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    <title>Quartic B-spline collocation method to the numerical solutions of the Burgers' equation</title>
    <description>Chaos, Solitons &amp; Fractals</description><link>http://www.bibsonomy.org/bibtex/27c8f6b032c5b2a66429ffdb9e914be51/smicha</link>
    <dc:creator>smicha</dc:creator>
    <dc:date>2008-04-22T12:52:29+02:00</dc:date>
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	    <![CDATA[
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	      <div class="bmtitle">

  <a href="http://www.bibsonomy.org/bibtex/27c8f6b032c5b2a66429ffdb9e914be51/smicha">Quartic B-spline collocation method to the numerical solutions of the Burgers' equation</a>
</div>
<div class="bmdesc">
  <span style="color:#555555;"> 
    B{\&#034;u}lent <a href="http://www.bibsonomy.org/author/Saka">Saka</a>         	     	 
        	  and Idris <a href="http://www.bibsonomy.org/author/Dag">Dag</a>         	     	 
        	 </span> 
  <em>Chaos, Solitons \&amp; Fractals</em>
      <b>32</b>
      1125--1137
  (2007)
</div>
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          by <a href="http://www.bibsonomy.org/user/smicha">smicha</a> 
        
        
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	the Burgers&#039; equation</swrc:title><swrc:volume>32</swrc:volume><swrc:year>2007</swrc:year><swrc:keywords>imported </swrc:keywords><swrc:date>2008-04-22 12:52:29.0</swrc:date><swrc:author>
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<item rdf:about="http://www.bibsonomy.org/uri/bibtex/25119ca621ace7bd4f395a20f73ad1cd2/dblp">
    <title>A Web Usage Mining Framework for Mining Evolving User Profiles in Dynamic Web Sites.</title>
    <description>dblp</description><link>http://www.bibsonomy.org/bibtex/25119ca621ace7bd4f395a20f73ad1cd2/dblp</link>
    <dc:creator>dblp</dc:creator>
    <dc:date>2008-02-22T00:00:00+01:00</dc:date>
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	      <div class="bmtitle">

  <a href="http://www.bibsonomy.org/bibtex/25119ca621ace7bd4f395a20f73ad1cd2/dblp">A Web Usage Mining Framework for Mining Evolving User Profiles in Dynamic Web Sites.</a>
</div>
<div class="bmdesc">
  <span style="color:#555555;"> 
    Olfa <a href="http://www.bibsonomy.org/author/Nasraoui">Nasraoui</a>         	     	 
        	  and Maha <a href="http://www.bibsonomy.org/author/Soliman">Soliman</a>         	     	 
        	  and Esin <a href="http://www.bibsonomy.org/author/Saka">Saka</a>         	     	 
        	  and Antonio <a href="http://www.bibsonomy.org/author/Badia">Badia</a>         	     	 
        	  and Richard <a href="http://www.bibsonomy.org/author/Germain">Germain</a>         	     	 
        	 </span> 
  <em>IEEE Trans. Knowl. Data Eng.</em>
      <b>20</b>
      202-215
  (2008)
</div>
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          by <a href="http://www.bibsonomy.org/user/dblp">dblp</a> 
        
        
        on 2008-02-22 00:00:00 </span></div>
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    <title>Web Usage Mining in Noisy and Ambiguous Environments: Exploring the Role of Concept Hierarchies, Compression, and Robust User Profiles.</title>
    <description>dblp</description><link>http://www.bibsonomy.org/bibtex/201b9510ee558517cdada8f4c96b5a043/dblp</link>
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	    <![CDATA[
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	      <div class="bmtitle">

  <a href="http://www.bibsonomy.org/bibtex/201b9510ee558517cdada8f4c96b5a043/dblp">Web Usage Mining in Noisy and Ambiguous Environments: Exploring the Role of Concept Hierarchies, Compression, and Robust User Profiles.</a>
</div>
<div class="bmdesc">
  <span style="color:#555555;"> 
    Olfa <a href="http://www.bibsonomy.org/author/Nasraoui">Nasraoui</a>         	     	 
        	  and Esin <a href="http://www.bibsonomy.org/author/Saka">Saka</a>         	     	 
        	 </span> 
  <em>WebMine</em>
    82-101
  (2006)
</div>
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        to
        <span class="bmtags">
        <a href="http://www.bibsonomy.org/user/dblp/dblp">dblp</a>
        </span>
        

          by <a href="http://www.bibsonomy.org/user/dblp">dblp</a> 
        
        
        on 2007-09-05 00:00:00 </span></div>
	    ]]>
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<item rdf:about="http://www.bibsonomy.org/uri/bibtex/28600056ca6d51d12a4d8466fb3644cf2/dblp">
    <title>Mapping Modern Science Using Co-citation Analysis.</title>
    <description>dblp</description><link>http://www.bibsonomy.org/bibtex/28600056ca6d51d12a4d8466fb3644cf2/dblp</link>
    <dc:creator>dblp</dc:creator>
    <dc:date>2007-07-05T00:00:00+02:00</dc:date>
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	    <![CDATA[
        <div class="block">
	      <div class="bmtitle">

  <a href="http://www.bibsonomy.org/bibtex/28600056ca6d51d12a4d8466fb3644cf2/dblp">Mapping Modern Science Using Co-citation Analysis.</a>
</div>
<div class="bmdesc">
  <span style="color:#555555;"> 
    Ayaka <a href="http://www.bibsonomy.org/author/Saka">Saka</a>         	     	 
        	  and Masatsura <a href="http://www.bibsonomy.org/author/Igami">Igami</a>         	     	 
        	 </span> 
  <em>IV</em>
    453-458
  (2007)
</div>
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        to
        <span class="bmtags">
        <a href="http://www.bibsonomy.org/user/dblp/dblp">dblp</a>
        </span>
        

          by <a href="http://www.bibsonomy.org/user/dblp">dblp</a> 
        
        
        on 2007-07-05 00:00:00 </span></div>
	    ]]>
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        <swrc:booktitle>IV</swrc:booktitle><swrc:crossref>conf/iv/2007</swrc:crossref><swrc:pages>453-458</swrc:pages><swrc:publisher><swrc:Organization swrc:name="IEEE Computer Society"/></swrc:publisher><swrc:title>Mapping Modern Science Using Co-citation Analysis.</swrc:title><swrc:year>2007</swrc:year><swrc:keywords>dblp </swrc:keywords><swrc:date>2007-07-05 00:00:00.0</swrc:date><swrc:hasExtraField>
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<item rdf:about="http://www.bibsonomy.org/uri/bibtex/20544547c158948befdf74ae9d1439c5a/statphys23">
    <title>Relaxation of a Single Knotted Ring Polymer</title>
    <link>http://www.bibsonomy.org/bibtex/20544547c158948befdf74ae9d1439c5a/statphys23</link>
    <dc:creator>statphys23</dc:creator>
    <dc:date>2007-06-20T10:16:09+02:00</dc:date>
    <dc:subject>brownian dynamics effects knot polymer rates relaxation ring simulations statphys23 topic-7 topological </dc:subject>
    <content:encoded>
	    <![CDATA[
        <div class="block">
	      <div class="bmtitle">

  <a href="http://www.bibsonomy.org/bibtex/20544547c158948befdf74ae9d1439c5a/statphys23">Relaxation of a Single Knotted Ring Polymer</a>
</div>
<div class="bmdesc">
  <span style="color:#555555;"> 
    S. <a href="http://www.bibsonomy.org/author/Saka">Saka</a>         	     	 
        	  and H. <a href="http://www.bibsonomy.org/author/Takano">Takano</a>         	     	 
        	 </span> 
  <em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics</em>
    
  (2007)
</div>
<span class="bmmeta">
  
  
        to
        <span class="bmtags">
        <a href="http://www.bibsonomy.org/user/statphys23/brownian">brownian</a>
        <a href="http://www.bibsonomy.org/user/statphys23/dynamics">dynamics</a>
        <a href="http://www.bibsonomy.org/user/statphys23/effects">effects</a>
        <a href="http://www.bibsonomy.org/user/statphys23/knot">knot</a>
        <a href="http://www.bibsonomy.org/user/statphys23/polymer">polymer</a>
        <a href="http://www.bibsonomy.org/user/statphys23/rates">rates</a>
        <a href="http://www.bibsonomy.org/user/statphys23/relaxation">relaxation</a>
        <a href="http://www.bibsonomy.org/user/statphys23/ring">ring</a>
        <a href="http://www.bibsonomy.org/user/statphys23/simulations">simulations</a>
        <a href="http://www.bibsonomy.org/user/statphys23/statphys23">statphys23</a>
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        <a href="http://www.bibsonomy.org/user/statphys23/topological">topological</a>
        </span>
        

          by <a href="http://www.bibsonomy.org/user/statphys23">statphys23</a> 
        
        
        on 2007-06-20 10:16:09 </span></div>
	    ]]>
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      <swrc:InCollection>
        <swrc:address>Genova, Italy</swrc:address><swrc:booktitle>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics</swrc:booktitle><swrc:month>9-13 July</swrc:month><swrc:title>Relaxation of a Single Knotted Ring Polymer</swrc:title><swrc:year>2007</swrc:year><swrc:keywords>brownian dynamics effects knot polymer rates relaxation ring simulations statphys23 topic-7 topological </swrc:keywords><swrc:date>2007-06-20 10:16:09.0</swrc:date><swrc:abstract>The relaxation of a single knotted ring polymer
%with the trivial or the trefoil knot
is studied by Brownian dynamics simulations. 
The relaxation rate $\lambda_q$ for the wave number $q$ is estimated
by the least square fit of
the equilibrium time-displaced correlation function
	$C_q(t) = N^{-1} \sum_i \sum_j C_{i,j}(t)
	\exp [{2\pi}q(j-i)/N] $
to a double exponential decay at long times. 
Here,
$N$ is the number of segments of a ring polymer and
$C_{i,j}(t)$ denotes the equilibrium time-displaced correlation function
of the positions of the $i$th and the $j$th segments
relative to the center of mass of the polymer.
\par
Figure 1 shows log-log plots of $\lambda_q$ versus $q/N$
for the single ring polymer with
(a) the trivial knot and (b) the trefoil knot.
The solid symbols represent the relaxation rates for $q=1$ and
the open symbols represent those for $q&gt;1$.
The relaxation rate distribution
of a single ring polymer with the trivial or the trefoil knot
appears to behave as
$ \lambda_q \simeq A(1/N)^x $ for $q=1$ and
$ \lambda_q \simeq A&#039;(q/N)^{x&#039;} $ for $q&gt;1$. 
In the case of the trivial knot,
$x \simeq x&#039; \simeq 2.15$ and $ A &lt; A&#039;$.
These exponents are similar to that found for a linear polymer chain. 
The topological effect appears as the difference between
the amplitudes, which does not appear for a linear polymer chain. 
In the case of the trefoil knot,
$x \simeq 2.52$, $x&#039; \simeq 1.95$ and $A &gt; A&#039;$.
It is found that
the slowest relaxation rate for each $N$ is given by $\lambda_q$ 
with $q=2$ for the small values of $N$ and 
that with $q=1$ for the large values of $N$.
This transition is considered to be caused by
the change of the structure of the ring polymer 
from a ``uniform&#039;&#039; state for small $N$, 
where the knotted part is extended widely along the ring polymer,
to a ``phase segregated&#039;&#039; state for large $N$,
where the knotted part is localized to a part of the ring polymer 
and the rest of the ring polymer behaves like
a ring polymer with the trivial knot.
See figure 2.
\par
This localization of the knotted part is 
confirmed by the analysis of the ``average structure.&#039;&#039;
The ``average structure&#039;&#039; is obtained  self-consistently 
by averaging many structures obtained from simulations,
which are translated and rotated 
to be matched to the ``average structure.&#039;&#039;
Note that
the ``average structure&#039;&#039; does not necessarily 
preserve the topology of the original structures. 
The ``average structures&#039;&#039; of the ring polymer with the trefoil knot
are shown in figure 3 for $N=24$ and $192$.
The ``average structure&#039;&#039;
changes from the double-loop structure for small $N$
to the single-loop structure for large $N$.
This change corresponds to the localization of the knotted part
of the ring polymer.</swrc:abstract><swrc:author>
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  <a href="http://www.bibsonomy.org/bibtex/2c1d0c4a42aa62a0ee1b2803aa06e4bf4/dblp">On the fractional-order logistic equation.</a>
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    A. M. A. <a href="http://www.bibsonomy.org/author/El-Sayed">El-Sayed</a>         	     	 
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        	 </span> 
  <em>Appl. Math. Lett.</em>
      <b>20</b>
      817-823
  (2007)
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    <title>A small time solutions for the Korteweg-de Vries equation using spline approximation.</title>
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    Dursun <a href="http://www.bibsonomy.org/author/Irk">Irk</a>         	     	 
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  <em>Applied Mathematics and Computation</em>
      <b>173</b>
      834-846
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    Bülent <a href="http://www.bibsonomy.org/author/Saka">Saka</a>         	     	 
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  <em>Int. J. Comput. Math.</em>
      <b>81</b>
      727-739
  (2004)
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    Nese <a href="http://www.bibsonomy.org/author/Zayim">Zayim</a>         	     	 
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  <em>Educational Technology &amp; Society</em>
      <b>9</b>
      213-222
  (2006)
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    <title>Development of Image Processing Program for Yeast Cell Morphology.</title>
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  <a href="http://www.bibsonomy.org/bibtex/2b71782502f710ab01bb8f7338977677d/dblp">Development of Image Processing Program for Yeast Cell Morphology.</a>
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    Miwaka <a href="http://www.bibsonomy.org/author/Ohtani">Ohtani</a>         	     	 
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  <em>J. Bioinformatics and Computational Biology</em>
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