Sentence examples for calculus by using from inspiring English sources

(I'll note that while it is natural and effective to use calculus to solve the maximization problem in the induction step, it can be done without calculus by using substitution to put the function to be maximized in the form A – (f(x))^2, which is clearly maximized when f(x) = 0).

Numerical results illustrate the high speed up of the calculus by using GPUs and the coherence of the computations (asset evolution, default probabilities and so on).

Many researchers studied the properties of functions on fractal space and constructed many kinds of fractional calculus by using different approaches [16 18].

Many researchers studied the properties of functions on fractal space and constructed many kinds of fractional calculus by using different approaches [8 12].

In 2014, Baleanu and Agarwal [21] established some inequalities involving Saigo fractional q-integral operator in the theory of quantum calculus by using the two parameters of deformation.

By the same motivation of the above, we also discover both new and interesting applications of umbral calculus by using extended p-adic q-invariant integral on Z p. By virtue of which, we procure some new interesting equalities on the extended p-adic q-Bernoulli numbers and polynomials and extended p-adic q-Bernoulli polynomials of order k.

Researchers are trying to create new calculus on fractals by using some different approaches which are algorithmic or not.

Left ventricular dP/dt is the first derivative of left ventricular pressure, which is computed by software algorithms by using calculus.

Donaldson (1977) examined the classical no-shortage inventory model for deteriorating items with a linear trend in demand over a known and finite horizon by using calculus method.

By using calculus of variations, the governing equations for the construction of the specific flow pattern were derived from the functional extremum problem represented by the Lagrange multiplier equation.

Based on the theory of calculus on time scales, by using the properties of almost periodic functions and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained.