Solutions of Zakharov-Kuznetsov equation with power law nonlinearity in (1+3) dimensions

This paper studies the Zakharov-Kuznetsov equation in (1+3) dimensions with an arbitrary power law nonlinearity. The method of Lie symmetry analysis is used to carry out the integration of the Zakharov-Kuznetsov equation. The solutions obtained are cnoidal waves, periodic solutions, singular periodic solutions, and solitary wave solutions. Subsequently, the extended tanh-function method and the G′/G method are used to integrate the Zakharov-Kuznetsov equation. Finally, the nontopological soliton solution is obtained by the aid of ansatz method. There are numerical simulations throughout the paper to support the analytical development.     

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 novel approach to cutting decision trees

In data mining, binary classification has a wide range of applications. Cutting Decision Tree (CDT) induction is an efficient mathematical programming based method that tries to discretize the data set on hand by using multiple separating hyperplanes. A new improvement to CDT model is proposed in this study by incorporating the second goal of maximizing the distance of the correctly classified instances to the misclassification region. Computational results show that developed model achieves better classification accuracy for Wisconsin Breast Cancer database and Japanese Banks data set when compared to existing piecewise-linear models in literature. Furthermore, remarkable results are obtained for the well-known benchmarking data sets (Buba Liver Disorders, Blood Tranfusion and Pima Indian Diabetes) when compared to the original CDT model.     

A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system

Nonlinear Dynamics - Substitution Box (S-Box) is one of the most significant structures used to create an encryption which is strong and resistant against attacks in block encryption algorithms....     

Synthesis and proton conductivity studies of polystyrene‐based triazole functional polymer membranes

In this study, poly(vinylbenzylchloride) (PVBC) was produced by free‐radical polymerization of 4‐vinylbenzylchloride, and then it was functionalized with 3‐amino‐1,2,4‐triazole (ATri) and 1H‐1,2,4‐triazole (Tri). The composition of the polymers was verified by elemental analysis, and the structure was characterized by Fourier transform infrared and ¹³C‐nuclear magnetic resonance spectra. PVBC was modified by ATri with 68% and Tri with 50% yield. The polymers were doped with trifluoromethanesulfonic acid (TA) at various molar ratios, X = 0.5, 1, 2, and 3 with respect to aminotriazole and triazole units. Proton transfer from TA to the triazole rings was proved with Fourier transform infrared spectroscopy. Thermogravimetric analysis showed that the samples are thermally stable up to approximately 200 °C. Differential scanning calorimetry results illustrated the homogeneity of the materials. Under anhydrous conditions, PVBCATri3TA and PVBCTri3TA showed highest proton conductivity of 0.086 and 0.042 S/cm, respectively. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Synthesis,microwave‐promoted catalytic activity in Suzuki–Miyaura cross‐coupling reactions and antimicrobial properties of novel benzimidazole salts bearing trimethylsilyl group

A mixture of benzimidazole salts (2–7), Pd(OAc)₂ and K₂CO₃ in DMF–H₂O catalyzes the Suzuki–Miyaura cross‐coupling reactions promoted by microwave irradiation resulting in high yield within a short time. In particular, the yield of the Suzuki–Miyaura reactions with aryl bromides was found to be nearly quantitative. The synthesized benzimidazole salts (2–7) were identified by ¹H‐¹³C, NMR, IR spectroscopic methods and microanalysis. The molecular structure of 1 was determined by X‐ray crystallography. The antibacterial and antifungal activities of the novel benzimidazole derivatives (1–7) were also tested against standard strains. Copyright © 2011 John Wiley & Sons, Ltd.     

Poly(cyclohexene oxide)/clay nanocomposites by photoinitiated cationic polymerization via activated monomer mechanism

Poly(cyclohexene oxide) (PCHO)/clay nanocomposites were prepared by in situ photoinitiated activated monomer cationic polymerization. The polymerization of cyclohexene oxide through the interlayer galleries of the clay can provide distribution of the clay layers in the polymer matrix homogenously and results in the formation of PCHO/clay nanocomposites. The exfoliated structures were characterized by X‐ray diffraction spectroscopy, thermogravimetric analysis, transmission electron microscopy, and atomic force microscopy. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5328–5335, 2009     

Monitoring of Mycophenolic Acid in the Plasma of Transplant Patients by Capillary Electrophoresis

Plasma samples from 60 transplant patients on mycophenolate mofetil therapy were analysed using validated capillary electrophoresis (CE) method to determine mycophenolic acid (MPA) and its main metabolite mycophenolic acid glucuronide. Enzyme multiplied immunoassay technique (EMIT) values were available for the same samples. The differences between the results from the two methods was clarified by using Bland–Altman analysis and further statistical analysis. More than 90% of the results showed a positive bias, with EMIT giving higher levels than CE.     

Commuting elements and spaces of homomorphisms

This article records basic topological, as well as homological properties of the space of homomorphisms Hom(π,G) where π is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If π is a free abelian group of rank equal to n, then Hom(π, G) is the space of ordered n–tuples of commuting elements in G. If G = SU(2), a complete calculation of the cohomology of these spaces is given for n = 2, 3. An explicit stable splitting of these spaces is also obtained, as a special case of a more general splitting. Alejandro Adem was partially supported by the NSF and NSERC. Frederick R. Cohen was partially supported by the NSF, grant number 0340575.