Markovian representation of a bilinear time series model and maximum likelihood estimation of the parameters

A bilinear time series (BLTS) model is expressed in the form of Akaike's Markovian representation in order to use the Kalman recursive estimation approach. It is shown that Akaike's Markovian representation of autoregressive moving average models of orderp and q (ARMA(p,q)) and that of the bilinear model are equivalent. This equivalence facilitates the maximum likelihood estimation of the parameters involved in the bilinear model, which otherwise is an unwieldy problem. The present approach can easily be extended to take into account missing observations     

Experimental determination of the flexoelectric coefficients of some nematic liquid crystals

Abstract

We report measurements of the temperature variation of the flexoelectric coefficient (e ₁–e ₃) of a number of nematic liquid crystals like phenylcyclohexanes, cyanobiphenyls, etc. We have also measured (e ₁+e ₃) of a few systems using appropriate methods of applying an electric field gradient to the sample. In most of the systems, (e ₁–e ₃)/k, where k is a curvature elastic constant, is found to be positive and independent of temperature, as expected. However, in 4-heptyl-1-(4-cyanocyclohexyl)cyclohexane and a few other compounds with relatively flexible parts, |(e ₁–e ₃)/k| increases with temperature. We discuss the possible molecular origin of the sign and temperature dependence of the flexoelectric coefficients of the systems studied.     

A novel entry into a new class of spiroheterocyclic framework: regioselective synthesis of dispiro[oxindole-cyclohexanone]pyrrolidines and dispiro[oxindole-hexahydroindazole]pyrrolidines

2,6-Bis(arylmethylidene)cyclohexanones undergo a regioselective 1,3-dipolar cycloaddition reaction with the azomethine ylide derived from isatin and sarcosine by a decarboxylative route affording a series of 1-N-methyl-spiro[2.3¹]oxindole-spiro[3.2¹¹]6¹¹-arylmethylidenecyclohexanone-4-aryl-pyrrolidines which were further annulated to give a series of novel 1-N-methyl-spiro[2.3¹]oxindole-spiro[3.7¹¹](3¹¹-aryl)Δ^111,711a-hexahydro-2H-indazole-4-aryl-pyrrolidines. The structures of which were established by spectroscopic techniques as well as single crystal X-ray analysis.     

The Run-Off Condition for Rimming Flow of a Power-Law Fluid

The rimming flow of a power-law fluid in the inner surface of a horizontal rotating cylinder is investigated. Exploiting the fact that the liquid layer is thin, the simplest lubrication theory is applied. The generalized run-off condition for the steady-state flow of the power-law liquid is derived. In the bounds implied by this condition, film thickness admits a continuous solution. In the supercritical case when the mass of non-Newtonian liquid exceeds a certain value or the speed of rotation is less than an indicated limit, a discontinuous solution is possible and a hydraulic jump may occur in the steady-state regime. The location and height of the hydraulic jump for the power-law liquid is determined. Received 8 February 2001 and accepted 19 June 2001     

Application of empirical mode decomposition in the field of polymer physics

Noisy data has always been a problem to the experimental community. Effective removal of noise from data is important for better understanding and interpretation of experimental results. Over the years, several methods have evolved for filtering the noise present in the data. Fast Fourier transform (FFT) based filters are widely used because they provide precise information about the frequency content of the experimental data, which is used for filtering of noise. However, FFT assumes that the experimental data is stationary. This means that: (i) the deterministic part of the experimental data obtained from a system is at steady state without any transients and has frequency components which do not vary with respect to time and (ii) noise corrupting the experimental data is wide sense stationary, that is, mean and variance of the noise does not statistically vary with respect to time. Several approaches, for example, short time Fourier transform (STFT) and wavelet transform‐based filters, have been developed to handle transient data corrupted with nonstationary noise (mean and variance of noise varies with respect to time) data. Both these approaches provide time and frequency information about the data (time at which a particular frequency is present in the signal). However, these filtering approaches have the following drawbacks: (i) STFT requires identification of an optimal window length within which the data is stationary, which is difficult and (ii) there are theoretical limits on simultaneous time and frequency resolution. Hence, filtering of noise is compromised. Recently, empirical mode decomposition (EMD) has been used in several applications to decompose a given nonstationary data segment into several characteristic oscillatory components called intrinsic mode functions (IMFs). Fourier transform of these IMFs identifies the frequency content in the signal, which can be used for removal of noisy IMFs and reconstruction of the filtered signal. In this work, we propose an algorithm for effective filtering of noise using an EMD‐based FFT approach for applications in polymer physics. The advantages of the proposed approach are: (i) it uses the precise frequency information provided by the FFT and, therefore, efficiently filters a wide variety of noise and (ii) the EMD approach can effectively obtain IMFs from both nonstationary as well as nonlinear experimental data. The utility of the proposed approach is illustrated using an analytical model and also through two typical laboratory experiments in polymer physics wherein the material response is nonstationary; standard filtering approaches are often inappropriate in such cases. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Simultaneous quantitation of IC87114, roflumilast and its active metabolite roflumilast N‐oxide in plasma by LC‐MS/MS: application for a pharmacokinetic study

A sensitive and reliable high‐performance liquid chromatography–mass spectrometry (LC–MS/MS) was developed and validated for simultaneous quantification IC87114, roflumilast (RFM), and its active metabolite roflumilast N‐oxide (RFN) using tolbutamide as an internal standard. The analytes were extracted by using liquid–liquid extraction and separated on a reverse phase C₁₈ column (50 mm × 3 mm i.d., 4.6 µ) using methanol: 2 mM ammonium acetate buffer, pH 4.0 as mobile phase at a flow rate 1 mL/min in gradient mode. Selective reaction monitoring was performed using the transitions m/z 398.3 > 145.9, 403.1 >186.9, 419.1 > 187.0 and 271.1 > 155.0 to quantify quantification IC87114, RFM, RFN and tolbutamide, respectively. The method was validated over the concentration range of 0.1–60 ng.mL^?1 for RFM and RFN and 6 to 2980 ng.mL^?1 for IC87114. Intra‐ and inter‐day accuracy and precision of validated method were within the acceptable limits of <15% at all concentrations. Coefficients of correlation (r²) for the calibration curves were >0.99 for all analytes. The quantitation method was successfully applied for simultaneous estimation of IC87114, RFM and RFN in a pharmacokinetic drug–drug interaction study in Wistar rats. Copyright © 2012 John Wiley & Sons, Ltd.     

Homonuclear and heteronuclear NMR studies of a statherin fragment bound to hydroxyapatite crystals

Acidic proteins found in mineralized tissues act as nature's crystal engineers, where they play a key role in promoting or inhibiting the growth of minerals such as hydroxyapatite (HAP), Ca10(PO4)6(OH)2, the main mineral component of bone and teeth. Key to understanding the structural basis of protein-crystal recognition and protein control of hard tissue growth is the nature of interactions between the protein side chains and the crystal surface. In an earlier work we have measured the proximity of the lysine (K6) side chain in an SN-15 peptide fragment of the salivary protein statherin adsorbed to the Phosphorus-rich surface of HAP using solid-state NMR recoupling experiments. 15N{31P} rotational echo double resonance (REDOR) NMR data on the side-chain nitrogen in K6 gave rise to three different models of protein-surface interaction to explain the experimental data acquired. In this work we extend the analysis of the REDOR data by examining the contribution of interactions between surface phosphorus atoms to the observed 15N REDOR decay. We performed 31P-31P recoupling experiments in HAP and (NH4)2HPO4 (DHP) to explore the nature of dipolar coupled 31P spin networks. These studies indicate that extensive networks of dipolar coupled 31P spins can be represented as stronger effective dipolar couplings, the existence of which must be included in the analysis of REDOR data. We carried out 15N{31P} REDOR in the case of DHP to determine how the size of the dephasing spin network influences the interpretation of the REDOR data. Although use of an extended 31P coupled spin network simulates the REDOR data well, a simplified 31P dephasing system composed of two spins with a larger dipolar coupling also simulates the REDOR data and only perturbs the heteronuclear couplings very slightly. The 31P-31P dipolar couplings between phosphorus nuclei in HAP can be replaced by an effective dipolar interaction of 600 Hz between two 31P spins. We incorporated this coupling and applied the above approach to reanalyze the 15N{31P} REDOR of the lysine side chain approaching the HAP surface and have refined the binding models proposed earlier. We obtain 15N-31P distances between 3.3 and 5 A from these models that are indicative of the possibility of a lysine-phosphate hydrogen bond.     

Parameter estimation in metabolic flux balance models for batch fermentation—Formulation & Solution using Differential Variational Inequalities (DVIs)

Recent years have witnessed a surge in research in cellular biology. There has been particular interest in the interaction between cellular metabolism and its environment. In this work we present a framework for fitting fermentation models that include this interaction. Differential equations describe the evolution of extracellular metabolites, while a Linear Program (LP) models cell metabolism, and piecewise smooth functions model the links between cell metabolism and its environment. We show that the fermentation dynamics can be described using Differential Variational Inequalities (DVIs). Discretization of the system and reformulation of the VIs using optimality conditions converts the DVI to a Mathematical Program with Complementarity Constraints (MPCC). We briefly describe an interior point algorithm for solving MPCCs. Encouraging numerical results are presented in estimating model parameters to fit model prediction and data obtained from fermentation, using cultures of Saccharomyces cerevisiae reported in the literature.     

Phase transitions in novel disulphide-bridged alkoxycyanobiphenyl dimers

The synthesis, characterization and mesomorphic properties of the first examples of novel disulphide-bridged alkoxycyanobiphenyl dimers are reported. The thermal behaviour of these mesogens was investigated by polarizing optical microscopy, differential scanning calorimetry and X-ray diffractometry. The dimers with a shorter spacer exhibit only the nematic phase while dimers with a longer spacer display nematic as well as smectic phases. X-ray diffraction experiments reveal the intercalated structure of the SmA phase of these dimers and the presence of short range SmA-like order in the N phase (cybotactic nematic) of all the compounds, except the one with the shortest spacer.     

An expedient synthesis of pyrrolidinyl spirooxindole grafted 3-nitrochromanes through 1,3-dipolar cycloaddition reaction of azomethine ylides

A facile one-pot synthesis of pyrrolidinyl-spirooxindole grafted 3-nitrochromanes has been accomplished by 1,3-dipolar cycloaddition (1,3-DC) reaction of 3-nitrochromenes with azomethine ylides generated in situ from isatin and secondary amino acids. The regio- and stereochemical outcome of the cycloaddition reaction was ascertained by X-ray crystallographic analysis.