Sentence examples for properties of the integral from inspiring English sources

Consequently, the fuzzy Riemann integrability is a particular case of the fuzzy Henstock integrability, and therefore the properties of the integral (FH) will be valid for the integral (FR), too.

The properties of the integral operators are then investigated in the space of square integrable functions in order to obtain sufficient conditions for the uniqueness of solution of the system equations.

Next, we give semigroup properties of the integral operator.

Also the following properties of the integral are valid.

The following lemma is a straightforward application of the properties of the integral.

In the present paper, we aim at proving some inequality properties and convolution properties of the integral operator.

For basic properties of the integrals of vector-valued functions with respect to scalar measures and the integrals of scalar-valued functions with respect to vector measures, see Chapter II in [12].

This observation might be explained by the above-mentioned property of the Integral controller to "intelligently give up," i.e., a differential, or velocity, feedback controller.

Flexibilitas cerea (Bässler 1983), an interesting property observed in non-active animals characterized by a leg joint showing an extremely slow return movement after a disturbance and interpreted as mimesis behavior, may be a property of the integral controller which is equipped with an extremely sensitive sensor monitoring angular velocity of the joints.

Here, a direct application of the properties of the Cauchy integral operator and existing power series expansions allows one to represent the solution in terms of integral operators and Taylor series expansions.

For properties of the Bochner integral see Yosida [41].