Gravitational potentialIn classical mechanics, the gravitational potential at a point in space is equal to the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point. It is analogous to the electric potential with mass playing the role of charge. The reference point, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance.
Electrostatic lensAn electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens assists in the transport of light in an optical instrument. Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or converge the electron trajectories. An electrostatic lens can also be used to focus an ion beam, for example to make a microbeam for irradiating individual cells.
ElectrostaticsElectrostatics is a branch of physics that studies slow-moving or stationary electric charges. Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber, ἤλεκτρον (), was thus the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law.
Polymer capacitorA polymer capacitor, or more accurately a polymer electrolytic capacitor, is an electrolytic capacitor (e-cap) with a solid conductive polymer electrolyte. There are four different types: Polymer tantalum electrolytic capacitor (Polymer Ta-e-cap) Polymer aluminium electrolytic capacitor (Polymer Al-e-cap) Hybrid polymer capacitor (Hybrid polymer Al-e-cap) Polymer niobium electrolytic capacitors Polymer Ta-e-caps are available in rectangular surface-mounted device (SMD) chip style.
GeometryGeometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Aluminum electrolytic capacitorAluminum electrolytic capacitors are polarized electrolytic capacitors whose anode electrode (+) is made of a pure aluminum foil with an etched surface. The aluminum forms a very thin insulating layer of aluminum oxide by anodization that acts as the dielectric of the capacitor. A non-solid electrolyte covers the rough surface of the oxide layer, serving in principle as the second electrode (cathode) (-) of the capacitor. A second aluminum foil called “cathode foil” contacts the electrolyte and serves as the electrical connection to the negative terminal of the capacitor.
Solvable groupIn mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equation. Specifically, a polynomial equation is solvable in radicals if and only if the corresponding Galois group is solvable (note this theorem holds only in characteristic 0).
Reductive groupIn mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal group SO(n), and the symplectic group Sp(2n).
P-groupIn mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be different powers of p. Abelian p-groups are also called p-primary or simply primary. A finite group is a p-group if and only if its order (the number of its elements) is a power of p.
