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Rouse Dynamics of Topological Polymers through Gaussian Random Embeddings and Comparison with Experiments Deguchi, Tetsuo
Description
<p class=MsoNormal align=left style='text-align:left;line-height:14.0pt; mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family: "\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>Recently, polymers of complex chemical connectivity expressed with graphs have been synthesized in experiments [1-3]. It is indeed marvelous that even such polymers expressed with K<sub>3<span class=GramE>,3</span></sub> bipartite graph have been produced [2]. We call polymers with nontrivial structures in chemical connectivity <i style='mso-bidi-font-style:normal'>topological polymers</i>. We also call polymers with nontrivial topology of spatial graphs as embeddings in three dimensions<i style='mso-bidi-font-style:normal'> topological polymers</i> [4].</span></p> <p class=MsoNormal align=left style='text-align:left;line-height:14.0pt; mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family: "\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>The Rouse dynamics of a polymer plays an important role in the dynamical aspects of the polymer in dilute solution, and also in melts if the molecular weight is small [5]. In this talk, we formulate the Rouse dynamics of the topological polymer with a given graph. We derive several physical consequences of the model. In particular, we compare the experimental data of Size Exclusion Chromatography (SEC) of some topological polymers with their theoretical estimates of the mean-square radius of gyration obtained by the Gaussian method [6]. We argue physical backgrounds of SEC data and discuss how they are consistent.</span></p> <p class=MsoNormal align=left style='text-align:left;line-height:14.0pt; mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family: "\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>After reviewing the method for constructing Gaussian random configurations of a topological polymer, i.e. Gaussian random graph embeddings [6], we derive the normal coordinates and modes for the topological polymer. Here we remark that while the Moore-Penrose generalized inverse matrix has been addressed for general Gaussian molecules about three decades ago [7], it seems that important consequences were found later independently [8]. Moreover, it has not been known until quite recently how to generate Gaussian random configurations of a given topological polymer [6]. In fact, we can calculate any physical quantity at least numerically by taking the ensemble averages over generated configurations. It is quite nontrivial to generate such random walks that satisfy the constraints of all independent loops in the graph.</span></p> <p class=MsoNormal align=left style='text-align:left;line-height:14.0pt; mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family: "\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>The results of this talk are obtained in collaboration with Jason Cantarella, Clayton Shonkwiler, and Erica Uehara.</span></p> <p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l3 level1 lfo8'><![if !supportLists]><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:11.0pt; mso-bidi-font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-fareast-language: JA'><span style='mso-list:Ignore'>1)<span style='font:7.0pt "Times New Roman"'> </span></span></span></i><![endif]><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family: "\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>Topological Polymer Chemistry: Progress of cyclic polymers in synthesis, properties and</span></i></p> <p class=MsoNormal style='margin-left:18.0pt'><i style='mso-bidi-font-style: normal'><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt; mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'><span style="mso-spacerun:yes"> </span><span class=GramE>functions</span></span></i><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family: "\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>, Y. Tezuka ed., World Scientific, Singapore, 2013.<span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span></span></p> <p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd; text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace: none;word-break:break-all'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family: "Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span style='mso-list:Ignore'>2)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; mso-bidi-font-size:12.0pt;line-height:115%;color:black;mso-font-kerning:0pt; mso-fareast-language:JA'>T. Suzuki, T. Yamamoto and Y. Tezuka. <i>J. Am. Chem. Soc.</i>, 2014, <b style='mso-bidi-font-weight:normal'>136</b>, 10148–10155.</span><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%; mso-font-kerning:0pt;mso-fareast-language:JA'></span></p> <p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd; text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace: none;word-break:break-all'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family: "Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span style='mso-list:Ignore'>3)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; mso-bidi-font-size:12.0pt;line-height:115%;color:black;mso-font-kerning:0pt; mso-fareast-language:JA'>Y. Tezuka. <i>Acc. Chem. Res.</i>, 2017, <b style='mso-bidi-font-weight:normal'>50</b>, 2661–2672.</span><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%; mso-font-kerning:0pt;mso-fareast-language:JA'></span></p> <p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd; text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace: none;word-break:break-all'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family: "Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span style='mso-list:Ignore'>4)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language: JA'>E. Uehara and T. Deguchi, <i style='mso-bidi-font-style:normal'>J. Chem. Phys.</i> 2016, <b style='mso-bidi-font-weight:normal'>145</b>, 164905.</span></p> <p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd; text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace: none;word-break:break-all'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family: "Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span style='mso-list:Ignore'>5)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language: JA'>M. Doi and S. F. Edwards, <i style='mso-bidi-font-style:normal'>The Theory of Polymer Dynamics</i>, Oxford University Press, Oxford, 1986.<span style="mso-spacerun:yes"> </span></span></p> <p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd; text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace: none;word-break:break-all'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family: "Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span style='mso-list:Ignore'>6)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language: JA'>J. Cantarella, T. Deguchi, C. Shonkwiler and E. Uehara, in preparation.</span></p> <p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd; text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace: none;word-break:break-all'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family: "Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span style='mso-list:Ignore'>7)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language: JA'>B. E. Eichinger, <i style='mso-bidi-font-style:normal'>Macromolecules</i>, 1980, <b style='mso-bidi-font-weight:normal'>13</b>, 1-11.</span></p> <p class=MsoListParagraph style='margin-left:13.5pt;mso-para-margin-left:0gd; text-indent:-13.5pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace: none;word-break:break-all'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family: "Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span style='mso-list:Ignore'>8)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%; mso-font-kerning:0pt;mso-fareast-language:JA'>E. Estrada and N. Hatano, <i>Chem. Phys. Let. </i>2010, <b style='mso-bidi-font-weight:normal'>486</b>, 166–170.</span></p>
Item Metadata
Title |
Rouse Dynamics of Topological Polymers through Gaussian Random Embeddings and Comparison with Experiments
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2019-03-28T10:32
|
Description |
<p class=MsoNormal align=left style='text-align:left;line-height:14.0pt;
mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family:
"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>Recently, polymers of complex chemical
connectivity expressed with graphs have been synthesized in experiments [1-3]. It
is indeed marvelous that even such polymers expressed with K<sub>3<span
class=GramE>,3</span></sub> bipartite graph have been produced [2]. We call
polymers with nontrivial structures in chemical connectivity <i
style='mso-bidi-font-style:normal'>topological polymers</i>. We also call
polymers with nontrivial topology of spatial graphs as embeddings in three
dimensions<i style='mso-bidi-font-style:normal'> topological polymers</i> [4].</span></p>
<p class=MsoNormal align=left style='text-align:left;line-height:14.0pt;
mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family:
"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>The Rouse dynamics of a polymer
plays an important role in the dynamical aspects of the polymer in dilute
solution, and also in melts if the molecular weight is small [5]. In this talk,
we formulate the Rouse dynamics of the topological polymer with a given graph. We
derive several physical consequences of the model. In particular, we compare
the experimental data of Size Exclusion Chromatography (SEC) of some
topological polymers with their theoretical estimates of the mean-square radius
of gyration obtained by the Gaussian method [6]. We argue physical backgrounds
of SEC data and discuss how they are consistent.</span></p>
<p class=MsoNormal align=left style='text-align:left;line-height:14.0pt;
mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family:
"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>After reviewing the method for
constructing Gaussian random configurations of a topological polymer, i.e.
Gaussian random graph embeddings [6], we derive the normal coordinates and modes
for the topological polymer. Here we remark that while the Moore-Penrose
generalized inverse matrix has been addressed for general Gaussian molecules about
three decades ago [7], it seems that important consequences were found later
independently [8]. Moreover, it has not been known until quite recently how to
generate Gaussian random configurations of a given topological polymer [6]. In
fact, we can calculate any physical quantity at least numerically by taking the
ensemble averages over generated configurations. It is quite nontrivial to
generate such random walks that satisfy the constraints of all independent loops
in the graph.</span></p>
<p class=MsoNormal align=left style='text-align:left;line-height:14.0pt;
mso-line-height-rule:exactly;mso-layout-grid-align:none;text-autospace:none'><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family:
"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>The results of this talk are
obtained in collaboration with Jason Cantarella, Clayton Shonkwiler, and Erica
Uehara.</span></p>
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l3 level1 lfo8'><![if !supportLists]><i
style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:11.0pt;
mso-bidi-font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-fareast-language:
JA'><span style='mso-list:Ignore'>1)<span style='font:7.0pt "Times New Roman"'>
</span></span></span></i><![endif]><i style='mso-bidi-font-style:normal'><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family:
"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>Topological Polymer Chemistry:
Progress of cyclic polymers in synthesis, properties and</span></i></p>
<p class=MsoNormal style='margin-left:18.0pt'><i style='mso-bidi-font-style:
normal'><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;
mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'><span
style="mso-spacerun:yes"> </span><span class=GramE>functions</span></span></i><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;mso-fareast-font-family:
"\FF2D\FF33 \660E\671D";mso-fareast-language:JA'>, Y. Tezuka ed., World
Scientific, Singapore, 2013.<span style="mso-spacerun:yes"> </span><span
style="mso-spacerun:yes"> </span></span></p>
<p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd;
text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace:
none;word-break:break-all'><![if !supportLists]><span lang=EN-US
style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span
style='mso-list:Ignore'>2)<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;
mso-bidi-font-size:12.0pt;line-height:115%;color:black;mso-font-kerning:0pt;
mso-fareast-language:JA'>T. Suzuki, T. Yamamoto and Y. Tezuka. <i>J. Am. Chem.
Soc.</i>, 2014, <b style='mso-bidi-font-weight:normal'>136</b>, 10148–10155.</span><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;
mso-font-kerning:0pt;mso-fareast-language:JA'></span></p>
<p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd;
text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace:
none;word-break:break-all'><![if !supportLists]><span lang=EN-US
style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span
style='mso-list:Ignore'>3)<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;
mso-bidi-font-size:12.0pt;line-height:115%;color:black;mso-font-kerning:0pt;
mso-fareast-language:JA'>Y. Tezuka. <i>Acc. Chem. Res.</i>, 2017, <b
style='mso-bidi-font-weight:normal'>50</b>, 2661–2672.</span><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;
mso-font-kerning:0pt;mso-fareast-language:JA'></span></p>
<p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd;
text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace:
none;word-break:break-all'><![if !supportLists]><span lang=EN-US
style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span
style='mso-list:Ignore'>4)<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;
mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language:
JA'>E. Uehara and T. Deguchi, <i style='mso-bidi-font-style:normal'>J. Chem.
Phys.</i> 2016, <b style='mso-bidi-font-weight:normal'>145</b>, 164905.</span></p>
<p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd;
text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace:
none;word-break:break-all'><![if !supportLists]><span lang=EN-US
style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span
style='mso-list:Ignore'>5)<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;
mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language:
JA'>M. Doi and S. F. Edwards, <i style='mso-bidi-font-style:normal'>The Theory
of Polymer Dynamics</i>, Oxford University Press, Oxford, 1986.<span
style="mso-spacerun:yes"> </span></span></p>
<p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd;
text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace:
none;word-break:break-all'><![if !supportLists]><span lang=EN-US
style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span
style='mso-list:Ignore'>6)<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;
mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language:
JA'>J. Cantarella, T. Deguchi, C. Shonkwiler and E. Uehara, in preparation.</span></p>
<p class=MsoListParagraph style='margin-left:18.0pt;mso-para-margin-left:0gd;
text-indent:-18.0pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace:
none;word-break:break-all'><![if !supportLists]><span lang=EN-US
style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span
style='mso-list:Ignore'>7)<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt;
mso-bidi-font-size:12.0pt;line-height:115%;mso-font-kerning:0pt;mso-fareast-language:
JA'>B. E. Eichinger, <i style='mso-bidi-font-style:normal'>Macromolecules</i>,
1980, <b style='mso-bidi-font-weight:normal'>13</b>, 1-11.</span></p>
<p class=MsoListParagraph style='margin-left:13.5pt;mso-para-margin-left:0gd;
text-indent:-13.5pt;line-height:115%;mso-list:l3 level1 lfo8;text-autospace:
none;word-break:break-all'><![if !supportLists]><span lang=EN-US
style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;mso-fareast-font-family:
"Times New Roman";mso-font-kerning:0pt;mso-fareast-language:JA'><span
style='mso-list:Ignore'>8)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;line-height:115%;
mso-font-kerning:0pt;mso-fareast-language:JA'>E. Estrada and N. Hatano, <i>Chem.
Phys. Let. </i>2010, <b style='mso-bidi-font-weight:normal'>486</b>, 166–170.</span></p>
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Extent |
28.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
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Notes |
Author affiliation: Ochanomizu University
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Series | |
Date Available |
2019-09-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0380996
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
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