Time dependent transformations in deformation quantization

We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time dependent coordinate transformations. This result considerably enlarges the set of possible phase space representations of quantum mechanics and makes it possible to construct a causal representation for the distributional sector of Wigner quantum mechanics.Comment: 16 pages, to appear in the J. Math. Phy

Shintani descent for standard supercharacters of algebra groups

Let $\mathcal{A}(q)$ be a finite-dimensional nilpotent algebra over a finite field $\mathbb{F}_{q}$ with $q$ elements, and let $G(q) = 1+\mathcal{A}(q)$. On the other hand, let $\Bbbk$ denote the algebraic closure of $\mathbb{F}_{q}$, and let $\mathcal{A} = \mathcal{A}(q) \otimes_{\mathbb{F}_{q}} \Bbbk$. Then $G = 1+\mathcal{A}$ is an algebraic group over $\Bbbk$ equipped with an $\mathbb{F}_{q}$-rational structure given by the usual Frobenius map $F:G\to G$, and $G(q)$ can be regarded as the fixed point subgroup $G^{F}$. For every $n \in \mathbb{N}$, the $n$th power $F^{n}:G\to G$ is also a Frobenius map, and $G^{F^{n}}$ identifies with $G(q^{n}) = 1 + \mathcal{A}(q^{n})$. The Frobenius map restricts to a group automorphism $F:G(q^{n})\to G(q^{n})$, and hence it acts on the set of irreducible characters of $G(q^{n})$. Shintani descent provides a method to compare $F$-invariant irreducible characters of $G(q^{n})$ and irreducible characters of $G(q)$. In this paper, we show that it also provides a uniform way of studying supercharacters of $G(q^{n})$ for $n \in \mathbb{N}$. These groups form an inductive system with respect to the inclusion maps $G(q^{m}) \to G(q^{n})$ whenever $m \mid n$, and this fact allows us to study all supercharacter theories simultaneously, to establish connections between them, and to relate them to the algebraic group $G$. Indeed, we show that Shintani descent permits the definition of a certain ``superdual algebra'' which encodes information about the supercharacters of $G(q^{n})$ for $n \in \mathbb{N}$

Generalized Weyl-Wigner map and Vey quantum mechanics

The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations is still missing. In this paper we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.Comment: 15 pages, LaTe

Quantification of GHB and GHB-GLUC in an 1,4-butanediol intoxication: a case report

Gamma-hydroxybutyric acid (GHB) is an endogenous compound with known action at the neural level. Its psychoactive effects led to an illicit use context including recreational purposes, muscle building effects in bodybuilders and drug-facilitated crimes, specifically in sexual assaults. Besides the misuse of the main compound, there are precursors like Gammabutyrolactone (GBL) and 1,4-butanediol (1,4-BD), usually non controlled substances, becoming a much easier way to obtain the target-compound. The authors present the first reported intoxication case in Portugal with 1,4-Butanediol, including the quantification of GHB and GHB-GLUC in serum, by GC-MS/MS TQD. A suspicious liquid and a serum sample were sent by an hospital ER and analysed by GC-MS-single quadrupole and GC-MS/MS TQD, respectively. A methodology including protein precipitation and GC-MS/MS TQD analysis was used to detect and quantify GHB and GHB-GLUC in serum. Toxicological analysis revealed the presence of 1,4-Butanediol in the liquid and GHB [171 mg/L] and GHB-GLUC [13,7 mg/L] in serum. The victim reverted the coma with no neurological sequelae. This was the first detected case, in Portugal, with 1,4-Butanediol, suggesting that it is important to be aware that consumers have different options to obtain illicit compounds, such as GHB. On the other hand, GHB-GLUC was identified and quantified for the first time in a real case, due to intoxication. This case highlights the importance of analysing all samples for active compounds, precursors and metabolites that can lead to the main intoxication origin.publishe

Assessment of habitat suitability for common cockles in the Ria the Aveiro Lagoon under average and projected environmental conditions

The common cockle Cerastoderma edule is a widespread bivalve species inhabiting estuarine systems across the North East Atlantic, where it provides several ecosystem services, and represents a valuable fishery resource for local economies. However, anthropogenic pressure and more frequent extreme weather events threaten the resilience of the species. Spatially explicit information on species distribution is critical for the implementation of management and conservation practices. This study assessed the potential distribution of C. edule in the Ria de Aveiro by estimating the habitat suitability using an ensemble approach based on ecological niche modeling and recently developed hydrodynamic and water quality models to forecast both average and projected estuarine conditions. The models were developed for the summer of 2013 and spring of 2019 and potential range shifts in the species distribution were forecasted under projected environmental conditions: high and low estimates of freshwater discharge, a 2 °C increase in water temperature, and the combined effect of low freshwater discharge and increased water temperature. The results suggest that salinity, time of submersion, and current velocity play an important role in the distribution of cockles, and large areas were consistently classified with high habitat suitability. Increased freshwater discharge (both seasons) and low discharge coupled to increased temperature (spring) resulted in large decreases in suitable habitat. Conversely, low freshwater discharges and average (unchanged) temperatures increased the suitable habitat in the outermost regions of the Ria. The spatially explicit information provided contributes to a better understanding of the vulnerability of C. edule in the Ria de Aveiro to extreme weather events (e.g., droughts, river floods) and may support adaptive management strategies of the cockle fishery during these conditions. Moreover, this approach can be transferred to other estuarine ecosystems for which data describing the environmental conditions (e.g., derived from numerical models), and information about species presence are available (including data-poor species).publishe

Impact of nanoconfinement on the physical state and conductivity mechanisms of a 2-picolinium ionic liquid crystal

Funding Information: This work was supported by the Associate Laboratory for Green Chemistry LAQV ( UID/QUI/50006/2019 ), i3N (UID/ CTM / 50025/2019 ) and CeFEMA (UID/ CTM / 04540/2019 ), which are financed by national funds from FCT- MCTES and by FEDER funds through the COMPETE 2020 Program. The authors also thank the National Funds through FCT- MCTES and POR Lisboa 2020, under the project numbers PTDC/EAM - AMB / 2023/2021 ( SUSTECH4H2O ), POCI-01-0145-FEDER-007688 and European Interdisciplinary Action ( COST Action CA21159 , PhoBioS). A. F. M. Santos also acknowledges FCT- MCTES for the PhD Grant ( SFRH/BD/132551/2017 ) and I. Matos for the contract CEECIND/004431/2022 . Funding Information: This work was supported by the Associate Laboratory for Green Chemistry LAQV, Portugal, (LA/P/0008/2020, UIDB/50006/2020, UIDP/50006/2020), i3N, Portugal, (LA/P/0037/2020, UIDB/50025/2020, UIDP/50025/2020), CQE, Portugal, (UIDB/00100/2020, UIDP/00100/2020) and CeFEMA, Portugal, (UIDB/04540/2020, UIDP/04540/2020), which are financed by national funds from FCT-MCTES, Portugal, and by FEDER funds through the COMPETE 2020, Portugal, Program. The authors also thank the National Funds through FCT-MCTES, Portugal and POR Lisboa 2020, under the project numbers PTDC/EAM-AMB/2023/2021 (SUSTECH4H2O), POCI-01-0145-FEDER-007688 and European Interdisciplinary Action (COST Action, Belgium, CA21159, PhoBioS). A. F. M. Santos also acknowledges FCT-MCTES, Portugal, for the PhD Grant (SFRH/BD/132551/2017) and I. Matos for the contract CEECIND/004431/2022. Publisher Copyright: © 2024 The Author(s)Hybrid solid-like materials prepared from the incorporation of liquid-like ionic conductors into nanoporous matrices could represent an advantage for a variety of electronic applications. Aiming to obtain such materials, three composites of the polymorphic ionic liquid crystal (ILC) 1-hexadecyl-2-methylpyridinium bromide ([C16-2-Pic][Br]), loaded in the mesoporous inorganic silica SBA-15 (∼6.8 nm in pore diameter), were prepared at guest–host weight fractions of ∼ 40, 60 and 80% (w/w) and investigated by different techniques: ATR-FTIR, BET, TGA, XRD and DSC. Complete amorphisation was achieved for the 40 and 60% composites, while the 80% preparation was stabilised in the low-T morph of native C16, being in the liquid state at room temperature. Furthermore, through Dielectric Relaxation Spectroscopy, the ionic conductivity of the three hybrid materials was characterised, allowing to deconvolute this property in a pure ohmic contribution (conductivity I) and the overlapping of ac − dc transition with interfacial polarisation resulting from the coexistence of the ionic liquid and the quasi-insulating inorganic matrix (conductivity II). From –20 to 20 °C, the conductivity and the corresponding charge migration are faster in all composites relative to the neat ILC, as deduced from the inferior radii of Nyquist arcs. The 60% preparation stood out from the other materials, exhibiting direct conductivity unaffected by electrode polarisation over a larger T-range, leading to the assumption of a nearly continuous silica-mediated charge migration pathway, which is never reached for the 40% composite, while, in the 80% preparation, some C16 deposits on the outer surface of the pores. Incorporation into the silica matrix proved to be a good strategy for the production of cost-efficient materials with long-term stabilisation of the ionic liquid in a single phase over a large range of temperatures, enabling the prediction of flow and conductive properties.publishersversionpublishe

On the implementation of the gamma function for image correction on a endoscopic camera

This paper describes part of project that implemented the image processing of a CMOS sensor for endoscopic purposes. The sensor is a small sized device of 1x1mm2 and the image processing has been done inside a FPGA. This part of the work describes the implementation of the Gamma function with a balance between the resources needed and the accuracy. A linear piecewise solution was used that stores the values for 31 gamma functions with values ranging from 1 to 4 with 0.1 steps. The solution developed is 10 bit based, was coded in VHDL and is implemented in a Spartan 6 FPGA. The results show that it is an accurate solution that has a small footprint in terms of used resources.info:eu-repo/semantics/publishedVersio