Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces

We introduce a new method for proving the estimate

where solves the equation . The method can be applied to the Laplacian on . It also allows us to obtain similar estimates when we replace the Laplacian by an infinite-dimensional Ornstein-Uhlenbeck operator or other elliptic operators. These operators arise naturally in martingale problems arising from measure-valued branching diffusions and from stochastic partial differential equations.

     

Preparation, preservation and application of pure isotope-enriched phenyltin species

A method combining liquid/liquid extraction and chromatographic fractionation has been developed for the preparation of pure monophenyltin (MPhT), diphenyltin (DPhT), and triphenyltin (TPhT), synthesized from isotope-enriched Sn metal using phenylation of SnI₄ in diethylether (DEE) followed by quenching with HBr and water. After two successive extractions of the aqueous HBr phase with DEE, >99% of both DPhT and TPhT was recovered in the combined DEE phase and 94% of the MPhT remained in the aqueous phase. The MPhT in the aqueous phase was extracted into dichloromethane. The organic phases were vaporized and the PhTs were redissolved in MeOH/water/acetic acid/sodium acetate (59/30/6/8, v/v/v/w), which was also used as storing solution. Aliquots of the two solutions containing either DPhT and TPhT or MPhT were injected into a silica-based C₁₈ column for isolating and purifying single species. The yields of pure MPhT, DPhT, and TPhT, each synthesized from isotope-enriched ¹¹⁸Sn metal, ¹²²Sn metal, and ¹²⁴Sn metal, were better than 99%. After chromatographic separation, the single phenyltin compounds were mixed to prepare a spike for multiple-isotope species-specific isotope dilution (MI-SSID). MI-SSID was successfully used to determine phenyltin compounds in the certified reference material, mussel tissue BCR CRM-477. At −20 °C, all of the fractionated phenyltin species were stable in the storage solution for at least 197 days. When these standards were stored at 4 °C or 22 °C, 4–6% of the DPhT and TPhT degraded within 27 days. The degradation of DPhT and TPhT increased with the ionic strength and acidity of the storage solution.      

Influence of Sm<Superscript>3+</Superscript> ion in structural,morphological, and electrochemical properties of LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript> synthesized by microwave calcination

LiSm_xMn_2–xO₄ samples were synthesized via co-precipitation technique. The structural properties of the synthesized materials were studied using X-ray diffraction analysis and it confirmed the cubic spinel structure for all the compounds. The lattice parameter of LiMn₂O₄ was observed to be 8.2347 Ǻ and it decreased with Sm³⁺ concentration, due to the shrinkage in cell volume aided by higher binding energy between Sm-O bond. The SEM micrographs were analyzed using Image processing software (Image-J) to ascertain the pore and grain properties. The microwave synthesis had been observed to control the bulk grain formation and had yielded lesser porous and nanoparticles. The particle size distributions obtained through photocross correlation laser diffraction analysis had shown that LiMn₂O₄ with 60 nm and Sm-doped compounds with ∼30 nm, respectively. The cyclic voltammetry studies had revealed the decrease in electrocatalytic behavior in the initial cycle for compounds doped with Sm³⁺ ion. The initial capacities of LiMn₂O₄, LiSm_0.05Mn_1.95O₄ and LiSm_0.10Mn_1.90O₄ substituted compounds were observed to be 134.87 mAhg⁻¹, 132.22 mAhg⁻¹ and 126.41 mAhg⁻¹, respectively. The cells were simulated using 1D model namely Dualfoil5.1 program. The simulated results coincide well with the measured results. The cycle life studies reveal 93% capacity retention of samarium-0.05-doped samples when compared with 78.4% of the LiMn₂O₄.     

Characterization of Phyllanthus amarus herb by inductively coupled plasma mass spectrometric (ICP-MS) analysis,optical absorption and electron paramagnetic resonance (EPR) spectroscopic methods

A powdered sample of Phyllanthus amarus herb of Kadapa district of Andhra Pradesh, India, is used in the present study. ICP-MS analysis indicates that copper is present in higher concentration when compared to other elements. Although the Pb is toxic, it is within the permissible limit. The evaluated soil and herb physico-chemical parameters indicate that the sample is acidic in nature in comparison with the soil. An EPR study on powdered sample confirms the presence of Fe(III), Mn(II) and Cu(II). Optical absorption spectrum indicates that Fe(III) impurity is present in octahedral structure whereas Cu(II) is present in rhombically distorted octahedral environment. MIR results are due to carbonate fundamentals.     

Synthesis and Antimicrobial Activity of 1-Aryl-4-(arylimino)-6-iminohexahydro-1,3,5-triazine-2-thione Derivatives

Russian Journal of General Chemistry - A series of 6-imino-1-aryl-4-(arylimino)-1,3,5-triazinane-2-thione derivatives are synthesized by cyclization of 1-aryl-3-cyanoguanidine with aryl...     

Palladium‐catalysed room‐temperature Suzuki–Miyaura coupling in water extract of pomegranate ash,a bio‐derived sustainable and renewable medium

An agro waste‐derived, ‘water extract of pomegranate ash’ (WEPA), has been utilized for the first time as a renewable medium for Pd(OAc)₂‐catalysed Suzuki–Miyaura cross‐coupling at room temperature. This method offers a simple and sustainable synthesis of biaryls from aryl halides and arylboronic acids under ligand‐ and external base‐free aerobic and ambient conditions. This method has been found effective for both activated and unactivated aryl halides in the production of biaryls with moderate to nearly quantitative yields. The protocol shows high chemoselectivity over identical/similar reactive sites in aryl halides (i.e. selectivity over identical halogens or different halogens of aryl halides). This method exhibits high regioselectivity, i.e. the selective reactivity of a halogen over other identical halogens at different positions on the aromatic nucleus. Therefore, we disclose here a clean, benign, substantial chemo‐ and regioselective and highly economic alternative method for the palladium‐assisted synthesis of biaryls using an agro waste‐derived medium.     

Diindeno-Fused Dibenzo[a,h]anthracene and Dibenzo[c,l]chrysene: Syntheses,Structural Analyses,and Properties

Diindeno-fused dibenzo[a,h]anthracene 6 and diindeno-fused dibenzo[c,l]chrysene 9 contain the key moieties 1,4-quinodipropene (1,4-QDP) and 2,6-naphthoquinodipropene (2,6-NQDP), respectively, and they both have an open-shell singlet ground state. The latter compound exhibits a strong biradical character and interesting properties, including a low ΔE_T−S (2.44 kcal mol⁻¹), a small HOMO–LUMO gap (1.06 eV), a wide photoabsorption range (250–1172 nm), and a large two-photon absorption cross-section (σ=1342±56 GM). This work verifies that 6 has a slightly larger HOMO–LUMO gap and ΔE_T−S than its helical isomer diindeno[2,1-f:1′,2′-j]picene (DIP), but is a much stronger two-photon absorber, verifying the important effect of geometry on the photophysical properties.