Product integration of logarithmic singular integrands based on cubic splines

This paper is concerned with the practical evaluation of the product integral ∫¹_{? 1}f(x)k(x)dx for the case when k(x) = In|x - λ|, λ? (?1, +1) and f is bounded in [?1, +1]. The approximation is a quadrature rule

where the weights {w_n,n,i} are chosen to be exact when f is given by a linear combination of a chosen set of functions {φ_n,j}. In this paper the functions {φ_n,j} are chosen to be cubic B-splines. An error bound for product quadrature rules based on cubic splines is provided. Examples that test the performance of the product quadrature rules for different choices of the function are given. A comparison is made with product quadrature rules based on first kind Chebyshev polynomials.     

Ionic liquids as modulators of the critical micelle concentration of sodium dodecyl sulfate

Critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS), an anionic surfactant, has been investigated in aqueous solutions of a variety of room temperature ionic liquids (RTILs): 1,3-dimethylimidazolium iodide (Me2IM-I, 2), 1-butyl-3-methylimidazolium chloride (BMIM-Cl, 3), 1-hexyl-3-methylimidazolium chloride (HxMIM-Cl, 4), 1-methyl-3-octylimidazolium chloride (MOIM-Cl), 5, and 1-methyl-3-octylimidazolium tetrafluoroborate (MOIM-BF4, 6). The CMC of SDS is shown to correlate with the nature of the alkyl groups in the RTILs; SDS showed appreciably higher CMCs in presence of ionic liquids 2 and 3, whereas in the presence of ionic liquids 4, 5, and 6 much smaller CMCs were observed. The nature of the gigenions, Cl- or BF4-, has no noticeable effect on the observed CMC values.     

Photoactivatable Carbo- and Silicon-Rhodamines and Their Application in MINFLUX Nanoscopy

New photoactivatable fluorescent dyes (rhodamine, carbo- and silicon-rhodamines [SiR]) with emission ranging from green to far red have been prepared, and their photophysical properties studied. The photocleavable 2-nitrobenzyloxycarbonyl unit with an alpha-carboxyl group as a branching point and additional functionality was attached to a polycyclic and lipophilic fluorescent dye. The photoactivatable probes having the HaloTagTM amine (O2) ligand bound with a dye core were obtained and applied for live-cell staining in stable cell lines incorporating Vimentin (VIM) or Nuclear Pore Complex Protein NUP96 fused with the HaloTag. The probes were applied in 2D (VIM, NUP96) and 3D (VIM) MINFLUX nanoscopy, as well as in superresolution fluorescence microscopy with single fluorophore activation (VIM, live-cell labeling). Images of VIM and NUPs labeled with different dyes were acquired and their apparent dimensions and shapes assessed on a lower single-digit nanometer scale. Applicability and performance of the photoactivatable dye derivatives were evaluated in terms of photoactivation rate, labeling and detection efficiency, number of detected photons per molecule and other parameters related to MINFLUX nanoscopy.     

An exact solution for static scalar fields coupled to gravity in (2+1)-dimensions

We obtain an exact solution for the Einstein’s equations with cosmological constant coupled to a scalar, static particle in static, “spherically” symmetric background in (2+1)-dimensions.     

Chemical constituents and biological activities of Dianthus elegans var. elegans

Chemical investigation of the aerial parts of Dianthus elegans var. elegans afforded two previously undescribed saponins, named dianosides M-N (1–2), together with four oleanane-type triterpenoid glycosides (3–6). Their structures were elucidated as 3-O-α-L-arabinofuranosyl-16α-hydroxyolean-12-ene-23α, 28β-dioic acid (1) and 3-O-α-L-arabinofuranosyl-(1 → 3)-β-D-glucopyranosyl 16α-hydroxyolean-12-ene-23α-oic acid, 28-O-β-D-glucopyranosyl-(1 → 6)-β-D-glycosyl ester (2) by chemical and extensive spectroscopic methods including IR, 1D, 2D NMR and HRESIMS. Both of the saponins were evaluated for their cytotoxicities against HEK-293, A-549 and HeLa human cancer cells using the MTT method. All compounds showed no substantial cytotoxic activity against tested cell lines. However, dianosides M-N and the n-butanol fraction exhibited considerable haemolysis in human erythrocyte cells. The immunomodulatory properties of dianosides M-N were also evaluated in activated whole blood cells by PMA plus ionomycin. Dianosides M-N increased IL-1β concentration significantly whereas the n-butanol fraction slightly augmented IL-1β secretion. All compounds did not change IL-2 and IFN-γ levels considerably.     

Self-dual Yang-Mills fields in eight dimensions

Strongly self-dual Yang-Mills fields in even-dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fieldsF . We derive a topological bound on R⁸, , wherep1 is the first Pontryagin class of the SO(n) Yang-Mills bundle, andk is a constant. Strongly self-dual Yang-Mills fields realise the lower bound.     

Synthesis,Characterization, Crystal and Molecular Structure of 1,5‐Dihydro‐2H‐cyclopenta[1,2‐b:5,4‐b′]dipyridin‐2‐imine

The reaction of 1,5‐dihydro‐2H‐cyclopenta[1,2‐b:5,4‐b′]dipyridin‐2‐one ( 3 ) with an alkylamine (butylamine, hexylamine or ethylenediamine) yields, quite unexpectedly and in the absence of catalyst, the novel compound 1,5‐dihydro‐2H‐cyclopenta[1,2‐b:5,4‐b′]dipyridin‐2‐imine ( 4 ) as the sole, analytically pure, solid product, which was fully characterized. The structure of 4 was unequivocally solved by single‐crystal X‐ray‐diffraction analysis. The compound crystallizes in a monoclinic cell (space group P 2₁/c), with two molecules in the asymmetric unit, held together by intermolecular H‐bonds. Compound 4 could be interesting as a bi‐ or even tridentate ligand, and exhibits a strong fluorescence upon excitation at 310 nm. A mechanism, based on the observed C? N bond cleavage, is proposed.     

Silicon nanoparticle charge trapping memory cell

A charge trapping memory with 2 nm silicon nanoparticles (Si NPs) is demonstrated. A zinc oxide (ZnO) active layer is deposited by atomic layer deposition (ALD), preceded by Al₂O₃ which acts as the gate, blocking and tunneling oxide. Spin coating technique is used to deposit Si NPs across the sample between Al₂O₃ steps. The Si nanoparticle memory exhibits a threshold voltage (V_t) shift of 2.9 V at a negative programming voltage of –10 V indicating that holes are emitted from channel to charge trapping layer. The negligible measured V_t shift without the nanoparticles and the good re‐ tention of charges (>10 years) with Si NPs confirm that the Si NPs act as deep energy states within the bandgap of the Al₂O₃ layer. In order to determine the mechanism for hole emission, we study the effect of the electric field across the tunnel oxide on the magnitude and trend of the V_t shift. The V_t shift is only achieved at electric fields above 1 MV/cm. This high field indicates that tunneling is the main mechanism. More specifically, phonon‐assisted tunneling (PAT) dominates at electric fields between 1.2 MV/cm < E < 2.1 MV/cm, while Fowler–Nordheim tunneling leads at higher fields (E > 2.1 MV/cm). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Glucose Oxidase-dextran Conjugates with Enhanced Stabilities Against Temperature and pH

Multipoint covalent bonding of glucose oxidase (EC 1.1.3.4) to hydrophilic natural polymer dextran and optimization of procedures to obtain, with enhanced temperature and pH stabilities, were studied. Purified enzyme was conjugated with various molecular weight dextrans (17.5, 75, and188 kD) in a ratio of 20:1, 10:1, 1:1, 1:5, 1:10, 1:15, and 1:20. After 1 h of incubation at pH 7, the activities of purified enzyme and conjugates were determined at different temperatures (25°C, 30°C, 35°C, 40°C, 50°C, 60°C, 70°C, and 80°C), and the results were evaluated for thermal resistance. Increases in temperature from 25°C to 50°C did not change the activities of the conjugates. The conjugate, which was prepared with 75 kDa dextran in a molar ratio of 1:5, showed the highest thermal resistance and even the activity still remains at 80°C at pH 7.0. This conjugate also displayed activity in a wide pH range (pH 4.0–7.0) at high temperatures. Conjugate, which was synthesized with 75 kDa dextran in a molar ratio of 1:5, appears to be feasible and useful for biotechnological applications.