529 research outputs found
An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains
In this paper, we consider a generalized longest common subsequence problem
with multiple substring exclusion constrains. For the two input sequences
and of lengths and , and a set of constrains
of total length , the problem is to find a common subsequence of and
excluding each of constrain string in as a substring and the length of
is maximized. The problem was declared to be NP-hard\cite{1}, but we
finally found that this is not true. A new dynamic programming solution for
this problem is presented in this paper. The correctness of the new algorithm
is proved. The time complexity of our algorithm is .Comment: arXiv admin note: substantial text overlap with arXiv:1301.718
A note on the largest number of red nodes in red-black trees
In this paper, we are interested in the number of red nodes in red-black
trees. We first present an time dynamic programming solution for
computing , the largest number of red internal nodes in a red-black tree
on keys. Then the algorithm is improved to some time recursive
and nonrecursive algorithms. Based on these improved algorithms we finally find
a closed-form solution of
Complete Solutions for a Combinatorial Puzzle in Linear Time
In this paper we study a single player game consisting of black checkers
and white checkers, called shifting the checkers. We have proved that the
minimum number of steps needed to play the game for general and is . We have also presented an optimal algorithm to generate an optimal
move sequence of the game consisting of black checkers and white
checkers, and finally, we present an explicit solution for the general game
The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials
We derive the reconstruction formulae for the inflation model with the
non-minimal derivative coupling term. If reconstructing the potential from the
tensor-to-scalar ratio, we could obtain the potential without using the high
friction limit. As an example, we reconstruct the potential from the
parametrization , which is a general form of the
-attractor. The reconstructed potential has the same asymptotic
behavior as the T- and E-model if we choose and . We
also discuss the constraints from the reheating phase preceding the radiation
domination by assuming the parameter of state equation during
reheating is a constant. The scale of big-bang nucleosynthesis could put a up
limit on if and a low limit on if .Comment: 12 pages, 3 figure
Estimating Ion Temperatures at the Polar Coronal Hole Boundary
Physical quantities, such as ion temperature and nonthermal velocity, provide
critical information about the heating mechanism of the million-degree solar
corona. We determined the possible ion temperature intervals using
extreme ultraviolet (EUV) line widths, only assuming that the plasma nonthermal
velocity is the same for all ions. We measured ion temperatures at the polar
coronal hole boundary simultaneously observed in 2007 by the EUV Imaging
Spectrometer (EIS) on board the Hinode satellite and the Solar Ultraviolet
Measurements of Emitted Radiation (SUMER) on board the Solar and Heliospheric
Observatory (SOHO). The temperatures of ions with the charge-to-mass ratio
() less than 0.20 or greater than 0.33 are much higher than the local
electron temperature. The measured ion temperature decreases with the to
0.25 and then increases with the charge-to-mass ratio. We ran the Alfv\'en Wave
Solar Model-realtime (AWSoM-R) and the SPECTRUM module to validate the ion
temperature diagnostic technique and to help interpret the results. We suggest
that the widths of hot lines in the coronal hole (e.g., Fe XII, Fe XIII) are
also affected by the solar wind bulk motions along the line of sight. We
discussed the factors that might affect the line width fitting, including the
instrumental width and non-Gaussian wings in some bright SUMER lines that can
be fitted by a double-Gaussian or a distribution. Our study confirms
the presence of preferential heating of heavy ions in coronal holes and
provides new constraints to coronal heating models.Comment: Submitted to ApJ, 26 pages, 18 figures. Jupyter notebooks are
available at https://github.com/yjzhu-solar/EIS_SUMER_PCH_Ti. Comments are
welcom
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