Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations

By establishing a comparison result and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of solutions for systems of nonlinear fractional differential equations.     

Phase behaviour of thermotropic banana-shaped compounds under pressure

The phase behaviour of two achiral bent core banana-shaped compounds, the hexyloxy (compound I) and decyloxy (compound II) members of the 1,3-phenylene bis[N-(2-hydroxy-4-n-alkoxybenzylidene)-4′-aminobenzoate] series was investigated under hydrostatic pressures up to 300?MPa using high pressure differential thermal analysis and light transmission methods. The reversible transition sequence crystal (Cr₁)–B₁ phase–isotropic liquid (I), observed at room pressure for compound I, remains in the pressure region up to c 70?MPa. At higher pressures a pressure-induced crystalline phase (Cr_i) appears between the Cr₁ and B₁ phases, its temperature region becoming wider with increasing pressure. The temperature vs. pressure phase diagram shows a triple point of 72.9?MPa and 160.3°C for the Cr₁, Cr_i and B₁ phases, indicating the lower limit of pressure for the Cr_i phase. In compound II the reversible transition sequence crystal (Cr₁)–B₂ phase–I is seen over the whole pressure region, and the temperature range of the B₂ phase remains unaltered. It is concluded that both the B₁ and B₂ banana phases are stable over the whole pressure region studied.     

Analysis and numerical simulation for a class of time fractional diffusion equation via tension spline

In this work, we prove the weak and strong convergence of a sequence generated by a modified S-iteration process for finding a common fixed point of two G-nonexpansive mappings in a uniformly convex Banach space with a directed graph. We also give some numerical examples for supporting our main theorem and compare convergence rate between the studied iteration and the Ishikawa iteration.     

Spectro Analytical,Computational and In Vitro Biological Studies of Novel Substituted Quinolone Hydrazone and it’s Metal Complexes

Some novel transition metal [Cu (II), Ni (II) and Co (II)] complexes of nalidixic acid hydrazone have been prepared and characterized by employing spectro-analytical techniques viz: elemental analysis, ¹H-NMR, Mass, UV–Vis, IR, TGA-DTA, SEM-EDX, ESR and Spectrophotometry studies. The HyperChem 7.5 software was used for geometry optimization of title compound in its molecular and ionic forms. Quantum mechanical parameters, contour maps of highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) and corresponding binding energy values were computed using semi empirical single point PM3 method. The stoichiometric equilibrium studies of metal complexes carried out spectrophotometrically using Job’s continuous variation and mole ratio methods inferred formation of 1:2 (ML₂) metal complexes in respective systems. The title compound and its metal complexes screened for antibacterial and antifungal properties, exemplified improved activity in metal complexes. The studies of nuclease activity for the cleavage of CT- DNA and MTT assay for in vitro cytotoxic properties involving metal complexes exhibited high activity. In addition, the DNA binding properties of Cu (II), Ni (II) and Co (II) complexes investigated by electronic absorption and fluorescence measurements revealed their good binding ability and commended agreement of K_b values obtained from both the techniques. Molecular docking studies were also performed to find the binding affinity of synthesized compounds with DNA (PDB ID: 1N37) and “Thymidine phosphorylase from E.coli” (PDB ID: 4EAF) protein targets.     

An analysis of a widely used version of the CUSUM tracking signal

Tracking signals are used to determine whether a sequence of forecasts is unbiased. We analyse a version of the CUSUM tracking signal that is based on the unsmoothed average mean absolute deviation of forecasting errors. We make the common assumption that demand values in different periods are independently, identically, and normally distributed. We show that, when forecast errors in different periods are also normal iid, this version of the tracking signal can indicate that the sequence is not unbiased even when it is unbiased. We suggest a simple modification to the tracking signal that serves to eliminate this flaw.     

Spectroscopic Investigation of Tungsten Ions in Lead Scandium Phosphate Glass System

Lead scandium phosphate glasses (PbO-Sc₂O₃-P₂O₅) containing different concentrations of tungsten oxide (WO₃) ranging from 0 to 5 mol% were prepared. A number of studies, viz. differential thermal analysis (DTA), infrared spectra, optical absorption, and electron spin resonance (ESR) spectra, have been carried out. The results of DTA indicated the highest glass forming ability for the glass containing 5 mol% of WO₃. The results of spectroscopic studies have been analyzed in light of different oxidation states of tungsten ions.