Zeros of Unilateral Quaternionic Polynomials

The purpose of this paper is to show how the problem of finding the zeros of unilateral n-order quaternionic polynomials can be solved by determining the eigen-vectors of the corresponding companion matrix. This approach, probably superfluous in the case of quadratic equations for which a closed formula can be given, becomes truly useful for (unilateral) n-order polynomials. To understand the strehgth of this method, we compare it with the Niven algorithm and show where this (full) matrix approach improves previous methods based on the use of the Niven algorithm. For the convenience of the readers, we explicitly solve some examples of second and third order unilateral quaternionic polynomials. The leading idea of the practical solution method proposed in this work can be summarized in following three steps: translating the quaternionic polynomial in the eigenvalue problem for its companion matrix, finding its eigenvectors, and, finally, giving the quaternionic solution of the unilateral polynomial in terms of the components of such eigenvectors. A brief discussion on bilateral quaternionic quadratic equations is also presented.Comment: 14 page

A New Phase Time Formula for Opaque Barrier Tunneling

After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase time is in excellent agreement with the numerical simulations and shows that for wave packets whose upper limit of the momentum distribution is very close to the barrier height, the transit time is proportional to the barrier width.Comment: 9 pages, 2 figure

A Closed Formula for the Barrier Transmission Coefficient in Quaternionic Quantum mechanics

In this paper, we analyze, by using a matrix approach, the dynamics of a non-relativistic particle in presence of a quaternionic potential barrier. The matrix method used to solve the quaternionic Schrodinger equation allows to obtain a closed formula for the transmission coefficient. Up to now, in quaternionic quantum mechanics, almost every discussion on the dynamics of non-relativistic particle was motived by or evolved from numerical studies. A closed formula for the transmission coefficient stimulates an analysis of qualitative differences between complex and quaternionic quantum mechanics, and, by using the stationary phase method, gives the possibility to discuss transmission times.Comment: 10 pages, 2 figure

O tratado sobre os números, de Plotino : uma tradução comentada

Orientador: Prof. Dr. Bernardo Guadalupe dos Santos Lins BrandãoCoorientadora: Prof. Dr. Vivianne de Castilho MoreiraTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Humanas, Programa de Pós-Graduação em Filosofia. Defesa : Curitiba, 03/03/2023Inclui referências: p. 213-224Resumo: Este trabalho oferece ao público uma tradução comentada do Tratado sobre os números, o tratado VI 6, de Plotino. A compreensão desse importante e difícil texto de Metafísica exige algum conhecimento da influência exercida pela Matemática sobre a filosofia platônica. Para isso, descrevemos um breve histórico da Matemática grega e de sua relação com a Filosofia Antiga. Em seguida, fazemos um panorama das Doutrinas não escritas, incluindo a polêmica entre Aristóteles e os platônicos a respeito da natureza dos números. Por fim, depois de observar as semelhanças entre essas doutrinas e o médio-platonismo, apresentamos nossa tradução do Tratado sobre os números, bem como os necessários comentários e notas. Esperamos, ao fim, ter cumprido o objetivo de esclarecer as questões abordadas no tratado e de situá-lo como um ponto de referência na história da Filosofia Antiga.Abstract: This work offers the public an annotated translation of Plotinus' Treatise on Numbers, treatise VI 6. Understanding this important and difficult text of Metaphysics requires some knowledge of the influence exerted by mathematics on Platonic philosophy. For this purpose, we describe a brief history of Greek Mathematics and its relationship with Ancient Philosophy. Then, we make an overview of the unwritten Doctrines, including the polemic between Aristotle and the platonists about the numbers nature. Finally, after noting the similarities between these doctrines and Middle Platonism, we present our translation of the Treatise on Numbers, as well as the necessary comments and notes. We hope, in the end, to have fulfilled the objective of clarifying the issues addressed in the treatise and of placing it as a point of reference in the history of Ancient Philosophy

Immunohistochemical Analysis of IL-1 beta in the Discs of Patients with Temporomandibular Joint Dysfunction

Purpose: Interleukin-1 beta (IL-1β) is a cytokine that participates in the regulation of immune responses and inflammatory reactions. It is hypothesized that IL-1 levels may be elevated in patients suffering from temporomandibular joint dysfunction. The purpose of this study was to determine the association of IL-1β expression with TMD using an immunohistochemical approach to evaluate the joint disc. Materials and methods: A total of 39 human temporomandibular joint disc samples were collected, with 31 samples in the test group. Nineteen of the test group samples were from discs of patients with anterior disc displacement with reduction, and 12 of the samples were from patients with anterior disc displacement without reduction. Eight control samples were used in the control group. The samples were immunostained and evaluated on both quantity and intensity of staining. Results: There was a statistically significant difference (p \u3c 0.05) between the control and test groups for both quantity and intensity of staining. Conclusion: IL-1β plays a role in the inflammatory process and degradation of TMJ discs in patients with TMJ dysfunctions

Genomic positional conservation identifies topological anchor point RNAs linked to developmental loci.

BACKGROUND: The mammalian genome is transcribed into large numbers of long noncoding RNAs (lncRNAs), but the definition of functional lncRNA groups has proven difficult, partly due to their low sequence conservation and lack of identified shared properties. Here we consider promoter conservation and positional conservation as indicators of functional commonality. RESULTS: We identify 665 conserved lncRNA promoters in mouse and human that are preserved in genomic position relative to orthologous coding genes. These positionally conserved lncRNA genes are primarily associated with developmental transcription factor loci with which they are coexpressed in a tissue-specific manner. Over half of positionally conserved RNAs in this set are linked to chromatin organization structures, overlapping binding sites for the CTCF chromatin organiser and located at chromatin loop anchor points and borders of topologically associating domains (TADs). We define these RNAs as topological anchor point RNAs (tapRNAs). Characterization of these noncoding RNAs and their associated coding genes shows that they are functionally connected: they regulate each other's expression and influence the metastatic phenotype of cancer cells in vitro in a similar fashion. Furthermore, we find that tapRNAs contain conserved sequence domains that are enriched in motifs for zinc finger domain-containing RNA-binding proteins and transcription factors, whose binding sites are found mutated in cancers. CONCLUSIONS: This work leverages positional conservation to identify lncRNAs with potential importance in genome organization, development and disease. The evidence that many developmental transcription factors are physically and functionally connected to lncRNAs represents an exciting stepping-stone to further our understanding of genome regulation.VMC was supported by a PAICONICYT grant (PAI79170021) and a FONDECYT-CONICYT grant (11161020)

Measurement of the top quark forward-backward production asymmetry and the anomalous chromoelectric and chromomagnetic moments in pp collisions at √s = 13 TeV

Abstract The parton-level top quark (t) forward-backward asymmetry and the anomalous chromoelectric (d̂ t) and chromomagnetic (μ̂ t) moments have been measured using LHC pp collisions at a center-of-mass energy of 13 TeV, collected in the CMS detector in a data sample corresponding to an integrated luminosity of 35.9 fb−1. The linearized variable AFB(1) is used to approximate the asymmetry. Candidate t t ¯ events decaying to a muon or electron and jets in final states with low and high Lorentz boosts are selected and reconstructed using a fit of the kinematic distributions of the decay products to those expected for t t ¯ final states. The values found for the parameters are AFB(1)=0.048−0.087+0.095(stat)−0.029+0.020(syst),μ̂t=−0.024−0.009+0.013(stat)−0.011+0.016(syst), and a limit is placed on the magnitude of | d̂ t| < 0.03 at 95% confidence level. [Figure not available: see fulltext.