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.     

A Novel Coherent Multilevel Combined Phase and Polarization Shift Keying Modulation in Twisted Fibers

This article proposes a novel coherent multilevel modulation model that exploits polarization and phase of the field. This model is based on the possibility of coherent systems to use all the four degrees of freedom of the electromagnetic field. The proposed scheme is able, by applying a suitable twisting process to the optical fiber, to physically confine the polarization and the phase of the transmitted field within the phase sphere. In this way, with the same performances of existing systems, the receiver is considerably simplified because there is no longer need of birefringence tracking circuits.     

Symmetry Groups and Non-Planar Collisionless Action-Minimizing Solutions of the Three-Body Problem in Three-Dimensional Space

Periodic and quasi-periodic solutions of the n-body problem can be found as minimizers of the Lagrangian action functional restricted to suitable spaces of symmetric paths. The main purpose of this paper is to develop a systematic approach to the equivariant minimization for the three-body problem in three-dimensional space. First we give a finite complete list of symmetry groups fitting to the minimization of the action, with the property that any other symmetry group can be reduced to be isomorphic to one of these representatives. A second step is to prove that the resulting (local and global) symmetric action-minimizers are always collisionless (when they are not already bound to collisions). Furthermore, we prove some results which address the question of whether minimizers are planar or non-planar; as a consequence of our theory we will give general criteria for a symmetry group to yield planar or homographic minimizers (either homographic or not, as in the Chenciner-Montgomery eight solution). On the other hand we will provide a rigorous proof of the existence of some interesting one-parameter families of periodic and quasi-periodic non-planar orbits. These include the choreographic Marchal's P₁₂ family with equal masses – together with a less-symmetric choreographic family (which anyway probably coincides with the P₁₂ family).