Markoff-Rosenberger triples in arithmetic progression

We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and the classic Markoff equation x^2+y^2+z^2 = 3xyz over an arbitrary number field.Comment: To appear in Journal of Symbolic Computatio

Nuclear effects in electron- and neutrino-nucleus scattering within a relativistic quantum mechanical framework

We study the impact of the description of the knockout nucleon wave function on electron- and neutrino-induced quasielastic and single-pion production cross sections. We work in a fully relativistic and quantum mechanical framework, where the relativistic mean-field model is used to describe the target nucleus. The focus is on Pauli blocking and the distortion of the final nucleon, these two nuclear effects are separated and analyzed in detail. We find that a proper quantum mechanical treatment of these effects is crucial to provide the correct magnitude and shape of the inclusive cross section. Also, this seems to be key to predict the right ratio of muon- to electron-neutrino cross sections at very forward scattering angles.Comment: 14 pages, 14 figure

Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images

A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted by Q(I ), whose basic building blocks are vertices, edges, square faces and cubes. In Gonzalez-Diaz et al. (Discret Appl Math 183:59–77, 2015), we presented a method to “locally repair” Q(I ) to obtain a polyhedral complex P(I ) (whose basic building blocks are vertices, edges, specific polygons and polyhedra), homotopy equivalent to Q(I ), satisfying that its boundary surface is a 2D manifold. P(I ) is called a well-composed polyhedral complex over the picture I . Besides, we developed a new codification system for P(I ), encoding geometric information of the cells of P(I ) under the form of a 3D grayscale image, and the boundary face relations of the cells of P(I ) under the form of a set of structuring elements. In this paper, we build upon (Gonzalez-Diaz et al. 2015) and prove that, to retrieve topological and geometric information of P(I ), it is enough to store just one 3D point per polyhedron and hence neither grayscale image nor set of structuring elements are needed. From this “minimal” codification of P(I ), we finally present a method to compute the 2-cells in the boundary surface of P(I ).Ministerio de Economía y Competitividad MTM2015-67072-

Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images

We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) associated to a 3D binary image I, to obtain a “well-composed” polyhedral complex P(I), homotopy equivalent to Q(I). There, we developed a new codification system for P(I), called ExtendedCubeMap (ECM) representation, that encodes: (1) the (geometric) information of the cells of P(I) (i.e., which cells are presented and where), under the form of a 3D grayscale image gP ; (2) the boundary face relations between the cells of P(I), under the form of a set BP of structuring elements. In this paper, we simplify ECM representations, proving that geometric and topological information of cells can be encoded using just a 3D binary image, without the need of using colors or sets of structuring elements. We also outline a possible application in which well-composed polyhedral complexes can be useful.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-32706Ministerio de Economía y Competitividad MTM2015-67072-

Spatiotemporal Barcodes for Image Sequence Analysis

Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a spatiotemporal 0–barcode encoding lifetime of connected components on the image sequence over time. This information may not coincide with the one provided by the 0–barcode encoding the 0–persistent homology, since the latter does not respect the principle that it is not possible to move backwards in time. A cell complex K is computed from the given sequence, being the cells of K classified as spatial or temporal depending on whether they connect two consecutive frames or not. A spatiotemporal path is defined as a sequence of edges of K forming a path such that two edges of the path cannot connect the same two consecutive frames. In our algorithm, for each vertex v ∈ K, a spatiotemporal path from v to the “oldest” spatiotemporally-connected vertex is computed and the corresponding spatiotemporal 0–bar is added to the spatiotemporal 0–barcode.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-3270

Hacia una evolución de la concepción de analogía : aplicación al análisis de libros de texto

Las analogías han contribuido a la construcción y desarrollo del conocimiento científico y a su posterior comunicación, por lo que se consideran fundamentales en el proceso de enseñanza-aprendizaje de las ciencias. En este trabajo se analizan las posiciones acerca de la idea de analogía y se establece una propuesta de su concepción y estructura. Esto ha permitido identificar y estudiar la distribución de las analogías presentes en los libros de texto de enseñanza secundaria, atendiendo a las siguientes variables: fecha de publicación, etapa educativa, materia y curso.Analogies have contributed to the construction and development of scientific knowledge and to its ulterior presentation, because they are essential in the scientific teaching-learning process. In this work the positions about the idea of analogy are analysed and a suggestion about conception and structure analogy is proposed. This fact has permitted the identification and research of the analogy distribution in secondary education textbooks. All this in relation with the following variables: publication date, education level, subjet and school year

Distribution of critical metals in evolving pyrite from massive sulfide ores of the Iberian Pyrite Belt

Acknowledgements This research is a contribution to the projects CGL2016-79204-R, PID2019-111715GB-I00 which are supported by the Spanish Government, and 18/IF/6347 granted by Science Foundation Ireland (SFI). The authors thank Cambridge Minerals for access to drill core, sampling assistance and the ongoing collaboration. We are also grateful to Teodosio Donaire for his constructive suggestions in petrogenetic aspects of volcanogenic rocks in the IPB as well as Dany Savard and Audrey Lavoie of LabMaTer, UQAC, for their assistance during the laser ablation analyses. Authors would also like to acknowledge the use of Servicio General de Apoyo a la Investigación-SAI, Universidad de Zaragoza.Supplementary data to this article can be found online at https://doi. org/10.1016/j.oregeorev.2022.105275.With >90 known deposits containing original reserves of >2400 Mt of sulfide ore, the Iberian Pyrite Belt (IPB) is the largest volcanogenic massive sulfide (VMS) province on Earth. In these evolving mineral systems, texturally different pyrite exhibits characteristic mineralogy and trace element fingerprints. Pyrite (Py-1), which is well preserved in the polymetallic ores that crystallized at the earliest stage of VMS deposit formation, consists of kernels of pyrite framboids surrounded by concentric colloform bands and ended by faceted outlines. It is rich in some metals like Pb, Zn, Sb and As (mostly hosted as nano-to-micron-sized particles, including galena, tetrahedrite and arsenopyrite) but depleted in Cu, Co and Bi. In contrast, pyrite from the pyritic and Cu-rich ore overprinted by late fluids exhibits spongy-looking (Py-2) or homogenous (Py-3) cores surrounded by external facets with crystallographic continuity across the whole single grains due to re-crystallization. Py-2 is depleted in most trace elements with the exception of Au and Bi, which occur both in solid solutions and as nano-to-micron-sized inclusions. Py-3 has the highest Cu, Ag, Co and Ni (mainly associated to nano-to-micron-sized particles of tennantite, chalcopyrite and gersdorffite) and the lowest Au contents in the form of native gold. The progressive increase in metal contents from inner to outer parts of Py-1 matches with the onset of the economic metal endowment of VMS deposits in the IPB, whereas Py-2 and Py-3 are associated with metal shoot processes that led to both leached and high-grade ores, very likely when mafic rocks were emplaced into the footwall of the deposits.Projects CGL2016-79204-R, PID2019-111715GB-I00 which are supported by the Spanish Government, and 18/IF/6347 granted by Science Foundation Ireland (SFI

Design of injection locked frequency divider in 65nm CMOS technology for mmW applications

In this paper, an Injection Locking Frequency Divider (ILFD) in 65 nm RF CMOS Technology for applications in millimeter-wave (mm-W) band is presented. The proposed circuit achieves 12.69% of locking range without any tuning mechanism and it can cover the entire mm-W band in presence of Process, Voltage and Temperature (PVT) variations by changing the Injection Locking Oscillator (ILO) voltage control. A design methodology flow is proposed for ILFD design and an overview regarding CMOS capabilities and opportunities for mm-W transceiver implementation is also exposed.Postprint (published version

Nanomaterial accumulation in boiling brines enhances epithermal bonanzas

This work benefited from Grant NANOMET PID2022-138768OB-I00 funded by MCIN/AEI/10.13039/50110001133 and by “ERDF A way of making Europe” by the “European Union”, Grant IN 218323 funded by PAPIIT-DGAPA-UNAM, and Grant PID 2019-105625RB-C21 funded by MCIN/AEI/10.13039/501100011033. Additional funding was Granted by CONAHCyT (ongoing Ph.D. grant) and the Geological Society of America (Grant Number 13570-22) to the first author. Xavier Llovet, Laura Casado, Isabel Rivas, María del Mar Abad, and Cecilia de la Prada are acknowledged for their assistance during EPMA, FIB-SEM, and HRTEM analyses. We thank UNAM academicians Juan Tomás Vásquez and Edith Fuentes Guzmán for their help during sample preparation. We also thank Baltazar Chávez, Senén Benítez, and the team at Natividad (Oaxaca) for their assistance during the stay at the mine facilities. The manuscript has strongly benefited from insightful reviews by two anonymous reviewers and the handling Editor, Dr. Dan Zhu.Epithermal bonanza-type ores, characterized by weight-percent contents of e.g., gold and silver in a few mm to cm, are generated by mixtures of magmatic-derived hydrothermal brines and external fluids (e.g., meteoric) that transport a variety of metals to the site of deposition. However, the low solubilities of precious metals in hydrothermal fluids cannot justify the high concentrations necessary to produce such type of hyper-enriched metal ore. Here we show that boiling metal-bearing brines can produce, aggregate, and accumulate metal nanomaterials, ultimately leading to focused gold + silver ± copper over-enrichments. We found direct nano-scale evidence of nanoparticulate gold- and/or silver-bearing ores formed via nonclassical growth (i.e., nanomaterial attachment) during boiling in an intermediate-sulfidation epithermal bonanza. The documented processes may explain the generation of bonanzas in metal-rich brines from a range of mineral deposit types.MCIN/AEI/10.13039/50110001133: NANOMET PID2022-138768OB-I00ERDF A way of making Europe, European UnionPAPIIT-DGAPA-UNAM: IN 218323CONAHCyTGeological Society of America 13570-22Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México MCIN/AEI/10.13039/501100011033, PID 2019-105625RB-C21 DGAPA, UNA

Torsion of rational elliptic curves over quadratic fields II

“This is a post-peer-review, pre-copyedit version of an article published in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. The final authenticated version is available online at: http://dx.doi.org/10.1007/s13398-015-0223-9“Let (Formula presented.) be an elliptic curve defined over (Formula presented.) and let (Formula presented.) be the associated torsion group. In a previous paper, the authors studied, for a given (Formula presented.) , which possible groups (Formula presented.) could appear such that (Formula presented.) , for (Formula presented.). In the present paper, we go further in this study and compute, under this assumption and for every such (Formula presented.) , all the possible situations where (Formula presented.). The result is optimal, as we also display examples for every situation we state as possible. As a consequence, the maximum number of quadratic number fields (Formula presented.) such that (Formula presented.) is easily obtainedE. González-Jiménez was partially supported by the Grant MTM2012-35849. J. M. Tornero was partially supported by the Grant FQM–218 and P12–FQM–269