Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

Acylglycerols (=Glycerides) from the Glandular Trichome Exudate on the Leaves of Paulownia tomentosa

Chemical investigations of the glandular trichome exudates on the leaves of Paulownia tomentosa (Scrophulariaceae) led to the identification of the thirty acylglycerols (=glycerides) 1 – 30 , including five known ones ( 2, 3, 6, 9 , and 15 ) (Fig. 1). Spectroscopic analysis combined with GC/MS studies of the glycerides and the liberated fatty acids, in the form of trimethylsilyl ether derivatives and trimethylsilylated methyl esters, respectively, established that the constituents belonged to 1,3‐di‐O‐acetyl‐2‐O‐(fatty acyl)glycerols, 1‐O‐acetyl‐2‐O‐(fatty acyl)‐sn‐glycerols, and 2‐O‐(fatty acyl)glycerols, wherein the fatty acyl moiety was either an eicosanoyl or an octadecanoyl group bearing OH and/or AcO groups at the 3‐, 3,6‐, 3,7‐, 3,8‐, or 3,9‐positions. The 1‐O‐acetyl‐2‐O‐[(3R,6S)‐3‐(acetyloxy)‐6‐hydroxyeicosanoyl]‐sn‐glycerol ( 12 ; 20% of the total glycerides), 2‐O‐[(3R,8R)‐3,8‐bis(acetyloxy)eicosanoyl]glycerol ( 17 ; 14%), 2‐O‐[(3R,9R)‐3,9‐bis(acetyloxy)eicosanoyl]glycerol ( 18 ; 12%), and 2‐O‐[(3R)‐3‐(acetyloxy)eicosanoyl]glycerol ( 10 ; 12%) were relatively abundant constituents. The configurations of the stereogenic centers of the fatty acyl moieties were determined by ¹H‐NMR analysis of the monoesters obtained from (R)‐ and (S)‐2‐(naphthalen‐2‐yl)‐2‐methoxyacetic acid ((R)‐ and (S)‐2NMA? OH and the hydroxy‐substituted fatty acid methyl esters (Fig. 2). The configuration at C(2) of the glycerol moiety of the 1‐O‐acetyl‐2‐O‐(fatty acyl)glycerols was determined to be (2S) by chemical conversion of, e.g., G‐2 (= 2 / 3 1 : 10) to (+)‐3‐O‐[tert‐butyl)diphenylsilyl]‐sn glycerol of known absolute configuration.     

Chemical and Genetic Study of Ligularia cyathiceps in Yunnan Province of China

Root chemicals and evolutionarily neutral DNA regions in L. cyathiceps samples collected in the Zhongdian (Shangrila) County of Yunnan, P. R. China, were examined. Twenty compounds were isolated, including three new ones, 1β,10β‐epoxy‐6β‐(propionyloxy)furanoeremophilan‐9‐one ( 6 ), 1β,10β‐epoxy‐8α‐ethoxyeremophila‐6,11‐diene ( 14 ), and 11αH‐6β‐isobutyryloxy‐1β,10β,7β,8β‐diepoxyeremophilan‐12,8α‐olide ( 15 ). The chemical diversity was found to be limited, with cacalol ( 1 ) and 6‐(acyloxy)furanoeremophilan‐9‐ones ( 4 and/or 5 ) being major components in all the samples. The nuclear ribosomal RNA gene was also found to harbor little variation, although two distinct sequence types were found for the plastid atpB‐rbcL intergenic region.     

Total Synthesis of the Antibiotic Kendomycin: A Macrocyclization Using the Tsuji–Trost Etherification

A highly stereocontrolled, convergent total synthesis of kendomycin [(?)‐TAN2162], an ansa‐macrocyclic antibiotic, is reported. The key of the strategy is an unprecedented Tsuji–Trost macrocyclic etherification, followed by a transannular Claisen rearrangement to construct the 18‐membered carbocyclic framework. The oxa‐six‐ and five‐membered rings were also stereoselectively constructed respectively by a cascade oxidative cyclization at an unfunctionalized benzylic position and using a one‐pot epoxidation/5‐exo‐tet epoxide opening.     

Comparison of accuracy of intravoxel incoherent motion and apparent diffusion coefficient techniques for predicting malignancy of head and neck tumors using half-Fourier single-shot turbo spin-echo diffusion-weighted imaging

Purpose

To evaluate the use of the intravoxel incoherent motion (IVIM) technique in half-Fourier single-shot turbo spin-echo (HASTE) diffusion-weighted imaging (DWI), and to compare its accuracy to that of apparent diffusion coefficient (ADC) to predict malignancy in head and neck tumors.

Patients and methods

HASTE DW images of 33 patients with head and neck tumors (10 benign and 23 malignant) were evaluated. Using the IVIM technique, parameters (D, true diffusion coefficient; f, perfusion fraction; D*, pseudodiffusion coefficient) were calculated for each tumor. ADC values were measured over a range of b values from 0 to 1000 s/mm². IVIM parameters and ADC values in benign and malignant tumors were compared using Student's t test, receiver operating characteristics (ROC) analysis, and multivariate logistic regression modeling.

Results

Mean ADC and D values of malignant tumors were significantly lower than those of benign tumors (P < 0.05). Mean D* values of malignant tumors were significantly higher than those of benign tumors (P < 0.05). There was no significant difference in mean f values between malignant and benign tumors (P > 0.05). The technique of combining D and D* was the best for predicting malignancy; accuracy for this model was higher than that for ADC.

Conclusions

The IVIM technique may be applied in HASTE DWI as a diagnostic tool to predict malignancy in head and neck masses. The use of D and D* in combination increases the diagnostic accuracy in comparison with ADC.     

Real-time monitoring of monochlorinated benzene and polychlorinated biphenyls in the gas phase with on-line detection: High chemical selectivity of resonance-enhanced two-photon ionization.

The development of molecular spectroscopy has enabled us to select chlorinated aromatic hydrocarbons very rapidly. In particular, the laser ionization TOFMS (time-of-flight mass spectrometry) method is expected to be useful as an on-line, selective, and sensitive method. In the present work, real-time laser ionization TOFMS measurements were carried out on gaseous chlorinated aromatic hydrocarbons. The laser ionization method used resonance-enhanced two-photon ionization with the direct introduction of gas into the vacuum chamber. This method for analyzing aromatic hydrocarbons was developed using a pulsed supersonic molecular beam method. In the context of developing a highly selective and sensitive method, excitation of monochlorinated benzene at lambda = 263.07 nm was found to be effective in the wavelength region from 263 nm to 265 nm. Also the excitation of polychlorinated biphenyls at lambda = 266 nm was found to be substantially more effective than at lambda = 280, 300 or 320 nm. The achievable sensitivity for real-time (1 min) measurements using the laser ionization TOFMS technique was found to be in the ppbV range.