Sentence examples for by straightforward computations from inspiring English sources

Nevertheless, by straightforward computations we can prove: Proposition 1.

Then the following property is an immediate consequence by straightforward computations, see Lemma 2.4 in [10].

Note that the generator g can be obtained from (71), (72) and (73) by straightforward computations.

The set of the fixed points of this reflection is the circle x = b 2. Proof The proof follows by straightforward computations.

Using such coordinate maps, we can prove by straightforward computations that under Legendre transforms the Poincare forms l θ (Equation 57) and l ω (Equation 58) transform respectively into l ω ˘ Open image in new window (Equation107) and l ω ˘ Open image in new window (Equation 108).

Also we get by straightforward computation that (2.36).

(4.8) By straightforward computation, we have nablaboldsymbol{xi}=varphi^{1-beta}nabla^{2} varphi + 1- beta)varphi^{-beta}nablavarphiotimesnablavarphi.

By a straightforward computation we see that the polynomial is strictly decreasing on.

Since (( I-T^{dagger }T ) ) is a projection, then so is P, by a straightforward computation.

Indeed, for each (mathbf{c} in mathcal{H}), setting y(t)=frac{Gamma (alpha)(eta -2t)}{1-eta } mathbf{c} quad mbox{for } t in [0,1], we have (phi (y)=mathbf{c}), by a straightforward computation.

for any n 1, n 2, n 3, n 4 ∈ N, so we can show that the sequence ( φ n 1, n 2, n 3, n 4 ) fulfills (3.6) by a straightforward computation because of the continuity of the function R + → R, t → R t φ ( x ), for any φ ∈ C b, 1 ( H ).