301,091 research outputs found
The generalized 3-connectivity of Cartesian product graphs
The generalized connectivity of a graph, which was introduced recently by
Chartrand et al., is a generalization of the concept of vertex connectivity.
Let be a nonempty set of vertices of , a collection
of trees in is said to be internally disjoint trees
connecting if and for
any pair of distinct integers , where . For an integer
with , the -connectivity of is the
greatest positive integer for which contains at least internally
disjoint trees connecting for any set of vertices of .
Obviously, is the connectivity of . Sabidussi showed
that for any two connected graphs
and . In this paper, we first study the 3-connectivity of the Cartesian
product of a graph and a tree , and show that if
, then ;
if , then .
Furthermore, for any two connected graphs and with
, if , then ; if , then
. Our result could be seen as
a generalization of Sabidussi's result. Moreover, all the bounds are sharp.Comment: 17 page
Component-Enhanced Chinese Character Embeddings
Distributed word representations are very useful for capturing semantic
information and have been successfully applied in a variety of NLP tasks,
especially on English. In this work, we innovatively develop two
component-enhanced Chinese character embedding models and their bigram
extensions. Distinguished from English word embeddings, our models explore the
compositions of Chinese characters, which often serve as semantic indictors
inherently. The evaluations on both word similarity and text classification
demonstrate the effectiveness of our models.Comment: 6 pages, 2 figures, conference, EMNLP 201
Discussion on `Characterization of 1-3 piezoelectric polymer composites - a numerical and analytical evaluation procedure for thickness mode vibrations' by C.V. Madhusudhana Rao, G. Prasad, Condens. Matter Phys., 2010, Vol.13, No.1, 13703
In the paper entitled "Characterization of 1-3 piezoelectric polymer
composites - a numerical and analytical evaluation procedure for thickness mode
vibrations", the dependence of the thickness electromechanical coupling
coefficient on the aspect ratio of piezoceramic fibers is studied by finite
element simulation for various volume fractions of piezoceramic fibers in a 1-3
composite. The accuracy of the results is questionable because the boundary
condition claiming that `predefined displacements are applied perpendicularly
on plane on all nodes' is not suitable for the analysis of 1-3 composite
with comparatively large aspect ratio from 0.2 to 1. A discussion regarding
this problem and the suggested corrections are presented in this paper.Comment: 4 pages, 3 figure
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