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In this paper, we first prove that the problem in unbounded dimensions is NP-hard.
Therefore, there is a problem finding the optimal alignment of two structures in unbounded dimensions known as NP-hard [ 1].
Our results show that although the problem of searching for similar structures in a database based on the RMSD measure with indels is NP-hard in the case of unbounded dimensions, it can be solved in 3-D by a simple average-case linear time algorithm when the number of indels is bounded by a constant.
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A new, efficient, and accurate method has been developed for computing unsteady, incompressible, viscous flows in a domain where two dimensions are unbounded, the third dimension is periodic and the vorticity is rapidly decaying in the unbounded directions.
Baseball, Jeff Greenfield concludes in a self-described portentous digression from his personal reflections on three generations at Yankee Stadium, became the classic American game because it paid homage to two historic eras: "The outfield, unbounded by the strict dimensions that apply to other sports, was our tribute to our agricultural roots.
We also extend the R-G algorithm with blobs to problems which are periodic in one spatial dimension and unbounded in the other, and we document the performance of the resulting algorithm using some exact periodic solutions of the incompressible Euler equations.
Rather, in almost all cases, the number of colors needed to color a hypergraph embedabble in a certain dimension is unbounded.
For the three datasets, the set of plausible flux distributions – solutions to a linear system detailed in Eq. (1) – was an unbounded convex cone of dimension 5.
Cosmologists who have based their theories on general relativity have sometimes postulated a finite but unbounded space time (analogous, in four dimensions, to the surface of a sphere) as far as spacelike directions are concerned, but practically all cosmologists have assumed that space time is infinite in its timelike directions.
Dirichlet-to-Neumann (DtN) boundary conditions for unbounded wave guides in two and three dimensions are derived and analyzed, defining problems that are suitable for finite element analysis.
A method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com