Ruled quartic surfaces,models and classification

New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a ‘modern’ treatment of the classification of ruled quartic surfaces the classical one is corrected and completed. The string models of Series XIII of some ruled quartic surfaces (manufactured by L. Brill and by M. Schilling) are based on a result of Rohn concerning curves in \mathbbP¹×\mathbbP¹{\mathbb{P}^1\times \mathbb{P}^1} of bi-degree (2, 2). This is given here a conceptional proof.     

Weak Solutions for the Motion of a Self-propelled Deformable Structure in a Viscous Incompressible Fluid

We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.     

Analyticity and Gevrey-Class Regularity for the Second-Grade Fluid Equations

We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of the solutions that does not vanish as t → ∞, and which is independent of the Rivlin–Ericksen material parameter α. Applications to the damped incompressible Euler equations are also given.     

2,9-Diazadibenzoperylene and 2,9-Dimethyldibenzoperylene-1,3,8,10-tetratriflates: Key to Functionalized 2,9-Diazaperopyrenes

The synthesis of 2,9-diaza-1,3,8,10-tetratriflato-dibenzoperylene (DDP 3 a ) and corresponding 2,9-dimethyl-1,3,8,10-tetratriflato-dibenzoperylene (DBP 3 b ) has been developed at multigram scale via reduction of one of the industrially most important high-performance dyes, perylene-3,4,9,10-tetracarboxylic diimide (PTCDI), and of the corresponding dihydroxy peropyrenequinone precursor. The focus of this paper is on the reactivity pattern of 3 a as key intermediate towards highly functionalized 2,9-diazadibenzopyrelenes (DDPs) obtained via catalytic substitution of four triflate by aryl, heteroaryl, alkynyl, aminyl, and O-phosphanyl substituents. The influence of electron-donating substituents (OSiMe₃, OPt-Bu₂, N-piperidinyl), electron-withdrawing (OTf, 3,5-bis-trifluoromethyl-phenyl), and of electron-rich π-conjugated (2-thienyl, 4-tert-butylphenyl, trimethylsilyl-ethynyl) substituents on optoelectronic and structural properties of these functionalized DDPs has been investigated via XRD analyses, UV/Vis, PL spectroscopy, and by electroanalytical CV. These results were correlated to results of DFT and TD-DFT calculations. Thus, functionalized DPPs with easily tunable HOMO and LUMO energies and gap became available via a new and reliable synthetic strategy starting from readily available PTCDI.     

A Polyclonal Selex Aptamer Library Directly Allows Specific Labelling of the Human Gut Bacterium Blautia producta without Isolating Individual Aptamers

Recent studies have demonstrated that changes in the abundance of the intestinal bacterium Blautia producta, a potential probiotic, are closely associated with the development of various diseases such as obesity, diabetes, some neurodegenerative diseases, and certain cancers. However, there is still a lack of an effective method to detect the abundance of B. producta in the gut rapidly. Especially, DNA aptamers are now widely used as biometric components for medical testing due to their unique characteristics, including high chemical stability, low production cost, ease of chemical modification, low immunogenicity, and fast reproducibility. We successfully obtained a high-affinity nucleic acid aptamer library (B.p-R14) after 14 SELEX rounds, which efficiently discriminates B. producta in different analysis techniques including fluorometric suspension assays or fluorescence microscopy from other major gut bacteria in complex mixtures and even in human stool samples. These preliminary findings will be the basis towards aptamer-based biosensing applications for the fast and reliable monitoring of B. producta in the human gut microbiome.     

Synthesis,properties, and crystal structure of a novel 3-hydroxy-(4<Emphasis Type="Italic">H</Emphasis>)-benzopyran-4-one containing copper(II) complex,and its oxygenation and relevance to quercetinase

The preparation, spectroscopic properties, and crystal structure of [Cu(ind)(mco)] [ind is the anion of 1,3-bis(2-pyridylimino)isoindoline and mco is the anion of 3-hydroxy-(4H)-benzopyran-4-one] are reported. The complex exhibits a distorted square pyramidal geometry. The oxygenation of the title compound results in oxidative cleavage of the heterocyclic ring to give the (acetylsalicylato)copper(II) complex [Cu(asp)(ind)] (asp is the anion of acetylsalicylic acid) and CO as primary products, which reaction resembles the enzymatic reaction of quercetinase.     

Chloride‐Free Method to Synthesise New Ionic Liquids with Mixed Borate Anions

Chloride avoided! A new chloride‐free method to synthesise ionic liquids (ILs) with mixed borate anions, starting from tetrafluoroborate compounds, has been developed and a number of examples including some new ILs are presented (see scheme; [CAT]⁺=cation). It is widely applicable and allows access to mixed borates with various types of ligands in a straightforward manner.

     

Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.