Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Reaction of Dithiophosphoric Acid Chloride Betaine with Bifunctional Compounds - A New Route to Cyclic Dithiophosphates

Abstract

Dithiophosphoric acid chloride pyrididium betaine, Py. PS₂Cl (1)¹, can be widely used for the synthesis of various organophosphorus compounds. 1 reacts in the presence of a base with an excess of nucleophiles like amines, alcohols or thiols to the corresponding disubstituted thiophosphoric acid derivatives^2–3.     

Investigation of Matrix Effects on the Determination of Carbadox and Olaquindox in Feed by LC–MS/MS

A comprehensive survey of matrix effects on the LC–MS/MS analysis of the banned antibiotic growth promoters carbadox and olaquindox in feed was carried out. Various factors of sample preparation procedure and measurement were systematically investigated by pre- and post-extraction addition and postcolumn infusion experiments. In general, strong signal suppression up to 70 % for carbadox and up to 90 % for olaquindox was observed when using different extraction solvents and techniques as well as different chromatographic conditions. Reduction of matrix effects was achieved by SPE clean-up and dilution of sample extracts. Nevertheless, matrix effect profiles determined by postcolumn infusion revealed, that reduction of signal suppression at a respective retention time cannot guarantee improvement of the methods performance. If high variability of matrix effects is present along the chromatographic run, accuracy might decrease despite reduced signal suppression. Besides method parameters, different feedingstuffs were investigated and showed similar matrix effects.

     

Analysis of rotation curves in the framework of the gravitational suppression model

We present an analysis of suitable rotation curves (RCs) of eight galaxies, aimed at checking the consistency and universality of the gravitational suppression (GraS) hypothesis, a phenomenological model for a new interaction between dark matter and baryons. Motivated by the puzzle of the core versus cusp distribution of dark matter in the center of halos, this hypothesis claims to reconcile the predictions from N-body Lambda cold dark matter simulations with kinematic observations. The GraS model improves the kinematic fitting residuals, but the mass parameters are unphysical and put the theory in difficulty.     

A Bioorthogonal Small‐Molecule‐Switch System for Controlling Protein Function in Live Cells

Chemically induced dimerization (CID) has proven to be a powerful tool for modulating protein interactions. However, the traditional dimerizer rapamycin has limitations in certain in vivo applications because of its slow reversibility and its affinity for endogenous proteins. Described herein is a bioorthogonal system for rapidly reversible CID. A novel dimerizer with synthetic ligand of FKBP′ (SLF′) linked to trimethoprim (TMP). The SLF′ moiety binds to the F36V mutant of FK506‐binding protein (FKBP) and the TMP moiety binds to E. coli dihydrofolate reductase (eDHFR). SLF′‐TMP‐induced heterodimerization of FKBP(F36V) and eDHFR with a dissociation constant of 0.12 μM . Addition of TMP alone was sufficient to rapidly disrupt this heterodimerization. Two examples are presented to demonstrate that this system is an invaluable tool, which can be widely used to rapidly and reversibly control protein function in vivo.     

Contribution of CuxO distribution,shape and ratio on TiO2 nanotubes to improve methanol production from CO2 photoelectroreduction

Many studies are focused on the development of materials for converting carbon dioxide into multicarbon oxygenates such as methanol and ethanol, because of their higher energy density and wider applicability. In this work, TiO₂ nanotubes (NT/TiO₂) were modified with Cu_xO nanoparticles in order to investigate the contribution of different ratio of Cu₂O/CuO and its distribution over NT/TiO₂ for CO₂ photoelectro-conversion to methanol. The photoelectrodes were built by anodization process to obtain NT/TiO₂ layer, and the decoration with Cu_xO hybrid system was carried out by electrodeposition process, using Na₂SO₄ or acid lactic as electrolyte, followed by annealing at different temperatures. X-ray photoelectron spectroscopy analysis revealed the predominance of Cu⁺¹ and Cu⁺² at 150 °C and 300 °C, respectively. X-ray diffraction and scanning electron microscopy indicated that under lactic acid solution, the oxide nanoparticles exhibited small size, cubic shape, and uniform distribution on the nanotube wall. While under Na₂SO₄ electrolyte, large nanoparticles with two different morphologies, octahedral and cubic shapes, were deposited on the top of the nanotubes. All modified electrodes converted CO₂ in methanol in different quantities, identified by gas chromatograph. However, the NT/TiO₂ modified with CuO/Cu₂O (80:20) nanoparticles using lactic acid as electrolyte showed better performance in the CO₂ reduction to methanol (0.11 mmol L⁻¹) in relation to the other electrodes. In all cases, a blend among the structures and nanoparticle morphologies were achieved and essential to create new site of reactions what improved the use of light irradiation, minimization of charge recombination rate and promoted high selectivity of products.

     

Nanosized aerosols from consumer sprays: experimental analysis and exposure modeling for four commercial products

Consumer spray products are already on the market in the cosmetics and household sector, which suggest by their label that they contain engineered nanoparticles (ENP). Sprays are considered critical for human health, because the lungs represent a major route for the uptake of ENP into the human body. To contribute to the exposure assessment of ENP in consumer spray products, we analyzed ENP in four commercially available sprays: one antiperspirant, two shoe impregnation sprays, and one plant-strengthening agent. The spray dispersions were analyzed by inductively coupled plasma mass spectrometry (ICPMS) and (scanning-) transmission electron microscopy ((S)TEM). Aerosols were generated by using the original vessels, and analyzed by scanning mobility particle sizer (SMPS) and (S)TEM. On the basis of SMPS results, the nanosized aerosol depositing in the respiratory tract was modeled for female and male consumers. The derived exposure levels reflect a single spray application. We identified ENP in the dispersions of two products (shoe impregnation and plant spray). Nanosized aerosols were observed in three products that contained propellant gas. The aerosol number concentration increased linearly with the sprayed amount, with the highest concentration resulting from the antiperspirant. Modeled aerosol exposure levels were in the range of 10¹⁰ nanosized aerosol components per person and application event for the antiperspirant and the impregnation sprays, with the largest fraction of nanosized aerosol depositing in the alveolar region. Negligible exposure from the application of the plant spray (pump spray) was observed.     

High yielding microwave-assisted synthesis of tri-substituted 1,3,5-triazines using Pd-catalyzed aryl and heteroarylamination

A rapid and efficient Pd-catalyzed aryl and heteroarylamination under microwave irradiation has been developed for various tri-substituted triazines that can serve as versatile building blocks for both supramolecular and medicinal chemistry research. Particularly valuable features of this method included the short reaction time, good yield, and convenient operation.