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.     

Discrete exact solutions to some nonlinear differential-difference equations via the (G′/G)-expansion method

We extended the (G′/G)-expansion method to two well-known nonlinear differential-difference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. Discrete soliton and periodic wave solutions with more arbitrary parameters, as well as discrete rational wave solutions, are revealed. It seems that the utilized method can provide highly accurate discrete exact solutions to NDDEs arising in applied mathematical and physical sciences.     

Phenolic compounds from the aerial parts of Clematis viticella L. and their in vitro anti-inflammatory activities*

Phytochemical investigations on the EtOH extract of Clematis viticella led to the isolation of six flavonoid glycosides, isoorientin (1), isoorientin 3′-O-methyl ether (2), quercetin 7-O-α-L-rhamnopyranoside (3), quercetin 3,7-di-O-α-L-rhamnopyranoside (4), manghaslin (5) and chrysoeriol 7-O-β-D-glucopyranoside (6), one phenylethanol derivative, hydroxytyrosol (7), along with three phenolic acids, caffeic acid (8), (E)-p-coumaric acid (9) and p-hydroxybenzoic acid (10). The structures of the isolates were elucidated on the basis of NMR and HR-MS data. All compounds were isolated from C. viticella for the first time. Compounds 7 and 8 showed significant anti-inflammatory activity at 100 μM by reducing the release of NO in LPS-stimulated macrophages comparable to positive control indomethacin. Compounds 3 and 7 exhibited anti-inflammatory activity through lowering the levels of TNF-α while 1, 3 and 5 decreased the levels of neopterin better than the positive controls.     

Constructing rational and multi‐wave solutions to higher order NEEs via the Exp‐function method

In this paper, we present an application of some known generalizations of the Exp‐function method to the fifth‐order Burgers and to the seventh‐order Korteweg de Vries equations for the first time. The two examples show that the Exp‐function method can be an effective alternative tool for explicitly constructing rational and multi‐wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered. Copyright © 2011 John Wiley & Sons, Ltd.     

Palladium(II)?NHC complexes containing benzimidazole ligand as a catalyst for C?N bond formation

The reaction of 2‐(2‐bromoethyl)‐1,3‐dioxane with 1‐alkylbenzimidazole derivatives results in the formation of the new benzimidazolium salts (1). The reaction of Pd(OAc)₂ with 1,3‐dialkylbenzimidazolium salts (1a–c) yields palladium N‐heterocyclic carbene (NHC) complexes (2a–c). All synthesized compounds were characterized by ¹H NMR, ¹³ C NMR, IR and elemental analysis techniques which support the proposed structures. As catalysts, these new palladium complexes offer a simple and efficient methodology for the synthesis of triarylamines and secondary amines from anilines and amines and in a single step with potassium tertiary butoxide as a base. Copyright © 2010 John Wiley & Sons, Ltd.     

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).     

New olefinic centred binuclear clamshell type phthalocyanines: Design, synthesis, structural characterisation, the stability and the change in the electron cloud at olefine-based symmetrical diphthalonitrile fragment by the combined application of UV–Vis electronic structure and theoretical methods

The olefinic centred Schiff base (3) was obtained from the condensation of substituted dialdehyde (1) with 2-amino-4-methylphenol (2) in a 1:2 ratio. The diphthalonitrile derivative (5) was prepared by the reaction of 4-nitrophthalonitrile (4) and compound (3) in dry dimethylformamide/potassium carbonate. The key product (5) was obtained by nucleophilic substitution of an activated nitro group into an aromatic ring. The cyclotetramerization of compound (5) with phthalonitrile (6) in 1:6.15 ratio gave the expected metal-free phthalocyanine of clamshell type (7), and with metal salts of Zn(II), Ni(II), Co(II) and Cu(II) gave metallophthalocyanines of clamshell types (8-11), respectively in dimethylaminoethanol/1,8-diazabycyclo[5.4.0]undec-7-ene system. The products were purified by several techniques such as crystallization and preparative thin layer chromatography. The newly prepared compounds were characterised by a combination of elemental analyses, IR, ¹H/¹³C NMR, MS and UV-Vis spectroscopy.