Sentence examples for multiplicative integral from inspiring English sources

(Stieltjes multiplicative integral (from [18])).

We use the symbol (overset{curvearrowright}{int} ) to refer to the multiplicative integral, or product integral.

In Section 8, we proposed a criterion for checking when the multiplicative integral component in Section 5.1 was not necessary.

Next, we shall interpret the singular term represented as the multiplicative integral in Eq. (18) of Section 5.

The limit is denoted overset{curvearrowright}{ int_{a}}^{b} e^{f(t),dK t)} and is called the multiplicative integral.

This follows from the properties of the multiplicative integral defined in Eq. (45) of Appendix C.1.

Here init_para is set to sphere_init_para which sets the external parameters as multiplicative factors for the integrals.

If this is fulfilled, the solution of the Dirichlet problem will be given, up to a multiplicative constant, by the Cauchy integral of, namely, (5.10).

Grossman and Katz [1], introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and biogeometric calculus, etc. Bashirov et al. [2] gave results with applications to the well-known properties of derivative and integral in the multiplicative calculus.

A third layer of multiplicative uncertainty would require a double integral over a more complicated product, and so on.

Despite the extreme irregularity of these stochastic integrators, the Skorohod integral is shown to be uniquely defined, and to be useful: an Ito formula is established; it is employed to derive a Tanaka formula for a corresponding local time; linear additive and multiplicative stochastic differential equations are solved; an analysis of existence for the stochastic heat equation is given.