Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Transition metal complexes of a hydrazone derived from hydralazine hydrochloride and 3,5-di-tert-butylsalicylaldehyde

Mononuclear Co(III), Ni(II) and Cu(II) coordination compounds of (E)-1-(3,5-di-tert-butyl-2-hydroxybenzylidene)-2-(phthalazin-1-yl)hydrazine (LH) were prepared and characterized by physicochemical and spectroscopic methods. The metal-to-ligand ratio was found to be 1:2 in [Co(L)₂]Cl·2H₂O (1) and [Ni(L)₂]·2H₂O (2), while it is 1:1 in [Cu(L)Cl]·2CH₃OH (3). The X-ray crystal structures of LH and complex 1 is are reported. LH shows monobasic behavior, coordinating through NNO donor atoms. The complexes were investigated for their antimicrobial properties. Complexes 1 and 3 show excellent antibacterial and antifungal activities, respectively.     

Dithiobissuccinimidyl propionate self assembled monolayer based cholesterol biosensor

A dithiobissuccinimidyl propionate (DTSP) self-assembled monolayer (SAM) prepared onto a gold (Au) surface has been utilized for covalent immobilization of cholesterol oxidase (ChOx) and cholesterol esterase (ChEt). These ChOx-ChEt/DTSP/Au bio-electrodes have been characterized using electrochemical impedance and cyclic voltammetric (CV) techniques, respectively. Differential pulse voltammetry (DPV) has been used for enzymatic assay of immobilized ChOx and ChEt onto the DTSP modified gold surface as a function of cholesterol oleate concentration. The response measurement conducted on ChOx-ChEt/DTSP/Au bio-electrode reveal the value of Michaelis-Menten constant (Km) as 0.95 mM suggesting enhanced affinity of enzymes (ChOx and ChEt). The ChOx-ChEt/DTSP/Au bio-electrodes show linearity in range of 50 to 400 mg dl(-1) of cholesterol oleate and the shelf-life of more than 50 days when stored at 4 degrees C. This biosensing electrode shows correlation coefficient of 0.9973 and standard deviation of regression as 0.859 microA.     

Liquid chromatography-tandem mass spectrometry method for identification and quantification of two biologically active polyisoprenylated benzophenones, isoxanthochymol and camboginol, in Garcinia species

A sensitive liquid chromatography/electrospray ionization tandem mass spectrometrical (LC/ESI-MS/MS) method was developed for simultaneous identification and quantification of two polyisoprenylated benzophenones, isoxanthochymol and camboginol, in the extracts of the fruit rinds, stem bark, seed and leaves of Garcinia indica and in the fruit rinds of Garcinia cambogia. The separation of isoxanthochymol and camboginol was achieved on an RP-8 column using the solvent system consisting of a mixture of acetonitrile-water (80:20) and methanol-acetic acid (99.0:1.0) as a mobile phase in a gradient elution mode. A multiple reaction monitoring (MRM) method was developed for quantification of isoxanthochymol and camboginol in the above extracts of Garcinia species. Based on a signal-to-noise ratio of 3, the limits of detection in MRM mode for isoxanthochymol and camboginol were 2.0 and 5.0 ng/mL respectively. The method was validated in terms of linearity, accuracy and precision for 6 days. The method developed was found to be useful for identification and quantification of isoxanthochymol and camboginol in the extracts of the fruit rinds, stem bark, seed and leaves of Garcinia indica and in the fruit rinds of Garcinia cambogia.     

A rapid liquid chromatography-tandem mass spectrometry method for quantification of a biologically active molecule camboginol in the extract of Garcinia cambogia

A liquid chromatography-tandem mass spectrometry (LC-MS/MS) method for the determination of camboginol in the extract of fruit rinds of Garcinia cambogia has been developed. Separation was achieved isocratically on an RP C(18) column using a solvent system consisting of a mixture of acetonitrile-water (9:1) and methanol-acetic acid (99.5:0.5) in the ratio of 30:70 as mobile phase at a flow rate of 0.4 mL/min. A multiple reaction monitoring (MRM) method was developed for quantification of camboginol in the fruit rinds extract of G. cambogia using MRM transitions of m/z 601.4 --> m/z 176.7 and m/z 601.4 --> m/z 448.9, respectively. The calibration curve based on peak area against concentration was linear up to 50 ng/mL with a detection limit of 0.5 ng/mL. The method showed satisfactory reproducibility with a coefficient of variation of less than 6%. The method was successfully applied for quantification of camboginol in different Garcinia extracts.     

Rainbow Connection Number and Radius

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) ≤  r(r + 2). We demonstrate that this bound is the best possible for rc(G) as a function of r, not just for bridgeless graphs, but also for graphs of any stronger connectivity. It may be noted that for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius (K _1,n for instance). We further show that for every bridgeless graph G with radius r and chordality (size of a largest induced cycle) k, rc(G) ≤  rk. Hitherto, the only reported upper bound on the rainbow connection number of bridgeless graphs is 4n/5 ? 1, where n is order of the graph (Caro et al. in Electron J Comb 15(1):Research paper 57, 13, 2008). It is known that computing rc(G) is NP-Hard (Chakraborty and fischer in J Comb Optim 1–18, 2009). Here, we present a (r + 3)-factor approximation algorithm which runs in O(nm) time and a (d + 3)-factor approximation algorithm which runs in O(dm) time to rainbow colour any connected graph G on n vertices, with m edges, diameter d and radius r.     

An accurate numerical method for solving the linear fractional Klein–Gordon equation

In this article, an implementation of an efficient numerical method for solving the linear fractional Klein–Gordon equation (LFKGE) is introduced. The fractional derivative is described in the Caputo sense. The method is based upon a combination between the properties of the Chebyshev approximations and finite difference method (FDM). The proposed method reduces LFKGE to a system of ODEs, which is solved using FDM. Special attention is given to study the convergence analysis and deduce an error upper bound of the proposed method. Numerical example is given to show the validity and the accuracy of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.     

A novel lip reading algorithm by using localized ACM and HMM: Tested for digit recognition

Lip contour tracking is an integral part of lip reading application. Fast and accurate lip tracking is an important step in lip reading. This paper uses a novel active contour model for lip tracking and proposes geometrical feature extraction approach for lip reading. Effect of individual features are compared and a joint feature model is obtained by combining weighted decision obtained by a feature vector of difference in inner area, height and width of lip. Ergodic hidden markov model (HMM) is used as a classifier. For each digit Markov Model is tested for 3 states and 5 states. Videos of English digit from 0 to 9 have been recorded for recognition test. Cuave database is used for comparison along with an in-house database. While doing computation of feature vectors, only significant frames are used to reduce the computation complexity. Results of experimentations on digit utterances are given to show that the maximum recognized digit can be used for important programming command of computerized numerical control machines.     

Nondestructive evaluation of helicopter rotor blades using guided Lamb modes

This paper presents an application for turning and direct modes in a complex composite laminate structure. The propagation and interaction of turning modes and fundamental Lamb modes are investigated in the skin, spar and web sections of a helicopter rotor blade. Finite element models were used to understand the various mode conversions at geometric discontinuities such as web-spar joints. Experimental investigation was carried out with the help of air coupled ultrasonic transducers. The turning and direct modes were confirmed with the help of particle displacements and velocities. Experimental B-Scans were performed on damaged and undamaged samples for qualitative and quantitative assessment of the structure. A strong correlation between the numerical and experimental results was observed and reported.     

Nonequilibrium forces between dragged ultrasoft colloids

The dynamical deformation of ultrasoft colloids as well as their dynamic frictional forces are numerically investigated, when one colloid is dragged past another at constant velocity. Hydrodynamic interactions are captured by a particle-based mesoscopic simulation method. At vanishing relative velocity, the equilibrium repulsive force-distance curve is obtained. At large drag velocities, in contrast, we find an apparent attractive force for departing colloids along the dragging direction. The deformation, in the close encounter of colloids, and the energy dissipation are examined as a function of the drag velocity and their separation.