Bianchi type II,VIII, and IX cosmological models in Lyra's geometry

The Bianchi type II, VIII, and IX models are investigated in Lyra's geometry (in normal gauge) when the gauge function is time dependent. The physical behavior of these models in vacuum and in the presence of the Zeldovich fluid is discussed.     

Degree of Approximation for Bivariate Chlodowsky–Szasz–Charlier Type Operators

We consider a combination of Chlodowsky polynomials with generalized Szasz operators involving Charlier polynomials. We give the degree of approximation for these bivariate operators by means of the complete and partial modulus of continuity, and also by using weighted modulus of continuity. Furthermore, we construct a GBS (Generalized Boolean Sum) operator of bivariate Chlodowsky–Szasz–Charlier type and estimate the order of approximation in terms of mixed modulus of continuity.     

GBS Operators of Lupaş–Durrmeyer Type Based on Polya Distribution

In this paper, we study an extension of the bivariate Lupa?–Durrmeyer operators based on Polya distribution. For these operators we get a Voronovskaja type theorem and the order of approximation using Peetre’s K-functional. Then, we construct the Generalized Boolean Sum operators of Lupa?–Durrmeyer type and estimate the degree of approximation in terms of the mixed modulus of smoothness.     

Observation of bulk like magnetic ordering below the blocking temperature in nanosized zinc ferrite

We investigated the magnetic behavior of nanosized zinc ferrite with the help of vibrating sample magnetometry and in-field Mössbauer spectroscopy. The nanoparticles of zinc ferrite with crystallite size ranging from 10 to 62 nm were synthesized by a nitrate method. The structure and phase were determined with the help of X-ray diffraction. Attributes of cation inversion were found with the calculated values of lattice parameter. The saturation magnetization decreases with the increase in crystallite size at room temperature, while these values are almost the same at 10 K for all the samples except the one with crystallite size of 10 nm. The thermal magnetization measurement shows a decrease in blocking temperature with increase in particle size for these samples. The synthesized samples exhibit the presence of antiferromagnetic ordering below the blocking temperature as investigated by in-field Mössbauer spectroscopy.     

Potts ferromagnets on coexpressed gene networks: identifying maximally stable partitions

Clustering gene expression data by exploiting phase transitions in granular ferromagnets requires transforming the data to a granular substrate. We present a method using the recently introduced homogeneity order parameter Lambda [H. Agrawal, Phys. Rev. Lett. 89, 268702 (2002)]] for optimizing the parameter controlling the "granularity" and thus the stability of partitions. The model substrates obtained for gene expression data have a highly granular structure. We explore properties of phase transition in high q ferromagnetic Potts models on these substrates and show that the maximum of the width of superparamagnetic domain, corresponding to maximally stable partitions, coincides with the minimum of Lambda.     

A Fractional Schrödinger Equation and Its Solution

This paper presents a fractional Schrödinger equation and its solution. The fractional Schrödinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrödinger equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Schrödinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function.     

Projective synchronization between different fractional‐order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique

In the present article, the authors have proposed a modified projective adaptive synchronization technique for fractional‐order chaotic systems. The adaptive projective synchronization controller and identification parameters law are developed on the basis of Lyapunov direct stability theory. The proposed method is successfully applied for the projective synchronization between fractional‐order hyperchaotic Lü system as drive system and fractional‐order hyperchaotic Lorenz chaotic system as response system. A comparison between the effects on synchronization time due to the presence of fractional‐order time derivatives for modified projective synchronization method and proposed modified adaptive projective synchronization technique is the key feature of the present article. Numerical simulation results, which are carried out using Adams–Boshforth–Moulton method show that the proposed technique is effective, convenient and also faster for projective synchronization of fractional‐order nonlinear dynamical systems. Copyright © 2013 John Wiley & Sons, Ltd.     

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

Nature and properties of ultrathin nanocrystalline gold films formed at the organic-aqueous interface

Ultrathin nanocrystalline films of gold formed at different temperatures at the organic-aqueous interface have been investigated by X-ray diffraction, electron microscopy, atomic force microscopy, and electronic spectroscopy. The films are smooth and continuous over relatively large length scales and are generally approximately 100 nm thick. The size of the nanocrystals is sensitive to the reaction temperature, which also determines whether the film is metallic or an activated conductor. The surface plasmon band of gold is highly red-shifted in the films. Alkanethiols perturb the structure of the films, with the magnitude of the effect depending on the chain length. Accordingly, the position of the plasmon band and the electrical resistance of the films are affected by interaction with alkanethiols; the plasmon band approaches that of isolated nanocrystals in the presence of long-chain thiols.     

Biligand metal chelates of 1,10-phenanthroline and several salicyclic acid derivatives in solution

Summary Mixed ligand complexes of copper(II), zinc(II), nickel(II) and cobalt(II) ions involving 1,10-phenanthroline (phen) as primary and 3,5-dinitrosalicylic acid (dnsa), 5-nitrosalicylic acid (nsa), 5-chlorosalicylic acid (csa) and 3,5-dibromosalicylic acid (dbsa) as secondary ligands in solution have been investigated potentiometrically [25°, µ = 0.1 M [NaClO₄], medium 50% v: v aqueous ethanol]. The stability order of mixed ligand complexes with respect to the metal ions obeys the natural order: cobalt(II) < nickel(II) < copper(II) > zinc(II). The stabilities of the heterometal chelates have been compared with the corresponding homometal chelates of the secondary ligands and have been interpreted in terms of metal-ligand effects and coulombic interactions between various ligand anion species present.