Sentence examples for manifold setting from inspiring English sources

As (I_{f,g}) is not bounded on X, we consider the behaviors of (I_{f,g}) on the Nehari manifold setting N_{f,g}=bigl{ (omega_{1},omega_{2})in X backslashbigl{ (0,0 bigr} ;I'_{f,g}( omega_{1},omega_{2}) (omega_{1}, omega_{2})=0bigr}.

A conjugate gradient algorithm on the appropriate manifold setting is developed.

Following the proof techniques discussed in the appendix, we can straightforwardly show that the bound in (14) in this manifold setting holds with pmin=pmax=1/m since all target classes are assumed to be equally likely here, and dmin=mini∈{1,…,M}diwhere d i = min f ~ i , f ~ i ( k ) ∈ D y i, ℓ ≠ k ∥ f ~ i − f ~ i ( k ) ∥.

The control action of the system is the inlet air velocity of the cathode air flow manifold, set by the cooling fan, and the system output is the stack voltage.

If one imagines that a manifold set of causes produces a complex multiplicity of effects, then one is saying in effect that each component of the complex cause is producing one component of the complex effect, and this amounts to saying that there are many instances of one cause producing one effect.

Solid-phase extraction (SPE) was performed using a 12-position vacuum manifold set (Cat. No. AHO-6023) and the solvents were removed using an SPE 12-position drying attachment with nitrogen supply (Cat. No. AHO-6050), all from Phenomenex.

Edelman et al. [25] proved that for Stiefel manifolds (set of all orthonormal k-frames in (mathbb {R}^{N}), (V_{k}(mathbb {R}^{n}) = left {mathbf {A} in mathbb {R}^{n times k}: mathbf {A}^{top } mathbf {A} = mathbf {I}right })), e.g., SO(3), their canonical Riemannian structure makes possible to generalize a Riemannian Newton's method on them.

Credo (1968) The shock here is manifold: firstly, in setting a religious text in Soviet times, in quoting Bach, and in fusing a wild diversity of styles into a 12-minute explosion of musical and spiritual energy.

They have had to manufacture all of these devices on the fly, including the manifold they are currently setting next to the wellhead.

I understand the technical complexity and risk in an incident of this magnitude in this depth of water, but, for heaven's sake, the kill manifold has been set for something like 2 weeks.

Rubin and Wechselberger [1] applied a center manifold reduction to (32) by setting (m=m_{infty } v)) to eliminate m and obtain a three-dimensional reduced model.