Sentence examples for a second relation of from inspiring English sources

For (c) notice that we can prove that for every x 1 ∗ ∈ S Fix ( T 1 ), there exists x 2 ∗ ∈ S Fix ( T 2 ), such that d ( x 1 ∗, x 2 ∗ ) ≤ η 1 − a 2. A second relation of this type will be obtained by interchanging the role of T 1 and T 2. Hence, the conclusion follows by the properties of the functional H. □.

A second relation expresses the continuity of mass i.e., if M is the mass of matter within a sphere of radius r, the mass added, ΔM, when encountering an increase in distance Δr through a shell of volume 4πr2Δr, equals the volume of the shell multiplied by the density, ρ.

Also like Augustine, he seems to leave unexplained this second relation of being "present as a whole" in every place.

Second, relation of these words are mined.

Suppose that (3.5), the first relation of (3.2) and the second relation of (3.8) are satisfied.

It follows from (8) and the second relation of condition (7) that all the eigenvalues of D F ( O ) have absolute values larger than 1 in norm.

(i) If (3.2) and either (3.1) and (3.3) or (3.5) are satisfied, then for the solution of system (1.7) we have that (3.9) holds and obviously tends to the unique zero equilibrium of (1.7) as.   (ii) Suppose that (3.5), the first relation of (3.2) and the second relation of (3.8) are satisfied.

Letting n → ∞ in the first (or second) relation of (3.1), we obtain, with the help of continuity of m 1, m = R ( m 1, m, m 2 ), which means that m is ( m 1, m 2 ) -stabilizable.

A third relation, termed the equation of state, expresses an explicit relation between the temperature, density, and pressure of a star's internal matter.

It follows from the first relation of (7) that | a j β | < 1, 1 ≤ j ≤ k + 1.

Remark 3.1 H = ( H 00 J ∗ = ( H 0 J ∗ follows from (3.3) and the first relation of (3.8) in the special case that a = − ∞ and b = + ∞.