A fixed point theorem for local pseudo-contractions in uniformly convex spaces

It is proved that if D is a bounded open subset of a uniformly convex Banach space X and is a continuous mapping which is a local pseudo-contraction (e.g., locally nonexpansive) on D, then T has a fixed point in D if there exists xD such that z–Tz相似文献   

Acetone and perdeuterated acetone in UV-IMS

Measuring a mixture of acetone and perdeuterated acetone (acetone-d6) with an ultra-high resolution drift time ion mobility spectrometer (resolving power of R_p?=?235) and ultraviolet ionization (10.6 eV) at ambient pressure reveals three separated peaks. Two of the peaks can easily be associated with acetone and perdeuterated acetone. In a former publication several findings indicated an exchange of a methyl group and the formation of a H₃COCD₃ related peak. In this work the formed ion species were analyzed with a high resolution drift time ion mobility time of flight mass spectrometer. The mass spectra clearly show the formation of three proton-bound dimer peaks whereas the peak between acetone and acetone-d6 is a proton-bound mixed dimer consisting of one acetone and one acetone-d6 molecule.     

Quantitative determination of sodium stearyl fumarate in a tablet formulation from continuous manufacturing using a high-pH reversed-phase HPLC method

This study demonstrates the first use of a reversed-phase (RP) high-performance liquid chromatography method with a high-pH buffer for the analysis of sodium stearyl fumarate (SSF) from a tablet formulation. After examining the retention time and peak shape using various buffer concentrations, buffer pH, and RP stationary phases, an optimized method was established using the XBridge® BEH C18 at high pH. This column was further evaluated for method specificity, accuracy, precision, linearity, stability, and sensitivity. Finally, the method was successfully used as a convenient and robust analytical procedure to accurately quantitate SSF in stratified tablets from a continuous manufacturing process to confirm the excipient uniformity throughout the process.     

Nitrogen Doping and Carbon Coating Affects Substrate Selectivity of TiO2 Photocatalytic Organic Pollutant Degradation

A series of carbon-coated, nitrogen-doped titanium dioxide photocatalysts was produced and characterized. N-doped TiO₂ powder samples were prepared using a sol-gel method and subsequently used for making doped-TiO₂ thin films on glass substrates. Carbon layers were coated on the films by a thermal decomposition method using catechol. Diffuse reflectance spectra and Mott-Schottky analyses of the samples proved that nitrogen doping and carbon coating can slightly lower the band gap of TiO₂, broaden its absorption to visible light and enhance its n-type character. According to photocatalytic tests against model contaminants, carbon-coated nitrogen-doped TiO₂ films have better performance than simple TiO₂ on the degradation of Rhodamine B dye molecules, but are poorly effective for degrading 4-chlorophenol molecules. Several possible explanations are proposed for this result, supported by scavenging experiments. This reveals the importance of a broad substrate scope when assessing new photocatalytic materials for water treatment, something which is often overlooked in many literature studies.     

Copper‐Catalyzed Amidation of Primary and Secondary Alkyl Boronic Esters

The oxidative copper‐catalyzed cross‐coupling of functionalized alkyl boronic esters with primary amides is reported. Through the identification of appropriate diketimine ligands, conditions for efficient coupling of both primary and secondary alkyl boronic esters with diverse primary amides, including acetamide, have been developed.     

Transient spike adding in the presence of equilibria

Many models of neuronal activity exhibit complex oscillations in response to an input from other neurons in a network or to an input from a stimulus. We consider the effect of a single short stimulus on a simple model designed to mimic some features of neuronal dynamics. We focus on the transient response induced by the stimulus, particularly on the spike-adding behaviour of the response. Our main goal is to explain how the transient response is affected by the presence of unstable equilibria. We also investigate the dependence of the number of spikes on the amplitude and duration of the stimulus. In our analysis, we use numerical continuation methods and exploit the presence of different time scales in the model.     

Performance monitoring of a mammalian cell based bioprocess using Raman spectroscopy

Being able to predict the final product yield at all stages in long-running, industrial, mammalian cell culture processes is vital for both operational efficiency, process consistency, and the implementation of quality by design (QbD) practices. Here we used Raman spectroscopy to monitor (in terms of glycoprotein yield prediction) a fed-batch fermentation from start to finish. Raman data were collected from 12 different time points in a Chinese hamster ovary (CHO) based manufacturing process and across 37 separate production runs. The samples comprised of clarified bioprocess broths extracted from the CHO cell based process with varying amounts of fresh and spent cell culture media. Competitive adaptive reweighted sampling (CoAdReS) and ant colony optimization (ACO) variable selection methods were used to enhance the predictive ability of the chemometric models by removing unnecessary spectral information. Using CoAdReS accurate prediction models (relative error of predictions between 2.1% and 3.3%) were built for the final glycoprotein yield at every stage of the bioprocess from small scale up to the final 5000 L bioreactor. This result reinforces our previous studies which indicate that media quality is one of the most significant factors determining the efficiency of industrial CHO-cell processes. This Raman based approach could thus be used to manage production in terms of selecting which small scale batches are progressed to large-scale manufacture, thus improving process efficiency significantly.     

Magnetism in geometrically frustrated YMnO3 under hydrostatic pressure studied with muon spin relaxation

The ferroelectromagnet YMnO3 consists of weakly coupled triangular layers of S=2 spins. Below T(N) approximately equal to 70 K muon-spin relaxation data show two oscillatory relaxing signals due to magnetic order, with no purely relaxing signals resolvable (which would require different coexisting spin distributions). The transition temperature T(N) increases with applied hydrostatic pressure, even though the ordered moment decreases. These results suggest that pressure increases both the exchange coupling between the layers and the frustration within the layers.     

Dramatic Influence of an Anionic Donor on the Oxygen‐Atom Transfer Reactivity of a MnV–Oxo Complex

Addition of an anionic donor to an Mn^V(O) porphyrinoid complex causes a dramatic increase in 2‐electron oxygen‐atom‐transfer (OAT) chemistry. The 6‐coordinate [Mn^V(O)(TBP₈Cz)(CN)]^? was generated from addition of Bu₄N⁺CN^? to the 5‐coordinate Mn^V(O) precursor. The cyanide‐ligated complex was characterized for the first time by Mn K‐edge X‐ray absorption spectroscopy (XAS) and gives Mn?O=1.53 Å, Mn?CN=2.21 Å. In combination with computational studies these distances were shown to correlate with a singlet ground state. Reaction of the CN^? complex with thioethers results in OAT to give the corresponding sulfoxide and a 2e^?‐reduced Mn^III(CN)^? complex. Kinetic measurements reveal a dramatic rate enhancement for OAT of approximately 24 000‐fold versus the same reaction for the parent 5‐coordinate complex. An Eyring analysis gives ΔH^≠=14 kcal mol^?1, ΔS^≠=?10 cal mol^?1 K^?1. Computational studies fully support the structures, spin states, and relative reactivity of the 5‐ and 6‐coordinate Mn^V(O) complexes.