Frobenius pairs in abelian categories: correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts

In this work, we revisit Auslander-Buchweitz Approximation Theory and find some relations with cotorsion pairs and model category structures. From the notions of relatives generators and cogenerators in Approximation Theory, we introduce the concept of left Frobenius pairs $(\mathcal{X},\omega)$ in an abelian category $\mathcal{C}$. We show how to construct from $(\mathcal{X},\omega)$ a projective exact model structure on $\mathcal{X}^\wedge$, as a result of Hovey-Gillespie Correspondence applied to two compatible and complete cotorsion pairs in $\mathcal{X}^\wedge$. These pairs can be regarded as examples of what we call cotorsion pairs relative to a thick subcategory of $\mathcal{C}$. We establish some correspondences between Frobenius pairs, relative cotorsion pairs, exact model structures and Auslander-Buchweitz contexts. Finally, some applications of these results are given in the context of Gorenstein homological algebra by generalizing some existing model structures on the categories of modules over Gorenstein and Ding-Chen rings, and by encoding the stable module category of a ring as a certain homotopy category. We also present some connections with perfect cotorsion pairs, covering classes, and cotilting modules.Comment: 54 pages, 10 figures. The statement and proof of 2.6.21 was corrected. Typos corrected. Section 4 was improved, and new results in Section 5 were adde

Non-relativistic Extended Gravity and its applications across different astrophysical scales

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to Newton's gravity and to a MOND-like description in two different mass and length regimes. It is shown that a modification on the force sector (and not in the dynamical one as MOND does) is more convenient and can reproduce and predict different phenomena usually ascribed to dark matter at the non-relativistic level.Comment: 4 pages, 2 figures. To appear in the proceedings of the 2011 Spanish Relativity Meeting (ERE2011) held in Madrid, Spai

A cosmological dust model with extended f(chi) gravity

Introducing a fundamental constant of nature with dimensions of acceleration into the theory of gravity makes it possible to extend gravity in a very consistent manner. At the non-relativistic level a MOND-like theory with a modification in the force sector is obtained, which is the limit of a very general metric relativistic theory of gravity. Since the mass and length scales involved in the dynamics of the whole universe require small accelerations of the order of Milgrom's acceleration constant a_0, it turns out that the relativistic theory of gravity can be used to explain the expansion of the universe. In this work it is explained how to use that relativistic theory of gravity in such a way that the overall large-scale dynamics of the universe can be treated in a pure metric approach without the need to introduce dark matter and/or dark energy components.Comment: 7 pages, 1 figure. Accepted for publication in the European Physical Journal

Right-Sided Endocarditis Secondary to Aeromonas hydrophila: A Case Report

Right-sided endocarditis represents a distinct clinical condition observed in individuals with a history of parenteral drug use or those with implanted pacemakers or other intracardiac devices. Aeromonas infections, although uncommon in humans, particularly endocarditis cases, are exceedingly rare. Here, we report the case of a 72-year-old female with a medical history of arterial hypertension and chronic kidney disease undergoing hemodialysis via a tunneled permanent central venous catheter. She presented with chills and a fever of 38.3°C. Physical examination revealed a grade 3 protosystolic murmur at the tricuspid focus. Blood cultures from central and peripheral sites yielded growth of Aeromonas hydrophila. Transthoracic echocardiography demonstrated a fusiform, semi-mobile vegetation measuring 16 x 15 mm at the outlet of the superior vena cava, suggestive of endocarditis. Intravenous fluoroquinolones were initiated based on antibiogram results, leading to resolution of imaging findings after a 21-day treatment course

A Computational Approach to Multistationarity of Power-Law Kinetic Systems

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the "Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg's "deficiency one algorithm" to such systems

Gravitational lensing with f(χ)=χ3/2 f(\chi)=\chi^{3/2} gravity in accordance with astrophysical observations

In this article we perform a second order perturbation analysis of the gravitational metric theory of gravity $f(\chi) = \chi^{3/2}$ developed by Bernal et al. (2011). We show that the theory accounts in detail for two observational facts: (1) the phenomenology of flattened rotation curves associated to the Tully-Fisher relation observed in spiral galaxies, and (2) the details of observations of gravitational lensing in galaxies and groups of galaxies, without the need of any dark matter. We show how all dynamical observations on flat rotation curves and gravitational lensing can be synthesised in terms of the empirically required metric coefficients of any metric theory of gravity. We construct the corresponding metric components for the theory presented at second order in perturbation, which are shown to be perfectly compatible with the empirically derived ones. It is also shown that under the theory being presented, in order to obtain a complete full agreement with the observational results, a specific signature of Riemann's tensor has to be chosen. This signature corresponds to the one most widely used nowadays in relativity theory. Also, a computational program, the MEXICAS (Metric EXtended-gravity Incorporated through a Computer Algebraic System) code, developed for its usage in the Computer Algebraic System (CAS) Maxima for working out perturbations on a metric theory of gravity, is presented and made publicly available.Comment: 13 pages, 1 table. Accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS

Porcine Reproductive and Respiratory Syndrome Virus Infects Mature Porcine Dendritic Cells and Up-Regulates Interleukin-10 Production

Porcine reproductive and respiratory syndrome virus (PRRSV) infects mature dendritic cells (mDCs) derived from porcine monocytes and matured with lipopolysaccharide. The infection of mDCs induced apoptosis, reduced the expression of CD80/86 and major histocompatibility complex class II molecules, and increased the expression of interleukin-10, thus suggesting that such mDC modulation results in the impairment of T-cell activation

An Active Learning Didactic Proposal with Human-Computer Interaction in Engineering Education: A Direct Current Motor Case Study

Engineering education requires learning strategies to engage students and improve the development of disciplinary and transversal competencies. Additionally, as economic resources are generally limited, it is sought to avoid investing large sums of money in software and hardware, as well as in fitting out laboratories. This work presents a didactic proposal within the framework of active and collaborative learning that includes the flipped classroom technique to be applied in the curriculum of undergraduate engineering programs and inside a massive flexible digital master class. The activity is the mathematical modeling, simulation, and control system of a direct current motor where simulation work is carried out in open license computational packages. Students understand the physical phenomena involved in the motor’s modeling and the input–output variables’ relations. Moreover, an analogy between an electromechanical and a pure electrical model is carried out, where the relevant variables respond in an agile and reliable manner. To validate the modeling, the differential equations are solved by applying numerical methods, and tested for control purposes. The activity has been validated with a rule-based system applied to a Likert scale survey data. This type of human–computer interaction, in the context of active learning, could engage students and motivate them to develop competencies that are highly appreciated by industry practitioners. View Full-Tex