Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra

We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the $1$-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, including a counterpart of the Schur algorithm, extension of matrices and rational functions. Other topics considered include Wiener algebra, reproducing kernels Banach modules, and Blaschke factors.Comment: 35 page

The Levi-Civita spacetime as a limiting case of the Gamma spacetime

It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the Gamma metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics.Comment: LaTeX2e 17 page

Multiperiodic magnetic structures in Hubbard superlattices

We consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard-U couplings arranged in a repeated pattern of repulsive (i.e., U>0) and free (U=0) sites. Density Matrix Renormalization Group (DMRG) diagonalization of finite systems is used to calculate the local moment and the magnetic structure factor in the ground state. We have found four regimes for magnetic behavior: uniform local moments forming a spin-density wave (SDW), `floppy' local moments with short-ranged correlations, local moments on repulsive sites forming long-period SDW's superimposed with short-ranged correlations, and local moments on repulsive sites solely with long-period SDW's; the boundaries between these regimes depend on the range of electronic densities, rho, and on the SL aspect ratio. Above a critical electronic density, rho_{uparrow downarrow}, the SDW period oscillates both with rho and with the spacer thickness. The former oscillation allows one to reproduce all SDW wave vectors within a small range of electronic densities, unlike the homogeneous system. The latter oscillation is related to the exchange oscillation observed in magnetic multilayers. A crossover between regimes of `thin' to `thick' layers has also been observed.Comment: 9 two-column pages, 10 figure

Topological bound states for quantum charges

We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where two solenoids are sufficient to create bound states.Comment: Close to published versio

Cryopreservation of Byrsonima intermedia embryos followed by room temperature thawing

Byrsonima intermedia is a shrub from the Brazilian Cerrado with medicinal properties. The storage of biological material at ultra-low temperatures (-196°C) is termed cryopreservation and represents a promising technique for preserving plant diversity. Thawing is a crucial step that follows cryopreservation. The aim of this work was to cryopreserve B. intermedia zygotic embryos and subsequently thaw them at room temperature in a solution rich in sucrose. The embryos were decontaminated and desiccated in a laminar airflow hood for 0-4 hours prior to plunging into liquid nitrogen. The embryo moisture content (% MC) during dehydration was assessed. Cryopreserved embryos were thawed in a solution rich in sucrose at room temperature, inoculated in a germination medium and maintained in a growth chamber. After 30 days, the embryo germination was evaluated. No significant differences were observed between the different embryo dehydration times, where they were dehydrated for at least one hour. Embryos with a MC between 34.3 and 20.3% were germinated after cryopreservation. In the absence of dehydration, all embryos died following cryopreservation. We conclude that B. intermedia zygotic embryos can be successfully cryopreserved and thawed at room temperature after at least one hour of dehydration in a laminar airflow bench

On Quantum Effects of Vector Potentials and Generalizations of Functional Analysis

This is a dissertation in two parts. In the first one, the Aharonov-Bohm effect is investigated. It is shown that solenoids (or flux lines) can be seen as barriers for quantum charges. In particular, a charge can be trapped in a sector of a long cavity by two flux lines. Also, grids of flux lines can approximate the force associated with continuous two-dimensional distributions of magnetic fields. More, if it is assumed that the lines can be as close to each other as desirable, it is explained how the classical magnetic force can emerge from the Aharonov-Bohm effect. Continuing, the quantization of the source of the magnetic field, and not just of the degrees of freedom of the particle interacting with it, is considered. Special attention is given to the cases where the source has a relatively small spreading and is post-selected. As it will be discussed, in those cases, the weak value plays a role in the determination of the effective vector potential experienced by the particle. In the second part of this work, notions from functional analysis are extended to Banach algebras and completions of Grassmann algebras. A notion of analyticity is given to the functions of a single Banach algebra variable. This notion allows the introduction of holomorphic polynomials, power series, and rational functions. With that, the analogous of Hilbert spaces of power series are also considered. Finally, closures of Grassmann algebras with respect to the 1 and the 2-norms are explored. The analogous of the complex analysis in the open disk or a half-plane (usually referred to as Schur analysis) is presented in the 1-norm closure. Also, a Wiener-like algebra, interpolation problems, and a process known as the Schur algorithm are studied in this setting. Now, an inner product between two elements can be introduced in the 2-norm closure, revealing similarities between this space and the non-commutative Fock-Bargamann-Segal space. It is, then, defined a class of stochastic processes. To conclude, the derivatives of these processes are analyzed in an analogous of the space of stochastic distributions

Multiscale model for the effects of adaptive immunity suppression on the viral therapy of cancer

Oncolytic virotherapy - the use of viruses that specifically kill tumor cells - is an innovative and highly promising route for treating cancer. However, its therapeutic outcomes are mainly impaired by the host immune response to the viral infection. In the present work, we propose a multiscale mathematical model to study how the immune response interferes with the viral oncolytic activity. The model assumes that cytotoxic T cells can induce apoptosis in infected cancer cells and that free viruses can be inactivated by neutralizing antibodies or cleared at a constant rate by the innate immune response. Our simulations suggest that reprogramming the immune microenvironment in tumors could substantially enhance the oncolytic virotherapy in immune-competent hosts. Viable routes to such reprogramming are either in situ virus-mediated impairing of CD$8^+$ T cells motility or blockade of B and T lymphocytes recruitment. Our theoretical results can shed light on the design of viral vectors or new protocols with neat potential impacts on the clinical practice.Comment: 14 pages, 4 figure

The case study as a teaching tool in management and accounting education: the case of the Pestana group sustainability report

This paper aims to discuss the relevance of the case study methodology as a tool in management accounting education through the presentation of a case study on the Pestana Group. Case studies can be an effective learning tool in class and are popular in higher education, particularly, in business schools. They generally follow a narrative that includes: a problem or a question to solve; the description of the problem and some information about the company's background, sector, etc.; and some data to support the case study, such as, links to URls, images, videos, etc. The Pestana Group case study is based on its sustainability report. The Pestana Group is the largest hospitality company in Portugal. The analysis of this case in class will permit the discussion of strategic topics such as the disclosure of information in a sustainability report in the tourism industry. The case study is divided into three sections: first, we introduce the theoretical support about the use of case study methodology to teach management and accounting topics. Secondly, we present the instructional case study of the Pestana Group, learning objectives, learning outcomes and questions; and finally we conclude with some remarks and reflections.info:eu-repo/semantics/publishedVersio