A pseudo‐spectral method that uses an overlapping multidomain technique for the numerical solution of sine‐Gordon equation in one and two spatial dimensions

In this article, we study an explicit scheme for the solution of sine‐Gordon equation when the space discretization is carried out by an overlapping multidomain pseudo‐spectral technique. By using differentiation matrices, the equation is reduced to a nonlinear system of ordinary differential equations in time that can be discretized with the explicit fourth‐order Runge–Kutta method. To achieve approximation with high accuracy in large domains, the number of space grid points must be large enough. This yields very large and full matrices in the pseudo‐spectral method that causes large memory requirements. The domain decomposition approach provides sparsity in the matrices obtained after the discretization, and this property reduces storage for large matrices and provides economical ways of performing matrix–vector multiplications. Therefore, we propose a multidomain pseudo‐spectral method for the numerical simulation of the sine‐Gordon equation in large domains. Test examples are given to demonstrate the accuracy and capability of the proposed method. Numerical experiments show that the multidomain scheme has an excellent long‐time numerical behavior for the sine‐Gordon equation in one and two dimensions. Copyright © 2013 John Wiley & Sons, Ltd.     

Vibration based algorithm for crack detection in cantilever beam containing two different types of cracks

In this paper, a simple method for detection of multiple edge cracks in Euler–Bernoulli beams having two different types of cracks is presented based on energy equations. Each crack is modeled as a massless rotational spring using Linear Elastic Fracture Mechanics (LEFM) theory, and a relationship among natural frequencies, crack locations and stiffness of equivalent springs is demonstrated. In the procedure, for detection of m cracks in a beam, 3m equations and natural frequencies of healthy and cracked beam in two different directions are needed as input to the algorithm.     

Calix[4]phyrins. Effect of peripheral substituents on conformational mobility and structure within a series of related systems

A new, stepwise synthesis of calix[4]phyrins is described. It relies on the condensation of a ketone with pyrrole to form a dipyrromethane containing a quaternary carbon center that is subsequently condensed with an aromatic aldehyde. This methodology, in contrast to the previous rational approach described by this group (involving formation of a trisubstituted dipyrromethane via the condensation of an aldehyde with pyrrole, followed by condensation of this dipyrromethane with acetone), allows for a variety of bulky, ketone-derived substituents to be incorporated into the meso-like positions. The resulting systems, while all containing the same central macrocyclic core, display conformational properties that reflect the nature of these meso-like substituents; these conformational features were independently assessed by X-ray diffraction analysis, NMR spectroscopy, and quantum chemical calculations.     

calix-Tris-Tröger's bases--a new cavitand family

The first members of a new cavitand family, represented by calix-shaped tris Tr?ger's base diastereoisomers, are prepared via step-by-step synthesis as well as one-pot mixed troegeration.     

The investigation on phytochemicals from Ferulago angulata (Schlecht) Boiss,indigenous to central parts of Iran

Ferulago angulata (Schlecht) Boiss (Apiaceae) is a perennial herb distributed in the central parts of Iran. In this work, the essential oil of Ferulago angulat a aerial parts collected from the central parts of Iran was obtained by using hydrodistillation analysed by GC and GC–MS. Air-dried and powdered plant roots were extracted with n-hexane, dichloromethane and methanol, respectively, using a Soxhlet apparatus. The n-hexane extract was subjected to preparative thin-layer chromatography using chloroform–acetone (95:5) as solvent system to yield two linear furanocoumarins, prantschimgin and oxypeucedanin. The structure of theisolated compounds was elucidated by using spectroscopic data such as ¹H NMR, ¹³C NMR, UV and IR. The results of GC–MS analyses showed that γ-terpinolene (11.97%), α-pinene (10.00%), sabinene (6.89%), linalool (5.56%) and cis-ocimene (4.41%) were the main components among 51 constituents characterised in the oil. The oil exhibits considerable phytotoxic activity.     

Construction and Application of an Electrochemical Sensor for Simultaneous Determination of Cd(II), Cu(II) and Hg(II) in Water and Foodstuff Samples

By incorporation of synthesized magnetite nanoparticles (Fe₃O₄ NPs) coated with a new Schiff base into carbon paste electrode, a novel modified electrode was constructed for simultaneous determination of ultra trace amounts of Cd(II), Cu(II) and Hg(II). The complexation reaction of Schiff base with metal ions was studied spectrophotometrically. Under optimal conditions a detection limit of 0.20, 0.90 and 1.00 ng mL^?1 for Cd(II), Cu(II) and Hg(II), respectively, was obtained. We take the advantages of the proposed method for simple, rapid, sensitive and selective simultaneous determination of trace amounts of hazardous Cd(II), Cu(II) and Hg(II) in water and foodstuff samples.     

Supramolecular photocatalyst of Palladium (II) Encapsulated within Dendrimer on TiO2 nanoparticles for Photo‐induced Suzuki‐Miyaura and Sonogashira Cross‐Coupling reactions

In this study, synthesis, characterization and catalytic performance of a novel supramolecular photocatalytic system including palladium (II) encapsulated within amine‐terminated poly (triazine‐triamine) dendrimer modified TiO₂ nanoparticles (Pd (II) [PTATAD] @ TiO₂) is presented. The obtained nanodendritic catalyst was characterized by FT‐IR, ICP‐AES, XPS, EDS, TEM, TGA and UV‐DRS. The as‐prepared nanodendritic catalyst was shown to be highly active, selective, and recyclable for the Suzuki–Miyaura and Sonogashira cross‐coupling of a wide range of aryl halides including electron‐rich and electron‐poor and even aryl chlorides, affording the corresponding biaryl compounds in good to excellent yields under visible light irradiation. This study shows that visible light irradiation can drive the cross‐coupling reactions on the Pd (II) [PTATAD] @ TiO₂ under mild reaction conditions (27–30 °C) and no additional additives such as cocatalysts or phosphine ligands. So, we propose that the improved photoactivity predominantly benefits from the synergistic effects of Pd (II) amine‐terminated poly (triazine‐triamine) dendrimer on TiO₂ nanoparticles that cause efficient separation and photogenerated electron–hole pairs and photoredox capability of nanocatalyst which all of these advantages due to the tuning of band gap of catalyst in the visible light region.     

Anchoring of Cu (II)-Schiff base complex on magnetic mesoporous silica nanoparticles: catalytic efficacy in one-pot synthesis of 5-substituted-1H-tetrazoles,antibacterial activity evaluation and immobilization of α-amylase

Magnetic mesoporous silica nanocomposite, Fe₃O₄@MCM-41, was prepared and functionalized with N-(2-aminoethyl)-3-aminopropyltrimethoxysilane (AEAPS). Then Schiff base grafted nanoparticles were synthesized by the condensation of 5,5'-methylene bis (salicylaldehyde) and then benzhydrazide with Fe₃O₄@MCM-41-AEAPS. Finally, by adding Cu (CH₃COOH)₂.H₂O, the magnetic nanoparticles (MNPs) functionalized with Cu (II) Schiff base complex were synthesized. The new organic–inorganic hybrid nanocomposite was characterized by FT-IR, PXRD, AAS, BET, TGA, VSM, FE-SEM, HRTEM and EDX techniques. Then, the performance of this copper based magnetic nanocatalyst was investigated for the synthesis of 5-substituted 1H-tetrazole derivatives using one pot three-component reactions of various aldehydes, hydroxyl amine hydrochloride and sodium azide. The catalyst can be easily isolated from the reaction mixture by applying an external magnet and reused for at least 5 times without significant loss in catalytic activity. Also, the antibacterial activity of the streptomycin loaded magnetic nanoparticles against Gram-positive (S. aureus) and Gram-negative (E. coli) bacteria in the presence and absence of a magnetic field were studied. Results revealed that when these materials exposed to the magnetic field, bacteriostatic activity of nanocomposites was increased. Furthermore, the enzyme immobilization ability of the synthesized compounds was investigated and the results showed that these nanoparticles efficiently immobilized amylase enzyme.     

Spatial arrangements of dorsal root ganglion cells after sciatic nerve crush

The present study explores 3D spatial arrangements of the A- and B-cells within the fifth lumbar dorsal root ganglion (DRG) of rat in order to test for differences after sciatic nerve crush (SNC). The pair correlation and cross-correlation functions were estimated through counting dipole probes superimposed on DRG sections. The data showed that the A- and B-cells were clustered at distances below 40 and 35 μm in sham-operated animals, respectively. These values were 35 and 25 μm in SNC animals. Beyond these distances, the cells of the control group were arranged neither clustered nor repulsed. The A- and B-cells showed a negative correlation (repulsion) at r = 270–290 μm and r = 100 in SNC ganglions, respectively. The plot of the cross-correlation function showed that the first maximum curve was r = 51 μm and 41 μm in sham-operated and SNC rats, respectively. The other differences were seen at r = 51–61 μm and r = 165 μm between cross-covariance of the cells. The “degree of order” for the A- and B-cells showed no significant difference and the low values of the two groups indicated the random distribution of cells in them.

Conclusion

The obtained data revealed that cellular spatial patterns in the dorsal root ganglion of the sciatic nerve crush were changed.