25,708 research outputs found
A q-Analog of Dual Sequences with Applications
In the present paper combinatorial identities involving q-dual sequences or
polynomials with coefficients q-dual sequences are derived. Further,
combinatorial identities for q-binomial coefficients(Gaussian coefficients),
q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.Comment: 14 page
Critical Current Density and Resistivity of MgB2 Films
The high resistivity of many bulk and film samples of MgB2 is most readily
explained by the suggestion that only a fraction of the cross-sectional area of
the samples is effectively carrying current. Hence the supercurrent (Jc) in
such samples will be limited by the same area factor, arising for example from
porosity or from insulating oxides present at the grain boundaries. We suggest
that a correlation should exist, Jc ~ 1/{Rho(300K) - Rho(50K)}, where Rho(300K)
- Rho(50K) is the change in the apparent resistivity from 300 K to 50 K. We
report measurements of Rho(T) and Jc for a number of films made by hybrid
physical-chemical vapor deposition which demonstrate this correlation, although
the "reduced effective area" argument alone is not sufficient. We suggest that
this argument can also apply to many polycrystalline bulk and wire samples of
MgB2.Comment: 11 pages, 3 figure
The Degasperis-Procesi equation with self-consistent sources
The Degasperis-Procesi equation with self-consistent sources(DPESCS) is
derived. The Lax representation and the conservation laws for DPESCS are
constructed. The peakon solution of DPESCS is obtained.Comment: 15 page
PADS: A simple yet effective pattern-aware dynamic search method for fast maximal frequent pattern mining
While frequent pattern mining is fundamental for many data mining tasks, mining maximal frequent patterns efficiently is important in both theory and applications of frequent pattern mining. The fundamental challenge is how to search a large space of item combinations. Most of the existing methods search an enumeration tree of item combinations in a depth-first manner. In this paper, we develop a new technique for more efficient max-pattern mining. Our method is pattern-aware: it uses the patterns already found to schedule its future search so that many search subspaces can be pruned. We present efficient techniques to implement the new approach. As indicated by a systematic empirical study using the benchmark data sets, our new approach outperforms the currently fastest max-pattern mining algorithms FPMax* and LCM2 clearly. The source code and the executable code (on both Windows and Linux platforms) are publicly available at http://www.cs.sfu.ca/~jpei/Software/PADS.zip. © Springer-Verlag London Limited 2008
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