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The evaluation of the transverse shear stresses is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration.

The evaluation of the transverse shear stresses at any interior point is accomplished by direct differentiation of this function, while the coordinates of the shear center are obtained from this function using only boundary integration.

The numerical gradient is obtained by exploiting the available Finite Element Method discretization data, and by direct differentiation of the GB parameters, such as its angle of incidence and the position of the center.

Activity coefficients, as well as their first derivatives with respect to composition at infinite dilution, have been estimated by our method for three binary systems, both by direct differentiation of the excess Gibbs free energy data and through the use of the first and second composition derivatives of the pressure in the infinite dilution limit.

In contrast to the J-integral method, which would require the computation of stresses and strains at a series of internal points, here by direct differentiation of the structural response the strain energy release rates at the existing crack tip and new cracks for the period of crack growth are determined.

Pluripotency is tested by direct differentiation of the cells into multiple cell types in-vivo and in-vitro.

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To answer these questions, we generated human cortical glutamatergic neurons by directed differentiation of embryonic stem cells (see Methods).

As a means of addressing multiple pathological changes with a single therapeutically-relevant approach, we employed delayed transplantation of a unique class of astrocytes, GDAsBMP, that are generated in vitro by directed differentiation of glial precursors.

It is essential that future orthopedic devices are able to withstand micromotion by directing differentiation of locally derived mesenchymal (specifically skeletal) stem cells (MSCs) and osteoprogenitors (OPGs) into bone-matrix-secreting osteoblasts.

For instance, Doltsinis et al. [12] applied the perturbation technique and the incremental loading procedure for the response analysis of path-dependent non-linear structural systems with random parameters, and evaluated the sensitivities of the mean and variance of the structural performance function by direct differentiation in the framework of stochastic finite element analysis.

However, these cells might have been derived from the small number of NGN3+ cells detected on day 0 (recognized as KIT−/GFRα1− cells) by the action of RA, rather than by the direct differentiation of GFRα1+ to KIT+ cells.

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