Numerical stability study and error estimation for two implicit schemes in a moving boundary problem

Two algorithms are described [Ferris D. H. (fixed time‐step method) and Gupta and Kumar (variable time‐step method)] that solve a mathematical model for the study of the one‐dimensional moving boundary problem with implicit boundary conditions. Landau's transformation is used, in order to work with a fixed number of nodes at each time‐step. The p.d.e. is discretized using an implicit finite difference scheme. The mathematical model describes the oxygen diffusion in absorbing tissues. An important application is the estimation of time‐variant radiation treatments of cancerous tumors. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 42–61, 2000     

Über Umlagerungen bei der Cyclialkylierung von Arylpentanolen zu 2,3‐Dihydro‐1H‐inden‐Derivaten, 1. Mitteilung

On Rearrangements by Cyclialkylations of Arylpentanols to 2,3‐Dihydro‐1 H ‐indene Derivatives. Part 1. An Unexpected Rearrangement by the Acid‐Catalyzed Cyclialkylation of 4‐(2‐Chlorophenyl)‐2,4‐dimethyl pentan‐2‐ol under Formation of trans ‐4‐Chloro‐2,3‐dihydro‐1,1,2,3‐tetramethyl‐1 H ‐indene The acid‐catalyzed cyclialkylation of 2,4‐dimethyl‐4‐phenylpentan‐2‐ol led exclusively to the expected product, 2,3‐dihydro‐1,1,3,3‐tetramethyl‐1H‐indene. However, analogous cyclialkylation of 4‐(2‐chlorophenyl)‐2,4‐dimethylpentan‐2‐ol ( 1 ) gave a ca. 1 : 1 mixture of 4‐chloro‐2,3‐dihydro‐1,1,3,3‐tetramethyl‐1H‐indene ( 2 ) and of trans‐4‐chloro‐2,3‐dihydro‐1,1,2,3‐tetramethyl‐1H‐indene ( 3 ; Scheme 1). The specific action of the Cl substituent is investigated and a mechanism for this unexpected frame‐work transposition proposed.     

Über Umlagerungen bei der Cyclialkylierung von Arylpentanolen zu 2,3‐Dihydro‐1H‐inden‐Derivaten, 4. Mitteilung

On Rearrangements by Cyclialkylations of Arylpentanols to 2,3‐Dihydro‐1 H ‐indene Derivatives. Part 4. The Acid‐Catalyzed Cyclialkylation of 2,4‐Dimethyl‐2‐phenyl[3‐ ¹³ C]pentan‐3‐ol The cyclialkylation of 2,4‐dimethyl‐2‐phenyl[3‐¹³C]pentan‐3‐ol ( 4 ) gives only 2,3‐dihydro‐1,1,2,3‐tetramethyl‐1H‐[3‐¹³C]indene ( 6 ) (cf. Scheme 2) and not a trace of the isotopomeric 2,3‐dihydro‐1,1,2,3‐tetramethyl‐1H‐[2‐¹³C]indene ( 5 ). The mechanism proposed in [3] for the cyclialkylation of 4 (cf. Scheme 2, Path A) has, therefore, to be abandoned. The mechanism of Scheme 2, Path B, is proposed and may be considered as definitively established.     

A characteristic property of the Euclidean disc

In this paper the following is proved: Let K ⊂ $ \mathbb{E}^2 $ \mathbb{E}^2 be a smooth strictly convex body, and let L ⊂ $ \mathbb{E}^2 $ \mathbb{E}^2 be a line. Assume that for every point x ∈ L/K the two tangent segments from x to K have the same length, and the line joining the two contact points passes through a fixed point in the plane. Then K is an Euclidean disc.     

New Rh derivatives of s-indacene active in dehydrogenative silylation of styrene

The mono- and bimetallic complexes [(2,6-diethyl-4,8-dimethyl-s-indacenide){Rh(COD)}] (1), anti-[(2,6-diethyl-4,8-dimethyl-s-indacenediide){Rh(COD)}₂] (2a), syn-[(2,6-diethyl-4,8-dimethyl-s-indacenediide){Rh(COD)}₂] (2b) were synthesized and characterized spectroscopically and in the case of complex 2b, by means of X-ray diffraction. The ¹³C and ¹⁰³Rh NMR studies suggest that the bonding mode of the indacenediide ligand can be described as intermediate between η³- and η⁵-coordination. This result was confirmed by the crystal structure of 2b as evidenced by the slippage of the rhodium atom towards the periphery of the ligand. Cyclic voltammetry studies revealed a strong intermetallic communication through the fused ring ligand. This property was further illustrated by higher activity and selectivity of binuclear complexes 2 for the catalytic dehydrogenative silylation of styrene.     

Development of a selective chemical etch to improve the conversion efficiency of Zn-rich Cu2ZnSnS4 solar cells

Improvement of the efficiency of Cu(2)ZnSnS(4) (CZTS)-based solar cells requires the development of specific procedures to remove or avoid the formation of detrimental secondary phases. The presence of these phases is favored by the Zn-rich and Cu-poor conditions that are required to obtain device-grade layers. We have developed a selective chemical etching process based on the use of hydrochloric acid solutions to remove Zn-rich secondary phases from the CZTS film surface, which are partly responsible for the deterioration of the series resistance of the cells and, as a consequence, the conversion efficiency. Using this approach, we have obtained CZTS-based devices with 5.2% efficiency, which is nearly twice that of the devices we have prepared without this etching process.     

Liquid chromatographic/electrospray ionization tandem mass spectrometric study of polyphenolic composition of four cultivars of Fragaria vesca L. berries and their comparative evaluation

High-performance liquid chromatography coupled with ion spray mass spectrometry in the tandem mode with both negative and positive ionization was used for investigating a variety of polyphenolic compounds in four genotypes of Fragaria vesca berries. About 60 phenolic compounds belonging to the compound classes of phenolic acids, ellagitannins, ellagic acid derivatives, flavonols, monomeric and oligomeric flavanols, dihydrochalcones and anthocyanins were reported, providing for the first time a quite complete picture of polyphenolic composition of F. vesca berries. Some of the polyphenols herein investigated, such as a tris-galloyl-hexahydroxydiphenoyl-hexose, two castalagin/vescalagin-like isomers and peonidin-malonylglucoside, were described for the first time. Principal component analysis applied on original HPLC-MS/MS data, acquired in multiple reaction monitoring mode, successfully discriminated the four investigated cultivars on the basis of their polyphenolic composition, highlighting the fundamental role of mass spectrometry for food characterization. Copyright ? 2012 John Wiley & Sons, Ltd.     

Theoretical study of the conformational energy hypersurface of cyclotrisarcosyl

The multidimensional Conformational Potential Energy Hypersurface (PEHS) of cyclotrisarcosyl was comprehensively investigated at the DFT (B3LYP/6-31G(d), B3LYP/6-31G(d,p) and B3LYP/6-311++G(d,p)), levels of theory. The equilibrium structures, their relative stability, and the Transition State (TS) structures involved in the conformational interconversion pathways were analyzed. Aug-cc-pVTZ//B3LYP/6-311++G(d,p) and MP2/6-31G(d)//B3LYP/6-311++G(d,p) single point calculations predict a symmetric cis-cis-cis crown conformation as the energetically preferred form for this compound, which is in agreement with the experimental data. The conformational interconversion between the global minimum and the twist form requires 20.88 kcal mol-1 at the MP2/6-31G(d)//B3LYP/6-311++G(d,p) level of theory. Our results allow us to form a concise idea about the internal intricacies of the PEHSs of this cyclic tripeptide, describing the conformations as well as the conformational interconversion processes in this hypersurface. In addition, a comparative analysis between the conformational behaviors of cyclotrisarcosyl with that previously reported for cyclotriglycine was carried out     

Multistep conformational interconversion mechanism of cyclododecane. A simple and fast analysis using potential energy curves

An ab initio and Density Functional Theory (DFT) study of the conformational properties of cyclododecane was carried out. The energetically preferred equilibrium structures, their relative stability, and some of the transition state (TS) structures involved in the conformational interconversion pathways were analyzed from RHF/6‐31G(d), B3LYP/6‐31G(d,p) and B3LYP/6311++G(d,p) calculations. Aug‐cc‐pVDZ//B3LYP/6311++G(d,p) single point calculations predict that the multistep conformational interconversion mechanism requires 11.07 kcal/mol, which is in agreement with the available experimental data. These results allow us to form a concise idea about the internal intricacies of the preferred forms of cyclododecane, describing the conformations as well as the conformational interconversion processes in the conformational potential energy hypersurface. Our results indicated that performing an exhaustive analysis of the potential energy curves connecting the most representative conformations is a valid alternate tool to determine the principal conformational interconversion paths for cyclododecane. This methodology represents a satisfactory first approximation for the conformational analysis of medium‐ and large‐size flexible cyclic compounds. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012