There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Concise Guide to PHARMACOLOGY 2017/18 provides concise overviews of the key properties of nearly 1800 human drug targets with an emphasis on selective pharmacology (where available), plus links to an open access knowledgebase of drug targets and their ligands (www.guidetopharmacology.org), which provides more detailed views of target and ligand properties. Although the Concise Guide represents approximately 400 pages, the material presented is substantially reduced compared to information and links presented on the website. It provides a permanent, citable, point-in-time record that will survive database updates. The full contents of this section can be found at http://onlinelibrary.wiley.com/doi/10.1111/bph.13877/full. Enzymes are one of the eight major pharmacological targets into which the Guide is divided, with the others being: G protein-coupled receptors, ligand-gated ion channels, voltage-gated ion channels, other ion channels, nuclear hormone receptors, catalytic receptors and transporters. These are presented with nomenclature guidance and summary information on the best available pharmacological tools, alongside key references and suggestions for further reading. The landscape format of the Concise Guide is designed to facilitate comparison of related targets from material contemporary to mid-2017, and supersedes data presented in the 2015/16 and 2013/14 Concise Guides and previous Guides to Receptors and Channels. It is produced in close conjunction with the Nomenclature Committee of the Union of Basic and Clinical Pharmacology (NC-IUPHAR), therefore, providing official IUPHAR classification and nomenclature for human drug targets, where appropriate.

/pdf/the-concise-guide-to-pharmacology-2017-18-enzymes-5f548bda69.pdf

THE CONCISE GUIDE TO PHARMACOLOGY 2017/18: Enzymes

Many dynamical systems have an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differential equations. In this work we present a new approach via variational methods and critical point theory to obtain the existence of solutions to impulsive problems. We consider a linear Dirichlet problem and the solutions are found as critical points of a functional. We also study the nonlinear Dirichlet impulsive problem.

Variational approach to impulsive differential equations

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results

This work performs a computational investigation of the energy variations given by a powered Swing-By maneuver realized in an elliptical system. It extends previous works by giving the freedom to choose the location and the direction of the thrust vector, aspects that were not considered before in the literature. Those variations are obtained numerically as a function of the parameters related to the thrust (magnitude, direction and location of the application) and the orbital parameters of the primaries (eccentricity and true anomaly). The maneuver is realized around the smaller primary, and the energy variations are measured with respect to the main body of the system. The initial orbit of the space vehicle is defined by its periapsis distance, angle and approach velocity with respect to the smaller primary. The study is applied to a system composed of two primaries that are in elliptic orbits around the center of mass of the system. The eccentricity is varied as a free parameter, to measure its effects. The results show that the best maneuvers apply the thrust at a point inside the sphere of influence of the secondary body, but not in the periapsis of the orbit. The best direction of the thrust is not aligned with the motion of the space vehicle. The techniques studied here are applied in situations where it is desired to increase the energy of the space vehicle. Empirical equations are obtained for the energy variations, based on the simulations made in the present paper. The numerical approach makes the results more accurate and not limited to particular regions of the eccentricity.

A computational approach to the powered Swing-By in the elliptic restricted problem

Low-thrust transfers between given orbits within the two-body problem are considered; the thrust is assumed power limited A simple method for obtaining the transfer trajectories based on the linearization of the motion near reference orbits is suggested Required calculation accuracy can be reached by means of use of a proper number of the reference orbits The method may be used in the case of a large number of the orbits around the attracting center; no averaging is necessary in this case The suggested method also is applicable to the cases of partly given final orbit and if there are constraints on the thrust direction The method gives an optimal solution to the linearized problem which is not optimal for the original nonlinear problem; the difference between the optimal solutions to the original and linearized problems is estimated using a numerical example Also examples illustrating the method capacities are given

https://downloads.hindawi.com/journals/mpe/2012/905209.pdf

Low-Thrust Orbital Transfers in the Two-Body Problem

Orbital maneuvers to form a constellation of small satellites from a single large spacecraft

The role of small inexpensive satellites continuously grows in the modern space exploration. Their use can significantly reduce the cost of the mission. However, the control of such satellites is a challenge. One of the major issues here is that such satellites usually do not possess a complex attitude control system, and three-axis stabilization might be unavailable. As a consequence, the thrust vector of the orbit control system cannot be arbitrary oriented in space and rather involved mathematical methods are needed in order to compensate the control system’s simplicity. The most frequently used simple and lightweight passive systems of one-axis stabilization are spin, passive magnetic or aerodynamic stabilization. In this case, one or two orbit control thrusters can be installed along the stabilized axis, so the orientation of the thrust vector at any given moment of time is determined by the orientation of stabilized axis. A very similar situation we face if the satellite uses the radiation pressure from the Sun as a motive force. Recently, a serious progress was achieved in the analysis and solution of the respective control problems. For example, dampers which use magnetic hysteresis rods in order to dissipate the energy of undesired angular motions — occurred during deployment or caused by perturbations — are used in attitude control systems of small satellites since the 1960s (Fischell and Mobley, 1964). The mathematical modeling of such systems is quite a difficult task, since the majority of existent hysteresis models result in differential equations with discontinuous right-hand side. The analysis of dynamics for attitude control systems with magnetic hysteresis dampers and optimization of their parameters have been done in Sarychev et al. (1988) and Guerman et al. (1989), and the results of these studies have been implemented in real missions (Ovchinnikov et al., 2000; Santoni and Zelli, 2009). However, these studies lacked an accurate theoretical basis for application of

http://www.jatm.com.br/ojs/index.php/jatm/article/download/442/368

Antonio F. B. A. Prado

Papers

A computational approach to the powered Swing-By in the elliptic restricted problem

Low-Thrust Orbital Transfers in the Two-Body Problem

Orbital maneuvers to form a constellation of small satellites from a single large spacecraft

Mathematics of Nanosatellites

On the scattering of comets by a planet