Sentence examples for integral that from inspiring English sources

This approach will, in many cases, result in an integral, usually being two-dimensional integral even three-dimensional integral, that cannot be integrated into a closed form and hence must be integrated numerically.

Arrow et al. (2003) define sustainability as a utility integral that increases over time.

The kernel function (4.18) is an infinite integral that has a rather slow of convergence.

An explicit expression is derived for a classical integral that is frequently encountered in the electrical and electronic engineering literature.

end{aligned} (32) The analytic solution given in (32) involves an integral that may be numerically calculated.

It follows from (2.46) and and the absolute continuity of Lebesgue integral that is equicontinuous on any finite subinterval of.

The fractional q-derivative of the Riemann-Liouville type of order α ≥ 0 is defined by ( D q 0 f ) ( x ) = f ( x ) and ( D q α f ) ( x ) = ( D q p I q p − α f ) ( x ), α > 0, where p is the smallest integer greater than or equal to α. Next, we list some properties about q-derivative and q-integral that are already known in the literature.

The hypersingular integrals that result from the implementation of the TBEM are computed analytically.

In Section 2, we define and state some results about stochastic convolution integrals that will be used in the sequel.

There are two main techniques for dealing with the integrals that appear in the derivative: the free-weighting matrix method and the integral inequality method.

For example, the objects f(x) = δ(x) and g(x) = 0 are equal everywhere except at x = 0 yet have integrals that are different.