Exact solutions in general relativityIn general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
FieldbusA fieldbus is a member of a family of industrial digital communication networks used for real-time distributed control. Fieldbus profiles are standardized by the International Electrotechnical Commission (IEC) as IEC 61784/61158. A complex automated industrial system is typically structured in hierarchical levels as a distributed control system (DCS). In this hierarchy the upper levels for production managements are linked to the direct control level of programmable logic controllers (PLC) via a non-time-critical communications system (e.
Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.
Time travelTime travel is the hypothetical activity of traveling into the past or future. Time travel is a widely recognized concept in philosophy and fiction, particularly science fiction. In fiction, time travel is typically achieved through the use of a hypothetical device known as a time machine. The idea of a time machine was popularized by H. G. Wells' 1895 novel The Time Machine. It is uncertain if time travel to the past is physically possible, and such travel, if at all feasible, may give rise to questions of causality.
Atypical depressionAtypical depression is defined in the DSM IV as depression that shares many of the typical symptoms of major depressive disorder or dysthymia but is characterized by improved mood in response to positive events. In contrast to those with atypical depression, people with melancholic depression generally do not experience an improved mood in response to normally pleasurable events. Atypical depression also often features significant weight gain or an increased appetite, hypersomnia, a heavy sensation in the limbs, and interpersonal rejection sensitivity that results in significant social or occupational impairment.
Reverse osmosisReverse osmosis (RO) is a water purification process that uses a semi-permeable membrane to separate water molecules from other substances. RO applies pressure to overcome osmotic pressure that favors even distributions. RO can remove dissolved or suspended chemical species as well as biological substances (principally bacteria), and is used in industrial processes and the production of potable water. RO retains the solute on the pressurized side of the membrane and the purified solvent passes to the other side.
Time zoneA time zone is an area which observes a uniform standard time for legal, commercial and social purposes. Time zones tend to follow the boundaries between countries and their subdivisions instead of strictly following longitude, because it is convenient for areas in frequent communication to keep the same time. All time zones are defined as offsets from Coordinated Universal Time (UTC), ranging from UTC−12:00 to UTC+14:00. The offsets are usually a whole number of hours, but a few zones are offset by an additional 30 or 45 minutes, such as in India, South Australia and Nepal.
Gödel metricThe Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles (dust solution), and the second associated with a negative cosmological constant (see Lambdavacuum solution). This solution has many unusual properties—in particular, the existence of closed time-like curves that would allow time travel in a universe described by the solution.
