force through magnetic actuation.