A simple multi-scroll hyperchaotic system

We propose a simple autonomous hyperchaotic system that can generate multi-scroll attractors. The proposed system has a canonical structure, one control parameter, and a switching-type nonlinearity. If multiple breakpoints are added to the system nonlinearity, multi-scroll behavior can be obtained. We numerically demonstrate hyperchaotic behavior of the proposed system, under different nonlinearities, as its control parameter is changed. Furthermore, we study hyperchaos in the proposed system when it assumes a fractional order, and demonstrate that hyperchaotic behavior can be obtained in systems less than fourth order. Throughout the study, hyperchaos is verified by examining the Lyapunov spectrum, where the presence of multiple positive Lyapunov exponents in the spectrum is indicative of hyperchaos.     

A de Vries (SmC*) Phase in a Novel Series of Chiral Fluorinated Organosiloxane Liquid Crystals

The synthesis and characterization of a series of five chiral fluorinated low molar mass (bifurcated tail) organosiloxane materials is presented. The mesogenic moiety is similar to that in the TSiKN65F mesogen reported by Naciri et al., which displays a de Vries-type SmA* phase. The one parameter varied across the series reported herein is the length of the alkyl chain linking the mesogen's core to the bifurcated siloxane tail. One of the five materials displays a de Vries SmC* phase upon cooling from SmA*.     

Structure, magnetic properties and M?ssbauer spectra of La0.67Sr0.33FexMn1???xO3 manganites oxide prepared by mechanical ball milling method

La_0.67Sr_0.33Fe_xMn_1-xO₃, with x = 0.0, 0.1, 0.2 and 1 have been elaborated by mechanical system. X-ray diffraction, Scanning electron microscopy, Magnetic measurements and M?ssbauer spectroscopy for the systems have been investigated. Rietveld analysis of the X-ray powder diffraction show that the samples crystallise in the orthorhombic perovskite system with Pnma space group. The average particle size of about 60 nanometre was obtained from scanning electron microscopy and X-ray diffraction. The investigated samples exhibit a ferromagnetic to paramagnetic transition with increasing temperature. The presence of manganese in the structure leads to an increase of the Curie temperature as well as to spontaneous magnetization. The magnetization versus applied magnetic field shows a small coercive field and an unsaturated magnetization which indicates that the nanoparticles of all samples are superparamagnetic at around room temperature. Room temperature M?ssbauer spectra show that the samples with x = 0.1 and x = 1.0 contain minority α-Fe₂O₃ and other spinel ferrite species. Also, they indicate that Fe^3?+? ions are present in slightly distorted octahedral sites in the samples with x = 0.1 and 0.2, while mixed Fe valency was observed for the sample with x = 1.0.     

Oligomerization,Isomerization and Carboxylation of Alkanes and Alkenes with Galvanostatically Generated Superoxide in the Al/O2 Electrochemical Cell

Conversion of low‐value, but thermodynamically stable chemical byproducts such as alkanes or CO₂ to more valuable feedstocks is of broad‐based interest. These so‐called up‐conversion processes are expensive because they require energy‐intensive and catalytic interventions to drive reactions against thermodynamic gradients. Here we show that the nucleophilic characteristics of superoxides, generated galvanostatically in an Aluminum/O₂ electrochemical cell, can be used in tandem with the intrinsic catalytic properties of an imidazolium/AlCl₃ electrolyte to facilely upgrade alkanes (n‐decane), alkenes (1‐decene), and CO₂ feedstocks. The aluminum/O₂ electrochemical cell used to generate the superoxide intermediate is also reported to deliver large amounts of electrical energy and therefore offers a system for high‐energy density storage and for chemical up‐conversion of low‐value compounds. Chronopotentiometry, mass spectrometry and nuclear magnetic resonance were used to investigate the electrochemical features of the system and to analyze the discharge products. We find that even at room temperature, alkanes and alkenes are facilely oligomerized and isomerized at high conversions (>97 %), mimicking the traditionally produced refined products. Incorporating CO₂ in the alkane feed leads to formation of esters and formates at moderate yields (21 %).     

Fixed Point Theorems for (p,q)-Quasi-Contraction Mappings in Cone Metric Spaces

In this work, the authors introduce the concept of $(p,q)$-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a $(p,q)$-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order $2$.     

Some Results on Stability and Stabilization of Homogeneous Time-Varying Systems

In this paper, we study the stability and stabilization of time-varying homogeneous systems that are affine in the control using some results on differentiable manifolds.     

Hyperchaos in fractional order nonlinear systems

We numerically investigate hyperchaotic behavior in an autonomous nonlinear system of fractional order. It is demonstrated that hyperchaotic behavior of the integer order nonlinear system is preserved when the order becomes fractional. The system under study has been reported in the literature [Murali K, Tamasevicius A, Mykolaitis G, Namajunas A, Lindberg E. Hyperchaotic system with unstable oscillators. Nonlinear Phenom Complex Syst 3(1);2000:7–10], and consists of two nonlinearly coupled unstable oscillators, each consisting of an amplifier and an LC resonance loop. The fractional order model of this system is obtained by replacing one or both of its capacitors by fractional order capacitors. Hyperchaos is then assessed by studying the Lyapunov spectrum. The presence of multiple positive Lyapunov exponents in the spectrum is indicative of hyperchaos. Using the appropriate system control parameters, it is demonstrated that hyperchaotic attractors are obtained for a system order less than 4. Consequently, we present a conjecture that fourth-order hyperchaotic nonlinear systems can still produce hyperchaotic behavior with a total system order of 3 + ε, where 1 > ε > 0.     

Infrared, 1H and 13C NMR spectra, structural charcterization and DFT calculations of novel adenine-cyclodiphosp(V)azane derivatives

Adenine tetrachlorocyclodiphospha(V)zane derivatives (III(a-c)) were prepared by the reaction of hexachlorocyclodiphospha(V)zane derivatives (I(a-c)) and adenine (II) as precursors. The synthesized compound's and their structures (III(a-c)) were firmly characterized (based on the presence of an inversion center) using FT-IR (4000-200 cm(-1)), UV-vis. (190-800 nm), (1)H, (13)C NMR and Mass spectral measurements in addition to C, H, N, P elemental analysis. The compounds (III(a-c)) were found to be a 1:2 molar ratio of (I(a-c)) and adenine (II) adducts, respectively. Confident and complete vibrational assignments are proposed for nearly all fundamental vibrations, along with detailed interpretation for all observed signals in both (1)H and (13)C NMR spectra of the investigated phospha(V)zanes (III(a-c)). In addition, unconstrained geometry optimization of III(a-c) were carried out by means of DFT-B3LYP/3-21G(d) calculations to provide new insight into the structural parameters and molecular geometries of compounds III(a-c). The results are reported herein and compared with similar molecules whenever appropriate.