Sentence examples for homogeneous function from inspiring English sources

The normal derivation of the Gibbs-Duhem equation is performed using the theorem of Euler under the presupposition that the energy is a homogeneous function of order one.

It is a homogeneous function of degree (−2), and then for 2πN-symmetric vortex configurations can be expressed in terms of the so-called correlation coefficient.

To prove this, we consider the analogous Sobolev space W̊k,1 of the homogeneous type and show that a nonconstant homogeneous function of degree zero cannot be a Fourier multiplier of W̊k,1(Rn) (Theorem 2).

This representation is the sum of a first term involving the absolutely continuous component of the measure and of a second one which is a positively homogeneous function of the singular part.

The yield surface is represented by a recently developed generic format, combining the section forces into a homogeneous function of degree one and permitting smooth transition between regions with large and more moderate curvature.

The homogeneous function of degree has the following key property.

Sign invariance is satisfied by every positive homogeneous function of degree \(2m\) \((m = 1, 2, 3, \ldots)\).

If, is a nonnegative homogeneous function of degree in with, and for any,, then and (2.1).

(a) is the homogeneous function of degree zero on, that is, (1.1).

Theorem 1. Suppose that is a homogeneous function of -degree, and is a positive number.

If is a measurable function, satisfying for then we call the homogeneous function of -degree.