A Generalization of Noncommuting Graph via Automorphisms of a Group

Let G be a group. By using a family 𝒜 of subsets of automorphisms of G, we introduced a simple graph Γ_𝒜(G), which is a generalization of the non-commuting graph. In this paper, we study the combinatorial properties of Γ_𝒜(G).     

Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory

This paper deals with an analytical approach of the buckling behavior of a functionally graded circular cylindrical shell under axial pressure with external axial and circumferential stiffeners. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations and equilibrium and stability equations are derived using the third-order shear deformation theory. The resulting equations are employed to obtain the closed-form solution for the critical buckling loads. A simply supported boundary condition is considered for both edges of the shell. The comparison of the results of this study with those in the literature validates the present analysis. The effects of material composition (volume fraction exponent), of the number of stiffeners and of shell geometry parameters on the characteristics of the critical buckling load are described. The analytical results are compared and validated using the finite-element method. The results show that the inhomogeneity parameter, the geometry of the shell and the number of stiffeners considerably affect the critical buckling loads.     

The Effect of Space Dimensions on a Generalized Hydrogen-Atom Specific Heat in the Generalized Boltzmann-Gibbs Statistics

In this article, the effect of the space dimensions on the generalized hydrogen-atom specific heat in the generalized Boltzmann-Gibbs statistics is studied. The temperature dependence of the specific heat for a few different values of q and for different low space dimensions using Tsallis statistics is numerically calculated. The results indicate that for a fixed value of q, as the space dimension increases the temperature range where the specific heat has a nonzero value, decreases, while the general behavior of the specific heat does not show any change. Also, there exits a q-independent quantity related to two specific temperatures of the system which is almost linearly dependent on the space dimensions.     

Synthesis of a novel tetracationic acidic organic salt based on DABCO and its applications as catalyst in the Knoevenagel condensation reactions in water

Synthesis of a novel tetracationic acidic organic salt based on DABCO containing two sulfonic acid groups in the skeleton and four hydrogensulfate groups as counterion is described. Its catalytic efficiency in the Knoevenagel condensation of aldehydes with active cyclic methylene compounds in water is investigated. While 2,2'-(phenylmethylene)bis(3-hydroxy-5,5-dimethylcyclohex-2-enone) derivatives were obtained in 40–98% isolated yields in the reaction of aldehydes with dimedone, the corresponding Knoevenagel adducts were provided in 85–95% yields using 1,3-dimethylbarbituric acid. In addition, a DABCO-based polycationic organic salt polymer was prepared and characterized for the first time.     

Synthesis and crystal structure of the dinuclear copper(II) Schiff base complex μ‐hydroxido‐μ‐chlorido‐bis{[bis(trans‐2‐nitrocinnamaldehyde)ethylenediamine]chloridocopper(II)} dichloromethane sesquisolvate

Transition metal complexes of Schiff base ligands have been shown to have particular application in catalysis and magnetism. The chemistry of copper complexes is of interest owing to their importance in biological and industrial processes. The reaction of copper(I) chloride with the bidentate Schiff base N,N′‐bis(trans‐2‐nitrocinnamaldehyde)ethylenediamine {Nca₂en, systematic name: (1E,1′E,2E,2′E)‐N,N′‐(ethane‐1,2‐diyl)bis[3‐(2‐nitrophenyl)prop‐2‐en‐1‐imine]} in a 1:1 molar ratio in dichloromethane without exclusion of air or moisture resulted in the formation of the title complex μ‐chlorido‐μ‐hydroxido‐bis(chlorido{(1E,1′E,2E,2′E)‐N,N′‐(ethane‐1,2‐diyl)bis[3‐(2‐nitrophenyl)prop‐2‐en‐1‐imine]‐κ²N,N′}copper(II)) dichloromethane sesquisolvate, [Cu₂Cl₃(OH)(C₂₀H₁₈N₄O₄)₂]·1.5CH₂Cl₂. The dinuclear complex has a folded four‐membered ring in an unsymmetrical Cu₂OCl₃ core in which the approximate trigonal bipyramidal coordination displays different angular distortions in the equatorial planes of the two Cu^II atoms; the chloride bridge is asymmetric, but the hydroxide bridge is symmetric. The chelate rings of the two Nca₂en ligands have different conformations, leading to a more marked bowing of one of the ligands compared with the other. This is the first reported dinuclear complex, and the first five‐coordinate complex, of the Nca₂en Schiff base ligand. Molecules of the dimer are associated in pairs by ring‐stacking interactions supported by C—H…Cl interactions with solvent molecules; a further ring‐stacking interaction exists between the two Schiff base ligands of each molecule.     

Preparation of uniform TiO2 nanostructure film on 316L stainless steel by sol-gel dip coating

Sol was prepared by the mixing of tetra-η-butyle titanat, ethyl aceto acetate, and ethanol in an optimized condition. Polished 316L specimens were coated with the sol by dip-coating method. The influences of drying condition, withdrawal speed, calcination temperature, addition of dispersant, and pH of sol on TiO₂ nanostructure coating were investigated. Choosing of alcohol as drying atmosphere hindered the crack formation. The relation between coating thickness and withdrawal speed was evaluated. The optimum temperature to create a uniform distribution of nanoparticles of anatase was derived as 400 °C. Average roughness of coating was found about 10.61 nm by AFM analysis. Dispersant addition promoted formation of a uniform film as well as prevention of agglomeration. Acidic sol provided smaller particles than neutral sol.     

Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams

This article deals with the wave propagation analysis of single/double layered functionally graded (FG) size-dependent nanobeams in elastic medium and subjected to a longitudinal magnetic field employing nonlocal elasticity theory. Material properties of nanobeam change gradually according to the sigmoid function. Applying an analytical solution, the acoustical and optical dispersion relations are explored for various wave number, nonlocality parameter, material composition, elastic foundation constants, and magnetic field intensity. It is found that frequency and phase velocity of waves propagating in S-FGM nanobeam are significantly affected by these parameters. Also, presence of cut-off and escape frequencies in wave propagation analysis of embedded S-FGM nanobeams is investigated.     

Acoustic Multi Emission Lens via Transformation Acoustics

Based on transformation acoustic methodology, we propose an algorithm for designing acoustic non-resonant lens antenna, which is competent to generate multiple directive beams that are pointing at the desired direction.Unattainable with previous works, the present approach is capable of adjusting the directivity of each radiated beam individually, which is of the utmost importance in several acoustic applications such as in sonar systems. A linear transformation function is intentionally used for eliminating the inhomogeneity of the obtained materials and to pave the way towards more general acoustic patterns. Several numerical simulations are performed to show the capability of the proposed method in manipulating the acoustic waves. To authenticate the concept,a structure that can generate four beams with different directivities is realized with non-resonant meta-fluid bi-layered structure through effective medium theory.     

Designing of an efficient multi-aperture,edge pumped thin-disk laser

In this article the operation of a composite Yb:YAG/YAG asymmetric hexagonal thin disk laser is optimized. This structure consists an Yb:YAG thin sheet as laser material and a diffusion bonded undoped material on top of thin sheet. Three diodes are placed outside the asymmetric hexagonal shape disk, and the emitting light is coupled via three lens ducts through its three edges and propagates through the disk along the zigzag path and repeatedly passes the gain medium, thus pump uniformity and absorption efficiency are improved. A Monte Carlo ray tracing code and Finite Element Analysis is utilized for calculation of absorbed pump density and volume temperature distribution and also thermal and mechanical stresses, respectively. Finally the output power is calculated. The triplet designing parameters, namely absorbed power efficiency, absorption uniformity and temperature distribution are optimized. Results show this edge-facet pumped geometry is a high efficient configuration for thin gain lasers.     

Carbon dots with strong excitation-dependent fluorescence changes towards pH. Application as nanosensors for a broad range of pH

In this study, preparation of novel pH-sensitive N-doped carbon dots (NCDs) using glucose and urea is reported. The prepared NCDs present strong excitation-dependent fluorescence changes towards the pH that is a new behavior from these nanomaterials. By taking advantage of this unique behavior, two separated ratiometric pH sensors using emission spectra of the NCDs for both acidic (pH 2.0 to 8.0) and basic (pH 7.0 to 14.0) ranges of pH are constructed. Additionally, by considering the entire Excitation–Emission Matrix (EEM) of NCDs as analytical signal and using a suitable multivariate calibration method, a broad range of pH from 2.0 to 14.0 was well calibrated. The multivariate calibration method was independent from the concentration of NCDs and resulted in a very low average prediction error of 0.067 pH units. No changes in the predicted pH under UV irradiation (for 3 h) and at high ionic strength (up to 2 M NaCl) indicated the high stability of this pH nanosensor. The practicality of this pH nanosensor for pH determination in real water samples was validated with good accuracy and repeatability.