On the fractional counterpart of the higher-order equations

In this work, we study the solutions of some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be expressed by means of the transition laws of stable subordinators and their inverse processes. In particular, we establish connections between fractional and higher-order equations.     

Interrelations between charging, structure and electrokinetics of nanometric polyelectrolyte films

Streaming current, surface conductivity and swelling data of poly(acrylic acid) (PAA) and poly(ethylene imine) (PEI) thin films are analyzed on the basis of the theory for diffuse soft interfaces (J.F.L. Duval, R. Zimmermann, A. L. Cordeiro, N. Rein, C. Werner, Langmuir 25 (2009) 10691). Focus is put on ways to unravel the electroosmotic and migration contributions of the measured surface conductivity, which is crucial for appropriate electrokinetic analysis of films carrying high densities of dissociable groups. Results demonstrate that the osmotically-driven swelling of the PAA films with increasing pH is accompanied by an increase in diffuseness for the interphasial polymer segment density distribution. This heterogeneity is particularly marked at low ionic strength with a non-monotonous dependence of the streaming current on pH and the presence of a maximum at pH～6.5. The analysis of the PEI films evidences heterogeneous swelling with lowering pH, i.e. upon protonation of the amine groups. The characteristic decay length in the interphasial PEI segment density distribution is found to be nearly independent of the pH, which is in line with the moderate swelling determined by ellipsometry. A critical discussion is given on the strengths and limitations of electrokinetics/surface conductivity for quantifying the coupled electrohydrodynamic and structural properties of moderately to highly swollen polyelectrolyte thin films.     

LC-MS based quantification of 2'-ribosylated nucleosides Ar(p) and Gr(p) in tRNA

RNA nucleosides are often naturally modified into complex non-canonical structures with key biological functions. Here we report LC-MS quantification of the Ar(p) and Gr(p) 2'-ribosylated nucleosides in tRNA using deuterium labelled standards, and the first detection of Gr(p) in complex fungi.     

Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions

Summary. We prove convergence of a class of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions. The result is applied to the discontinuous Galerkin method due to Cockburn, Hou and Shu. Received April 15, 1993 / Revised version received March 13, 1995     

Structural elucidation of new ferulic acid-containing phenolic dimers and trimers isolated from maize bran

Four new phenolic dimers and trimers that contain ferulic acid moieties were isolated from the alkaline hydrolyzate of insoluble maize bran fiber and their structures were established by 1D/2D NMR and mass spectrometry. The biological role of one dimer remains unclear whereas the dimeric vanillin-ferulic acid-cross-product probably represents an oxidative degradation product from the corresponding diferulate. Both ferulic acid dehydrotrimers are able to cross-link polysaccharide chains. However, the 5-5/8-O-4(H₂O)-triferulic acid may be a cross-link in its identified structure whereas we assume that the identified 8-O-4/8-5(non-cyclic)-triferulic acid arose from a natural 8-O-4/8-5(cyclic)-triferulate analog during the saponification process.     

Combining different theoretical perspectives for analyzing students’ difficulties in vector spaces theory

This paper originates from our doctorate research project, in which we investigated graduate and undergraduate students’ errors and difficulties in vector space theory (VST). After a brief account of the whole study, we will focus on the analyses carried out through the lenses of two different theoretical frameworks: Fischbein’s Theory of Tacit Models and Sfard’s process/object duality theory. We also propose a retrospective reflection concerning the reasons why we chose to carry out our analysis according to more than one theoretical framework and why we chose those specific theoretical frameworks as well. Hence this contribution has a double focus: on the one hand it reports on the results drawn from our study on students’ difficulties in VST; on the other hand it presents a personal retrospective reflection on the use of theoretical frames within that study.     

Microwave spectrum of 18O14NF in excited vibrational states: Equilibrium structure of nitrosyl fluoride

The rotational spectra of ¹⁸O¹⁴NF were observed in the vibrationally excited ν₁, ν₂, and ν₃ states. The equilibrium structure of nitrosyl fluoride was determined using the equilibrium rotational constants of the two isotopic species, ¹⁶O¹⁴NF and ¹⁸O¹⁴NF. The newly determined spectroscopic parameters of ¹⁸O¹⁴NF were used to refine the quadratic and cubic force fields of nitrosyl fluoride.     

In situ study of the thermoresponsive behavior of micropatterned hydrogel films by imaging ellipsometry

A patterned hydrogel was immobilized on a polymer substrate by low-pressure argon plasma treatment using a masking technique. The polymer sample showed a thermoresponsive aggregation behavior in the region of 35-37 degrees C. The micropatterned, thermoresponsive hydrogel film has been characterized with imaging ellipsometry. The characterization was carried out on the dry film as well as on a swollen sample in water. The thermoresponsive behavior was studied in deionized water by temperature-dependent measurements in a solid-liquid cell. Through imaging ellipsometry, it was possible to distinguish the different regions of interest on a micrometer scale and to follow the swelling of the hydrogel part as a function of the temperature. It was possible to visualize the swelling as 3D profiles of Delta at various temperatures. Long-term changes of the sample could also be detected, which cannot be picked up by conventional ellipsometry.