Sentence examples for a constant equation from inspiring English sources

Current observational data from the cosmic microwave background anisotropy (CMB), galaxy surveys and type Ia supernovae (SNe Ia) strongly constrain the curvature of the universe to be close to zero for a universe dominated by a cosmological constant or dark energy with a constant equation of state.

From analysis of 60 supernovae from the first four years of ESSENCE data, in conjunction with constraints from baryonic acoustic oscillations and geometric flatness, we obtain a value for a constant equation of state parameter of w=-1.05 +- 0.13 (stat) +- 0.11 (sys).

In equation (1.5), when (alpha z)) is a constant, then equation (1.5) reduces to equation (1.4).

In equation (1.6), when (Q z)) is non-zero constant and (alpha z)) is a constant, then equation (1.6) reduces to equation (1.3).

When M is not a constant function, equation (1.1) without the damping and source terms is often called a Kirchhoff-type wave equation; it has first been introduced by Kirchhoff [7] in order to describe the nonlinear vibrations of an elastic string.

As a solution of a constant coefficient equation, is a sum of characteristic solutions.

For b̂ equal to a constant B, equation (2) has constant coefficients and it can easily be solved analytically [6].

We show that the situation is similar as in the case of a constant coefficients equation treated in Section 3.

Finally, we note that we have also investigated another special case of wide interest in which (b(x)=D/x^{2}) (where D is a constant) in equation (3).

Remark 1 In this section, for the sake of simplicity, we have considered a constant coefficients equation in the form (9), i.e., with c = 0, r = 1, and w = p − 1.

Because the potential field is defined relative to a constant (from Equation 1), the whole field is then shifted by the value of this drop.