Incorporating engineering intuition for parameter estimation in thermal sciences

This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient (h _θ ) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ _(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of h _θ , first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of h _θ . The estimate of h _θ is then used as an informative prior for solving the inverse problem of determining h _θ and α from θ _(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ _(x,t) is generated using liquid crystal thermography and these data are used to estimate h _θ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of (h _θ , α) to solve the governing equation to the problem is also done.     

Approximating stationary points of stochastic optimization problems in Banach space

In this paper, we present a uniform strong law of large numbers for random set-valued mappings in separable Banach space and apply it to analyze the sample average approximation of Clarke stationary points of a nonsmooth one stage stochastic minimization problem in separable Banach space. Moreover, under Hausdorff continuity, we show that with probability approaching one exponentially fast with the increase of sample size, the sample average of a convex compact set-valued mapping converges to its expected value uniformly. The result is used to establish exponential convergence of stationary sequence under some metric regularity conditions.     

First total synthesis of achaetolide

The first total synthesis of achaetolide, a 10-membered macrolactone was achieved using Mitsunobu reaction and Grubbs ring-closing metathesis reaction as the key steps for ring construction. The desired stereo centres were generated by Jacobsen hydrolytic kinetic resolution, dihydroxylation and Sharpless asymmetric epoxidation reactions.     

On Gaussian HJM framework for Eurodollar Futures

One of the standard tools for the theoretical analysis of fixed income securities and their associated derivatives is the term structure model of Heath, Jarrow and Morton. In this paper the question, what specific HJM model is consistent with the observed price of an Eurodollar Futures contract? is discussed. Eurodollar Futures, apart from being the most heavily traded futures are connected to London Inter Bank Offered Rate (LIBOR) and to domestic monetary conditions. The answer to the above question will help in pricing any new derivative on Eurodollar Futures or the one that is not heavily traded. A simple tool to measure the adequacy of different HJM structures that may be used to model Eurodollar Futures price process is suggested. Moreover, the question of estimation of parameters of these models by different methods—method of realized volatility, method of maximum likelihood (ML) and a two‐stage method that combines both the realized volatility and ML—is addressed. Although it sounds like a typical statistical procedure, one must be careful in applying standard statistical techniques that are not suitable under arbitrage theory, in particular, ML method. Copyright © 2010 John Wiley & Sons, Ltd.     

Photoluminescence Spectra of Eu3+-Doped Certain Powder Phosphors

The fluorescence properties of Eu³⁺-doped CaS, LaOCl, LaOF, YOCl and YOF powder phosphors are reported. These phosphors exhibited a reddish orange colour when excited in the UV. The photoluminescence spectra have been characterized by determining their stimulated emission cross-section values.     

A Stability-Indicating LC Method for Assay of Topotecan Hydrochloride

This paper describes the development of a stability-indicating high-performance liquid chromatographic (HPLC) method for quantitative determination of topotecan hydrochloride, a semi-synthetic derivative of camptothecin and anti-tumor drug with topoisomerase I-inhibitory activity. Chromatographic separation was achieved on a C₁₈ column with a mixture of phosphate buffer and acetonitrile as mobile phase. The method was validated for linearity, accuracy, precision, and robustness. Forced degradation studies were performed by treating bulk samples of topotecan hydrochloride with acid (0.5 M hydrochloric acid), base (0.5 M sodium hydroxide), oxidizing agent (10% v/v hydrogen peroxide), heat (60 °C), and UV light (254 nm).     

An efficient synthesis of β-aminoketone compounds through three-component Mannich reaction catalyzed by calcium chloride

Abstract  

Various β-aminoketones were synthesized in a three-component reaction of ketones, aldehydes, and amines in the presence of calcium chloride as catalyst in ethanol in high yields as compared to other synthetic methods. The advantages of this new method are a short reaction time (2 h), high yields, easy workup, convenience, low cost, and eco-friendly protocol.     

Synthesis and properties of thienopyrrole based heteroacenes--indolodibenzothienopyrrole and dicarbazolodithienopyrrole

We report the syntheses and properties of thienopyrrole based unsymmetrical and extended heteroacenes, which are isoelectronic with heptacene (30π) and nonacene (38π), respectively. Optical and electrochemical properties of these seven and nine rings fused systems are studied. The optoelectronic properties of the syn and anti-isomers of the unsymmetrical heteroacenes are also compared. The influence of the position of the heteroatoms in the fused corona, upon the optical and electrochemical properties, is rationalized based on the contributions from the benzenoid vs. quinonoid-type structures of these molecules.     

Photophysical properties of hydroxylated amphiphilic poly(p-phenylene)s

A homologous series of polyhydroxylated poly(p-phenylene)s with different alkoxy groups (C6PPPOH, C12PPPOH, and C18PPPOH) were synthesized with use of the Suzuki polycondensation reaction. Comparative studies of the structure correlation between their photophysical properties and film morphology is described. The absorption and emission spectra of polymers in solution and thin films showed similar features indicating that the electronic properties in solution were retained in the film state. Compared to the polymer with the short alkoxy chains (C6PPPOH), the polymers with long alkoxy groups (C12PPPOH and C18PPPOH) showed improved film forming properties with continuous and smooth film morphology. The absorption properties of the C12PPPOH showed an enhanced effective conjugation length and high quantum yield implying planarization of the backbone through alkoxy chain packing (C12H25O-) and potential hydrogen bonds. No overlap in the absorption and emission spectra was observed, which indicated minimized excimer formation or excitation energy transfer in the films. Time-resolved fluorescence measurements showed that the decay times increased from 43 ps (C6PPPOH) to 78 ps (C12PPPOH) and 99 ps (C18PPPOH). Electrochemical studies were performed for all polymers and the observed oxidation potential for C6PPPOH was higher than that of C12PPPOH and C18PPPOH. In addition, the C12PPPOH has the lowest band gap of DeltaE = 2.59 eV when compared to the 3.1 (C6PPPOH) and 2.61 eV (C18PPPOH) gaps. The optical band gaps estimated from the absorption onset of the polymers are significantly higher than those obtained from electrochemical data. C12PPPOH was chosen for investigating the charge carrier mobility by the time-of-flight (TOF) technique. The observed results also showed negative field dependent values of the drift mobility for the polymer C12PPPOH.     

Interfacial adhesion mechanisms in incompatible semicrystalline polymer systems

The mechanism of adhesion at semicrystalline polymer interfaces between isotactic polypropylene (iPP) and linear low‐density polyethylene (PE) was studied with transmission electron microscopy (TEM) and an asymmetric‐double‐cantilever‐beam test. From the TEM images, both the interfacial width and the lamellar thickness of the polymers were extracted. During annealing, the interfacial width increased with the annealing temperature, and this indicated the accumulation of amorphous polymers at the interface. The interfacial strength, determined from the critical fracture energy (G_c), also increased with the annealing temperature and reached a maximum above the melting temperatures of iPP and PE, whereas the smallest G_c value was obtained below the melting temperatures of the two materials. A mechanism of interfacial strengthening was proposed accounting for the competition between the interdiffusion of PE and crystallization of iPP. As the annealing temperature increased, the rates of PE diffusion and iPP crystallization increased. Although the crystallization of iPP hindered the interdiffusion of PE, both the interfacial width and the fracture energy increased with the temperature, and this indicated that PE interdiffusion dominated iPP crystallization. Below the critical temperature, the fracture surfaces of both iPP and PE were smooth, and chain pullout dominated the fracture mechanism. Above the critical temperature, iPP crystallization still hindered the interdiffusion, and crazes could be seen on the iPP side. Above the melting temperatures of the two materials, ruptured surfaces could also be seen on the PE side, and crazing was the fracture mechanism. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2667–2679, 2004