Converging strong shock waves in magnetogasdynamics under isothermal condition

The similarity solutions to the problem of cylindrically symmetric strong shock waves in an ideal gas with a constant azimuthal magnetic field are presented. The flow behind the shock wave is assumed to spatially isothermal rather than adiabatic. We use the method of Lie group invariance to determine the possible class of self-similar solutions. Infinitesimal generators of Lie group transformations are determined by using the invariance surface conditions to the system and on the basis of arbitrary constants occurring in the expressions for the generators, four different possible cases of the solutions are reckoned and we observed that only two out of all possibilities hold self-similar solutions, one of which follows the power law and another follows the exponential law. To obtain the similarity exponents numerical calculations have been performed and comparison is made with the existing results in the literature. The flow patterns behind the shock are analyzed graphically.

     

Analysis of a combat problem: The turret game

The turret game is defined and solved to illustrate the nature of games of combat. This game represents a highly simplified version of air combat, yet it is sufficiently complex so as to exhibit a rich variety of combat phenomena. A review of the formulation of -combat games is included in this paper.on sabbatical leave from Technion, Israel Institute of Technology, Haifa, Israel.     

Tellurium azamacrocycles: synthesis, characterization and coordination studies

The metal-free condensation of bis(2-formylphenyl) telluride (1) with a series of diamines affords macrocyclic tellurium ligands 2-7. Crystals of the protonated macrocycle 8 are monoclinic, space group P2/n with a=10.890(5), b=7.414(4), c=24.334(13) Å, Z=2. The reaction of tellurium containing macrocyclic Schiff base 2 with Pd(C₆H₅CN)₂Cl₂ gives the expected 1:1 product [Pd(II) 2] Cl₂ (9). Complex 9 was treated with excess of NH₄PF₆ in methanol to give the analogous PF₆⁻ salt [Pd(II) 2] (PF₆)₂ (10). The crystals of 10 are monoclinic, space group P2₁/n, a=8.2250(10), b=21.280 (4), c=21.150 (4), Z=4. However, the reaction of 2 with Pt(COD)Cl₂ proceeds via novel transmetallation to yield an organoplatinum complex (11). The crystals of 11 are also monoclinic, space group P2₁/n, a=12.3253 (14), b=14.6557 (14), C=13.4054 (11), Z=4. The octahedral Ni(II) complex 12 was prepared by the reaction of NiCl₂ · 6H₂O with 2 and NH₄PF₆ under an inert atmosphere. For 12: triclinic, space group ; Z=2; a=10.800(8), b=13.468(9), c=13.918(11), α=89.67(6)°, β=101.53(7)°, γ=81.49(3)° and V=1961(3). Cyclic voltammetry of 12 in MeCN solution shows a well-behaved quasi-reversible (ΔE=100 mV) Ni(III) ↔ Ni(II) couple.     

Bridging C−H Activation: Mild and Versatile Cleavage of the 8‐Aminoquinoline Directing Group

8‐Aminoquinoline has emerged as one of the most powerful bidentate directing groups in history of C?H activation within the last decade. However, cleavage of its robust amide bond has shown to be challenging in several cases, thus jeopardizing the general synthetic utility of the method. To overcome this limitation, we herein report a simple oxidative deprotection protocol. This transformation rapidly converts the robust amide to a labile imide, allowing subsequent cleavage in a simple one‐pot fashion to rapidly access carboxylic acids or amides as final products.     

A Highly Oxidized Cobalt Porphyrin Dimer: Spin Coupling and Stabilization of the Four‐Electron Oxidation Product

A highly oxidized cobalt porphyrin dimer is reported. Each cobalt(II) ion and porphyrin ring underwent 1e oxidation with iodine as the oxidant to give a 4e‐oxidized cobalt(III) porphyrin π‐cation radical dimer. The bridging ethylene group allows for substantial conjugation of the porphyrin macrocycles, thus leading to a strong antiferromagnetic coupling between the π‐cation radicals and to stabilization of the singlet state. X‐ray crystallography clearly showed that the complex may be considered as a real supramolecule rather than two cobalt(III) porphyrin π‐cation radicals that interact through space.     

Synchronization of memristor‐based delayed BAM neural networks with fractional‐order derivatives

This article deals with the problem of synchronization of fractional‐order memristor‐based BAM neural networks (FMBNNs) with time‐delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional‐order 0 < α < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master‐slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite‐time synchronization of FMBNNs with fractional‐order 1 < α < 2, using Mittag‐Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time‐delay and fractional‐order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity 21: 412–426, 2016     

Clustering intelligent transportation sensors using public transportation

Advanced transportation sensors use a wireless medium to communicate and use data fusion techniques to provide complete information. Large-scale use of intelligent transportation sensors can lead to data bottlenecks in an ad-hoc wireless sensor network, which needs to be reliable and should provide a framework to sensors that constantly join and leave the network. A possible solution is to use public transportation vehicles as data fusion nodes or cluster heads. This paper presents a mathematical programming approach to use public transportation vehicles as cluster heads. The mathematical programming solution seeks to maximize benefit achieved by covering both mobile and stationary sensors, while considering cost/penalty associated with changing cluster head locations. A simulation is developed to capture realistic considerations of a transportation network. This simulation is used to validate the solution provided by the mathematical model.     

Fractal Jacobi Systems and Convergence of Fourier–Jacobi Expansions of Fractal Interpolation Functions

The fractal interpolation function (FIF) is a special type of continuous function on a compact subset of \({\mathbb{R}}\) interpolating a given data set. They have been proved to be a very important tool in the study of irregular curves arising from financial series, electrocardiograms and bioelectric recording in general as an alternative to the classical methods. It is well known that Jacobi polynomials form an orthonormal system in \({\mathcal{L}^{2}(-1,1)}\) with respect to the weight function \({\rho^{(r,s)}(x)=(1-x)^{r} (1+x)^{s}}\), \({r > -1}\) and \({s > -1}\). In this paper, a fractal Jacobi system which is fractal analogous of Jacobi polynomials is defined. The Weierstrass type theorem providing an approximation for square integrable function in terms of \({\alpha}\)-fractal Jacobi sum is derived. A fractal basis for the space of weighted square integrable functions \({\mathcal{L}_{\rho}^{2}(-1,1)}\) is found. The Fourier–Jacobi expansion corresponding to an affine FIF (AFIF) interpolating certain data set is considered and its convergence in uniform norm and weighted-mean square norm is established. The closeness of the original function to the Fourier–Jacobi expansion of the AFIF is proved for certain scale vector. Finally, the Fourier–Jacobi expansion corresponding to a non-affine smooth FIF interpolating certain data set is considered and its convergence in uniform norm and weighted-mean square norm is investigated as well.     

Structure of Nano‐sized CeO2 Materials: Combined Scattering and Spectroscopic Investigations

The structure of several nano‐sized ceria, CeO₂, systems was investigated using neutron and X‐ray diffraction and X‐ray absorption spectroscopy. Whilst both diffraction and total pair distribution functions (PDFs) revealed that in all of the samples the occupancy of both Ce⁴⁺ and O^2? are very close to the ideal stoichiometry, the analysis using Reverse Monte Carlo technique revealed significant disorder around oxygen atoms in the nano‐sized ceria samples in comparison to the highly crystalline NIST standard. In addition, the analysis revealed that the main differences observed in the pair correlations from various X‐ray and neutron diffraction techniques were attributable to the particle size of the CeO₂ prepared by the reported three methods. Furthermore, detailed analysis of the Ce L₃‐ and K‐edge EXAFS data support this finding; in particular the decrease in higher shell coordination numbers with respect to the NIST standard, is attributed to differences in particle size.     

Cobalt and magnesium ferrite nanoparticles: preparation using liquid foams as templates and their magnetic characteristics

An easy and convenient method for the synthesis of cobalt and magnesium ferrite nanoparticles is demonstrated using liquid foams as templates. The foam is formed from an aqueous mixture of an anionic surfactant and the desired metal ions, where the metal ions are electrostatically entrapped by the surfactant at the thin borders between the foam bubbles and their junctions. The hydrolysis is carried out using alkali resulting in the formation of desired nanoparticles, with the foam playing the role of a template. However, in the formation of ferrites with the formula MFe(2)O(4), where the metal ion and iron possess oxidation states of +2 and +3, respectively, forming a foam from a 1:2 mixture of the desired ionic solutions would lead to a foam composition at variance with the original solution mixture because of greater electrostatic binding of ions possessing a greater charge with the surfactant. In our procedure, we circumvent this problem by preparing the foam from a 1:2 mixture of M(2+) and Fe(2+) ions and then utilizing the in situ conversion of Fe(2+) to Fe(3+) under basic conditions inside the foam matrix to get the desired composition of the metal ions with the required oxidation states. The fact that we could prepare both CoFe(2)O(4) and MgFe(2)O(4) particles shows the vast scope of this method for making even multicomponent oxides. The magnetic nanoparticles thus obtained exhibit a good crystalline nature and are characterized by superparamagnetic properties. The magnetic features observed for CoFe(2)O(4) and MgFe(2)O(4) nanoparticles are well in accordance with the expected behaviors, with CoFe(2)O(4) particles showing higher blocking temperatures and larger coercivities. These features can easily be explained by the contribution of Co(2+) sites to the magnetocrystalline anisotropy and the absence of the same from the Mg(2+) ions.