Generalization of the spherical harmonic method to radiative transfer in multi-dimensional space

The basic radiative transfer equation in three-dimensional space is expressed in terms of three commonly used coordinate systems, namely, Cartesian, cylindrical and spherical coordinates. The concept of a transformation matrix is applied to the transformation processes between the Cartesian system and two other systems. The spherical harmonic method is then applied to decompose the radiative transfer equation into a set of coupled partial differential equations for all three systems in terms of partial differential operators. By truncating the number of partial differential equations into four along with further mathematical analyses, we obtain a modified Helmholtz equation. For each coordinate system, analytical solutions in terms of infinite series are obtained whenever the equation is solvable by the technique of separation of variables with proper boundary conditions. Numerical computations are carried out for one dimensional radiative transfer to illustrate the applicability of the technique developed in the present study.     

Indium‐promoted Conversion of Allylic Bromide to Alcohol Moiety and Synthesis of Pipermethystine Skeletons

Dihydropyridone bromide ( 2 ) was converted to the corresponding alcohol ( 1 ) by reaction with indium in air or with indium followed by treatment with a sulfonyloxaziridine. The alcohol ( 1 ) was transformed in four steps to a phenylsulfone‐substituted pipermethystine derivative ( 10 ). Reductive cleavage of the phenylsulfone did not yield the pipermethystine natural product. Several new pyridone derivatives were synthesized.     

New Oxygenated Lignans from Kadsura philippinensis

Seven new oxygenated lignans, kadsuphilins G–M ( 1 – 7 , resp.), were isolated by chromatographic fractionation of an AcOEt extract of the aerial part of Kadsura philippinensis including four compounds with a dibenzocyclooctadiene skeleton, two with a bicyclooctane ring system, and one of 1,4‐biphenyldimethylbutane type. The structures of the isolated compounds were elucidated through extensive spectroscopic analyses, particularly 2D‐NMR experiments (HMQC, HMBC, and NOESY). The configuration of the chiral centers and the biphenyl moiety were determined by NOESY as well as CD spectroscopy, respectively.     

Simultaneous analysis of urinary 4,4'-methylenebis(2-chloroaniline) and N-acetyl 4,4'-methylenebis(2-chloroaniline) using solid-phase extraction and liquid chromatography/tandem mass spectrometry

Analysis of 4,4'-methylenebis(2-cholroaniline) (MOCA) or its metabolites in urine has been considered as the appropriate method to assess MOCA exposures through inhalation and skin absorption. MOCA and its metabolite, N-acetyl 4,4'-methylenebis(2-chloroaniline) (acetyl-MOCA), are analyzed using methods either limited by sensitivity or sample preparation. Therefore, a solid-phase extraction (SPE) and liquid chromatography/tandem mass spectrometry (LC/MS/MS) method was developed to simultaneously analyze MOCA and acetyl-MOCA in urine to serve as biomarkers for MOCA exposure. Protein was precipitated by using acetonitrile, and SPE were applied to clean up samples to eliminate the matrix effect and to improve the recovery. The limit of quantitation of this method was at 1.0 ng/mL for MOCA and 0.03 ng/mL for acetyl-MOCA (signal-to-noise (S/N) ratio = 10). Urinary MOCA and acetyl-MOCA levels in MOCA-exposed workers were analyzed and quantitated to be 191.9 +/- 373.2 (mean +/- standard deviation (SD)) and 11.79 +/- 23.8 ng/mL (N = 54) with the median values 38.6 and 1.8 ng/mL, respectively. MOCA concentrations are significantly correlated with their corresponding acetyl-MOCA levels in urine (Spearman correlation coefficient r = 0.916, p < 0.001). These results show that this method has been successfully developed and provides high-throughput potential to analyze MOCA and acetyl-MOCA to serve as exposure biomarkers for future study of the potential health effects associated with MOCA exposures.     

Seven New Lignan Esters from Kadsura philippinensis

Five new oxygenated lignans with a dibenzocyclooctadiene skeleton, kadsuphilols P–T ( 1 – 5 ), and two new C₁₉ homolignans, kadsuphilols U and V ( 6 and 7 ), were isolated by chromatographic fractionation of an AcOEt extract of the stems of Kadsura philippinensis. The structures of the isolated metabolites were elucidated through extensive spectroscopic analysis including HR‐ESI‐MS and 2D‐NMR (HMQC, COSY, and HMBC). The configuration at the chiral centers and at the biphenyl moiety were determined by interpretation of NOESY and CD data, respectively.     

Micro‐Raman spectroscopic study of cord‐marked pottery decorated with red coatings from Taiwan,ca 2600–1700 B.C.

Micro‐Raman spectroscopy is applied for the first time to identify mineralogical characteristics of ceramic bodies and red coatings on decorative cord‐marked pottery (ca 2600–1700 B.C.) from an archeological site in northern Taiwan. X‐ray diffraction and scanning electron microscopy‐energy dispersive X‐ray spectrometry were used as complementary techniques. The combined results of mineralogical and elemental composition suggest that the pottery items were produced from illitic clays and fired to a temperature less than 800 °C under oxidizing conditions. The slight discrepancy in composition between the red coatings and ceramic bodies possibly indicates a somewhat different source of raw materials and/or clay refining processes used by ancient potters. Additionally, feldspar, hornblende, and pyroxenes detected in the samples are closely related to the main compositions of nearby volcanic rocks, implying that the raw materials could have come from a local source. Copyright © 2010 John Wiley & Sons, Ltd.     

Moduli Spaces and Grassmannian

We calculate the homomorphism of the cohomology induced by the Krichever map of moduli spaces of curves into infinite-dimensional Grassmannian. This calculation can be used to compute the homology classes of cycles on moduli spaces of curves that are defined in terms of Weierstrass points.     

Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications

In this paper, we introduce a new iterative scheme for finding a common element of the set of common solutions of a finite family of equilibrium problems with relaxed monotone mappings, of the set of common solutions of a finite family of variational inequalities and of the set of common fixed points of an infinite family of nonexpansive mappings in a Hilbert space. Strong convergence for the proposed iterative scheme is proved. As an application, we solve a multi-objective optimization problem using the result of this paper. Our results improve and extend the corresponding ones announced by others.