An ultra-small heterostructure wavelength division multiplexer (WDM) with the ability to select two wavelengths from the s-band

In this article, a photonic crystal channel drop filter (CDF) based on \(2\times 3\) ring resonators is presented. At first, the effects of changing the radius of lattice rods and the lattice dielectric constant on the dropping efficiency of a 3-port CDF with one resonator are investigated. Then by developing this base structure, a new 4-port heterostructure CDF composed of two regions with rods made of silicone and germanium is presented, which can operate in the ‘S’ band of the communication window. The photonic crystal heterostructure CDF consists of a horizontal waveguide and two ring resonators that have been installed, in symmetry to the horizontal axis, in two regions with different refractive indices. These ring resonators act as energy couplers and capture at their resonant frequencies the electromagnetic energy which is propagated in the bus waveguide. For the analysis of transmission characteristics and the band structure of the filter, two methods have been employed: the two-dimensional Finite–difference time domain method and the Plane Wave Expansion method. In the final structure, dropping efficiencies of 97 and 89 % can be achieved at ports D and B, respectively, and also an acceptable quality factor can be obtained in the communication window. The overall size of this device is 174.14  \(\upmu \hbox {m}^{2}\) . Due to its small size, this structure can be used in Wavelength Division Multiplexer applications in the Optical Integrated Circuits.     

Catalytic application of sulfonic acid‐functionalized titana‐coated magnetic nanoparticles for the preparation of 1,8‐dioxodecahydroacridines and 2,4,6‐triarylpyridines via anomeric‐based oxidation

We have developed green, efficient and powerful protocols for the preparation of 2,4,6‐triarylpyridines and 1,8‐dioxodecahydroacridines in the presence of Fe₃O₄@TiO₂@O₂PO₂(CH₂)₂NHSO₃H as a sulfonic acid‐functionalized titana‐coated magnetic nanoparticle catalyst under mild and solvent‐free reaction conditions. These protocols furnished the desired products in short reaction times with good to high yields (20–40 min and 80–86% in the case of 2,4,6‐triarylpyridines; 15–90 min and 80–93% in the case of 1,8‐dioxodecahydroacridines). The final step of the mechanistic route in the synthesis of 2,4,6‐triarylpyridines proceeds via an anomeric‐based oxidation. Also, the nanomagnetic core–shell catalyst can be recycled and reused in both cases of the scrutinized one‐pot multicomponent reactions with high turnover number and turnover frequency.     

A multi-step class of iterative methods for nonlinear systems

In this article, the numerical solution of nonlinear systems using iterative methods are dealt with. Toward this goal, a general class of multi-point iteration methods with various orders is constructed. The error analysis is presented to prove the convergence order. Also, a thorough discussion on the computational complexity of the new iterative methods will be given. The analytical discussion of the paper will finally be upheld through solving some application-oriented problems.     

Synthesis and characterization of nanocrystalline α-Al2O3 using Al and Fe2O3 (hematite) through mechanical alloying

In this present work, the synthesis of nanocrystalline α-Al₂O₃ using pure aluminum (Al) and Fe₂O₃ (hematite) as the precursors by mechanical alloying technique has been studied. The formation of α-Al₂O₃ nanocrystallites occurs during the solid-state reaction and through the reduction treatment. Also in this paper, effects of milling time on particle size and the lattice strain nanocrystalline α-Al₂O₃ have been investigated. Obtained powders were evaluated by scanning electron microscopy (SEM), transmission electron microscopy (TEM), differential thermal analysis (DTA), thermal gravimetric analysis (TGA) and X-ray diffraction (XRD). The obtained results indicated that a reduction reaction was completed after 2 h milling in a planetary mill. The crystallite size of obtained α-alumina (α-Al₂O₃) was in general about 12 nm. Finally, the results showed appropriate homogeneity and dispersion of related nanocrystalline.     

Transitivity of generic semigroups of area-preserving surface diffeomorphisms

We prove that the action of the semigroup generated by a C ^r generic pair of area-preserving diffeomorphisms of a compact orientable surface is transitive.     

Altermatic number of categorical product of graphs

In this paper, we prove some relaxations of Hedetniemi’s conjecture in terms of altermatic number and strong altermatic number of graphs, two combinatorial parameters introduced by the present authors Alishahi and Hajiabolhassan (2015) providing two sharp lower bounds for the chromatic number of graphs. In terms of these parameters, we also introduce some sharp lower bounds for the chromatic number of the categorical product of two graphs. Using these lower bounds, we present some new families of graphs supporting Hedetniemi’s conjecture.