A note on Hardy’s theorem and rotations

Semigroup Forum - We give a very short proof, using the Hermite semigroup, to a generalized version of Hardy’s theorem due to Hogan and Lakey. We characterize $$fin L^2({mathbb {R}}^n)$$...     

Anomalous magnetic response of a quasi-periodic mesoscopic ring in presence of Rashba and Dresselhaus spin-orbit interactions

We investigate the properties of persistent charge current driven by magnetic flux in aquasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus spin-orbitinteractions. Within a tight-binding framework we work out individual state currentstogether with net current based on second-quantized approach. A significant enhancement ofcurrent is observed in presence of spin-orbit coupling and sometimes it becomes orders ofmagnitude higher compared to the spin-orbit interaction free Fibonacci ring. We alsoestablish a scaling relation of persistent current with ring size, associated with theFibonacci generation, from which one can directly estimate current for any arbitrary flux,even in presence of spin-orbit interaction, without doing numerical simulation. Thepresent analysis indeed gives a unique opportunity of determining persistent current andhas not been discussed so far.     

Crystal plasticity-based constitutive modelling of irradiated bcc structures

A constitutive crystal plasticity model is proposed and developed for the inelastic deformation of irradiated bcc ferritic/martensitic steels. Defects found in these irradiated materials are used as substructure variables in the model. Insights from lower length- and time-scale simulations are used to frame the kinematic and substructure evolution relations of the governing deformation mechanisms. Models for evolution of mobile and immobile dislocations, as well as interstitial loops (formed due to irradiation), are developed. A rate theory-based approach is used to model the evolution of point defects generated during irradiation. The model is used to simulate the quasi-static tensile and creep response of a martensitic steel over a range of loading histories.     

Carbon-13 NMR signals of some benzodiazepine drugs

Some carbon-13 NMR signal assignments of diazepam, flurazepam, clonazepam and chlordiazepoxide have been revised and the assignments of nitrazepam are reported. The assignments of the various resonances were made by considering the changes in chemical shifts produced by the change of substituents and also by comparison with the chemical shifts of model compounds.     

Understanding the influence of nanoenvironment on luminescence of rare-earth ions

This paper presents an overview of the recent results on upconversion and photoluminescence of rare-earth ions in nanoenvironments. The role of the rare-earth ion concentration, crystal size and crystal phase on the up and downconversion emission of rare-earth ions in oxide nanocrystals and their underlying mechanisms are discussed. It is also found that the luminescence lifetime of the excited state rare-earth ions is sensitive to the particle crystalline phase and size. The analysis suggests that the modifications of radiative and nonradiative relaxation mechanisms are due to local symmetry structure of the host lattice and crystal size respectively     

Structural Transformation of Bovine Serum Albumin Induced by Dimethyl Sulfoxide and Probed by Fluorescence Correlation Spectroscopy and Additional Methods

Determining the structure of a protein and its transformation under different conditions is key to understanding its activity. The structural stability and activity of proteins in aqueous–organic solvent mixtures, which is an intriguing topic of research in biochemistry, is dependent on the nature of the protein and the properties of the medium. Herein, the effect of a commonly used cosolvent, dimethyl sulfoxide (DMSO), on the structure and conformational dynamics of bovine serum albumin (BSA) protein is studied by fluorescence correlation spectroscopy (FCS) measurements on fluorescein isothiocyanate (FITC)‐labeled BSA. The FCS study reveals a change of the hydrodynamic radius of BSA from 3.7 nm in the native state to 7.0 nm in the presence of 40 % DMSO, which suggests complete unfolding of the protein under these conditions. Fluorescence self‐quenching of FITC has been exploited to understand the conformational dynamics of BSA. The time constant of the conformational dynamics of BSA is found to change from 35 μs in its native state to 50 μs as the protein unfolds with increasing DMSO concentration. The FCS results are corroborated by the near‐UV circular dichroism spectra of the protein, which suggest a loss of its tertiary structure with increasing concentration of DMSO. The intrinsic fluorescence of BSA and the fluorescence response of 1‐anilinonaphthalene‐8‐sulfonic acid, used as a probe molecule, provide information that is consistent with the FCS measurements, except that aggregation of BSA is observed in the presence of 40 % DMSO in the ensemble measurements.     

Four‐Center Oxidation State Combinations and Near‐Infrared Absorption in [Ru(pap)(Q)2]n (Q=3,5‐Di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine,pap=2‐Phenylazopyridine)

The complex series [Ru(pap)(Q)₂]ⁿ ([ 1 ]ⁿ–[ 4 ]ⁿ; n=+2, +1, 0, ?1, ?2) contains four redox non‐innocent entities: one ruthenium ion, 2‐phenylazopyridine (pap), and two o‐iminoquinone moieties, Q=3,5‐di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine (aryl=C₆H₅ ( 1⁺ ); m‐(Cl)₂C₆H₃ ( 2⁺ ); m‐(OCH₃)₂C₆H₃ ( 3⁺ ); m‐(tBu)₂C₆H₃ ( 4 ⁺)). A crystal structure determination of the representative compound, [ 1 ]ClO₄, established the crystallization of the ctt‐isomeric form, that is, cis and trans with respect to the mutual orientations of O and N donors of two Q ligands, and the coordinating azo N atom trans to the O donor of Q. The sensitive C? O (average: 1.299(3) Å), C? N (average: 1.346(4) Å) and intra‐ring C? C (meta; average: 1.373(4) Å) bond lengths of the coordinated iminoquinone moieties in corroboration with the N?N length (1.292(3) Å) of pap in 1 ⁺ establish [Ru^III(pap⁰)(Q^.?)₂]⁺ as the most appropriate electronic structural form. The coupling of three spins from one low‐spin ruthenium(III) (t_2g⁵) and two Q^.? radicals in 1 ⁺– 4 ⁺ gives a ground state with one unpaired electron on Q^.?, as evident from g=1.995 radical‐type EPR signals for 1 ⁺– 4 ⁺. Accordingly, the DFT‐calculated Mulliken spin densities of 1 ⁺ (1.152 for two Q, Ru: ?0.179, pap: 0.031) confirm Q‐based spin. Complex ions 1 ⁺– 4 ⁺ exhibit two near‐IR absorption bands at about λ=2000 and 920 nm in addition to intense multiple transitions covering the visible to UV regions; compounds [ 1 ]ClO₄–[ 4 ]ClO₄ undergo one oxidation and three separate reduction processes within ±2.0 V versus SCE. The crystal structure of the neutral (one‐electron reduced) state ( 2 ) was determined to show metal‐based reduction and an EPR signal at g=1.996. The electronic transitions of the complexes 1 ⁿ– 4 ⁿ (n=+2, +1, 0, ?1, ?2) in the UV, visible, and NIR regions, as determined by using spectroelectrochemistry, have been analyzed by TD‐DFT calculations and reveal significant low‐energy absorbance (λ_max>1000 nm) for cations, anions, and neutral forms. The experimental studies in combination with DFT calculations suggest the dominant valence configurations of 1 ⁿ– 4 ⁿ in the accessible redox states to be [Ru^III(pap⁰)(Q^.?)(Q⁰)]²⁺ ( 1 ²⁺– 4 ²⁺)→[Ru^III(pap⁰)(Q^.?)₂]⁺ ( 1 ⁺– 4 ⁺)→[Ru^II(pap⁰)(Q^.?)₂] ( 1 – 4 )→[Ru^II(pap^.?)(Q^.?)₂]^? ( 1 ^?– 4 ^?)→[Ru^III(pap^.?)(Q^2?)₂]^2? ( 1 ^2?– 4 ^2?).     

Total synchronous fluorescence scan spectra of petroleum products

Extending the two-dimensional synchronous fluorescence scan to a three-dimensional total synchronous fluorescence scan (TSFS) spectral measurement gives the total synchronous fluorescence characteristics of a multifluorophoric sample at various possible wavelength intervals (Deltalambda), which could help to characterize multifluorophoric systems better. TSFS spectra of petroleum products such as diesel, kerosene, petrol, engine oil etc., available in the Indian market, are reported. Fluorescence in these samples is due to the presence of polycyclic aromatic hydrocarbons (PAHs) of various ring sizes. The TSFS contour plot profiles of the neat samples measured at right-angle geometry is a result of various energy-degrading photophysical processes such as inner filter effect, light attenuation, resonance energy transfer, collisional quenching etc. TSFS plots make it easy to obtain the optimized Deltalambda of an unknown sample of analytical interest. TSFS and the excitation-emission matrix (EEM) techniques are similar, but the contour profiles generated are different. The response of the TSFS contour profiles to dilution is different from that in the EEM contour profiles. Thus, TSFS can provide an alternative way of presenting the fluorescence response of concentrated multifluorophoric samples.     

Colloidal Microcapsules: Self‐Assembly of Nanoparticles at the Liquid–Liquid Interface

Colloidal microcapsules (MCs) are highly modular, inherently multiscale constructs of capsules stabilized by nano‐/microparticle shells, with applications in many areas of materials and biological sciences, such as drug delivery, encapsulation, and microreactors. Until recently, fabrication of colloidal MCs focused on the use of submicron‐sized particles because the smaller nanoparticles (NPs) are inherently unstable at the interface owing to thermal disorder. However, stable microcapsules can now be obtained by tuning the interactions between the nanometer‐sized building blocks at the liquid–liquid interface. This Review highlights recent developments in the fabrication of colloidal MCs using NPs.