Results on uniqueness of entire functions whose difference polynomials share a polynomial

In this paper, we use the concept of weighted sharing of values to investigate the uniqueness results when two difference polynomials of entire functions share a nonzero polynomial or a small function with a finite weight.We also investigate the situation when the original functions share 0 CM. The obtained results improve some recent related results of X. Li et al. [Ann. Polon. Math, 102 (2011), 111-127] and that of W. Li et al. [Bull. Malay. Math. Sci. Soc., 39 (2016), 499-515].     

Light-induced excited spin-state trapping in spin crossover model system

We computationally investigate the light-induced excited spin-state trapping (LIESST) in a spin crossover (SCO) model system, derived out of [Fe(abpt)₂(NCS)₂] consisting of Fe(II) SCO center coordinated by bidenate as well as monodentate ligands. For this purpose, we use two complementary techniques: (a) time-dependent density functional theory (TDDFT) with the choice of different exchange-correlation functional and (b) multireference approach of complete active space self-consistent field and complete active-space second-order perturbation (CASPT2) theory. We calculate the potential energy curves (PECs) of low-energy states, as well as spin-orbit couplings at crossing points of these PECs. Inputting these pieces of information, and the information related to nuclear degrees of freedom within the Franck-Condon theory, we compute the relaxation rates of possible LIESST mechanisms, as suggested by the two approaches. Based on our findings, we conclude that TDDFT may not be an unreasonable approach to estimate the relaxation rates of real complexes, consisting of several tens to several hundreds of atoms, given its computationally inexpensive nature compared with that of the multireference approaches.     

Phenolic composition, antioxidant capacity and antibacterial activity of selected Irish Brassica vegetables

Vegetables belonging to the Brassicaceae family are rich in polyphenols, flavonoids and glucosinolates, and their hydrolysis products, which may have antibacterial, antioxidant and anticancer properties. In the present study, phenolic composition, antibacterial activity and antioxidant capacity of selected Brassica vegetables, including York cabbage, Brussels sprouts, broccoli and white cabbage were evaluated after extraction with aqueous methanol. Results obtained showed that York cabbage extract had the highest total phenolic content, which was 33.5, followed by 23.6, 20.4 and 18.4 mg GAE/g of dried weight (dw) of the extracts for broccoli, Brussels sprouts and white cabbage, respectively. All the vegetable extracts had high flavonoid contents in the order of 21.7, 17.5, 15.4 and 8.75 mg QE/g of extract (dw) for York cabbage, broccoli, Brussels sprouts and white cabbage, respectively. HPLC-DAD analysis showed that different vegetables contain a mixture of distinct groups of phenolic compounds. All the extracts studied showed a rapid and concentration dependent antioxidant capacity in diverse antioxidant systems. The antibacterial activity was determined against Gram-positive and Gram-negative bacteria. York cabbage extract exhibited significantly higher antibacterial activity against Listeria monocytogenes (100%) and Salmonella abony (94.3%), being the most susceptible at a concentration of 2.8%, whereas broccoli, Brussels sprouts and white cabbage had moderate to weak activity against all the test organisms. Good correlation (r2 0.97) was found between total phenolic content obtained by spectrophotometric analysis and the sum of the individual polyphenols monitored by HPLC-DAD.     

Natural Convection in a Nanofluid Saturated Rotating Porous Layer: A Nonlinear Study

The present paper deals with linear and nonlinear analysis of thermal instability in a rotating porous layer saturated by a nanofluid. Momentum equation with Brinkman term, involving the Coriolis term and incorporating the effect of Brownian motion along with thermophoresis has been considered. Linear stability analysis is done using normal mode technique, while for nonlinear analysis, a minimal representation of the truncated Fourier series, involving only two terms, has been used. Stationary and oscillatory modes of convection have been studied. A weak nonlinear analysis is used to obtain the concentration and thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is investigated by solving the finite amplitude equations using a numerical method. Obtained results have been presented graphically and discussed in details.     

Nonlinear Two-Dimensional Convection in a Nanofluid Saturated Porous Medium

In this article, we study the linear and nonlinear thermal instability in a horizontal porous medium saturated by a nanofluid. For this, the momentum equation with Brinkman model has been used. Also, it incorporates the effect of Brownian motion along with thermophoresis. The linear stability is based on normal mode technique, and for nonlinear analysis, the truncated Fourier series involving only two terms has been used. The expression of Rayleigh number for linear theory has been derived, and the effects of various parameters on Rayleigh number have been presented graphically. Weak nonlinear theory is used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is investigated and depicted graphically, by solving the finite amplitude equations using a numerical method.     

NMR studies of carbon dioxide and methane self-diffusion in ZIF-8 at elevated gas pressures

Self-diffusion measurements with methane and carbon dioxide adsorbed in the Zeolitic Imidazolate Framework-8 (ZIF-8) were performed by ¹H and ¹³C pulsed field gradient nuclear magnetic resonance (PFG NMR). The experiments were conducted at 298 K and variable pressures of 7 to 15 bar in the gas phase above the ZIF-8 bed. Via known adsorption isotherms these pressures were converted to loadings of the adsorbed molecules. The self-diffusion coefficients of carbon dioxide measured by PFG NMR are found to be independent of loading. They are in good agreement with results from molecular dynamic (MD) simulations and resume the trend previously found by IR microscopy at lower loadings. Methane diffuses in ZIF-8 only slightly slower than carbon dioxide. Its experimentally obtained self-diffusion coefficients are about a factor of two smaller than the corresponding values determined by MD simulations using flexible frameworks.     

Effect of pH on the photophysical and redox properties of a ruthenium(II) mixed chelate derived from imidazole-4,5-dicarboxylic acid and 2,2'-bipyridine: an experimental and theoretical investigation

Combined experimental and DFT-TD-DFT computational studies were utilized to investigate the structural and electronic properties of mixed-ligand monometallic ruthenium(II) complexes of compositions [(bpy)(2)Ru(H(2)Imdc)](+) (1(+)), its N-H deprotonated form [(bpy)(2)Ru(HImdc)] (1), and COOH deprotonated form [(bpy)(2)Ru(Imdc)](-) (1(-)), where H(3)Imdc = imidazole-4,5-dicarboxylic acid and bpy = 2,2'-bipyridine. The optimized geometrical parameters for the complexes computed both in the gas phase and in solution are reported and compared with the previously reported X-ray data. The influence of pH on the absorption, emission, and redox properties of [(bpy)(2)Ru(H(2)Imdc)](+) (1(+)) has been thoroughly investigated. The absorption titration data were used to determine the ground state pK values, whereas the luminescence data were utilized for the determination of excited state acid dissociation constants. The proton-coupled redox activity of 1(+) has been studied over the pH range 2-12 in acetonitrile-water (3:2). From the E(1/2) versus pH profile, the equilibrium constants of the variously deprotonated complex species in Ru(II) and Ru(III) oxidation states have been determined. As compared to the protonated complex (1(+)), which undergoes reversible oxidation at 0.96 V (vs Ag/AgCl) in acetonitrile, the redox potential of the fully deprotonated complex (1(-)) is shifted to a much lower value, viz., 0.52 V. Density functional theory (DFT) and time-dependent DFT (TD-DFT) study provides insight into the nature of the ground and excited states with resulting detailed assignments of the orbitals involved in absorption and emission transitions. In particular, the red-shifts of the absorption and emission bands and the cathodic shift in the oxidation potential of 1(+) compared to 1 and 1(-) are also reproduced by our calculations.     

Eigensolutions of cyclopolyacene graphs

A graph of {X, Y}-cyclopolyacene with n of hexagonal rings has been presented that contains four orbits, of which orbits 1 and 4 are occupied by the X-type of vertex and orbits 2 and 4 are occupied by the Y-type, or vice versa. Eigensolutions for such a graph have been derived in analytical form through the use of rotational symmetry followed by a plane of symmetry. Varying X ( = C, N, B, …) and Y ( = C, N, B, …) several types of cyclopolyacene graph may be obtained. Eigenvalue-expressions for such systems containing C, N and B have been shown in analytical form and their total π-electron energies with 2–6 hexagonal rings have been calculated with the help of the expressions developed.     

Measurement of improved pressure dependence of superconducting transition temperature

We describe a technique for making electrical transport measurements in a diamond anvil cell at liquid helium temperature having in situ pressure measurement option, permitting accurate pressure determination at any low temperature during the resistance measurement scan. In general, for four-probe resistivity measurements on a polycrystalline sample, four fine gold wires are kept in contact with the sample with the help of the compression from the soft solid (usually alkali halides such as NaCl, KCl, etc.) acting as a pressure-transmitting medium. The actual pressure on the sample is underestimated if not measured from a ruby sphere placed adjacent to the sample and at that very low temperature. Here, we demonstrate the technique with a quasi-four-probe resistance measurement on an Fe-based superconductor in the temperature range 1.2–300 K and pressures up to 8 GPa to find an improved pressure dependence of the superconducting transition temperature.     

Natural Convection in a Nanofluid-Saturated Rotating Porous Layer: A More Realistic Approach

The present work aims at studying the thermal instability in a rotating porous layer saturated by a nanofluid based on a new boundary condition for the nanoparticle fraction, which is physically more realistic. The model used for nanofluid combines the effect of Brownian motion along with thermophoresis, while for a porous medium Brinkman model has been used. A more realistic set of boundary conditions where the nanoparticle volume fraction adjusts itself including the contributions of the effect of thermophoresis so that the nanoparticle flux is zero at the boundaries has been considered. Using linear stability analysis, the expression for critical Rayleigh number has been obtained in terms of various non-dimensional parameters. The effect of various parameters on the onset of instability has been presented graphically and discussed in detail.