Sentence examples for subsequently we derive from inspiring English sources

Subsequently, we derive worst-case bounds on the approximation of the optimum social welfare achieved in (strong) equilibrium by the mechanism.

Subsequently, we derive from the above conclusions that textstylebegin{cases} x_{n_{i}}rightharpoonup z, y_{n_{i}}rightharpoonup z, u_{n_{i}}rightharpoonup z end{cases} (3.30) and textstylebegin{cases} mathcal{A}x_{n_{i}}rightharpoonupmathcal{A}z, mathcal{A}y_{n_{i}}rightharpoonupmathcal{A}z, mathcal{A}u_{n_{i}}rightharpoonupmathcal{A}z.

Subsequently, we derive the unconditional likelihood contributions by integrating V out: {l}_s={int}_Vleft[{l}_s V /{D}_0 V right]mathrm{d}G V kern1.5em mathrm{for} s=1,dots, 5 (3)where G V) is the joint distribution function of the unobserved heterogeneity terms and D 0 is the conditioning event taking into account that there is neither treatment nor exit to employment in the first month.

Subsequently, we derive the variances when parents are unknown, for queens and sires.

Subsequently, we derive the local bounded properties of the Jacobian, tensor and Hessian matrices of the system.

Subsequently, we will derive recommendations for policies.

Subsequently we will derive another form of the model, which starts from a model for study specific ROCs and has a different parametrization.

(65) This confirms Eq. (7), with the added information that the diagonal coefficients are independent of time, which is a property of the equation of motion that we subsequently derive for (rho _{Q}) (Eq. (39)).

We subsequently derive 'complex participation' for individual proteins by counting the number of complexes that they belong to, in our large combined collection of protein complex samples.

Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary.

We subsequently derived a set of ribl matrices from genome-wide exon annotations.