Sentence examples for I b where from inspiring English sources

Since ( ( D - z ) - 1 y a ) = e - i a ξ ( ( D - i b ) - 1 y ) , where y a = e - i a ξ y , we can suppose that z = i b where b ∈ R. We have to check the inequality ‖ v ( D - i b ) - 1 v - 1 w ‖ ≤ C ‖ w ‖ (3.14 on a dense in L 2 ( R ) set of elements w with compact supports.

ρ ij ( kl ) = q kl ( 1 - 2 | e ij | ) 2. In method 1 (EBS), H(X(b)) is the block entropy defined as H X X ( b ) ) = - ∑ i h i ( b ) log h i ( b ), where h i ( b ) is the normalized histogram of all non-zero DCT coefficients in block X(b).

Corollary 3 The following identity holds true: ∑ i = 0 m ( m i ) a i − 1 b m − i G i ( b x ) S m − i ( a ) = ∑ i = 0 m ( m i ) b i − 1 a m − i G i ( a x ) S m − i ( b ), where S m ( a ) = ∑ j = 0 a − 1 ( − 1 ) j j m and G n ( x ) are called the ordinary Genocchi polynomials which are defined via the following generating function: ∑ n = 0 ∞ G n ( x ) t n n !

It assigns the class with the minimum regression residual to b. Mathematically, it is expressed as j = min1 ≤i≤C r i (b ) where r i (b ) is the regression residual corresponding to the i-th class and is computed as r i b   = b - A δ i x 2 2, where δ i (x ) is defined analogically as in Equation (21).

We then computed the average distance in pixels that the MF travels between adjacent columns as μ = 1 n ∑ i = 1 n x i a − x i b where x ia and x ib are the x coordinates in pixel values for the i th pair of R8 cell centroids, and n is the total number of R8 pairs.

In this case, for each SNP, the median of the values of the control samples is used as reference i.e, the median of (θ C, i A + θ C, i B ) where C is a subset of control samples within the experiment.

Using a different social-psychological approach, Miller and Pasta (1994, 1995) adopt the traits-desires-intentions-behavior framework (T-D-I-B), where fertility intentions are placed within a complex decision-making framework.

The optimization problem is similar with the linear separation case, and following the Lagrange formulation and given a solution of Lagrange multipliers α i, the discriminant function is given by f (x ) = ∑ i N s α i y i K (x, x i ) + b, where x i, i=1,…, N s are the support vectors.

Linear SVM can then applied to this feature space based on the following decision function: f x = s i g n ∑ i = 1 l α i 0 y i K ( x, x i ) + b, where the coefficients α i 0 and b are determined by maximizing the following Langrangian expression: ∑ i = 1 l α i − 1 2 ∑ i = 1 l ∑ j = 1 l α i α j y i y j K x i, x j under the conditions α i  ≥ 0 and ∑ i = 1 l α i y i = 0.

In the dual representation, the function values f(x) in the KLR logit models can be computed as follows: (4) f (x ) = ∑ i = 1 N α i K (x, x i ) + b, where   K x, x i ) = φ(x) T φ(x i ).

The decision function of SVM is listed as follows: (7) h (x ) = sgn ⁡ (∑ i = 1 sv α i y i K (x, x i ) + b ), where sv represents the number of support vectors, α i is the Lagrange multiplier, b is the bias of optimum classification hyperplane, and K x, x i ) denotes the kernel function.