Sentence examples for divergence integral from inspiring English sources

The divergence integral (delta^{alpha}) is the adjoint of (D^{alpha}).

In 2012, Shen and Chen [13] defined a stochastic integral with respect to sub-fractional Brownian motion (S^{H}) with index (H in 0, 1/2)) that extends the divergence integral from Malliavin calculus, and established versions of the formulas of Itô and Tanaka that hold for all (Hin 0, 1/2)).

The divergence integral (delta^{B}) is the adjoint of the derivative operator (D^{B}) given by the duality relationship E bigl[Fdelta^{B} u) bigr]=Ebigllangle D^{B}F,ubigrrangle _{mathcal {H}} (2.3) for any element (Fin{mathbb {D}}^{1,2}) and any (uin L^{2}(Omega;{mathcal {H}})) in (delta^{B}).

Property (iii) follows from the slow fast nature of the global return mechanism: the divergence integral computation is dominated by the passages along the slow branches (S_{a}^{pm}), which are both attracting and yield a contribution of the order (-K/varepsilon ), for some (K>0), while the fast parts and the parts near the folds yield an (O(1)) contribution.

The emergence of an SNPO branch from the resonant saddle homoclinic is standard (see [24]), and based on three features: (i) the ratio of eigenvalues is perturbed regularly upon variation of a parameter (C), (ii) the separatrix connection breaks regularly upon variation of another parameter (A), and (iii) the divergence integral along the homoclinic loop is nonzero.

The exact distance travelled along the middle branch can be computed using slow-divergence integrals and exit entry relations; we refer to the literature [21].

The divergence operator (integral) δ is defined as the adjoint of D. A random variable (uin L^{2}(Omega;{mathcal {H}})) belongs to the domain (operatorname{Dom}(delta)) of δ, provided {E}biglvert langle Ddigamma,urangle_{mathcal {H}}bigrvert leq C| digamma|_{L^{2}(Omega)} for all (digammainmathcal {C}).

In this section we discuss the divergence of integrals analogous to (5).

The finite volume method is locally conservative because it is based on a "balance" approach: a local balance is written on each discretization cell that is often called "control volume;" by the divergence formula, an integral formulation of the fluxes over the boundary of the control volume is then obtained.

Clearly then y ( t ) → 0 as t → ∞, otherwise we get a contradiction with the divergence of the integral in (15).

The divergence of the integral for a sufficiently large τ follows then in the same way as before, namely, (11) (R Δ χ Λ − τ ) (λ (s ) ) ≈ ∫ (0, 1 ) d r r m − 1 (s + | r | 2 ) τ I (s, r ) where I (s, r ) approaches, uniformly in s, a fixed, positive constant for r → 0. In this section, we will establish some consequences of the hypothesis T p (G ⋅ p ) ⊂ T p c (b M ).