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.     

Design,Synthesis and Anticancer Activity of 1,2,4-Thiadiazole Derivatives Bearing 1,2,4-Oxadiazole

Russian Journal of General Chemistry - A series of novel 1,2,4-thiadiazole derivatives bearing 1,2,4-oxadiazole is synthesized. Structures of the synthesized compounds are confirmed by 1H and 13C...     

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.     

A sensitive LC‐MS/MS method for the quantification of febuxostat in human plasma and its pharmacokinetic application

An improved, simple and highly sensitive LC‐MS/MS method has been developed and validated for quantification of febuxostat with 100 μL human plasma using febuxostat‐d₇ as an internal standard (IS) according to regulatory guidelines. The analyte and IS were extracted from human plasma via liquid–liquid extraction using diethyl ether. The chromatographic separation was achieved on a Zorbax C₁₈ column using a mixture of acetonitrile and 5 mm ammonium formate (60:40, v/v) as the mobile phase at a flow rate of 0.5 mL/min. The total run time was 5.0 min and the elution of febuxostat and IS occurred at 1.0 and 1.5 min, respectively. A linear response function was established for the range of concentrations 1–6000 ng/mL (r > 0.99). The precursor to product ion transitions monitored for febuxostat and IS were m/z 317.1 → 261.1 and 324.2 → 262.1, respectively. The intra‐ and inter‐day precisions (%RSD) were within 1.29–9.19 and 2.85–7.69%, respectively. The proposed method was successfully applied to pharmacokinetic studies in humans. Copyright © 2013 John Wiley & Sons, Ltd.     

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.