Volume change of bulk metals and metal clusters due to spin-polarization

The stabilized jellium model (SJM) provides us a method to calculate the volume changes of different simple metals as a function of the spin polarization, $\zeta$, of the delocalized valence electrons. Our calculations show that for bulk metals, the equilibrium Wigner-Seitz (WS) radius, $\bar r_s(\zeta)$, is always a n increasing function of the polarization i.e., the volume of a bulk metal always increases as $\zeta$ increases, and the rate of increasing is higher for higher electron density metals. Using the SJM along with the local spin density approximation, we have also calculated the equilibrium WS radius, $\bar r_s(N,\zeta)$, of spherical jellium clusters, at which the pressure on the cluster with given numbers of total electrons, $N$, and their spin configuration $\zeta$ vanishes. Our calculations f or Cs, Na, and Al clusters show that $\bar r_s(N,\zeta)$ as a function of $\zeta$ behaves differently depending on whether $N$ corresponds to a closed-shell or an open-shell cluster. For a closed-shell cluster, it is an increasing function of $\zeta$ over the whole range $0\le\zeta\le 1$, whereas in open-shell clusters it has a decreasing behavior over the range $0\le\zeta\le\zeta_0$, where $\zeta_0$ is a polarization that the cluster has a configuration consistent with Hund's first rule. The resu lts show that for all neutral clusters with ground state spin configuration, $\zeta_0$, the inequality $\bar r_s(N,\zeta_0)\le\bar r_s(0)$ always holds (self-compression) but, at some polarization $\zeta_1>\zeta_0$, the inequality changes the direction (self-expansion). However, the inequality $\bar r_s(N,\zeta)\le\bar r_s(\zeta)$ always holds and the equality is achieved in the limit $N\to\infty$.Comment: 7 pages, RevTex, 10 figure

A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus

The final version is published in Complex Analysis and Operator Theory, 13-No.6, (2019). Received: 8 May 2018 / Accepted: 24 December 2018 / Published online: 11 January 2019.In this paper, we develop a time-fractional operator calculus in fractional Clifford analysis. Initially, we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogs of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems.UID/MAT/04106/2019. A-15/17 / DAAD-PPP IF/00271/2014info:eu-repo/semantics/publishedVersio

Fractional gradient methods via ψ-Hilfer derivative

Motivated by the increasing of practical applications in fractional calculus, we study the classical gradient method under the perspective of the $\psi$-Hilfer derivative. This allows us to cover in our study several definitions of fractional derivatives that are found in the literature. The convergence of the $\psi$-Hilfer continuous fractional gradient method is studied both for strongly and non-strongly convex cases. Using a series representation of the target function, we develop an algorithm for the $\psi$-Hilfer fractional order gradient method. The numerical method obtained by truncating higher-order terms was tested and analyzed using benchmark functions. Considering variable order differentiation and optimizing the step size, the $\psi$-Hilfer fractional gradient method shows better results in terms of speed and accuracy. Our results generalize previous works in the literature.publishe

A fractional analysis in higher dimensions for the Sturm-Liouville problem

In this work, we consider the n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.publishe

Dirac’s method applied to the time-fractional diffusion-wave equation

Acknowledgments: The work of the authors was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within projects UIDB/04106/2020 and UIDP/04106/2020. N. Vieira was also supported by FCT via the 2018 FCT program of Stimulus of Scientific Employment - Individual Support (Ref: CEECIND/01131/2018).We compute the fundamental solution for time-fractional diffusion Dirac-like equations, which arise from the factorization of the multidimensional time-fractional diffusion-wave equation using Dirac’s factorization approach.info:eu-repo/semantics/publishedVersio

Distributed-order relaxation-oscillation equation

Acknowledgments The work of the authors was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within projects UIDB/04106/2020 and UIDP/04106/2020. N. Vieira was also supported by FCT via the 2018 FCT program of Stimulus of Scientific Employment - Individual Support (Ref: CEECIND/01131/2018).In this short paper, we study the Cauchy problem associated with the forced time-fractional relaxation-oscillation equation with distributed order. We employ the Laplace transform technique to derive the solution. Additionally, for the scenario without external forcing, we focus on density functions characterized by a single order, demonstrating that under these conditions, the solution can be expressed using two-parameter Mittag-Leffler functions.info:eu-repo/semantics/publishedVersio

Rapid detection of microorganisms by peptide nucleic acids

Peptide nucleic acid (PNA) molecules are DNA mimics, where the negatively charged sugarphosphate backbone is replaced by an achiral, neutral polyamide backbone formed by repetitive units of N–(2-aminoethyl) glycine. Due to their superior hybridization properties, PNA probes to detect pathogens by fluorescence in situ hybridization (FISH) have been challenging DNA probes over the last few years. In our lab, we have already designed and developed several new probes for the specific detection of bacterial species such as Helicobacter pylori, Cronobacter spp., Staphylococcus epidermidis, Salmonella spp. and Proteus spp. [1, 2]. During development and validation, probes are tested against several related species, and have been shown to be highly specific for the microorganisms of interest. All techniques were optimized in slides and then adapted for different types of samples, depending on the microorganism: H. pylori probe has been developed to work on gastric biopsies and will soon be tested in a clinical trial for a potentially commercial application; Cronobacter spp. is a major contaminant of milk-based powdered infant formula, and as such a probe to detect the pathogen after pre-enrichment of contaminated milk was devised; S. epidermidis, which is frequently present on the skin of humans, had methods developed for its identification in blood samples and catheters; and analysis of interest for Salmonella and Proteus spp. included pipes of drinking water distribution systems and urinary samples. Future work with PNA probes will involve simultaneous detection of several species in a single sample and quantitative signal detection by flow cytometry

Origin and consequences of chromosomal inversions in the virilis group of Drosophila

In Drosophila, large variations in rearrangement rate have been reported among different lineages and among Muller’s elements. Nevertheless, the mechanisms that are involved in the generation of inversions, their increase in frequency, as well as their impact on the genome are not completely understood. This is in part due to the lack of comparative studies on species distantly related to Drosophila melanogaster. Therefore, we sequenced and assembled the genomes of two species of the virilis phylad (Drosophila novamexicana [15010-1031.00] and Drosophila americana [SF12]), which are diverging from D. melanogaster for more than 40 Myr. Based on these data, we identified the precise location of six novel inversion breakpoints. A molecular characterization provided clear evidence that DAIBAM (a miniature inverted–repeat transposable element) was involved in the generation of eight out of the nine inversions identified. In contrast to what has been previously reported for D. melanogaster and close relatives, ectopic recombination is thus the prevalent mechanism of generating inversions in species of the virilis phylad. Using pool-sequencing data for three populations of D. americana, we also show that common polymorphic inversions create a high degree of genetic differentiation between populations for chromosomes X, 4, and 5 over large physical distances. We did not find statistically significant differences in expression levels between D. americana (SF12) and D. novamexicana (15010-1031.00) strains for the three genes surveyed (CG9588, Fig 4, and fab1) flanking three inversion breakpoints.This article is a result of the project Norte-01-0145-FEDER-000008—Porto Neurosciences and Neurologic Disease Research Initiative at I3S, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (FEDER). N.P. and M.R. are funded by the Emmy Noether Programme of the Deutsche Forschungsgemeinschaft (Grant Number: PO 1648/3-1 to N.P.). We would like to thank the Transcriptome Analysis Lab (TAL) (University Medical Center Göttingen, UMG) in Göttingen for the Illumina sequencing