Differentiable Distance Spaces

The distance function \({\varrho(p, q) ({\rm or} d(p, q))}\) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over \({\mathbb{R}^n}\), whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are not Finsler spaces (which are special distance spaces). They are situated between general metric spaces (distance spaces) and Finsler spaces. We will investigate such curves of differentiable distance spaces, which possess the same properties as geodesics do in Finsler spaces. So these curves can be considered as forerunners of Finsler geodesics. They are in greater plenitude than Finsler geodesics, but they become geodesics in a Finsler space. We show some properties of these curves, as well as some relations between differentiable distance spaces and Finsler spaces. We arrive to these curves and to our results by using distance spheres, and using no variational calculus. We often apply direct geometric considerations.     

Antibacterial wollastonite supported excellent proliferation and osteogenic differentiation of human bone marrow derived mesenchymal stromal cells

Journal of Sol-Gel Science and Technology - Biocompatibility and bacterial infections are the primary concerns associated with the current bone graft substitutes. The application of...     

The Extended Hadamard Transform: Sensitivity-Enhanced NMR Experiments Among Labile and Non-Labile 1Hs of SARS-CoV-2-derived RNAs

Hadamard encoded saturation transfer can significantly improve the efficiency of NOE-based NMR correlations from labile protons in proteins, glycans and RNAs, increasing the sensitivity of cross-peaks by an order of magnitude and shortening experimental times by ≥100-fold. These schemes, however, fail when tackling correlations within a pool of labile protons – for instance imino-imino correlations in RNAs or amide-amide correlations in proteins. Here we analyze the origin of the artifacts appearing in these experiments and propose a way to obtain artifact-free correlations both within the labile pool as well as between labile and non-labile ¹Hs, while still enjoying the gains arising from Hadamard encoding and solvent repolarizations. The principles required for implementing what we define as the extended Hadamard scheme are derived, and its clean, artifact-free, sensitivity-enhancing performance is demonstrated on RNA fragments derived from the SARS-CoV-2 genome. Sensitivity gains per unit time approaching an order of magnitude are then achieved in both imino-imino and imino-amino/aromatic protons 2D correlations; similar artifact-free sensitivity gains can be observed when carrying out extended Hadamard encodings of 3D NOESY/HSQC-type experiments. The resulting spectra reveal significantly more correlations than their conventionally acquired counterparts, which can support the spectral assignment and secondary structure determination of structured RNA elements.     

Carboxylic acid–pyridine supramolecular heterocatemer in a co-crystal

Robustness of carboxylic acid–pyridine supramolecular heterosynthon was examined in three 1:2 binary co-crystals of 4,4′-bipyridine with monocarboxylic acids, (4,4′-bipyridine)·(dl-hydroxyphenylacetic acid)₂, 1; (4,4′-bipyridine)_0.5·(4-bromonaphthalene-1-carboxylic acid), 2 and (4,4′-bipyridine)_0.5·(4-methylbenzoic acid), 3. All the three co-crystals form “two-component supermolecules” (consisting of one molecule of 4,4′-bipyridine and two molecules of the relevant carboxylic acid) stabilized through carboxylic acid–pyridine heterosynthons. Co-crystals 1 and 2 exhibits the expected carboxylic acid–pyridine dimer (heterodimer I) whereas co-crystal 3 forms a novel carboxylic acid–pyridine catemer (heterocatemer II).     

Energy dispersive X-ray fluorescence analysis of gallstones

The elemental analysis of south Indian gallstones has been carried out using energy dispersive X-ray fluorescence (EDXRF) spectroscopy. A number of important elements including Fe, Cu, Zn, Br, and Pb were estimated from the EDXRF spectra. The results are presented and discussed.     

Study of theS-matrix near bound states in the continuum

The behaviour ofS-matrix for potentials generating bound states in continuum in the neighbourhood of the positive bound state energies is studied. It is shown that unlike the case of usual negative energy bound states, theS-matrix does not have a pole at the positive bound state energy but becomes unity at the energy corresponding to bound states in continuum. Calculations ofS-waveS-matrix for a local potential constructed by Stillinger and Herrick and a separable nonlocal potential constructed by the present authors verify these results. Our results indicate that the bound states embedded in continuum constructedvia the von Neumann and Wigner procedure cannot be interpreted as resonances with zero width.