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.

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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

An analytical and a numerical study of the perturbation imparted to a spacecraft by a third body is developed. There are several important applications of the present research, such as calculation of the effect of lunar and solar perturbations on high-altitude Earth satellites. The goal is to study the evolution of orbits around some important natural satellites of the solar system, such as the moon, the Galilean satellites of Jupiter, Titan, Titania, Triton, and Charon. There is special interest in learning under which conditions a near-circular orbit remains near circular. The existence of circular, equatorial, and frozen orbits are also considered for a lunar satellite, but the results are valid for any system of primaries by making a time transformation that depends on the masses of the bodies involved. Several plots will show the time histories of the Keplerian elements of the orbits involved. Then, a study is performed to estimate the lifetime of orbits around those natural satellites.

Third-Body Perturbation in Orbits Around Natural Satellites

Close-Approach Trajectories in the Elliptic Restricted Problem

In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites. We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed, considering that the perturbations are acting together or one at a time.

Some orbital characteristics of lunar artificial satellites

1 INPE-DMC, Avenida dos Astronautas 1758, 12227-010 Sao Jose dos Campos, SP, Brazil 2 IEEC and Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain 3 Universidade Estadual Paulista, UNESP, CEP 12516-410, Campus de Guaratingueta, Guaratingueta, SP, Brazil 4Universidade Estadual Paulista, UNESP, Caixa Postal 178, CEP 13500-970, Campus de Rio Claro, Rio Claro, SP, Brazil

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Antonio F. B. A. Prado

Papers

Third-Body Perturbation in Orbits Around Natural Satellites

Close-Approach Trajectories in the Elliptic Restricted Problem

Some orbital characteristics of lunar artificial satellites

Mathematical Methods Applied to the Celestial Mechanics of Artificial Satellites

Traveling between the lagrangian points and the earth