Sentence examples for in equivalent form from inspiring English sources

The rest of this paper is organized as follows: in Section 2, we describe the analytic setting where we restate the problems in equivalent form by replacing ε p with λ − 1 other than the usual scaling (see [38]), due to the non-autonomy of nonlinearities.

Indeed, equation (21) can be written in equivalent form, Vert xVert cdot Vert x+yVert ^{2}le bigl Vert x Vert ^{2} +langle x,yranglebigr) bigl Vert xVert -Vert y Vert bigr)+biglVert v x,y bigrVert cdot Vert xVert cdot Vert yVert cdot Vert x+yVert.

Following the Floquet approach[29, 30], the space-translated version of the Schrödinger equation, Equation 1, can be cast in equivalent form of a system of coupled time independent differential equations for the Floquet components of the wave function φ, containing the (in general complex) quasi-energy E.

Indeed, equation (22) can be written in equivalent form, bigl Vert yVert ^{2} +langle x,yranglebigr) bigl Vert x Vert -Vert yVert bigr)+Vert yVert cdot Vert x+yVert ^{2}lebiglVert v x,y bigrVert cdot Vert xVert cdot Vert yVert cdot Vert x+yVert, and then biglVert v x,y bigrVert ^{2}lebiglVert v x,y bigrVert cdotfrac{2Vert x+yVert }{Vert xVert +Vert yVert }.

Biologic drugs in equivalent forms are unavailable in the United States because they were not part of the 1984 Hatch-Waxman law, which paved the way for cheaper generic copies of prescription drugs derived from chemicals.

Next we give some useful theorems about writing the generalized differential transform in equivalent forms under certain conditions.

For example, Newton's classical identity, f = ma, can be rewritten in equivalent forms such as a = f/m or f/a = m.

In sum, mental imagery activates many of the brain systems involved in equivalent forms of perception, and when the imagery is emotional in content brain systems involved in processing emotional information, in much the same way as with perceived events.

The first model used to estimate repeatability and competing ability of horses in simulations was the underlying model proposed in (1) in its equivalent form (4).

Based on the Ermentrout Kopell transformation, the quadratic integrate-and-fire can be written in its equivalent form in terms of a new variable called the phase of a neuron.

In the equivalent form in the CIS the score is calculated automatically and gets stored in the patient's electronic health record (EHR).