A new two-point scheme for multiple roots of nonlinear equations

In most of the earlier research for multiple zeros, in order to obtain a new iteration function from the existing scheme, the usual practice is to make no change at the first substep. In this paper, we explore the idea that what are the advantages if the flexibility of choice is also given at the first substep. Therefore, we present a new two-point sixth-order scheme for multiple roots (m>1). The main advantages of our scheme over the existing schemes are flexibility at both substeps, simple body structure, smaller residual error, smaller error difference between two consecutive iterations, and smaller asymptotic error constant. The development of the scheme is based on midpoint formula and weight functions of two variables. We compare our methods with the existing methods of the same order with real-life applications as well as standard test problems. From the numerical results, we find that our methods can be considered as better alternates for the existing methods of the same order. Finally, dynamical study of the proposed schemes is presented that confirms the theoretical results.     

Doping radius effects on an erbium-doped fiber amplifier

In an erbium-doped fiber amplifier(EDFA), erbium ions act as a three-level system. Therefore, much higher pump energy is required to achieve the population inversion in an erbium-doped fiber(EDF). This higher pump energy requirement complicates the efficient design of an EDFA. However, efficient use of the pump power can improve the EDFA performance. The improved performance of an EDFA can be obtained by reducing the doping radius of the EDF. A smaller doping radius increases pump–dopant interactions and subsequently increases the pump–photon conversion efficiency. Decreasing the doping radius allows a larger proportion of dopant ions,which are concentrated near the core, to interact with the highest pump intensity. However, decreasing the doping radius beyond a certain limit will bring the dopant ions much closer and introduce detrimental ion–ion interaction effects. In this Letter, we show that an optimal doping radius in an EDF can provide the best gain performance. Moreover, we have simulated the well-known numerical aperture effects on EDFA gain performance to support our claim.     

Physico-Chemical Properties of Magnetic Dicationic Ionic Liquids with Tetrahaloferrate Anions

A series of imidazolium-based symmetrical and asymmetrical dicationic ionic liquids (DcILs) with alkyl spacers of different length and with [FeCl₃Br]⁻ as counter ion have been synthesized. The synthesized DcILs are characterized by using FTIR and Raman spectroscopy as well as mass spectrometry, along with single-crystal XRD analysis. Physicochemical properties such as solubility, thermal stability and magnetic susceptibility are also measured. These compounds show low melting points, good solubility in water and organic solvents, thermal stability, and paramagnetism. The products of molar susceptibility and temperature (χ_mol⋅T) for the synthesized DcILs have been found between 4.05 to 4.79 emu mol⁻¹ K Oe⁻¹ and effective magnetic moment values have also been determined to be compared to that expected from the spin-only approximation.     

Optimization and Validation of RP-LC/UV–VIS Detection Method for Simultaneous Determination of Fat-Soluble Anti-Oxidant Vitamins, all-trans-Retinol and α-Tocopherol in Human Serum: Effect of Experimental Parameters

A versatile isocratic reversed-phase liquid chromatographic/ultraviolet–visible detection method for simultaneous determination of all-trans-retinol and α-tocopherol in human serum was developed and validated after optimization of various chromatographic conditions and other experimental parameters. Analytes were separated on a Kromasil 100 RP₁₈ (150 × 4.6 mm, 5 μm) analytical column protected by a Perkin Elmer RP₁₈ (30 × 4.6 mm, 10 μm) guard cartridge. The mobile phase, methanol–water (96:04 v/v) was pumped at a flow rate of 2.2 mL min^?1 and the column eluents were monitored at the wavelength of 292 nm using retinyl acetate (1.0 μg mL^?1) as the internal standard for both analytes. Sample preparation was based on protein precipitation and stabilization with 2,6-bis(1,1-dimethylethyl)-4-methylphenol/ethanol and a two step extraction process using n-hexane followed by dichloromethane as extraction solvents. Sample size was kept 20 μL and separation of analytes was achieved in less than 7 min. The present method demonstrated acceptable values for specificity/selectivity, linearity within the expected concentration range, recovery, precision, sensitivity, stability of solutions, robustness, and system suitability specifications and tests. The method was used for monitoring all-trans-retinol and α-tocopherol concentrations in human serum samples and could also be applied to other sample matrices such as brain slices and cosmetic products if attention is paid to the extraction procedure.     

Longitudinal distribution of trace elements in the atmosphere of an industrial area from neutron activation analysis

Industrial units play a significant role in atmospheric pollution. Industrial exhausts deteriorate the atmospheric quality causing unhygienic environment for the people working in the vicinity. This work presents a study of the longitudinal distribution of trace elements of the Sheikhupura industrial area. Three kinds of distribution patterns were observed and are discussed in detail. The results are based on the neutron activation analysis of 16 trace elements.     

Mass spectra of complexes of 8-quinolinol with trivalent metals (AL,Ga, In,Sc, Cr and Fe)

The main fragmentation of the compounds MX_3-nox_n (oxH=8-quinolinol. n = 3; M=AL, Ga, In, Sc, Cr or Fe. n = 2; M=In or Fe; X=Cl or Br. InIox₂. n = 1; M=AL, In or Fe; X= Cl or Br) involves loss of X and intact ox_. radicals. The comparative abundances of the fragments are primarily related to the common oxidation states of the metals. For example, all the Mox₃ compounds show the ions [Mox₃]⁺ and [Mox₂]⁺. The ions [Mox]⁺ and [M]⁺ are present when M=Ga, In, Cr or Fe but for the elements with only one oxidation state (Al or Sc) [M]⁺ is absent and [Mox]⁺ has only very low abundance. When M= Cr or Fe metal-containing ions arising from loss of species such as CO, H₂O, HX, C₂H₂, H and OH by fragmentation of the ox ligand are also present; this behaviour is rationalised in terms of the ability of these metals to undergo a unit change in oxidation state. When n=1 the ions [MXox₂]⁺ and [Mox₂]⁺ and when n= 2 the ions [MX₂ox]⁺ and [Mox₃]⁺ are present; these ions arise by ionization and fragmentation of species formed by redistribution reactions in the mass spectrometer.     

A divergent approach to highly substituted benzothiepinones and to 2,3-dihydrothieno[2,3-b]thiopyran-4-ones

The radical addition-transfer of S-(2-fluoro-phenacyl)xanthates can be used to construct rapidly benzothiepinones, including libraries of complex aza-bridged derivatives, and highly functionalized 2,3-dihydrothieno[2,3-b]thiopyran-4-ones.     

Formulation of Piperine–Chitosan-Coated Liposomes: Characterization and In Vitro Cytotoxic Evaluation

The present research work is designed to prepare and evaluate piperine liposomes and piperine–chitosan-coated liposomes for oral delivery. Piperine (PPN) is a water-insoluble bioactive compound used for different diseases. The prepared formulations were evaluated for physicochemical study, mucoadhesive study, permeation study and in vitro cytotoxic study using the MCF7 breast cancer cell line. Piperine-loaded liposomes (PLF) were prepared by the thin-film evaporation method. The selected liposomes were coated with chitosan (PLFC) by electrostatic deposition to enhance the mucoadhesive property and in vitro therapeutic efficacy. Based on the findings of the study, the prepared PPN liposomes (PLF3) and chitosan coated PPN liposomes (PLF3C1) showed a nanometric size range of 165.7 ± 7.4 to 243.4 ± 7.5, a narrow polydispersity index (>0.3) and zeta potential (−7.1 to 29.8 mV). The average encapsulation efficiency was found to be between 60 and 80% for all prepared formulations. The drug release and permeation study profile showed biphasic release behavior and enhanced PPN permeation. The in vitro antioxidant study results showed a comparable antioxidant activity with pure PPN. The anticancer study depicted that the cell viability assay of tested PLF3C2 has significantly (p < 0.001)) reduced the IC₅₀ when compared with pure PPN. The study revealed that oral chitosan-coated liposomes are a promising delivery system for the PPN and can increase the therapeutic efficacy against the breast cancer cell line.     

Convergent synthesis of carbonic anhydrase inhibiting bi-heterocyclic benzamides: Structure–activity relationship and mechanistic explorations through enzyme inhibition,kinetics, and computational studies

By using a convergent methodology, a novel series of N-arylated 4-yl-benzamides containing a bi-heterocyclic thiazole–triazole core was synthesized, and the structures of these hybrid molecules, 9a–k , were corroborated through spectral analyses. The in vitro studies of these multifunctional molecules demonstrated their potent carbonic anhydrase inhibition relative to the standard used. The kinetics mechanism was exposed by Lineweaver–Burk plots, which revealed that 9j inhibited carbonic anhydrase non-competitively by forming an enzyme-inhibitor complex. The inhibition constants K_i calculated from Dixon plots for this compound was 1.2 μM. The computational study was also persuasive with the experimental results, and these molecules disclosed good results of all scoring functions and interactions, which suggested a good binding to carbonic anhydrase. So, it was predicted from the inferred results that these molecules might be considered as promising medicinal scaffolds for various diseases related to the uncontrolled production of this enzyme.