Sentence examples for continuation with respect from inspiring English sources

We write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters.

The recently developed generalized Fourier Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the nonlinear modes.

The isometry theorem involves integration over a tube of radius R in the complexification, followed by analytic continuation with respect to R. A cancellation of singularities allows the relevant integral to have a nonsingular extension to large R, even though the function being integrated has singularities.

Continuation of a steady state, periodic solution or solution of a general boundary value problem with respect to a parameter provides a solution diagram; simultaneous stability analysis identifies bifurcation points and these may be continued with respect to a second parameter to obtain a bifurcation diagram.

Over the study period, no significant differences were observed between the abacavir-switch or PI-continuation arms with respect to LDL subfractions (particle size A and major class) or HDL-cholesterol (LSM change from baseline at week 28, +0.2 vs +1.3 mg/dL, P = 0.583; LSM at week 28, 40 vs 41 mg/dL).

Then f θ : I θ → R is called the fractal continuation of f with respect to θ (and W ), and { f θ : θ ∈ I ∞ } is the set of fractal continuations (w.r.t. W ) of the fractal function f.

The author uses continuation of solution with respect to a parameter using the implicit function theorem and hence requires the autonomous part of the nonlinear perturbations to be C 2 smooth.

This study is a continuation of previous studies with respect to the Malay landscape in the state of Perak.

Finally, we also exhibit a holomorphic continuation of the kernels with respect to the Sobolev parameter to the entire complex plane.

The second possibility is eliminated if the paths remain bounded or equivalently by the properness of the exponential mapping (i.e., the initial adjoint vectors p 0,λ that are computed along the continuation procedure remain bounded uniformly with respect to λ).

Otherwise, the continuation of the current situation with respect to the powers of the president will harm the AKP more than the other parties, and Davutoglu will face serious problems of governance.