Integer latticeIn mathematics, the n-dimensional integer lattice (or cubic lattice), denoted \mathbb{Z}^n, is the lattice in the Euclidean space \mathbb{R}^n whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. \mathbb{Z}^n is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice. The automorphism group (or group of congruences) of the integer lattice consists of all permutations and sign changes of the coordinates, and is of order 2n n!.
DiagramA diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram.
Metallic hydrogenMetallic hydrogen is a phase of hydrogen in which it behaves like an electrical conductor. This phase was predicted in 1935 on theoretical grounds by Eugene Wigner and Hillard Bell Huntington. At high pressure and temperatures, metallic hydrogen can exist as a partial liquid rather than a solid, and researchers think it might be present in large quantities in the hot and gravitationally compressed interiors of Jupiter and Saturn, as well as in some exoplanets.
Kinetic energyIn physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
Coordination numberIn chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/molecule/atom is called a ligand. This number is determined somewhat differently for molecules than for crystals. For molecules and polyatomic ions the coordination number of an atom is determined by simply counting the other atoms to which it is bonded (by either single or multiple bonds).
Classical musicClassical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" also applies to non-Western art music. Classical music is often characterized by formality and complexity in its musical form and harmonic organization, particularly with the use of polyphony.
Bravais latticeIn geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by where the ni are any integers, and ai are primitive translation vectors, or primitive vectors, which lie in different directions (not necessarily mutually perpendicular) and span the lattice. The choice of primitive vectors for a given Bravais lattice is not unique.
Monte Carlo methodMonte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.
Classical period (music)The Classical period was an era of classical music between roughly 1750 and 1820. The Classical period falls between the Baroque and the Romantic periods. Classical music has a lighter, clearer texture than Baroque music, but a more varying use of musical form, which is, in simpler terms, the rhythm and organization of any given piece of music. It is mainly homophonic, using a clear melody line over a subordinate chordal accompaniment, but counterpoint was by no means forgotten, especially in liturgical vocal music and, later in the period, secular instrumental music.
Mean motionIn orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. The concept applies equally well to a small body revolving about a large, massive primary body or to two relatively same-sized bodies revolving about a common center of mass.
Control-flow diagramA control-flow diagram (CFD) is a diagram to describe the control flow of a business process, process or review. Control-flow diagrams were developed in the 1950s, and are widely used in multiple engineering disciplines. They are one of the classic business process modeling methodologies, along with flow charts, drakon-charts, data flow diagrams, functional flow block diagram, Gantt charts, PERT diagrams, and IDEF. A control-flow diagram can consist of a subdivision to show sequential steps, with if-then-else conditions, repetition, and/or case conditions.
Particle filterParticle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system.
