Higher order equations related to thin films: Blow-up and global existence, the influence of the initial data

We are interested in the following class of equations:

     

Determination of higher carboxylic acids in snow samples using solid-phase extraction and LC/MS-TOF

The objective of this work was to develop a method to determine the concentrations of higher organic acids in snow samples. The target species are the homologous aliphatic alpha,omega-dicarboxylic acids from C(5) to C(13), pinonic acid, pinic acid and phthalic acid. A preconcentration procedure utilizing solid phase extraction was developed and optimized using solutions of authentic standards. The influences of different parameters such as flow rate during extraction and the concentration of the eluent on the efficiency of the extraction procedure were investigated. The compounds of interest were separated by HPLC and detected by a quadrupole time-of-flight mass spectrometer (qTOF-MS). The recovery rate (extraction efficiency) of the extraction procedure was found to vary between 41% for tridecanedioic acid and 102% for adipic acid. The limits of detection were determined for all compounds and were between 0.9 nmol/L (dodecanedioic acid) and 29.5 nmol/L (pinonic acid). An exception is pinic acid, for which a considerably higher detection limit of 103.9 nmol/L was calculated. Snow samples were collected in December 2006 and January 2007 at the Fee glacier (Switzerland) from locations at heights from 3056 to 3580 m asl and from different depths within the snow layer. In total, the analysis of 61 single snow samples was performed, and the following compounds could be quantified: homologous aliphatic alpha,omega-dicarboxylic acids with 5-12 carbon atoms and phthalic acid. Tridecanedioic acid, pinonic and pinic acid were identified in the samples but were not quantified due to their low concentrations. The three most abundant acids found in the molten snow samples were glutaric acid (C(5)-di; 3.90 nmol/L), adipic acid (C(6)-di; 3.35 nmol/L) and phthalic acid (Ph; 3.04 nmol/L).     

On-line size exclusion chromatography-pyrolysis-gas chromatography-mass spectrometry for copolymer characterization and additive analysis

On-line coupled size exclusion chromatography-pyrolysis gas chromatography mass spectrometry (SEC-Py-GC-MS) is studied as a novel tool for the characterization of complex polymer samples. An automated system for on-line SEC-Py-GC-MS allowing transfer of multiple fractions was developed based on stop-flow operation of the SEC dimension, syringe-based transfer of the SEC fraction to the GC instrument and solvent elimination with subsequent pyrolysis in a programmed temperature vaporization (PTV) injector. After optimization the system was applied to the characterization of a complex terpolymer composed of very similar monomers. The use of the system for combined pyrolysis and additive analyses in polycarbonate was also demonstrated. Results obtained with the new method indicate the interesting potentials of the method for detailed characterization of polymeric materials.     

Plumbonacrite Identified by X‐ray Powder Diffraction Tomography as a Missing Link during Degradation of Red Lead in a Van Gogh Painting

Red lead, a semiconductor pigment used by artists since antiquity, is known to undergo several discoloration phenomena. These transformations are either described as darkening of the pigment caused by the formation of either plattnerite (β‐PbO₂) or galena (PbS) or as whitening by which red lead is converted into anglesite (PbSO₄) or (hydro)cerussite (2 PbCO₃?Pb(OH)₂; PbCO₃). X‐ray powder diffraction tomography, a powerful analytical method that allows visualization of the internal distribution of different crystalline compounds in complex samples, was used to investigate a microscopic paint sample from a Van Gogh painting. A very rare lead mineral, plumbonacrite (3 PbCO₃? Pb(OH)₂?PbO), was revealed to be present. This is the first reported occurrence of this compound in a painting dating from before the mid 20th century. It constitutes the missing link between on the one hand the photoinduced reduction of red lead and on the other hand (hydro)cerussite, and thus sheds new light on the whitening of red lead.     

A heterobimetallic ruthenium-gadolinium complex as a potential agent for bimodal imaging

Trinuclear heterobimetallic Ln(III)-Ru(II) complexes (Ln = Eu, Gd) based on a 1,10-phenanthroline ligand bearing a diethylenetriaminepentaacetic acid (DTPA) core have been synthesized and fully characterized by a range of experimental techniques. The (17)O NMR and proton nuclear magnetic relaxation dispersion (NMRD) measurements of Gd(III)-Ru(II) show that, in comparison to the parent Gd-DTPA, this complex exhibits improved relaxivity, which is the result of an increase of the rotational correlation time. Relaxometry and ultrafiltration experiments indicate that the 1,10-phenanthroline ligand has a high affinity for noncovalent binding to human serum albumin, which results in a high relaxivity r(1) of 14.3 s(-1) mM(-1) at 20 MHz and 37 °C. Furthermore, the Ln(III)-Ru(II) complexes (Ln = Eu, Gd) show an intense light absorption in the visible spectral region due to metal-to-ligand charge transfer (MLCT) transitions. Upon excitation into the MLCT band at 440 nm, the complexes exhibit a bright-red luminescence centered at 610 nm, with a quantum yield of 4.7%. The luminescence lifetime equals 540 ns and is therefore long enough to exceed the fluorescent background. Monometallic lanthanide complexes have also been synthesized, and the Eu(III) analogue shows a characteristic red luminescence with a quantum yield of 0.8%. Taking into account the relaxometric and luminescent properties, the developed Gd(III)-Ru(II) complex can be considered as a potential in vitro bimodal imaging agent.     

Photochemistry and photophysics of n-butanal, 3-methylbutanal, and 3,3-dimethylbutanal: experimental and theoretical study

Dilute mixtures of n-butanal, 3-methylbutanal, and 3,3-dimethylbutanal in synthetic air, different N(2)/O(2) mixtures, and pure nitrogen (up to 100 ppm) were photolyzed with fluorescent UV lamps (275-380 nm) at 298 K. The main photooxidation products were ethene (n-butanal), propene (3-methylbutanal) or i-butene (3,3-dimethylbutanal), CO, vinylalcohol, and ethanal. The photolysis rates and the absolute quantum yields were found to be dependent on the total pressure of synthetic air but not of nitrogen. At 100 Torr, the total quantum yield Φ(100) = 0.45 ± 0.01 and 0.49 ± 0.07, whereas at 700 Torr, Φ(700) = 0.31 ± 0.01 and 0.36 ± 0.03 for 3-methylbutanal and 3,3-dimethybutanal, respectively. Quantum yield values for n-butanal were reported earlier by Tadi? et al. (J. Photochem. Photobiol. A2001143, 169-179) to be Φ(100) = 0.48 ± 0.02 and Φ(700) = 0.32 ± 0.01. Two decomposition channels were identified: the radical channel RCHO → R + HCO (Norrish type I) and the molecular channel CH(3)CH(CH(3))CH(2)CHO → CH(2)CHCH(3) + CH(2)═CHOH or CH(3)C(CH(3))(2)CH(2)CHO → CHC(CH(3))CH(3) + CH(2)═CHOH, (Norrish type II) having the absolute quantum yields of 0.123 and 0.119 for 3-methybutanal and 0.071 and 0.199 for 3,3-dimethylbutanal at 700 Torr of synthetic air. The product ethenol CH(2)═CHOH tautomerizes to ethanal. We have performed ab initio and density functional quantum (DFT) chemical computations of both type I and type II processes starting from the singlet and triplet excited states. We conclude that the Norrish type I dissociation produces radicals from both singlet and triplet excited states, while Norrish type II dissociation is a two-step process starting from the triplet excited state, but is a concerted process from the singlet state.     

A new metallostar complex based on an aluminum(iii) 8-hydroxyquinoline core as a potential bimodal contrast agent

A ditopic DTPA monoamide derivative containing an 8-hydroxyquinoline moiety was synthesized and the corresponding gadolinium(iii) complex ([Gd(H5)(H(2)O)](-)) was prepared. After adding aluminum(iii), the 8-hydroxyquinoline part self-assembled into a heteropolymetallic triscomplex [(Gd5)(3)Al(H(2)O)(3)](3-). The magnetic and optical properties of this metallostar compound were investigated in order to classify it as a potential in vitro bimodal contrast agent. The proton nuclear magnetic relaxation dispersion measurements indicated that the relaxivity r(1) of [Gd(H5)(H(2)O)](-) and [(Gd5)(3)Al(H(2)O)(3)](3-) at 20 MHz and 310 K equaled 6.17 s(-1) mM(-1) and 10.9 s(-1) mM(-1) per Gd(iii) ion respectively. This corresponds to a relaxivity value of 32.7 s(-1) mM(-1) for the supramolecular complex containing three Gd(iii) ions. The high relaxivity value is prominently caused by an increase of the rotational tumbling time τ(R) by a factor of 2.7 and 5.5 respectively, in comparison with the commercially used MRI contrast agent Gd(iii)-DTPA (Magnevist?). Furthermore, upon UV irradiation, [(Gd5)(3)Al(H(2)O)(3)](3-) exposes green broad-band emission with a maximum at 543 nm. Regarding the high relaxivity and the photophysical properties of the [(Gd5)(3)Al(H(2)O)(3)](3-) metallostar compound, it can be considered as a lead compound for in vitro bimodal applications.     

New insights into churn prediction in the telecommunication sector: A profit driven data mining approach

Customer churn prediction models aim to indicate the customers with the highest propensity to attrite, allowing to improve the efficiency of customer retention campaigns and to reduce the costs associated with churn. Although cost reduction is their prime objective, churn prediction models are typically evaluated using statistically based performance measures, resulting in suboptimal model selection. Therefore, in the first part of this paper, a novel, profit centric performance measure is developed, by calculating the maximum profit that can be generated by including the optimal fraction of customers with the highest predicted probabilities to attrite in a retention campaign. The novel measure selects the optimal model and fraction of customers to include, yielding a significant increase in profits compared to statistical measures.In the second part an extensive benchmarking experiment is conducted, evaluating various classification techniques applied on eleven real-life data sets from telecom operators worldwide by using both the profit centric and statistically based performance measures. The experimental results show that a small number of variables suffices to predict churn with high accuracy, and that oversampling generally does not improve the performance significantly. Finally, a large group of classifiers is found to yield comparable performance.