A general framework for the construction of piecewise-polynomial local interpolants of minimum degree

In this paper we consider the problem of designing piecewise polynomial local interpolants of non-uniformly spaced data. We provide a constructive approach that, for any assigned degree of polynomial reproduction, continuity order, and support width, allows for generating the fundamental spline functions of minimum degree having the desired properties. Finally, the proposed construction is extended to handle open sets of data and to the case of multiple knots.     

Harnack’s inequality for a class of non-divergent equations in the Heisenberg group

We prove an invariant Harnack’s inequality for operators in non-divergence form structured on Heisenberg vector fields when the coe?cient matrix is uniformly positive definite, continuous, and symplectic. The method consists in constructing appropriate barriers to obtain pointwise-to-measure estimates for supersolutions in small balls, and then invoking the axiomatic approach developed by Di Fazio, Gutiérrez, and Lanconelli to obtain Harnack’s inequality.     

A certain critical density property for invariant Harnack inequalities in H-type groups

We consider second order linear degenerate elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Gutiérrez and Tournier (2011) for the Heisenberg group, we prove a critical density estimate by assuming a condition of Cordes–Landis type. We then deduce an invariant Harnack inequality for the non-negative solutions from a result by Di Fazio, Gutiérrez, and Lanconelli (2008).     

Synthesis of Indenes via Graphene Oxide Mediated Manipulation of Morita-Baylis-Hillman Alcohols

A new metal-free synthetic approach to functionalized indenes is documented. The use of commercially available graphene oxide (GO) allowed the direct access to indenyl cores (yield up to 80 %) via intramolecular Friedel-Crafts-type allylic alkylations with readily available Morita-Baylis-Hillman alcohols. Combined experimental and spectroscopic investigations contributed to shed light on the reaction mechanism dealing with a nanostructured carbon material-based C−C bond forming reaction.     

Controlling the Assembly of Cellulose-Based Oligosaccharides through Sequence Modifications

Peptides and nucleic acids with programmable sequences are widely explored for the production of tunable, self-assembling functional materials. Herein we demonstrate that the primary sequence of oligosaccharides can be designed to access materials with tunable shapes and properties. Synthetic cellulose-based oligomers were assembled into 2D or 3D rod-like crystallites. Sequence modifications within the oligosaccharide core influenced the molecular packing and led to the formation of square-like assemblies based on the rare cellulose IV_II allomorph. In contrast, modifications at the termini generated elongated aggregates with tunable surfaces, resulting in self-healing supramolecular hydrogels.     

Optical sensing in microfluidic lab-on-a-chip by femtosecond-laser-written waveguides

We use direct femtosecond laser writing to integrate optical waveguides into a commercial fused silica capillary electrophoresis chip. High-quality waveguides crossing the microfluidic channels are fabricated and used to optically address, with high spatial selectivity, their content. Fluorescence from the optically excited volume is efficiently collected at a 90° angle by a high numerical aperture fiber, resulting in a highly compact and portable device. To test the platform we performed electrophoresis and detection of a 23-mer oligonucleotide plug. Our approach is quite powerful because it allows the integration of photonic functionalities, by simple post-processing, into commercial LOCs fabricated with standard techniques. Figure Femtosecond laser written waveguides can selectively excite fluorescence in a microfluidic channel of a commercial lab-on-a-chip. A compact scheme for on-chip detection by laser induced fluorescence is applied to capillary electrophoresis of a 23-mer Cy3-labeled oligonucleotide     

The coevolution theory of the origin of the genetic code

A review of the coevolution theory of the origin of the genetic code is presented. This theory maintains that the origin of the code should be sought in the biosynthetic relationships between amino acids. In particular, some amino acids, the precursors, occupied the structure of the genetic code early on. As the product amino acids developed from these precursors, part or all of the codon domain of the precursor amino acid was ceded to the product amino acids, which resulted in the structuring of the genetic code. This paper therefore reviews the evidence in favour of this theory. The existence of some molecular fossils representing the biosynthetic pathways on which the coevolution theory suggests biosynthetic transformations took place (precursor amino acid → product amino acid) seems to be a strong corroboration of this theory. A generalisation imposed by this theory on the ancestral metabolic state is then discussed and, finally, the main prospects that seem to stem from the coevolution theory are presented.     

Inter-method comparison for the determination of antimony and arsenic in peat samples

Four analytical approaches, based on different physical principles, for the determination of antimony (Sb) and arsenic (As) in ancient peat samples were critically evaluated: (a) open vessel digestion/hydride generation-atomic absorption spectrometry (HG-AAS), (b) closed-pressurized digestion in a microwave oven followed by sector field-inductively coupled plasma-mass spectrometry (SF-ICP-MS), (c) digestion in a microwave autoclave and subsequent quadrupole-inductively coupled plasma-mass spectrometry (Q-ICP-MS) measurements and (d) instrumental neutron activation analysis (INAA). The quality control scheme applied, always included the use of adequate plant reference materials to ensure the accuracy and precision of the analytical procedures. Additionally, two internal peat reference materials were analyzed using all four analytical approaches, generally showing good agreement for both elements. Method detection limits for As and Sb provided by all procedures were approximately 5 and 2 ng g⁻¹ which is sufficiently low for the reliable quantification of both elements in ancient, pre-anthropogenic peat samples. A comparison of As and Sb concentrations in a set of peat samples determined by INAA, HG-AAS and SF-ICP-MS revealed that INAA underestimated the values in a systematic manner, whereas HG-AAS and SF-ICP-MS data agreed very well. Best precision of the results was obtained by analytical procedures involving HG-AAS or Q-ICP-MS and varied from 3.6 to 4.3% and 7.1 to 7.5% for As (at about 0.5 μg g⁻¹) and Sb (at about 0.1 μg g⁻¹), respectively. The highest sample throughput (40 samples per run accomplished in 2 h) combined with low risk of sample contamination could be realized in the high-pressure microwave autoclave. The amount of sample required by all approaches was 200 mg, except for INAA which needed at least 25 times more sample mass to achieve comparable detection limits. For the quantification of As and Sb, inductively coupled plasma-mass spectrometry (ICP-MS) was preferred over INAA and HG-AAS, mainly because (a) less sample is needed and (b) As and Sb can be determined simultaneously. In addition, ICP-MS offers the possibility to measure concurrently a wide range of other elements which also are of environmental interest.