Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Relaxation Processes and Exciton-Phonon Interactions in Nanocomposites Based on CdSe/ZnS Semiconductor Quantum Dots and Porphyrin Molecules

Russian Physics Journal - Using spectral-kinetic data obtained for nanoassemblies based on CdSe/ZnS semiconductor quantum dots and tetrapyridylporphyrin molecules in methylcyclohexane-toluene...     

Lewis acid-base adducts of zwitterionic alkali metal methanides and silanides with BH3

The synthesis, structures and spectroscopic properties of M(MeOCH₂CH₂OMe₂Si)₃CBH₃ (M-1-BH₃) and M(MeOCH₂CH₂OMe₂Si)₃SiBH₃ (M-2-BH₃) (M?=?Li, Na, K) derived from reactions of BH₃ with the alkali metal zwitterions [M(MeOCH₂CH₂OMe₂Si)₃C] (M-1) and [M(MeOCH₂CH₂OMe₂Si)₃Si] (M-2) (M?=?Li, Na, K), resp., are reported. X-ray analysis and DFT calculations reveal discrete zwitterionic structures with the octahedral alkali metal cations rigidly locked and charge separated from the BH₃ units via pendant donors groups. Solution experiments with the hydride acceptors B(C₆F₅)₃ and [Ph₃C]₂[B₁₂C₁₂] indicate that Na-1-BH₃ can donate hydrides to form cations of formula [Na(MeOCH₂CH₂OMe₂Si)₃CBH₂]⁺.     

Cellulose Iβ investigated by IR-spectroscopy at low temperatures

Highly crystalline oriented Halocynthia roretzi cellulose Iβ films were investigated by IR-spectroscopy between ?180 and +10 °C. Changes in the IR-spectra induced by temperature were compared to published changes induced by mechanical stretching. This made it possible to conclude that frequency shifts in the O–H stretching region of the IR-spectra due to temperature were not predominantly an indirect effect of thermal expansion leading to greater O–O distances, but were due directly to the effect of temperature on the O–H···O hydrogen bonds. Temperature induced frequency shifts of C–H stretching bands were consistent with the presence of weak inter-sheet C–H···O bonds. Furthermore, no phase transition in cellulose Iβ was found between ?180 and +10 °C.     

Nanotechnology for Electroanalytical Biosensors of Reactive Oxygen and Nitrogen Species

Over the past several decades, nanotechnology has contributed to the progress of biomedicine, biomarker discovery, and the development of highly sensitive electroanalytical / electrochemical biosensors for in vitro and in vivo monitoring, and quantification of oxidative and nitrosative stress markers like reactive oxygen species (ROS) and reactive nitrogen species (RNS). A major source of ROS and RNS is oxidative stress in cells, which can cause many human diseases, including cancer. Therefore, the detection of local concentrations of ROS (e. g. superoxide anion radical; O₂^•−) and RNS (e. g. nitric oxide radical; NO^• and its metabolites) released from biological systems is increasingly important and needs a sophisticated detection strategy to monitor ROS and RNS in vitro and in vivo. In this review, we discuss the nanomaterials‐based ROS and RNS biosensors utilizing electrochemical techniques with emphasis on their biomedical applications.     

Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances

A Bayesian inference for a linear Gaussian random coefficient regression model with inhomogeneous within-class variances is presented. The model is motivated by an application in metrology, but it may well find interest in other fields. We consider the selection of a noninformative prior for the Bayesian inference to address applications where the available prior knowledge is either vague or shall be ignored. The noninformative prior is derived by applying the Berger and Bernardo reference prior principle with the means of the random coefficients forming the parameters of interest. We show that the resulting posterior is proper and specify conditions for the existence of first and second moments of the marginal posterior. Simulation results are presented which suggest good frequentist properties of the proposed inference. The calibration of sonic nozzle data is considered as an application from metrology. The proposed inference is applied to these data and the results are compared to those obtained by alternative approaches.     

The Formation of Methyl Ketones during Lipid Oxidation at Elevated Temperatures

Lipid oxidation and the resulting volatile organic compounds are the main reasons for a loss of food quality. In addition to typical compounds, such as alkanes, aldehydes and alcohols, methyl ketones like heptan-2-one, are repeatedly described as aroma-active substances in various foods. However, it is not yet clear from which precursors methyl ketones are formed and what influence amino compounds have on the formation mechanism. In this study, the formation of methyl ketones in selected food-relevant fats and oils, as well as in model systems with linoleic acid or pure secondary degradation products (alka-2,4-dienals, alken-2-als, hexanal, and 2-butyloct-2-enal), has been investigated. Elevated temperatures were chosen for simulating processing conditions such as baking, frying, or deep-frying. Up to seven methyl ketones in milk fat, vegetable oils, and selected model systems have been determined using static headspace gas chromatography-mass spectrometry (GC-MS). This study showed that methyl ketones are tertiary lipid oxidation products, as they are derived from secondary degradation products such as deca-2,4-dienal and oct-2-enal. The study further showed that the position of the double bond in the precursor compound determines the chain length of the methyl ketone and that amino compounds promote the formation of methyl ketones to a different degree. These compounds influence the profile of the products formed. As food naturally contains lipids as well as amino compounds, the proposed pathways are relevant for the formation of aroma-active methyl ketones in food.     

Structural,Magnetic and Catalytic Properties of a New Vacancy Ordered Perovskite Type Barium Cobaltate BaCoO2.67

A new vacancy ordered, anion deficient perovskite modification with composition of BaCoO_2.67 (Ba₃Co₃O₈□₁) has been prepared via a two-step heating process. Combined Rietveld analysis of neutron and X-ray powder diffraction data shows a novel ordering of oxygen vacancies not known before for barium cobaltates. A combination of neutron powder diffraction, magnetic measurements, and density functional theory (DFT) studies confirms G-type antiferromagnetic ordering. From impedance measurements, the electronic conductivity of the order of 10⁻⁴ S cm⁻¹ is determined. Remarkably, the bifunctional catalytic activity for oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) is found to be comparable to that of Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3–y, confirming that charge-ordered anion deficient non-cubic perovskites can be highly efficient catalysts.