Synthesis and evaluation of a novel pyrenyl-appended triazole-based thiacalix[4]arene as a fluorescent sensor for Ag+ ion

New fluorescent chemosensors 1,3-alternate-1 and 2 with pyrenyl-appended triazole-based on thiacalix[4]arene were synthesized. The fluorescence spectra changes suggested that chemosensors 1 and 2 are highly selective for Ag+ over other metal ions by enhancing the monomer emission of pyrene in neutral solution. However, other heavy metal ions, such as Cu2+, and Hg2+ quench both the monomer and excimer emission of pyrene acutely. The 1H NMR results indicated that Ag+ can be selectively recognized by the triazole moieties on the receptors 1 and 2 together with the ionophoricity cavity formed by the two inverted benzene rings and sulfur atoms of the thiacalix[4]arene

Eigenvectors of tensors and algorithms for Waring decomposition

A Waring decomposition of a (homogeneous) polynomial f is a minimal sum of powers of linear forms expressing f. Under certain conditions, such a decomposition is unique. We discuss some algorithms to compute the Waring decomposition, which are linked to the equation of certain secant varieties and to eigenvectors of tensors. In particular we explicitly decompose a general cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem).Comment: 32 pages; three Macaulay2 files as ancillary files. Revised with referee's suggestions. Accepted JS

Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Geometric Entanglement of Symmetric States and the Majorana Representation

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science (LNCS

Catalysts based on Co-Birnessite and Co-Todorokite for the efficient production of hydrogen by ethanol steam reforming

[EN] Two structured manganese oxides (Birnessite and Todorokite) containing Co have been studied in the steam reforming of ethanol. It has been found that both materials are active in the hydrogen production, exhibiting high values of conversion of ethanol and selectivities to hydrogen (100% and 70%, respectively). The best results have been obtained with the catalyst based on Todorokite material. Characterization by DRX, BET area, TPR and TEM has allowed to find that the excellent performance exhibited by this material could be attributed to the lower size of the Co metallic particles present in this sample (6 nm vs 12 nm in Birnessite). This lower size could be related to the especial microporous structure of Todorokite precursor, which could provide high-quality positions for the stabilization of the Co metal particles during calcination and reduction steps. Catalytic deactivation has also been considered. Deactivation was found higher for Todorokite-based catalyst, which presented the largest amount of deposited carbon (26.2 wt% for Co-TOD vs 10.6 wt% for Co-BIR). On the other hand, the degree of metal sintering was found similar in both catalysts. Therefore, the deactivation of the catalysts has been attributed primarily to the deposition of coke. The results presented here show that it is possible to prepare new catalysts based on manganese oxides with Birnessite and Todorokite structure and promoted with Co with high catalytic performance in the steam reforming of ethanol. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.The doctor Javier Francisco Da Costa Serra acknowledges the CSIC for granted the scholarship predoctoral-JAE-CSIC. Moreover, Electronic Microscopy Service of UPV for TEM images.Da Costa Serra, JF.; Chica, A. (2018). Catalysts based on Co-Birnessite and Co-Todorokite for the efficient production of hydrogen by ethanol steam reforming. International Journal of Hydrogen Energy. 43(35):16859-16865. https://doi.org/10.1016/j.ijhydene.2017.12.114S1685916865433