<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">APM</journal-id><journal-title-group><journal-title>Advances in Pure Mathematics</journal-title></journal-title-group><issn pub-type="epub">2160-0368</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/apm.2014.412077</article-id><article-id pub-id-type="publisher-id">APM-52798</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Physics&amp;Mathematics</subject></subj-group></article-categories><title-group><article-title>
 
 
  Erratum to “Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5)” [Advances in Pure Mathematics 4 (2014), 494-497]
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>oshikatsu</surname><given-names>Sasaki</given-names></name><xref ref-type="aff" rid="aff1"><sub>1</sub></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>Department of Mathematics, Hiroshima University, Higashi-Hiroshima, Japan</addr-line></aff><author-notes><corresp id="cor1">* E-mail:<email>sasakiyo@hiroshima-u.ac.jp</email></corresp></author-notes><pub-date pub-type="epub"><day>18</day><month>12</month><year>2014</year></pub-date><volume>04</volume><issue>12</issue><fpage>680</fpage><lpage>681</lpage><history><date date-type="received"><day>1</day>	<month>June</month>	<year>2014</year></date><date date-type="rev-recd"><day>3</day>	<month>July</month>	<year>2014</year>	</date><date date-type="accepted"><day>15</day>	<month>July</month>	<year>2014</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.
 
</p></abstract><kwd-group><kwd>Painlev&#233; Hierarchy</kwd><kwd> String Equation</kwd><kwd> Elliptic Function</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>References</title></sec></body><back><ref-list><title>References</title><ref id="scirp.52798-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Douglas, M.R. (1990) String in Less than One-Dimensions and K-dV Hierarchies. Physics Letters B, 238, 176-180.http://dx.doi.org/10.1016/0370-2693(90)91716-O</mixed-citation></ref><ref id="scirp.52798-ref2"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Moore, G. (1990) Geometry of the String Equations. Communications in Mathematical Physics, 133, 261-304. http://dx.doi.org/10.1007/BF02097368</mixed-citation></ref><ref id="scirp.52798-ref3"><label>3</label><mixed-citation publication-type="other" xlink:type="simple">Moore, G. (1991) Matrix Models of 2D Gravity and Isomonodromic Deformations. Progress of Theoretical Physics Supplement, 102, 255-285. http://dx.doi.org/10.1143/PTPS.102.255</mixed-citation></ref><ref id="scirp.52798-ref4"><label>4</label><mixed-citation publication-type="other" xlink:type="simple">Fukuma, M., Kawai, H. and Nakayama, R. (1991) Infinite Dimensional Grassmannian Structure of Two Dimensional String Theory. Communications in Mathematical Physics, 143, 371-403. http://dx.doi.org/10.1007/BF02099014</mixed-citation></ref><ref id="scirp.52798-ref5"><label>5</label><mixed-citation publication-type="other" xlink:type="simple">Kac, V. and Schwarz, A. (1991) Geometric Interpretation of Partition Functions of 2D Gravity. Physics Letters B, 257, 329-334. http://dx.doi.org/10.1016/0370-2693(91)91901-7</mixed-citation></ref><ref id="scirp.52798-ref6"><label>6</label><mixed-citation publication-type="other" xlink:type="simple">Schwarz, A. (1991) On Solutions to the String Equations. Modern Physics Letters A, 29, 2713-2725.http://dx.doi.org/10.1142/S0217732391003171</mixed-citation></ref><ref id="scirp.52798-ref7"><label>7</label><mixed-citation publication-type="other" xlink:type="simple">Adler, M. and van Moerbeke, P. (1992) A Matrix Integral Solution to Two-Dimensional Wp-Gravity. Communications in Mathematical Physics, 147, 25-26. http://dx.doi.org/10.1007/BF02099527</mixed-citation></ref><ref id="scirp.52798-ref8"><label>8</label><mixed-citation publication-type="book" xlink:type="simple">van Moerbeke, P. (1994) Integrable Foudations of String Theory. In: Babelon, O., et al., Ed., Lectures on Integrable Systems, World Science Publisher, Singapore, 163-267.</mixed-citation></ref><ref id="scirp.52798-ref9"><label>9</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Takasaki</surname><given-names> K. </given-names></name>,<etal>et al</etal>. (<year>2007</year>)<article-title>Hamiltonian Structure of PI Hierarchy</article-title><source> SIGMA</source><volume> 3</volume>,<fpage> 42</fpage>-<lpage>116</lpage>.<pub-id pub-id-type="doi"></pub-id></mixed-citation></ref><ref id="scirp.52798-ref10"><label>10</label><mixed-citation publication-type="other" xlink:type="simple">Ince, E.L. (1956) Ordinary Differential Equations. Dover Publications, New York.</mixed-citation></ref><ref id="scirp.52798-ref11"><label>11</label><mixed-citation publication-type="other" xlink:type="simple">Conte, R. and Mussette, M. (2008) The Painlevé Handbook. Springer Science + Business Media B.V., Dordrecht.</mixed-citation></ref><ref id="scirp.52798-ref12"><label>12</label><mixed-citation publication-type="other" xlink:type="simple">Weiss, J. (1984) On Classes of Integrable Systems and the Painlevé Property. Journal of Mathematical Physics, 25, 13-24. http://dx.doi.org/10.1063/1.526009</mixed-citation></ref><ref id="scirp.52798-ref13"><label>13</label><mixed-citation publication-type="other" xlink:type="simple">Kudryashov, N.A. (1997) The First and Second Painlevé Equations of Higher Order and Some Relations between Them. Physics Letters A, 224, 353-360. http://dx.doi.org/10.1016/S0375-9601(96)00795-5</mixed-citation></ref><ref id="scirp.52798-ref14"><label>14</label><mixed-citation publication-type="other" xlink:type="simple">Gromak, V.I., Laine, I. and Shimomura, S. (2002) Painlevé Differential Equations in the Complex Plane. Walter de Gruyter, Berlin. http://dx.doi.org/10.1515/9783110198096</mixed-citation></ref><ref id="scirp.52798-ref15"><label>15</label><mixed-citation publication-type="other" xlink:type="simple">Shimomura, S. (2004) Poles and α-Points of Meromorphic Solutions of the First Painlevé Hierarchy. Publications of the Research Institute for Mathematical Sciences, Kyoto University, 40, 471-485. http://dx.doi.org/10.2977/prims/1145475811</mixed-citation></ref><ref id="scirp.52798-ref16"><label>16</label><mixed-citation publication-type="other" xlink:type="simple">Kimura, H. (1989) The Degeneration of the Two Dimensional Garnier System and the Polynomial Hamiltonian Structure. Annali di Matematica Pura ed Applicata, 155, 25-74. http://dx.doi.org/10.1007/BF01765933</mixed-citation></ref><ref id="scirp.52798-ref17"><label>17</label><mixed-citation publication-type="other" xlink:type="simple">Suzuki, M. (2006) Spaces of Initial Conditions of Garnier System and Its Degenerate Systems in Two Variables. Journal of the Mathematical Society of Japan, 58, 1079-1117. http://dx.doi.org/10.2969/jmsj/1179759538</mixed-citation></ref><ref id="scirp.52798-ref18"><label>18</label><mixed-citation publication-type="other" xlink:type="simple">Shimomura, S. (2000) Painlevé Property of a Degenerate Garnier System of (9/2)-Type and a Certain Fourth Order Non-Linear Ordinary Differential Equation. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 29, 1-17.</mixed-citation></ref></ref-list></back></article>