New Exact Solutions of Fractional Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations Using Fractional Sub-Equation Method

In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.     

Phonon confinement and substitutional disorder in Cd1−xZnxS nanocrystals

1‐longitudinal optical (LO) phonons in free‐standing mixed Cd_1−xZn_xS nanocrystals, synthesized using chemical precipitation, are investigated using Raman spectroscopy. As expected for the nanocrystals, the 1‐LO modes are found to appear at slightly lower wavenumbers than those in the bulk mixed crystals and exhibit one‐mode behavior. On the other hand, the line broadening is found to be much more than that can be accounted on the basis of phonon confinement. From the detailed line‐shape analysis it turns out that the substitutional disorder in the mixed crystals contributes much more to the line broadening than the phonon confinement. The linewidth arising from these mechanisms are also extracted from the analysis. Copyright © 2009 John Wiley & Sons, Ltd.     

Inhomogeneous Plane Symmetric String Cosmological Models in Bimetric Theory

It is shown that the inhomogeneous plane symmetric perfect fluid distribution and cosmic strings do not survive in frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). Hence vacuum models are presented and studied.     

Nano-graphitic clustering and break down of phonon selection rule in diamond-like carbon films

Diamond-like carbon films are deposited on silicon substrates at different substrate bias using ECR-CVD technique. Raman spectroscopic studies show the presence of broad G and D peaks. In contrast to the position of D peak, the G peak shows a systematic red-shift with increase in the bias voltage. From the analysis it is found that an increase in bias voltage decreases the sp² cluster diameter. Furthermore, two additional Raman peaks at around 690 and 880 cm^?1 are also observed. These peaks, forbidden in the first order Raman scattering, arise due to the breakdown of phonon selection rule in graphitic nanoclusters.     

Excited State Intramolecular Proton Transfer in Methyl and Methoxy Substituted Salicylic Acid

The excited state intramolecular proton transfer (ESIPT) processes in 3‐methylsalicyclic acid (3‐MeSA) and 3‐methoxysalicyclic acid (3‐MeOSA) have been investigated in cyclohexane medium by emission spectroscopic techniques. The ESIPT process was characterized in 3‐MeSA from the large Stokes fluorescent band (455 nm), but it was suppressed by 3‐MeOSA in cyclohexane. The ESIPT process was found to be accelerated both in 3‐MeSA and 3‐MeOSA in the presence of a hydrogen bond accepting agent, triethylamine (TEA). Further, theoretical calculations were carried out at the ground and excited states to complement the experimental evidences.     

Dye–Surfactant Interaction: Modulation of Photophysics of an Ionic Styryl Dye

The interesting modulation of multibond rotation–induced intramolecular charge transfer photophysics of 2-(4-(dimethylamino) styryl)-1-methylpyridinium iodide in different micelles due to different contributions of twisted intramolecular charge transfer (TICT) and hydrogen bonding deactivation channels have been reported in this paper. 2-(4-(dimethylamino) styryl)-1-methylpyridinium iodide enters into all the micelles in different positions from the water solution due to active hydrophobic force and electrostatic field, as revealed from the shift and intensity of intramolecular charge transfer (ICT) band. The presence of mechanically trapped water with the addition of salt and inherent thermodynamic water controls the ICT emission. Analysis of spectral data before and after the addition of salt confirms the orientation of 2-(4-(dimethylamino) styryl)-1-methylpyridinium iodide in cationic and anionic micelles.     

Decomposing capacity utilization in data envelopment analysis: An application to banks in India

This paper briefly reviews the existing methods of capacity utilization in nonparametric framework from economic perspectives, and then suggests an alternative in the light of limitations therein. In the spirit of work by Coelli et al. [Coelli, T.J., Grifell-Tatje, E., Perelman, S., 2002. Capacity utilisation and profitability: A decomposition of short run profit efficiency. International Journal of Production Economics 79, 261–278], we propose two methods, radial and non-radial, to decompose the input-based physical (technological) capacity utilization into various meaningful components viz., technical inefficiency, ray economic capacity utilization and optimal capacity idleness. A case study of Indian banking industry is taken as an example to illustrate the potential application of these two methods of decomposition. Our two broad empirical findings are that first, competition created after financial sector reforms generates high efficiency growth, and reduces excess capacity; second, the cost gap of the short-run cost from the actual cost is higher for the nationalized banks over the private banks indicating that the former banks, though old, do not reflect their learning experience in their cost minimizing behavior.     

On the order of a non-abelian representation group of a slim dense near hexagon

In this paper we study the possible orders of a non-abelian representation group of a slim dense near hexagon. We prove that if the representation group R of a slim dense near hexagon S is non-abelian, then R is a 2-group of exponent 4 and |R|=2 ^β , 1+NPdim(S)≤β≤1+dimV(S), where NPdim(S) is the near polygon embedding dimension of S and dimV(S) is the dimension of the universal representation module V(S) of S. Further, if β=1+NPdim(S), then R is necessarily an extraspecial 2-group. In that case, we determine the type of the extraspecial 2-group in each case. We also deduce that the universal representation group of S is a central product of an extraspecial 2-group and an abelian 2-group of exponent at most 4. This work was partially done when B.K. Sahoo was a Research Fellow at the Indian Statistical Institute, Bangalore Center with NBHM fellowship, DAE Grant 39/3/2000-R&D-II, Govt. of India.     

Effects of partial slip,viscous dissipation and Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid

The steady Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid is extended to the case where the disk surface admits partial slip. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The constitutive equation of the non-Newtonian fluid is modeled by that for a Reiner–Rivlin fluid. The momentum equations give rise to highly non-linear boundary value problem. Numerical solutions for the governing non-linear equations are obtained over the entire range of the physical parameters. The effects of slip, magnetic parameter and non-Newtonian fluid characteristics on the velocity and temperature fields are discussed in detail and shown graphically. Emphasis has been laid to study the effects of viscous dissipation and Joule heating on the thermal boundary layer. It is interesting to find that the non-Newtonian cross-viscous parameter has an opposite effect to that of the slip and the magnetic parameter on the velocity and the temperature fields.     

Modified ion exchange separation for tungsten isotopic measurements from kimberlite samples using multi-collector inductively coupled plasma mass spectrometry

Tungsten isotope composition of a sample of deep-seated rock can record the influence of core-mantle interaction of the parent magma. Samples of kimberlite, which is known as a carrier of diamond, from the deep mantle might exhibit effects of core-mantle interaction. Although tungsten isotope anomaly was reported for kimberlites from South Africa, a subsequent investigation did not verify the anomaly. The magnesium-rich and calcium-rich chemical composition of kimberlite might engender difficulty during chemical separation of tungsten for isotope analyses. This paper presents a simple, one-step anion exchange technique for precise and accurate determination of tungsten isotopes in kimberlites using multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS). Large quantities of Ca and Mg in kimberlite samples were precipitated and removed with aqueous H(2)SO(4). Highly pure fractions of tungsten for isotopic measurements were obtained following an anion exchange chromatographic procedure involving mixed acids. That procedure enabled efficient removal of high field strength elements (HFSE), such as Hf, Zr and Ti, which are small ions that carry strong charges and develop intense electrostatic fields. The tungsten yields were 85%-95%. Advantages of this system include less time and less use of reagents. Precise and accurate isotopic measurements are possible using fractions of tungsten that are obtained using this method. The accuracy and precision of these measurements were confirmed using various silicate standard rock samples, JB-2, JB-3 and AGV-1.