Sentence examples for equality can be rewritten from inspiring English sources

In view of (2.3), the above equality can be rewritten as follows: L x,lambda,mu)=f(x)+operatorname{svec}bigl(mathcal{A}(x) bigr)^{mathrm{T}}lambda +h(x)^{mathrm{T}}mu, where (lambda: =operatorname{svec}(Lambda)).

Differentiating both sides of this equality with respect to t we get S ˙ t T J S t + S t T J S ˙ t = 0 or, equivalently, J S ˙ t S t − 1 = − (S t T ) − 1 S ˙ t T J = (J S ˙ t S t − 1 ) T. This equality can be rewritten J S ˙ t S t − 1 = (J S ˙ t S t − 1 ) T hence the matrix J S ˙ t S t − 1 is symmetric.

Then, the equation can be rewritten as (24).

The above equation can be rewritten as (7).

Since the function (langle W_{k},X^{T}X rangle) is a convex function on X, thus bigllangle W_{k},X_{k}^{T}X_{k} bigrrangle - bigllangle W_{k},X_{k + 1}^{T}X_{k + 1} bigrrangle ge2 langle X_{k + 1}W_{k},X_{k} - X_{k + 1} rangle, and the above equality also can be rewritten as bigllangle W_{k},X_{k}^{T}X_{k} - X_{k + 1}^{T}X_{k + 1} bigrrangle ge2 langle X_{k + 1}W_{k},X_{k} - X_{k + 1} rangle.

Using the above equality and (2), equation (5) can be rewritten as follows: mathcal{J}_{a+}^{alpha}mathcal{D}_{a+}^{alpha}Y t)=Y t) ominus _{g}frac{ t-a)^{alpha-1}}{Gamma(alpha)}{B}.

Then, similar to the M k case, the equality in (11) can be rewritten as KEE ( G ) = ∑ k = 0 ∞ L k k !. Thus the main result of the subsection is the following.

By noting that the equality in (17) can be rewritten as frac{z^{k_{i}}-w^{k_{i}}}{beta_{k_{i}}}-K^Kbigl z^{k_{i}}bigr)in N_{S}}-K^Kbigl z^{k_{i}}bigrnd that the graph of the maxinal moN_{S}e operator (N_{S}) is weakly-strongly closed, and biglassing to the limit in the last inclusions, w^{k_{i}}bigrom (44) and (45), that hathe} in S. Hence (hat{z} ingraph).

First, we consider the case h = 0. Equalities (2), (3) can be rewritten in the form: L ( x, t ; D ) u = f 1 : = f - u t in Q T, (38) u = 0 on S T. (39).

Equation (10b) can be rewritten as.

Equation (1.1) can be rewritten as (2.2).