Sentence examples for be defined as integral from inspiring English sources

Hankel operators can be defined as integral operators ( H f ) ( t ) = ∫ 0 ∞ h ( t + s ) f ( s ) d s (1.1 in the space L 2 ( R + ) with kernels h that depend on the sum of variables only.

Although the nongeometric spectral characteristics can generally be defined as integrals of the one-sided evolutionary auto- and cross-spectra of the nonstationary process and its derivatives, the study exploits their time-domain definitions as the variances and the covariance of the response and an "auxiliary" process.

where the intensities ISi-NC and IA are defined as integrals over ω of Equations 1 and 3, respectively.

Reflection and transmission coefficients have been defined as integrals over the circumference of a single rod, in terms of the velocity potential and auxiliary velocity terms on the surface of the rod.

(1) The (topological) dual X ∗ of an order continuous Banach function space X (when defined over a σ-additive measure μ) is again a Banach function space (the Köthe dual or associate space X, i.e., X ∗ = X ′. The second space is defined as integrals of some class of functions. (2) If X is a p-convex Banach function space, its p th power is again a Banach function space.  .

The (topological) dual X ∗ of an order continuous Banach function space X (when defined over a σ-additive measure μ) is again a Banach function space (the Köthe dual or associate space X, i.e., X ∗ = X ′. The second space is defined as integrals of some class of functions. If X is a p-convex Banach function space, its p th power is again a Banach function space.

The corresponding higher order integral operators have been defined as well and confirmed.

Their corresponding higher order integral operators have been defined as well and confirmed.

(v) Condition (E): The function can be defined as the integral of.

The integral can be defined as the difference of series and integral with the value (for r = 1), ∫ 0 ∞ 8 π r n Γ ( n + 1 ) d n = ∑ n = 0 ∞ 8 π r n Γ ( n + 1 ) - ∫ 0 ∞ 8 π e - n r n ( π 2 + ln 2 n ) d n r = 1 ≈ 56.

Information and decision-making are both aspects of a patient-centred approach to cancer care (this can also be defined as patient education) and are integral parts of the health-care process, although there is some controversy about the compatibility of these concepts (Bensing, 2000; Straus and McAlister, 2000; Stewart, 2001).