Family of counterexamples to King's conjecture

In this short Note we present an infinite family of arbitrary high dimensional counterexamples to the King's conjecture.     

Birkhoff normalization, bifurcations of Hamiltonian systems and the Deprits formula

We consider Hamiltonian autonomous systems with n degrees of freedom near a singular point. In the case of absence of resonances of order less than or equal to 4 we present a direct computation of the Birkhoff normal form. In the case of two degrees of freedom, we study 1–parameter deformations of the 0 : 1, 1 : 1 and 2 : 1 resonant singularities. The obtained results are used in a direct derivation of the Deprits formula for the isoenergetic degeneracy determinant in the restricted three–body problem.     

Electrochemical Dissolution of Silver Nanoparticles and Its Application in Metalloimmunoassay

This work demonstrates the use of silver nanoparticles as a simple electrochemical biolabel to induce 10⁶ signal enhancement. We propose a mechanism of measuring the silver nanoparticles on a specific screen‐printed planar carbon electrode, without the requirement for the harsh oxidant or toxic reagents described in prior‐art for gold sol methods. The possible measurement process was validated with orthogonal techniques such as UV/Vis spectroscopy, dynamic light scattering and by anodic stripping voltammetry (ASV). The findings were utilized to develop a novel electrochemical sandwich immunoassay where the analyte concentration is directly proportional to ASV oxidation peak of silver. This technique in the future is envisaged to form the foundation of a generic Point of Care platform. The assay was applied to cardiac marker: myoglobin with detection limit of 3 ng/mL.     

Triazole bridges as versatile linkers in electron donor-acceptor conjugates

Aromatic triazoles have been frequently used as π-conjugated linkers in intramolecular electron transfer processes. To gain a deeper understanding of the electron-mediating function of triazoles, we have synthesized a family of new triazole-based electron donor-acceptor conjugates. We have connected zinc(II)porphyrins and fullerenes through a central triazole moiety--(ZnP-Tri-C(60))--each with a single change in their connection through the linker. An extensive photophysical and computational investigation reveals that the electron transfer dynamics--charge separation and charge recombination--in the different ZnP-Tri-C(60) conjugates reflect a significant influence of the connectivity at the triazole linker. Except for the m4m-ZnP-Tri-C(60)17, the conjugates exhibit through-bond photoinduced electron transfer with varying rate constants. Since the through-bond distance is nearly the same for all the synthesized ZnP-Tri-C(60) conjugates, the variation in charge separation and charge recombination dynamics is mainly associated with the electronic properties of the conjugates, including orbital energies, electron affinity, and the energies of the excited states. The changes of the electronic couplings are, in turn, a consequence of the different connectivity patterns at the triazole moieties.     

An integrated experimental and analytical approach to the chemical state imaging of iron in brain gliomas using X-ray absorption near edge structure spectroscopy

X-ray absorption near-edge structure spectroscopy is used for human neoplastic tissues in order to investigate distributions and chemical states of iron. The specimens used in this study were obtained intraoperatively from brain gliomas of different types and various grades of malignancy and from a control subject. An integrated experimental and analytical approach toward topographic and quantitative analysis in thin freeze-dried cryo-sections is presented. The full XANES spectra at the Fe absorption K edge show the presence of both chemical forms of Fe in the analyzed points of the tissues. The main goal of the work is the chemical state imaging of Fe in tissue areas. Topographic analysis of Fe speciation in the tissues investigated with the use of the XANES technique indicates the presence of microstructures where Fe²⁺ is dominant as well as those with a high abundance of the oxidized form of Fe. The quantitative analysis shows that for all cases the content of the oxidized form of Fe is significantly higher in comparison with Fe²⁺. The highest level of Fe³⁺ is found in the control sample, and the lowest one for the glioma of the highest grade of malignancy. The content of either Fe²⁺ or Fe³⁺ is increased in low grade gliomas in comparison to high-grade malignant tumors.     

Local collection and end-extensions of models of compositional truth

We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the case of the induction scheme.We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate.     

Aiding the self-assembly of supramolecular polyoxometalates under hydrothermal conditions to give precursors of complex functional oxides

In?situ Raman spectroscopy allows insight into molecular processes under hydrothermal conditions during synthesis of complex nanostructured MoVTeNb oxides (see picture: Nb?yellow, Mo?blue, V/Mo?pale blue, Te?red). Based on the knowledge acquired, the synthesis can be more efficiently directed towards the desired product with improved functionality.