*** Parabolic cylinder function

*** Parabolic induction

*** Parabolic Lie algebra

*** Low partial pressure of oxygen in the lungs when switching from inhaled anesthesia to atmospheric air, due to the Fink effect, or diffusion hypoxia.

*** Tshu – Khwe ( or Kalahari ) Many of these languages have undergone partial click loss.

*** Uhl anomaly, very rare congenital heart disease with a partial or total loss of the myocardial muscle in the right ventricle

*** Analytic element method, a numerical method used to solve partial differential equations

* Parabolic partial differential equation

* Parabolic partial differential equation

Category: Parabolic partial differential equations

Category: Parabolic partial differential equations

* Parabolic partial differential equation

* Parabolic geometry ( differential geometry ): The homogeneous space defined by a semisimple Lie group modulo a parabolic subgroup, or the curved analog of such a space

we can write the partial differential equation as

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

This is in fact a special case of a more general result on the regularity of solutions of hypoelliptic partial differential equations.

In particular, the DFT is widely employed in signal processing and related fields to analyze the frequencies contained in a sampled signal, to solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers.

Many of the concepts in dynamical systems can be extended to infinite-dimensional manifolds — those that are locally Banach spaces — in which case the differential equations are partial differential equations.

In the late 20th century the dynamical system perspective to partial differential equations started gaining popularity.

* Elliptic partial differential equation

The 17-year-old Enrico Fermi chose to derive and solve the partial differential equation for a vibrating rod, applying Fourier analysis.

The behavior of fluids can be described by the Navier – Stokes equations — a set of partial differential equations which are based on:

This huge improvement made many DFT-based algorithms practical ; FFTs are of great importance to a wide variety of applications, from digital signal processing and solving partial differential equations to algorithms for quick multiplication of large integers.

Fourier analysis has many scientific applications – in physics, partial differential equations, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricing, cryptography, numerical analysis, acoustics, oceanography, sonar, optics, diffraction, geometry, protein structure analysis and other areas.

The relation is specified by the Einstein field equations, a system of partial differential equations.

This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives studied in differential geometry.

Einstein's equations are nonlinear partial differential equations and, as such, difficult to solve exactly.

** partial differential equations

If one identifies C with R < sup > 2 </ sup >, then the holomorphic functions coincide with those functions of two real variables with continuous first derivatives which solve the Cauchy-Riemann equations, a set of two partial differential equations.

Steam just above atmospheric pressure ( all that the boiler could stand ) was introduced into the lower half of the cylinder beneath the piston during the gravity-induced upstroke ; the steam was then condensed by a jet of cold water injected into the steam space to produce a partial vacuum ; the pressure differential between the atmosphere and the vacuum on either side of the piston displaced it downwards into the cylinder, raising the opposite end of a rocking beam to which was attached a gang of gravity-actuated reciprocating force pumps housed in the mineshaft.

One way of expressing the Lie bracket is through the formalism of Lie derivatives, which identifies a vector field X with a first order partial differential operator L < sub > X </ sub > acting on smooth functions by letting L < sub > X </ sub >( f ) be the directional derivative of the function f in the direction of X.

In fact, his interest in the geometry of differential equations was first motivated by the work of Carl Gustav Jacobi, on the theory of partial differential equations of first order and on the equations of classical mechanics.

The above conditions can be expressed as partial differential equations that constrain the fluid flow.

An online resource focusing on algebraic, ordinary differential, partial differential ( mathematical physics ), integral, and other mathematical equations.

If the partial pressure of A at x < sub > 1 </ sub > is P < sub > A < sub > 1 </ sub ></ sub > and x < sub > 2 </ sub > is P < sub > A < sub > 2 </ sub ></ sub >, integration of above equation,

* Partial differential equation, a differential equation involving partial derivatives of a function of several variables

That slow, partial decomposition is usually accelerated by the presence of water, since hydrolysis is the other half of the reversible reaction equation of formation of weak salts.

In partial differential equations, a semigroup is associated to any equation whose spatial evolution is independent of time.

** Separable partial differential equation, a class of equations that can be broken down into differential equations in fewer independent variables

He demonstrated that radio radiation had all the properties of waves ( now called electromagnetic radiation ), and discovered that the electromagnetic equations could be reformulated into a partial differential equation called the wave equation.

This wave can also be represented by the partial differential equation

The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves.

The one dimensional wave equation is unusual for a partial differential equation in that a relatively simple general solution may be found.

In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.

Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations.

Generally, to supply enough oxygen for respiration, a spacesuit using pure oxygen must have a pressure of about, equal to the partial pressure of oxygen in the Earth's atmosphere at sea level, plus and water vapor pressure, both of which must be subtracted from the alveolar pressure to get alveolar oxygen partial pressure in 100 % oxygen atmospheres, by the alveolar gas equation .< ref >

The single symbolic equation thus unravels into four coupled linear first-order partial differential equations for the four quantities that make up the wave function.

It remained mysterious until 1965, when Kruskal and Zabusky showed that, after appropriate mathematical transformations, the system can be described by the Korteweg-de Vries equation, which is the prototype of nonlinear partial differential equations that have soliton solutions.