Verified bounds for singular values,in particular for the spectral norm of a matrix and its inverse

The singular value decomposition and spectral norm of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the spectral norm of a matrix are mandatory. We present various approaches to this together with some auxiliary useful estimates.     

Electrochemical Synthesis of Pyrazolines and Pyrazoles via [3+2] Dipolar Cycloaddition

Pyrazolines and pyrazoles are common and important motifs of pharmaceutical agents and agrochemicals. Herein, the first electrochemical approach for their direct synthesis from easily accessible hydrazones and dipolarophiles up to decagram scale is presented. The application of a biphasic system (aqueous/organic) even allows for the conversion of highly sensitive alkenes, wherein inexpensive sodium iodide is employed in a dual role as supporting electrolyte and mediator. In addition, mechanistic insight into the reaction is given by the isolation of key step intermediates. The relevance of the presented reaction is underlined by the synthesis of commercial herbicide safener mefenpyr-diethyl in good yields.     

MEASUREMENT OF ADHESION FORCES IN AIR WITH THE VIBRATION METHOD

The vibration method represents a practical method for the measurement of adhesion forces and adhesion force distributions. This method causes sinusoidally altemating stresses and yields detachment and contact forces between particles and substrate of the same order of magnitude. Alternating contact forces of the vibration method can cause an adhesion force intensification through flattening of asperities. The measuring principle of the vibration method and the analysis of experimental results are described in the article. Normal adhesion forces (pull-off forces) are measured using the vibration method and the colloidal probe technique. The results of both methods show good agreement for small particle sizes. The influence of the detachment force direction is shown by comparing tangential and normal adhesion forces measured using particle reentrainment in a turbulent air flow and the vibration method, respectively. The surface roughness of the substrate and the relative humidity are shown to significantly influence the measured adhesion forces. For the calculation of the adhesion forces, an approach by Rabinovich was combined with approximations of plastic micro asperity flattening. The Rabinovich approach accounts for roughness effects on the van der Waals force by incorporating the rms roughness of the interacting surfaces. rms-values of the particles and substrates were measured with atomic force microscopy at different scanning areas.     

Dual-label autoradiographic analysis of human skin fibroblast and myoblast proteins by two-dimensional polyacrylamide gel electrophoresis using immobilised pH gradients in the first dimension

Horizontal two-dimensional polyacrylamide gel electrophoresis with immobilised pH gradients in the first dimension has been applied to the analysis of human skin fibroblast and muscle myoblast total cell proteins. Excellent two-dimensional separations of skin fibroblast proteins were obtained using pH 4-10 immobilised pH gradient gels with a long interelectrode distance (16 cm), but resolution was degraded, particularly of the more acidic proteins, by the use of shorter (10 cm) gels. Improved resolution of acidic and basic proteins was obtained using separate pH 4-7 and pH 7-10 immobilised pH gradient gels respectively in the first dimension. Two-dimensional protein maps of skin fibroblast proteins were visualised both by silver staining and by autoradiography of samples labelled synthetically with [35S]methionine. Horizontal two-dimensional electrophoresis, using pH 4-7 and pH 7-10 immobilised pH gradient gels in the first dimension, was applied to the analysis of protein samples from skin fibroblasts and muscle myoblasts dual-labelled synthetically with [35S]methionine and [75Se]selenomethionine in an attempt to identify sets of proteins specific to each cell type. In addition, two-dimensional maps or protein samples derived from normal individuals and patients with Duchenne muscular dystrophy were compared to search for protein changes associated with the disease state. Although sets of qualitative protein spot differences were observed by visual inspection of the two-dimensional gels, more rigorous qualitative and quantitative analysis of the patterns using a computerised analysis system will be required to obtain the maximum amount of information from these data.     

Effect of Chelate Ring Size in Iron(II) Isothiocyanato Complexes with Tetradentate Tripyridyl‐alkylamine Ligands on Spin Crossover Properties

Iron(II) complexes of the type [Fe(L)(NCS)₂] with tetradentate ligands L are well known to show spin crossover properties. However, this behavior is quite sensitive in regard to small changes of the ligand system. Starting from the thoroughly investigated complex [Fe(tmpa)(NCS)₂] [tmpa = tris(2‐pyridylmethyl)amine, also abbreviated as tpa in the literature] we modified the ligand by increasing systematically the chelate ring sizes from 5 to 6 thus obtaining complexes [Fe(pmea)(NCS)₂], [Fe(pmap)(NCS)₂], and [Fe(tepa)(NCS)₂] [pmea = N,N‐bis[(2‐pyridyl)methyl]‐2‐(2‐pyridyl)ethylamine, pmap = N,N‐bis[2‐(2‐pyridyl)ethyl]‐(2‐pyridyl)methylamine, and tepa = tris[2‐(2‐pyridyl)ethyl]amine]. All complexes were structurally characterized and spin crossover properties were investigated using Mößbauer spectroscopy, magnetic measurements, and IR/Raman analyses. The results demonstrated that only the iron complexes with tmpa and pmea showed spin crossover properties, whereas the complexes with the ligands pmap and tepa only formed high spin complexes. Furthermore, DFT calculations supported these findings demonstrating again the strong influence of ligand environment. Herein the effect of increasing the chelate ring sizes in iron(II) isothiocyanato complexes with tetradentate tripyridyl‐alkylamine ligands is clearly demonstrated.     

Metal-Free Twofold Electrochemical C−H Amination of Activated Arenes: Application to Medicinally Relevant Precursor Synthesis

The efficient production of many medicinally or synthetically important starting materials suffers from wasteful or toxic precursors for the synthesis. In particular, the aromatic non-protected primary amine function represents a versatile synthetic precursor, but its synthesis typically requires toxic oxidizing agents and transition metal catalysts. The twofold electrochemical amination of activated benzene derivatives via Zincke intermediates provides an alternative sustainable strategy for the formation of new C−N bonds of high synthetic value. As a proof of concept, we use our approach to generate a benzoxazinone scaffold that gained attention as a starting structure against castrate-resistant prostate cancer. Further improvement of the structure led to significantly increased cancer cell line toxicity. Thus, exploiting environmentally benign electrooxidation, we present a new versatile and powerful method based on direct C−H activation that is applicable for example the production of medicinally relevant compounds.     

Between Aromatic and Quinoid Structure: A Symmetrical UV to Vis/NIR Benzothiadiazole Redox Switch

Reversibly switching the light absorption of organic molecules by redox processes is of interest for applications in sensors, light harvesting, smart materials, and medical diagnostics. This work presents a symmetrical benzothiadiazole (BTD) derivative with a high fluorescence quantum yield in solution and in the crystalline state and shows by spectroelectrochemical analysis that reversible switching of UV absorption in the neutral state, to broadband Vis/NIR absorption in the 1st oxidized state, to sharp band Vis absorption in the 2nd oxidized state, is possible. For the one-electron oxidized species, formation of a delocalized radical is confirmed by electron paramagnetic resonance spectroelectrochemistry. Furthermore, our results reveal an increasing quinoidal distortion upon the 1st and 2nd oxidation, which can be used as the leitmotif for the development of BTD based redox switches.     

Synthesis of Highly Functionalized N,N-Diarylamides by an Anodic C,N-Coupling Reaction

We report an innovative, sustainable and straightforward protocol for the synthesis of N,N-diarylamides equipped with nonprotected hydroxyl groups by using electrosynthesis. The concept allows the application of various substrates furnishing diarylamides with yields up to 57 % within a single and direct electrolytic protocol. The method is thereby easy to conduct in an undivided cell with constant current conditions offering a versatile and short-cut alternative to conventional pathways.     

Brodie's or Hummers’ Method: Oxidation Conditions Determine the Structure of Graphene Oxide

Synthesis and studies of graphite oxide started more than 150 years ago and turned into a boom by the measurements of the outstanding physical properties of graphene. A series of preparation protocols emanated trying to optimize the synthesis of graphene oxide in order to obtain a less defective material, as source for graphene. However, over-oxidation of the carbon framework hampered establishing structure-property relationships. Here, the fact that two different synthetic methods for graphene oxide preparation lead to very similar types of graphene oxide with a preserved graphene lattice is demonstrated. Either sodium chlorate in nitric acid (similar to Brodie's method) or potassium permanganate in sulfuric acid (similar to Hummers’ method) treatment are possible; however, reaction conditions must be controlled. With a preserved carbon lattice analytical differences between the samples relate to the altered on-plane functionality. Consequently, terming preparation protocols “according to Brodie's/Hummers’ method” is not sufficient.