Sentence examples for bump function from inspiring English sources

An infinite-dimensional Banach space X has a Cp smooth (Lipschitz) bump function if and only if it has another Cp smooth (Lipschitz) bump function f such that its derivative does not vanish at any point in the interior of the support of f (that is, f does not satisfy Rolle's theorem).

g is a real-valued, C ∞ bump function on a compact support with length 2Π, which promises the energy of basis function is normalized ( ∥ ψ 0 ∥ 2 = 1 ).

We also study the related question as to how large the set of gradients of a bump function can be, and among other results we obtain the following new characterization of smoothness in Banach spaces: a Banach space X has a C1 Lipschitz bump function if and only if there exists another C1 smooth Lipschitz bump function whose set of gradients contains the unit ball of the dual space X*.

The niche-based genetic algorithm and the multiple local search approach are compared in the fifth illustrative problem involving a discrete ten-variable bump function problem.

The proposed shifting strategy takes advantage of the transmission architecture to achieve power-on shifting, which greatly improves the driving comfort compared with conventional automated manual transmission, with a bump function based shifting control method.

It is shown that on weakly compactly generated Banach spaces which admit a Lipschitz, Cp smooth bump function, one can uniformly approximate uniformly continuous, bounded, real-valued functions by Lipschitz, Cp smooth functions.

Starlike bodies are interesting in nonlinear functional analysis because they are strongly related to bump functions and to n-homogeneous polynomials on Banach spaces, and their geometrical properties are thus worth studying.

This result might also be relevant to the problem of finding an Asplund space with no smooth bump functions.

Steady inverse design of this cascade is performed to investigate the effects of two shape parameterization methods, namely Hicks–Henne bump functions and mesh points.

We use this parametrix to obtain asymptotic expansions for solutions of u= f and to obtain a uniform Lp estimate for a family of bump functions traveling to infinity.

The study of (10.4) also requires that we verify cancellation properties in terms of its action on "bump functions".