Sentence examples for order of continuity from inspiring English sources

Various local approximations are blended using novel pasting functions that provide any desired order of continuity.

The order of continuity at each knot is controlled via multiple knot insertions so that cusps and straight-line segments can be conveniently prescribed.

The order of continuity and connectivity degree for the macropore system from highest to lowest was alfalfa field, conservation tillage field, uncultivated field, and conventional tillage field.

It is a kind of modified Fourier series, which is able to represent any order of continuity of the vibration/buckling modes.

Multiple knots may be inserted to reduce the order of continuity to C1 or C0 at specified points, and by means of double knots the PH splines offer a linear precision and local shape modification capability.

end{aligned}We refer the reader to [5] for an analog of Theorem 1.7.2 for higher order moduli of continuity.

We establish a global approximation theorem in terms of second order modulus of continuity and a direct approximation theorem by means of the Ditzian Totik modulus of smoothness.

The constant M in the above inequality is independent of δ and f and (tilde{omega}_{2}(f;sqrt{delta})) is the second order modulus of continuity.

We also establish a local approximation theorem by means of the Steklov means in terms of the first and the second order modulus of continuity and Voronovskaya type asymtotic theorem.

For f ∈ C [ a, b ] and a positive integer k ≥ 1, the k th order modulus of continuity is defined as ω k ( f, δ ; a, b ) = sup { | Δ h k f ( x ) | : | h | ≤ δ  and  x, x + k h ∈ [ a, b ] }, where Δ h k f ( x ) is k th forward difference with step length h.

Then there exists a positive constant (mathcal{C}>0) such that (K_{2}(f,delta)leqmathcal{C}omega_{2}(f,delta^{frac{1}{2}})), (delta>0), where the second order modulus of continuity is given by omega_{2}bigl f,delta^{frac{1}{2}}bigr)=sup _{0< h< delta^{frac{1}{2}}sup_{xin[00,ell+1]}biglvert f(x+2h -2f(x+h)+f(x bigrvert.