Rectifiable oscillations in second-order linear differential equations

We study the linear differential equation , on I=(0,1), where the coefficient f(x) is strictly positive and continuous on I, and satisfies the Hartman-Wintner condition at x=0. The four main results of the paper are: (i) a criterion for rectifiable oscillations of (P), characterized by the integrability of on I; (ii) a stability result for rectifiable and unrectifiable oscillations of (P), in terms of a perturbation on f(x); (iii) the s-dimensional fractal oscillations (for which we assume also f(x)∼cx−α when x→0, α>2, and s=max{1,3/2−2/α}); and (iv) the co-existence of rectifiable and unrectifiable oscillations in the absence of the Hartman-Wintner condition on f(x). Explicit examples related to the above results are given.     

Electrical,structural, and thermal studies of antimony trioxide-doped poly(acrylic acid)-based composite polymer electrolytes

In this work, we investigate the electrical, structural, and thermal properties of composite polymer electrolytes (CPEs). Different mass fractions of antimony trioxide filler, Sb₂O₃, are added into poly(acrylic acid) (PAA)-based polymer electrolytes with N-lithiotrifluoromethane sulphonamide [LiN(SO₂CF₃)₂] (LiTFSI) as doping salt. Characteristics such as alternating current (AC)–impedance spectroscopy, attenuated total reflectance–Fourier transform infrared (ATR-FTIR), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA) are analyzed. The highest ionic conductivity of (2.15?±?0.01)?×?10^?4 S cm^?1 is achieved at room temperature with addition of 6 wt% of fillers. The ionic transportation is further proven in a transference number study under DC polarization, whereas ATR-FTIR is employed to explore the complexation between PAA, LiTFSI, and Sb₂O₃. TGA reveals the improved thermal stability of CPEs. The glass transition temperature (T _g) is reduced upon addition of Sb₂O₃ as shown in DSC analysis.     

Structural Manipulation of Ruthenium(II) Polypyridine Nitrone Complexes to Generate Phosphorogenic Bioorthogonal Reagents for Selective Cellular Labeling

We report a new class of ruthenium(II) polypyridine complexes functionalized with a nitrone group as phosphorogenic bioorthogonal probes. These complexes were very weakly emissive owing to rapid C=N isomerization of the nitrone moiety, but exhibited significant emission enhancement upon strain‐promoted alkyne–nitrone cycloaddition (SPANC) reaction with bicyclo[6.1.0]nonyne (BCN)‐modified substrates. The modification of nitrone with a dicationic ruthenium(II) polypyridine unit at the α‐C‐position and a phenyl ring at the N‐position led to remarkably accelerated reaction kinetics, which are substantially greater (up to ≈278 fold) than those of other acyclic nitrone–BCN systems. Interestingly, the complexes achieved specific cell membrane/cytosol staining upon specific labeling of an exogenous substrate, BCN‐modified decane (BCN‐C10), in live cells. Importantly, the in situ generation of the more lipophilic isoxazoline adduct in the cytoplasm resulted in increased cytotoxicity, highlighting a novel approach to apply the SPANC labeling technique in drug activation.     

Tuning of Supramolecular Architectures of l‐Valine‐Containing Dicyanoplatinum(II) 2,2′‐Bipyridine Complexes by Metal–Metal, π–π Stacking,and Hydrogen‐Bonding Interactions

A series of newly synthesized dicyanoplatinum(II) 2,2′‐bipyridine complexes exhibits self‐assembly properties in solution after the incorporation of the l ‐valine amino units appended with various hydrophobic motifs. These l ‐valine‐derived substituents were found to have critical control over the aggregation behaviors of the complexes in the solution state. On one hand, one of the complexes was found to exhibit interesting circularly polarized luminescence (CPL) signals at low temperature due to the formation of chiral spherical aggregates in the temperature‐dependent studies. On the other hand, systematic transformation from less uniform aggregates to well‐defined fibrous and rod‐like structures via Pt???Pt and π–π stacking interactions has also been observed in the mixed‐solvent studies. These changes were monitored by UV/Vis absorption, emission, circular dichroism (CD), and CPL spectroscopies, and morphologies were studied by electron microscopy.     

Multi-element analysis by ArF laser excited atomic fluorescence of laser ablated plumes: Mechanism and applications

A new multi-element analysis technique based on laser-excited atomic fluorescence was reviewed. However, the one-wavelength-one-transition constraint was overcome. Numerous elements were induced to fluoresce at a single excitation wavelength of 193 nm. This was possible provided that the analytes were imbedded in dense plumes, such as those produced by pulsed laser ablation. The underlying mechanism of the technique was explained and corroborated. Analytical applications to metals, plastics, ceramics and their composites were discribed. Detection limits in the ng/g range and mass limits of atto moles were demonstrated. Several real-world problems, including the analysis of paint coating for trace lead, the non-destructive analysis of potteries and ink, the chemical profiling of electrode-plastic interfaces, and the analysis of ingestible lead colloids were discussed.     

Potential-screening on atomic wavelengths

In this article, we review or report recent works on atomic wavelengths in screening environments. We mainly review recent works on the transition, tune-out and magic wavelengths with Coulomb and screened Coulomb potentials. We also present our investigation on tune-out and magic wavelengths for two-electron Yukawa atoms. The various transition wavelengths for two-electron systems with and without screening environments are also presented.