University students' discourse about irreducible polynomials

The purpose of this paper is to analyse, following Sfard’s theoretical framework, the students’ discourse about irreducible polynomials in order to understand their difficulties. Through the students’ explanations, given during the interviews conducted after carrying out the questionnaire, it is possible to study which processes were triggered by them to solve the task. In particular, we focused on the concept of the irreducible polynomials and the link between the roots of the polynomial and its reducibility in university students

Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system

Wind Speed and Direction Detection by Means of Solid-state Anemometers Embedded on Small Quadcopters

This work describes the application of a compact, MEMS-based, 2D anemometer to the estimation of a quadrotor's airspeed. Correcting for the vehicle's ground speed provided by internal GPS and inertial units allows this low cost, mobile platform to provide local wind speed estimates. A series of initial, bench-top tests were performed to characterize and calibrate the sensor, which is an improved version of a recently proposed and novel device. Additional full-scale wind tunnel experiments were performed with the sensor mounted on a fixed quadrotor to test the effect of the propellers on the sensor's performance. Keywords: wind sensor; quadcopter; MEMS; UA

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We derive the equations of motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B (GPB) complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters

Quantum time delay in the gravitational field of a rotating mass

We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test low-energy quantum gravity within the solar system

Self-Aligning Finger Exoskeleton for the Mobilization of the Metacarpophalangeal Joint

In the context of hand and finger rehabilitation, kinematic compatibility is key for the acceptability and clinical exploitation of robotic devices. Different kinematic chain solutions have been proposed in the state of the art, with different trade-offs between characteristics of kinematic compatibility, adaptability to different anthropometries, and the ability to compute relevant clinical information. This study presents the design of a novel kinematic chain for the mobilization of the metacarpophalangeal (MCP) joint of the long fingers and a mathematical model for the real-time computation of the joint angle and transferred torque. The proposed mechanism can self-align with the human joint without hindering force transfer or inducing parasitic torque. The chain has been designed for integration into an exoskeletal device aimed at rehabilitating traumatic-hand patients. The exoskeleton actuation the unit has a series-elastic architecture for compliant human-robot interaction and has been assembled and preliminarily tested in experiments with eight human subjects. Performance has been investigated in terms of (i) the accuracy of the MCP joint angle estimation through comparison with a video-based motion tracking system, (ii) residual MCP torque when the exoskeleton is controlled to provide null output impedance and (iii) torque-tracking performance. Results showed a root-mean-square error (RMSE) below 5 degrees in the estimated MCP angle. The estimated residual MCP torque resulted below 7 mNm. Torque tracking performance shows an RMSE lower than 8 mNm in following sinusoidal reference profiles. The results encourage further investigations of the device in a clinical scenario

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

Quantum time delay in the gravitational field of a rotating mass

We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test low-energy quantum gravity within the solar system

Clinical differences among the elderly admitted to the emergency department for accidental or unexplained falls and syncope

It is difficult to distinguish unexplained falls (UFs) from accidental falls (AFs) or syncope in older people. This study was designed to compare patients referred to the emergency department (ED) for AFs, UFs or syncope. Data from a longitudinal study on adverse drug events diagnosed at the ED (ANCESTRAL-ED) in older people were analyzed in order to select cases of AF, syncope, or UF. A total of 724 patients (median age: 81.0 [65–105] years, 66.3% female) were consecutively admitted to the ED (403 AF, 210 syncope, and 111 UF). The number of psychotropic drugs was the only significant difference in patients with AF versus those with UF (odds ratio [OR] 1.44; 95% confidence interval 1.17–1.77). When comparing AF with syncope, female gender, musculoskeletal diseases, dementia, and systolic blood pressure >110 mmHg emerged as significantly associated with AF (OR 0.40 [0.27–0.58], 0.40 [0.24–0.68], 0.35 [0.14–0.82], and 0.31 [0.20–0.49], respectively), while valvulopathy and the number of antihypertensive drugs were significantly related to syncope (OR 2.51 [1.07–5.90] and 1.24 [1.07–1.44], respectively). Upon comparison of UF and syncope, the number of central nervous system drugs, female gender, musculoskeletal diseases, and SBP >110 mmHg were associated with UF (OR 0.65 [0.50–0.84], 0.52 [0.30–0.89], 0.40 [0.20–0.77], and 0.26 [0.13–0.55]), respectively. These results indicate specific differences, in terms of demographics, medical/pharmacological history, and vital signs, among older patients admitted to the ED for AF and syncope. UF was associated with higher use of psychotropic drugs than AF. Our findings could be helpful in supporting a proper diagnostic process when evaluating older patients after a fall