Sentence examples for for any given σ from inspiring English sources

In this case, for any given σ: 0 < σ ≪ 1.

For any given Σ and u B ∑, we have two cases for the estimation of (CΣu) i (n).

Lemma 2.3 For any given σ ∈ C 1 [ 0, π ], the unique solution of the boundary value problem.

Under the basic assumptions (H1) and ( H ^ 2 ), for each Σ, the operator CΣ is completely continuous on B ∑. Proof For any given Σ and u ∈ B ∑, we have two cases for the estimation of (CΣu) i (n).

It is found that for a given σ h 2, the output SNR1 increases with the increase of σ g 2, while for a given σ g 2, SNR1 does not keep increasing with the increase of σ h 2. This is because as the quality of channels between transceiver 1 and the relays improves, i.e., σ h 2 increases, the desired transmission power at transceiver 2 to guarantee its output SNR increases [2].

Step 2. Hessian matrix calculation: For a given σ value, the Hessian matrix corresponding to pixel (x i, y i ) in the candidate is calculated as follows H σ x i, y i = L xx x i, y i, σ L xy x i, y i, σ L yx x i, y i, σ L yy x i, y i, σ (8).

For a given σ, a modified kernel, K_{boldsymbol{sigma}}(mathbf{u}, mathbf{v})=K(mathbf{u}bullet{boldsymbol {sigma}}, mathbf{v}bullet{boldsymbol{sigma}}), is used to build an SVM, where (tilde {mathbf {u}}=mathbf {u}bullet {boldsymbol {sigma }}in mathbb {R}^{k}) is a vector whose elements are those of u corresponding to the elements of σ which are equal to one.

Otherwise, for a given σ with 0< sigma< supbigl{ bigllangle I^{prime} u),hbigrrangle ;hin Ecap L^{infty }bigl(mathbb{H}^{N}bigr),Vert h Vert leq1 bigr}, there exists (hin Ecap L^{infty}(mathbb{H}^{N})) such that (Vert h Vert leq1) and (langle I^{prime} u),hrangle>sigma).

Figure 5a shows a typical dependence of nucleation rate J0 on time t for a given σ (see also Figures S2 and S3, Supporting Information).

The proportion of these S Δ DIC values larger than our chosen limit is an estimate of the power for a given σ u 2. In this section we illustrate the INLA methodology using a series of synthetic case studies for the models (described in the section Animal models).

In addition, for given σ and λ (or h and λ), the upper bounds of h (or σ) are listed in Tables 2 and 3.