Sentence examples for hence boundaries from inspiring English sources

Basal plane fracture is a dominant mechanism; hence, boundaries that disrupt the continuity of the basal plane are proposed to influence the crack propagation rate.

Hence boundary value problem (1 - 2) has the unique solution.

Hence boundary value problem (1.1 - 1.2 1.1 - 1.2east one solution.

Hence, boundary value problem (4.1) has at least one solution.

Hence, boundary value problem (1.1) has at least two positive solutions for (lambdain 0,lambda^)).

Hence, boundary value problem (1.1) has a positive solution u for (lambda=lambda^).

Hence, boundary conditions for the CFD simulations were well defined, and data for the validation of a reference model were generated.

Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

The water was of course not completely still, as small temperature gradients led to some convective flow; however, flow rates were very low (and hence boundary layers around the egg mass very large); drops of dye put into still water took many minutes to disperse.

Clearly the optimal coordinate systems for solving transport problems for magnetized ions and for neutrals are at odds with each other, with the former necessarily being related to (inhomogeneous) magnetic field properties, and the latter being simply Cartesian coordinates (in which also solid surfaces and hence boundary conditions for the ion transport are naturally formulated).

Hence, the boundaries of free speech cannot be set in stone by philosophical principles.