Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation

The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter epsilon. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1+1 dimension. We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions. Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic solutions show a fundamentally different behavior as the parameter epsilon is increased. We show that two distinct phases of periodic solutions exist which exhibit manifestly different behavior. Response functions for these phases are shown to behave differently, joining at an apparent phase transition point.     

Observational Constraints with Recent Data on the DGP Modified Gravity

We study one of the simplest covariant modified-gravity models based on the Dvali-Gabadadze-Porrati (DGP) brane cosmology, a self-accelerating universe. In this model gravitational leakage into extra dimensions is responsible of late-time acceleration. We mainly focus on the effects of the model parameters on the geometry and the age of universe. Also we investigate the evolution of matter density perturbations in the modified gravity model, and obtain an analytical expression for the growth index, f. We show that increasing leads to less growth of the density contrast δ, and also decreases the growth index. We give a fitting formula for the growth index at the present time and indicate that dominant term in this expression verifies the well-known approximation relation f≃Ω _m ^γ . As the observational test, the new Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and the Cluster Baryon Gas Mass Fraction (gas) are used to constrain the parameters of the DGP model. We also combine previous results with large scale structure formation (LSS) from the 2dFGRS survey. Finally to check the consistency of the DGP model, we compare the age of old cosmological objects with age of universe in this model.     

On the notion of Cohen–Macaulayness for non-Noetherian rings

There exist many characterizations of Noetherian Cohen–Macaulay rings in the literature. These characterizations do not remain equivalent if we drop the Noetherian assumption. The aim of this paper is to provide some comparisons between some of these characterizations in non-Noetherian case. Toward solving a conjecture posed by Glaz, we give a generalization of the Hochster–Eagon result on Cohen–Macaulayness of invariant rings, in the context of non-Noetherian rings.     

An output-feedback adaptive actuator failure compensation controller for systems with unknown state delays

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.     

Dye doped Eosin yellowish silica nanoparticles as novel fluorophore for a peroxyoxalate chemiluminescence system

In this work, we report the preparation and characterization of novel dye doped fluorophore Eosin yellowish silica nanoparticles (ESNPs). We synthesized ESNPs by the St?ber method via encapsulation of Eosin Yellowish in silica particles by the condensation of tetraethyl orthosilicate under alkaline condition at room temperature. The resulted ESNPs were characterized by transmission electron microscopy, atomic force microscopy; UV–Visible, fluorescence and Fourier transform infrared spectroscopy. The sizes of the nanoparticles have been found to be 300.0 (±1.0), 400.0 (±1.1) and 500.0 (±5.2) nm depending the reaction conditions under which they were synthesized. Furthermore, because of intense light emission, the ESNPs were used as fluorophore in a peroxyoxalate chemiluminescence system. The effect of solvent and concentrations of necessary reagents, bis(2,4,6-trichlorophenyl)oxalate, sodium salicylate, hydrogen peroxide and the effects of size of the ESNP and temperature on the luminescence efficiency of the system were examined. The activation kinetic parameters of the system were also evaluated from the temperature investigation.     

Preparation and characterization of polyphosphotungstate/ZrO2 nanocomposite and their sonocatalytic and photocatalytic activity under UV light illumination

Polyoxometalates (POM) supported on zirconia, H₃PW₁₂O₄₀/ZrO_2, were prepared by incorporating polyphosphotungstate into a zirconia matrix via sol-gel technique that involving the hydrolysis of zirconium (IV) n-butoxide, Zr (n-OBu)₄, as the ZrO₂ source. This insoluble and readily separable catalyst was characterized by using XRD, FT-IR, SEM, and UV diffuse reflectance spectroscopy (UV-DRS), indicating that the polyphosphotungstate was chemically attached to the zirconia supports, and primary Keggin structure remained intact. The photocatalytic and sonocatalytic activity of the supported polyphosphotungstate was tested via degradation of different dyes in aqueous solutions. The POM-ZrO₂ nanocomposite showed higher photocatalytic and sonocatalytic activity than pure polyoxometalate or pure ZrO₂.     

Efficient One‐pot Synthesis of Alkyl 3‐(alkyl)‐4‐methyl‐2‐thioxo‐2,3‐dihydrothiazole‐5‐carboxylates in a Multi Component Reaction

A simple and efficient one‐pot synthesis of alkyl 2‐(alkyl)‐4‐methyl‐2‐thioxo‐2,3‐dihydrothiazole‐5‐carboxylates from the reaction of primary alkylamines and carbon disulfide in the presence of 2‐chloro‐1,3‐dicarbonyl compounds is described. This new protocol has several advantages such as lack of necessity of the catalyst, good yields, mild conditions and short times for reaction.     

Antibacterial and antioxidant properties of phyto-synthesized silver nanoparticles using Lavandula stoechas extract

Due to environmentally friendly and cost- effective issues, biological methods for silver nanoparticles (AgNPs) synthesis are advantageous over chemical and physical ones. In this study, AgNPs synthesized using Lavandula stoechas extract as a reductant and its antioxidant capacity, antibacterial property and cytotoxicity effect were investigated. The phyto-synthesized AgNPs were characterized using various analyses such as transmission electron microscopy (TEM), scanning electron microscopy (SEM), x-ray diffraction (XRD) as well as Fourier transform infrared (FT-IR). The prepared nanoparticles were spherical on shape with the size about 20–50 nm. Antibacterial studies through agar disk diffusion method confirmed the antibacterial potential of phyto-synthesized AgNPs toward two clinical Staphylococus aureus and Pseudomonas aeruginosa bacteria, although MTT assay demonstrated that S. aureus (MIC = 125 μg/ml) was more susceptible to AgNPs than P. aeruginosa (MIC = 250 μg/ml). Moreover, the cytotoxicity assay of phyto-synthezied AgNPs showed a low cytotoxic effect on RAW264 cell line at 62.5 μg/ml as an effective concentration. Also the considerable antioxidant capacity of the AgNPs confirmed through DPPH assay. Great antibacterial and antioxidant properties along with biocompatibility make the suggested phyto-synthesized AgNPs a great candidate for different biomedical applications including wound healing.     

Coumarin-naphthohydrazone ligand with a rare coordination mode to form Mn(II) and Co(II) 1-D coordination polymers: synthesis,characterization, and crystal structure

The hydrazone (E)-3-hydroxy-N’-(1-(2-oxo-2H-chromen-3-yl)ethylidene)-2-naphthohydrazide (H₂L) was synthesized from the reaction of 3-acetylcoumarin and 3-hydroxy-2-naphthoic hydrazide in methanol. Compounds [Mn(H₂L)(NO₃)₂(CH₃OH)]·CH₃OH (1a), [Mn(HL)(NO₃)(CH₃OH)]_n (1b), [Co(HL)(NO₃)(CH₃OH)]_n (2), and [Cu(HL)(NO₃)] (3) were obtained by reaction of an equimolar amount of H₂L with nitrate salts of Mn(II), Co(II), or Cu(II) in methanol. The reaction of ligand and Mn(NO₃)₂·4H₂O was also carried out in the presence of sodium azide which led to the 1-D coordination polymer, [Mn(HL)(N₃)(CH₃OH)]_n (4). All of the synthesized compounds were characterized by elemental analyses and spectroscopic methods. Single-crystal X-ray analysis of 1–4 indicated that H₂L is neutral (in 1a) or mononegative ligand (in 1b, 2, 3 and 4). In 1b, 2 and 4 the 1-D polymeric chain is found by a rare coordination mode of this kind of hydrazone ligand since the naphtholic oxygen is coordinated to the neighboring metal ions while the NH moiety of hydrazone remains intact, also confirmed by FT-IR spectroscopic studies. The thermal stability of 2 and 4 were also studied from 30–1000 °C.