Bilayer grapheneBilayer graphene is a material consisting of two layers of graphene. One of the first reports of bilayer graphene was in the seminal 2004 Science paper by Geim and colleagues, in which they described devices "which contained just one, two, or three atomic layers" Bilayer graphene can exist in the AB, or Bernal-stacked form, where half of the atoms lie directly over the center of a hexagon in the lower graphene sheet, and half of the atoms lie over an atom, or, less commonly, in the AA form, in which the layers are exactly aligned.
Angular accelerationIn physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotation intersecting the body's centroid; and orbital angular acceleration, involving a point particle and an external axis. Angular acceleration has physical dimensions of angle per time squared, measured in SI units of radians per second squared (rads-2).
Peak ground accelerationPeak ground acceleration (PGA) is equal to the maximum ground acceleration that occurred during earthquake shaking at a location. PGA is equal to the amplitude of the largest absolute acceleration recorded on an accelerogram at a site during a particular earthquake. Earthquake shaking generally occurs in all three directions. Therefore, PGA is often split into the horizontal and vertical components. Horizontal PGAs are generally larger than those in the vertical direction but this is not always true, especially close to large earthquakes.
Inertial measurement unitAn inertial measurement unit (IMU) is an electronic device that measures and reports a body's specific force, angular rate, and sometimes the orientation of the body, using a combination of accelerometers, gyroscopes, and sometimes magnetometers. When the magnetometer is included, IMUs are referred to as IMMUs. IMUs are typically used to maneuver modern vehicles including motorcycles, missiles, aircraft (an attitude and heading reference system), including unmanned aerial vehicles (UAVs), among many others, and spacecraft, including satellites and landers.
Four-accelerationIn the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity). Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge. In inertial coordinates in special relativity, four-acceleration is defined as the rate of change in four-velocity with respect to the particle's proper time along its worldline.
Linear combinationIn mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.
Graphite oxideGraphite oxide (GO), formerly called graphitic oxide or graphitic acid, is a compound of carbon, oxygen, and hydrogen in variable ratios, obtained by treating graphite with strong oxidizers and acids for resolving of extra metals. The maximally oxidized bulk product is a yellow solid with C:O ratio between 2.1 and 2.9, that retains the layer structure of graphite but with a much larger and irregular spacing.
Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
Linear subspaceIn mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces. If V is a vector space over a field K and if W is a subset of V, then W is a linear subspace of V if under the operations of V, W is a vector space over K.
Proof theoryProof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
