Schwarzian derivative as a proof of the chaotic behaviour

In recent years, a sufficient condition for determining chaotic behaviours of the non-linear systems has been characterized by the negative Schwarzian derivative (Hac?bekiro?lu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, T _c, and paramagnetic Meissner transition temperature, T _PME, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The T _c, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the T _PME, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both T _c and T _PME which are in agreement with the chaotic behaviour of the system.     

A facile protocol for the preparation of 5-alkylidene and 5-imino substituted hydantoins from N,N′-disubstituted parabanic acids

A convenient procedure for the preparation of various substituted (thio)hydantoins is described. The method is based on Wittig and aza-Wittig reactions of parabanic acids with phosphonium ylides. The reactions occurred both regio- and stereo-selectively.     

Thermal decomposition kinetics of polypyrrole and its star shaped copolymer

Thermal behavior of 2,4,6-tris(4-(1H-pyrrol-1-yl)phenoxy)-1,3,5-triazine monomer, polypyrrole, and their star shaped copolymer, were investigated using TG and DTA methods. It was found that Tria melts at 517 K and after than it starts to decompose. Decomposition proceeded in two stages which were corresponding to removal of branched groups and remaining core structure degradation, respectively. Polypyrrole and copolymer showed similar thermal behaviors. These compounds decomposed in three stages which are removal of solvent, removal of dopant anion and rest of structure decomposition. The calculation of activation energies of all reactions were realized using model-free (KAS and FWO) methods. The graphs were prepared which show the alteration of activation energy with decomposition ratio. Thermal analysis results showed that dopant anion and solvent removal activation energy values for copolymer are lower than polypyrrole. Star shaped loose-packed novel structure greatly facilitates solvent and dopant anion removal from copolymer. It can be concluded also that thermal analysis can be used as predict package structure of conducting polymers.     

Performance of amperometric alcohol electrodes prepared by plasma polymerization technique

A single-layer alcohol electrode was prepared by plasma polymerization technique. Ethylenediamine was used to incorporate amino groups on tract-etched polycarbonate membranes in glow discharge reactor. In order to determine the plasma polymerization parameters (discharged power, monomer flow rate, exposure time) on membrane permeability, hydrogen peroxide was used as tracer. The single-layer alcohol electrode that was produced by 0.6% (w/v) of alcohol oxidase (AOx) solution on the polycarbonate membrane, which was modified at 30 W, 20 ml/min monomer flow rate and 15 min exposure time, was selected for optimum performance. Sensitivity, linearity and response time of that particular layer were 5.6 nA/mM, 2 mM and 50 s, respectively. The performance of the amperometric alcohol electrode was tested on commercial alcoholic beverages.     

Tauberian theorems for Abel limitability method

This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.      

On geometric interpretations of split quaternions

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).     

Theoretical investigation of triazine based a star shape pyrrole monomer

In this work, we report a comprehensive theoretical investigation of electroactive star shaped pyrrole functionalized triazine monomer with two main goals. First goal of this work is to explore the physical and chemical properties of the monomer, then to investigate correlation between the experimental and the theoretical properties of monomer. The scale factor which is calculated from B3LYP/cc-pVDZ was determined as 0.985 for FT-IR and it is an important and reliable contribution to the literature. It is determined that the most appropriate basis set for this molecule. The other novel objective of this research is to investigate temperature effect on displacement of chlorine atoms in 2,4,6-trichloro-1,3,5-triazine. This method applied for the first time in the literature for triazines is especially crucial to the synthesis of unsymmetrical triazines.