The critical exponent conjecture for powers of doubly nonnegative matrices

Doubly nonnegative matrices arise naturally in many setting including Markov random fields (positively banded graphical models) and in the convergence analysis of Markov chains. In this short note, we settle a recent conjecture by C.R. Johnson et al. [Charles R. Johnson, Brian Lins, Olivia Walch, The critical exponent for continuous conventional powers of doubly nonnegative matrices, Linear Algebra Appl. 435 (9) (2011) 2175–2182] by proving that the critical exponent beyond which all continuous conventional powers of n-by-n   doubly nonnegative matrices are doubly nonnegative is exactly n−2$n-2$. We show that the conjecture follows immediately by applying a general characterization from the literature. We prove a stronger form of the conjecture by classifying all powers preserving doubly nonnegative matrices, and proceed to generalize the conjecture for broad classes of functions. We also provide different approaches for settling the original conjecture.     

Low frequency dielectric spectroscopy of two room temperature chiral liquid crystal mixtures

Dielectric spectroscopy of two room temperature chiral liquid crystal mixtures (W-96 and W-97) have been carried out in the frequency range of 100?mHz–10?MHz. Low frequency dielectric relaxation modes corresponding to collective behavior of molecules (Goldstone- and soft-modes) in the SmC* phase have been found to be masked by the ionic conductance. Two slow modes of dielectric relaxation due to the ionic conductance have been detected (below 15?Hz) in planar-aligned samples. It has been observed that the effect of ionic conductance decreases with the number of thermal annealing cycles on the materials. With large number of thermal annealing cycles it has been possible to wipe out the effects of ionic conductance and then to detect other weak modes of dielectric relaxation which are otherwise masked.     

Landau theory of ferroelectric transition in long cylindrical nanoparticles

Using a phenomenological Landau theory, the size dependence on ferroelectric transition for free-standing long cylindrical nanoparticles is discussed. We derive the size dependence of the transition temperature, polarization profile as well as the static susceptibility. The transition temperature vanishes below a critical size where the static susceptibility shows divergence obeying Curie-Weiss law. In order to make this result compared with experiments, the average polarization and the susceptibility is computed with a Gaussian particle size distribution. The average polarization in such a case shows smearing with respect to the particle size whereas the divergence in the susceptibilty gets rounded. This might correspond to a size dependent soft mode which can be observed in Raman measurement.     

Optimization of a high-performance liquid chromatography method for the separation and identification of six different classes of phenolics

Flavonoids are chemical moieties widely distributed in certain plants that are important biologically active constituents of a daily human diet, with significant pharmacological potential (anti-hepatotoxic, anti-allergic, anti-inflammatory, anti-osteoporotic, and anti-tumor activities). Thus keeping in view the importance of this class of compounds, a rapid method for the separation and identification of fifteen phenols belonging to six different types of phenolics in a sole analysis has been developed and validated using selectivity, precision, recovery, and robustness as parameters. The method developed, which is rapid, accurate, and robust for the analysis of different classes of phenols, can be used in the quality control and standardization of plant extracts as well as herbal drugs, including compound herbal formulations.     

Accumulation and Toxicity of Nanoplastics in Photosynthetic-Species

This plastic waste degrades into nanoparticles, which are referred to as nanoplastics (NPs) pollutants, due to faulty reuse and recycling processes. These micro and nano plastic pollutants have the ability to absorb and interact with common pollutants and have a high surface area to volume ratio, which causes serious effects on the environment, especially plants. The size of pollutants is so small that they can cross the biological barriers and affect the cellular and molecular levels. Exposure to nanoplastics in photosynthetic species affects the growth and photosynthesis mechanism of the plants. Nanoplastics also affect humans through intake of the exposed plant materials. These pollutants can be plastic pellets, personal care products, marine coatings, synthetic textiles, etc. Plastic pollutants may enter the human body mainly through contaminated food and water. This review incorporates the toxicity of such pollutant and how their remediation is being done. The focus is also on the advancement of detection and remediation techniques.     

Characterization of Mn doped ZnS nanocrystalline powder dispersed in polyvinyl alcohol: 1st Nano Update

Manganese doped zinc sulfide nanocrystalline powder was synthesized with sodium citrate and its films were formed by mixing it with polyvinyl alcohol to study optical absorption of Mn doped ZnS dispersed in polyvinyl alcohol. The characteristics of the prepared powder and film samples were studied by X-ray diffraction, transmission electron microscopy and UV–visible absorption spectroscopy. Samples exhibited optical absorption at lower wavelength region and particle sizes were calculated from X-ray diffractogram.     

Synthesis of single-crystalline anatase nanorods and nanoflakes on transparent conducting substrates

Single-crystalline anatase nanorods and nanoflakes were grown on transparent conducting fluorine-doped tin oxide (FTO) substrates through hydrolysis of titanium tetrachloride (TiCl(4)) followed by heating to 450 °C.