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As expected, adaptive mesh refinement shows to be very efficient for studying singular structures compared to nonadaptive treatments.
Recent calculations related to the self-induced collapse of large-scale vortex structures into fine scale, possibly singular, structures in the Euler and Navier Stokes equations are described.
Proteins exist not as singular structures with precise coordinates, but rather as fluctuating bodies that move rapidly through an enormous number of conformational substates.
The assumption indicates that there exists a sequence of inclusions of the manifold and its singular structures, called a weak-Lyapunov filtration.
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Many eminent physicists believe that general relativity's prediction of singular structure signals a serious deficiency in the theory; singularities are an indication that the description offered by general relativity is breaking down.
As we have seen, there is no commonly accepted, strict definition of singularity, no physically reasonable definition of missing point, and no necessary connection of singular structure, at least as characterized by the presence of incomplete paths, to the presence of curvature pathology.
Many discussions of singular structure in relativistic spacetimes, therefore, are premised on the idea that a singularity represents a point or set of points that in some sense or other is "missing" from the spacetime manifold, that spacetime has a "hole" or "tear" in it that we could fill in or patch by the appendage of a boundary to it.
Who backed Roth in the construction of this singular structure?
It is a singular amenity offered by a singular structure.
None of them integrate the health system into a more manageable, singular structure, and none of them attempt to lower costs through a radical expansion of government bargaining power.
The consensus seems to be that, while it is easy in specific examples to conclude that incomplete paths of various sorts represent singular structure, no entirely satisfactory, strict definition of singular structure in their terms has yet been formulated.
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