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.     

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.     

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.     

Synthesis of chiral helical 1,3-oxazines

A series of novel 1,3-oxazines were prepared to construct a helical framework. The 1,3-oxazine attached to the phenanthrene unit showed a small bite angle θ (～12°), while the units attached to [4]helicene showed a larger θ (～35°) and exhibited helical isomers at ambient conditions. The diastereomers of the third type of helicene-like bis-oxazine attached to binaphthyl were easily separable and showed good thermal stability. All four diastereomers of bis-helicene were synthesized, and their absolute configuration was established.     

Gel sculpture: moldable, load-bearing and self-healing non-polymeric supramolecular gel derived from a simple organic salt

An easy access to a library of simple organic salts derived from tert-butoxycarbonyl (Boc)-protected L-amino acids and two secondary amines (dicyclohexyl- and dibenzyl amine) are synthesized following a supramolecular synthon rationale to generate a new series of low molecular weight gelators (LMWGs). Out of the 12 salts that we prepared, the nitrobenzene gel of dicyclohexylammonium Boc-glycinate (GLY.1) displayed remarkable load-bearing, moldable and self-healing properties. These remarkable properties displayed by GLY.1 and the inability to display such properties by its dibenzylammonium counterpart (GLY.2) were explained using microscopic and rheological data. Single crystal structures of eight salts displayed the presence of a 1D hydrogen-bonded network (HBN) that is believed to be important in gelation. Powder X-ray diffraction in combination with the single crystal X-ray structure of GLY.1 clearly established the presence of a 1D hydrogen-bonded network in the xerogel of the nitrobenzene gel of GLY.1. The fact that such remarkable properties arising from an easily accessible (salt formation) small molecule are due to supramolecular (non-covalent) interactions is quite intriguing and such easily synthesizable materials may be useful in stress-bearing and other applications.     

A convenient approach to β-heteroarylated (C-N bond) ketones from Cs2CO3 promoted reaction between propargyl alcohols and nitrogen-heterocycles

An efficient and direct approach to β-heteroarylated (C-N bond) ketones is demonstrated. Base promoted redox isomerization of propargyl alcohol to α,β-unsaturated ketone followed by conjugate addition to NH-heteroarenes affords a wide range of β-heteroarylated ketones in good to excellent yields. Aryl, heteroaryl, alkyl C(sp), and terminal alkynes containing unactivated propargyl alcohols effectively undergo redox-isomerization conjugate addition (RICA) with NH-heteroarenes. Reaction of 3-substituted pyrazoles or indazole with propargyl alcohols enables highly regioselective products. A diverse range of NH-bearing nucleophiles such as: pyrazoles, imidazole, triazoles, pyrrole, indoles and aniline participate in this reaction and deliver the corresponding β-heteroarylated ketones.