geometry, a density is a spatially varying quantity on a differentiable manifold that can be integrated in an intrinsic manner. Abstractly, a density is a section...

Engines that use a MAP sensor are typically fuel injected. The manifold absolute pressure sensor provides instantaneous manifold pressure information...

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional...

called asymptotic density) Dirichlet density Packing density Density (polytope) Density on a manifold Tensor density in differential geometry Dense set...

physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of...

coordinate change. For more on the intrinsic meaning, see Density on a manifold. A tensor density transforms like a tensor under a coordinate change, except...

Manifold vacuum, or engine vacuum in a petrol engine is the difference in air pressure between the engine's intake manifold and Earth's atmosphere. Manifold...

mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible...

oriented density. And so on. Integration of differential forms is well-defined only on oriented manifolds. An example of a 1-dimensional manifold is an interval...

manifold learning, is any of various related techniques that aim to project high-dimensional data, potentially existing across non-linear manifolds which...

automotive engineering, an exhaust manifold collects the exhaust gases from multiple cylinders into one pipe. The word manifold comes from the Old English word...

of calculus on manifolds, a theory of functions on manifolds. This section is a brief review of function theory in one-variable calculus. A real-valued...

z, t) or still more generally by a point s on a manifold. Often, a "Lagrangian density" is simply referred to as a "Lagrangian". For one scalar field...

geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises...

systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the...

construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). Kernel density estimates are closely related to histograms...

weaker notion of a density. A volume form provides a means to define the integral of a function on a differentiable manifold. In other words, a volume form...

densities on M. The point of this is that, while one can integrate a differential form only if the manifold is oriented, one can always integrate a density...

quantum field theory, a nonlinear σ model describes a field Σ that takes on values in a nonlinear manifold called the target manifold  T. The non-linear...

1967-1976 and first used on the VW 1600TL/E. The system was a speed/density system, using engine speed and intake manifold air density to calculate the amount...

dimensionality. Then learning can proceed using distances and densities defined on the manifold. The manifold assumption is practical when high-dimensional data...

generally a closed positive (p,p) current u on a complex manifold has a Lelong number n(u,x) for each point x of the manifold. Similarly a plurisubharmonic...

universe" could describe a universe that is a closed manifold. de Sitter space – Maximally symmetric Lorentzian manifold with a positive cosmological constant...

geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the...

i j {\displaystyle \pi ^{ij}} is invertible, one has an odd symplectic manifold. In that case, there exists an odd Darboux Theorem. That is, there exist...

fundamental properties of geometrically infinite hyperbolic 3-manifolds, together with the density theorem for Kleinian groups and the ending lamination theorem...

physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use...

stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is therefore a synthesis of...

geometry, a group of isometries of hyperbolic space is called geometrically finite if it has a well-behaved fundamental domain. A hyperbolic manifold is called...

complicated structure on larger scales. In this setting, a vector field gives a tangent vector at each point of the manifold (that is, a section of the tangent...