Solving proximal split feasibility problems without prior knowledge of operator norms

In this paper our interest is in investigating properties and numerical solutions of Proximal Split feasibility Problems. First, we consider the problem of finding a point which minimizes a convex function \(f\) such that its image under a bounded linear operator \(A\) minimizes another convex function \(g\) . Based on an idea introduced in Lopez (Inverse Probl 28:085004, 2012), we propose a split proximal algorithm with a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norm. Because the calculation or at least an estimate of the operator norm \(\Vert A\Vert \) is not an easy task. Secondly, we investigate the case where one of the two involved functions is prox-regular, the novelty of this approach is that the associated proximal mapping is not nonexpansive any longer. Such situation is encountered, for instance, in numerical solution to phase retrieval problem in crystallography, astronomy and inverse scattering Luke (SIAM Rev 44:169–224, 2002) and is therefore of great practical interest.     

Some bounds for integrals with refinements of the Grüss inequality

Some integral bounds are obtained which provide refinements and extensions of the Grüss type inequalities. We also get an alternative formulation of the Grüss inequality.     

Two-phase MFD flows in orthogonal curvilinear coordinate system

Steady flow of an inviscid, incompressible two-phase magnetofluid with infinite electrical conductivity is treated. With one ignorable coordinate in a general orthogonal curvilinear system, general solutions of the equations, considering number densityN constant throughout the motion, are obtained.     

Pressure dependence of thermodynamic properties of NaBr,NaI and AgCl

Various state-equations, derived by expanding energy as a function of volume in Taylor series and using different order Pade’s approximants, have been combined with quasi-harmonic approximation for free energy to reproduce the pressure dependence of thermodynamic properties of NaBr, NaI and AgCl crystals. We have used these state-equations to compute the reduced volume, the isothermal bulk modulus and the pressure derivative of isothermal bulk modulus for the three crystals at various pressures (up to 80 kbar) and at room temperature (T=298 K). The results obtained are reasonably good lending support to the state-equations and the technique used to extend their applicability. The significant results obtained in the present study include the unified reduced equation of state for the three crystals which generates almost a single curve for theP – V behaviour at room temperature.     

Ultrafast experiments on intermolecular electron transfer in the benzene - bromine atom charge transfer complex

Ultrafast pump - probe measurements have been made on the benzene - bromine atom charge transfer (CT) complex in CCl₄ and cyclohexane solutions. Ultrafast optical excitation of the CT band of the complex yields an ion pair, which is comprised of a benzene cation and a bromide anion. The rate of charge recombination between the bromide and the benzene cation in the ion pair has been observed to be much faster than the rate of diffusion apart. The charge recombination rate is accelerated at high benzene concentrations as a result of the formation of a benzene dimer cation - bromide ion pair which undergoes much faster charge recombination than the benzene cation - bromide ion pair.     

Serendipitous discovery of light-induced (<Emphasis Type="Italic">In Situ</Emphasis>) formation of an Azo-bridged dimeric sulfonated naphthol as a potent PTP1B inhibitor

Background

Protein tyrosine phosphatases (PTPs) like dual specificity phosphatase 5 (DUSP5) and protein tyrosine phosphatase 1B (PTP1B) are drug targets for diseases that include cancer, diabetes, and vascular disorders such as hemangiomas. The PTPs are also known to be notoriously difficult targets for designing inihibitors that become viable drug leads. Therefore, the pipeline for approved drugs in this class is minimal. Furthermore, drug screening for targets like PTPs often produce false positive and false negative results.

Results

Studies presented herein provide important insights into: (a) how to detect such artifacts, (b) the importance of compound re-synthesis and verification, and (c) how in situ chemical reactivity of compounds, when diagnosed and characterized, can actually lead to serendipitous discovery of valuable new lead molecules. Initial docking of compounds from the National Cancer Institute (NCI), followed by experimental testing in enzyme inhibition assays, identified an inhibitor of DUSP5. Subsequent control experiments revealed that this compound demonstrated time-dependent inhibition, and also a time-dependent change in color of the inhibitor that correlated with potency of inhibition. In addition, the compound activity varied depending on vendor source. We hypothesized, and then confirmed by synthesis of the compound, that the actual inhibitor of DUSP5 was a dimeric form of the original inhibitor compound, formed upon exposure to light and oxygen. This compound has an IC₅₀ of 36 μM for DUSP5, and is a competitive inhibitor. Testing against PTP1B, for selectivity, demonstrated the dimeric compound was actually a more potent inhibitor of PTP1B, with an IC₅₀ of 2.1 μM. The compound, an azo-bridged dimer of sulfonated naphthol rings, resembles previously reported PTP inhibitors, but with 18-fold selectivity for PTP1B versus DUSP5.

Conclusion

We report the identification of a potent PTP1B inhibitor that was initially identified in a screen for DUSP5, implying common mechanism of inhibitory action for these scaffolds.

     

A visual strip sensor for determination of iron

A visual strip has been developed for sensing iron in different aqueous samples like natural water and fruit juices. The sensor has been synthesized by UV-radiation induced graft polymerization of acrylamide monomer in microporous poly(propylene) base. For physical immobilization of iron selective reagent, the in situ polymerization of acrylamide has been carried out in the presence of 1,10-phenanthroline. The loaded strip on interaction with Fe(II) in aqueous solution turned into orange red color and the intensity of the color was found to be directly proportional to the amount of Fe(II) in the aqueous sample. The minimal sensor response with naked eye was found for 50 ng mL⁻¹ of Fe in 15 min of interaction. However, as low as 20 ng mL⁻¹ Fe could be quantified using a spectrophotometer. The detection limit calculated using the 3s/S criteria, where ‘s’ is the standard deviation of the absorbance of blank reagent loaded strip and ‘S’ is the slope of the linear calibration plot, was 1.0 ng mL⁻¹. The strip was applied to measure Fe in a variety of samples such as ground water and fruit juices.     

Pyrohydrolytic separation technique for fluoride and chloride from radioactive liquid wastes

A rapid method for simultaneous determination of fluorine and chlorine in radioactive liquid wastes with ion chromatography after pyrohydrolysis separation was proposed for routine analysis. The elements were separated from radioactive liquid wastes by pyrohydrolysis and were subsequently determined with ion chromatograpy. Total time taken to determine these elements is about 45 min including 30 min for the pyrohydrolysis and 15 min for ion chromatography. The results of recovery tests ranged 95% or above. The limits of detection for F and Cl are 0.5 and 0.8 mg kg⁻¹, respectively.     

Determination of Pu,Am, U and Cs in large soil samples in the vicinity of the USDOE Waste Isolation Pilot Plant

The determination of actinides in environmental soil and sediment samples are very important for environmental monitoring. A rapid actinide separation method has been developed and implemented that allows measurement of U, Pu and Am isotopes in large soil samples (10–15 g) with high chemical yields and effective removal of matrix interferences. The radiochemical procedures involve the total dissolution of soil samples, separation on anion-exchange resin, and separation and purification by extraction chromatography, e.g., UTEVA, TEVA, and TRU with measurements of radionuclides by alpha-spectrometry. The validation of the method is performed through the analysis of reference materials or by participating in laboratory intercomparison programs.