Hyperholomorphic polynomials are generalizations of holomorphic polynomials to higher dimensions in the framework of hypercomplex function theory. We consider a special sequence of hyperholomorphic polynomials whose c...
Hyperholomorphic polynomials are generalizations of holomorphic polynomials to higher dimensions in the framework of hypercomplex function theory. We consider a special sequence of hyperholomorphic polynomials whose coefficients can be arranged as triangular arrays of the Pascal type. Our main focus is a one-parameter sequence formed by partial alternating sums of their main diagonal elements that in the limit case is an extended Horadam sequence of rational numbers.
Managing type 1 diabetes presents a daily challenge for patients. Advanced technologies have emerged to simplify disease management and support patients and caregivers. Notably, dosing prandial insulin remains a compl...
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Managing type 1 diabetes presents a daily challenge for patients. Advanced technologies have emerged to simplify disease management and support patients and caregivers. Notably, dosing prandial insulin remains a complex and error-prone task. This study introduces a case-based reasoning system to predict postprandial blood glucose by considering several attributes that influence glycemic metabolism. The case-based reasoning system leverages the knowledge of historical cases to forecast blood glucose levels and use it to optimize insulin bolus calculation. The proposed approach holds promise for enhancing glycemic control, offering patients a more accurate and personalized insulin regimen.
We investigate static boson star solutions in the so-called Einstein-Friedberg-Lee-Sirlin (E-FLS) theory and perform a complete analysis of the solution space in this model. We study the phenomenological aspects of E-...
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We investigate static boson star solutions in the so-called Einstein-Friedberg-Lee-Sirlin (E-FLS) theory and perform a complete analysis of the solution space in this model. We study the phenomenological aspects of E-FLS stars with an emphasis on the analysis of circular timelike orbits and circular photon orbits. In order to study the astrophysical signatures of such stars, their images were obtained under the assumption that they are surrounded by a geometrically thin accretion disk. Here we consider two different accretion disk models, namely the optically thin and optically thick disk models. We present a selection of our findings for the astrophysical images of E-FLS stars and discuss their relevance as possible black hole mimickers.
We construct and explore the solution space of two non-spinning, mini-boson stars in equilibrium, in fully non-linear General Relativity (GR), minimally coupled to a free, massive, complex scalar field. The equilibriu...
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We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochasti...
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Within nonlinear electrodynamics (NED), photons follow null geodesics of an effective geometry, which is different from the geometry of the spacetime itself. Over the last years, several works were dedicated to invest...
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Within nonlinear electrodynamics (NED), photons follow null geodesics of an effective geometry, which is different from the geometry of the spacetime itself. Over the last years, several works were dedicated to investigate the motion of photons in the effective geometry of NED-based magnetically charged regular black hole (RBH) solutions. We study the light rings, shadows, and gravitational lensing of the electrically charged RBH solution proposed by Irina Dymnikova (ID), which is a static and spherically symmetric spacetime with a NED source. We show that the shadow associated with the effective geometry can be almost 10% bigger that the one associated with the standard geometry. We also find that the ID solution may mimic the shadow properties of the Reissner-Nordström BH, for low-to-extreme values of the electric charge. Besides that, by using the backwards ray-tracing technique, we obtain that ID and Reissner-Nordström BH solutions can have a very similar gravitational lensing, for some values of the correspondent electric charges. We also show that the motion of photons in the effective geometry can be interpreted as a nongeodesic curve submitted to a four-force term, from the perspective of an observer in the standard geometry.
The light rings (LRs) topological charge (TC) of a spacetime measures the number of stable LRs minus the number of unstable LRs. It is invariant under smooth spacetime deformations obeying fixed boundary conditions. A...
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The light rings (LRs) topological charge (TC) of a spacetime measures the number of stable LRs minus the number of unstable LRs. It is invariant under smooth spacetime deformations obeying fixed boundary conditions. Asymptotically flat equilibrium black holes (BHs) have, generically, TC=−1. In Einstein-Maxwell theory, however, the Schwarzschild-Melvin BH—describing a neutral BH immersed in a strong magnetic field—has TC=0. This allows the existence of BHs without LRs and produces remarkable phenomenological features, like panoramic shadows. Here we investigate the generalized Schwarzschild-Melvin solution in Einstein-Maxwell-dilaton theory, scanning the effect of the dilaton coupling a. We find that the TC changes discontinuously from TC=0 to TC=−1 precisely at the Kaluza-Klein value a=3, when the (empty) Melvin solution corresponds to a twisted Kaluza-Klein reduction of five-dimensional flat spacetime, i.e., the dilaton coupling a induces a topological transition in the TC. We relate this qualitative change to the Melvin asymptotics for different a. We also study the shadows and lensing of the generalized Schwarzschild-Melvin solution for different values of a, relating them to the TC.
The H-join of a family of graphs G = {G1, . . ., Gp}, also called the generalized composition, H[G1, . . ., Gp], where all graphs are undirected, simple and finite, is the graph obtained by replacing each vertex i of ...
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Regular black holes (RBHs)—geometries free from curvature singularities—arise naturally in theories of nonlinear electrodynamics. Here we study the absorption and superradiant amplification of a monochromatic planar...
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Regular black holes (RBHs)—geometries free from curvature singularities—arise naturally in theories of nonlinear electrodynamics. Here we study the absorption and superradiant amplification of a monochromatic planar wave in a charged, massive scalar field impinging on the electrically charged Ayón-Beato-García (ABG) RBH. Comparisons are drawn with absorption and superradiance for the Reissner-Nordström (RN) black hole in linear electrodynamics. We find that, in a certain parameter regime, the ABG absorption cross section is negative, due to superradiance, and moreover it is unbounded from below as the momentum of the wave approaches zero; this phenomenon of “unbounded superradiance” is absent in the RN case. We show how the parameter space can be divided into regions, using the bounded/unbounded and absorption/amplification boundaries. After introducing a high-frequency approximation based on particle trajectories, we calculate the absorption cross section numerically, via the partial-wave expansion, as a function of wave frequency, and we present a gallery of results. The cross section of the ABG RBH is found to be larger (smaller) than in the RN case when the field charge has the same (opposite) sign as the black hole charge. We show that it is possible to find “mimics”: situations in which the cross sections of both black holes are very similar. We conclude with a discussion of unbounded superradiance and superradiant instabilities.
Using q-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as i...
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