positive-definite

Some informal background: a Riemannian manifold is a differentiable manifold (where the tangent space at each point has an inner product) with a positive-definite metric tensor, d (x, y) ≥ 0.

Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

The Lorentzian manifold is a pseudo-Riemannian manifold, the generalization of the Riemannian manifold, such that the metric tensor need not be positive-definite.

Bad Language: “Riemannian Manifold” 2009

The Lorentzian manifold is a pseudo-Riemannian manifold, the generalization of the Riemannian manifold, such that the metric tensor need not be positive-definite.

Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

Some informal background: a Riemannian manifold is a differentiable manifold (where the tangent space at each point has an inner product) with a positive-definite metric tensor, d (x, y) ≥ 0.

Bad Language: “Riemannian Manifold” 2009

The thermal energy due to viscous dissipation appears as a positive-definite contribution to the various forms of the thermal energy conservation equation.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

Secondary organic condensation is solved simultaneously between the gas phase and among any number of aerosol size bins in any number of size distributions with the same unconditionally stable, noniterative, mass-conserving, positive-definite condensation scheme.

Climate Models – the Next Generation « Climate Audit 2006

The model calculates atmosphere-ocean exchange for any gas with a noniterative, mass-conserving, unconditionally-stable, positive-definite scheme that accounts for current ocean composition and pH.

Climate Models – the Next Generation « Climate Audit 2006

The aerosol-aerosol coagulation scheme is volume and volume concentration conserving, unconditionally stable, and positive-definite for any time step.

Climate Models – the Next Generation « Climate Audit 2006

The solution mechanism for simultaneous condensation/dissolution is unconditionally stable, exactly mass conserving, noniterative, and positive-definite.

Climate Models – the Next Generation « Climate Audit 2006

Functions obeying either (a) or (b) are known as positive-definite functions.

What's new 2009