Sentence examples for manifold products from inspiring English sources

This complex multi-scale discipline deals with the transformation of mass by energy to manifold products in different industrial fields under economical and ecological sustainable conditions.

With the virtual PPD-lab, users can test their design ideas on model-based computer-aided tools before performing experiments to validate the designed product; also, manifold product and process alternatives matching a priori defined targets can be generated.

We define a de Rham complex over a product manifold (infinite product of compact manifolds), and Dirichlet operators on differential forms, associated with differentiable measures (in particular, Gibbs measures), which generalize the notions of Bochner and de Rham Laplacians.

Let ({tilde{M}}=mathbb Rtimes _fmathbb C^4) be a warped product manifold between the product of real line (mathbb R) and the complex space (mathbb C^4).

In the field of World Cup studies, it is axiomatic that the competition itself and its manifold ancillary cultural products (songs especially) display what Frankfurt School philosopher Herbert Marcuse called repressive desublimation.

Then their warped product (M=N_{1}times_{f}N_{2}) is the product manifold (N_{1}times N_{2}) equipped with the Riemannian structure such that g=g_{1}+f^{2}g_{2}.

The warped product (M=M_{1}times _{f}M_{2}) is the product manifold (M_{1}times M_{2}) equipped with the Riemannian structure such that |U|^{2}=bigl| pi_{1}(U bigr | ^{2}+f^{2 bigl(pi_{1}(p)bigl)bigl| pi_{2}(U)bigr| ^{2} for any tangent vector (UinGamma(T_{t}M)), where ∗ is the symbol of the tangent maps.

Thus, the warped product (M=M_{1}times_{f}M_{2}) is defined based on the product manifold (M_{1}times M_{2}) equipped with a metric (g=g_{1}+f^{2}cdot g_{2}).

These manifolds are generalization of Riemannian product manifolds and occur naturally, e.g., surface of revolution is a warped product manifold.

A warped product manifold (M=M_{1}times _{f}M_{2}=(M_{1}times M_{2},g)) is said to be trivial or simply a Riemannian product if the warping function f is constant.

A warped product manifold M = N 1 × N 2 is said to be trivial or simply Riemannian product if the warping function f is constant.