• 検索結果がありません。

変換結果スキーマ指向のXML変換

N/A
N/A
Protected

Academic year: 2021

シェア "変換結果スキーマ指向のXML変換"

Copied!
8
0
0

読み込み中.... (全文を見る)

全文

(1)

(2) . .        .   .              ' ( ' ( 2 6  3 7 $ + 1 9 * , " 4 " 8 ! 0 / & )  . 5 # % ' ' ( : @ H = ? < C C I J ; > > E B 8 ! ! & F G A A D M0>}A&l]~N-^Om>AEn_8*`u&Rv*w0'5€x/(P&:4o‚pa;]-^>b<py4=35-TPƒqQc„*R >0†8_Ap:zS!;-.b<"^T={&4<*Y5='Z|>‡(8Uˆr0VdW9eXfT+g*&,>"-h‰YiŠZj3>&45sTD*(t-&K)[Lk\  Œ Ž ‹ – š œ ‘ “ ’ ™ ”  ˜ • › ž Ÿ —   ¨ ­ “   ¬ ¯ ¯ ® ± ¥ ° ¡ ¦ « © £ ¤ ¤ ª ¢ § ”§¤±˜»«Ä²½¨ Å¤³©µÃؕÓҕª“ÀÔ´”Çž«µ¾±²Õœ³¶ÖÝ·•×¸Ù´Æȕš¹²ÞžÉ¥ßƤκ¦Ú¯»¡¢¸¼Û•Ê›¹±Ë¢Ü½ºžÏݾ»¥Âм¿Ò̤Õ Íà½ÑÀ•¤Ò¤Á´¬˜§­š–º¨—¾»©¼á˜°ª ٠㠜 å ç ä × ä âý²Ò¾ž×ùᳲҠ⢡Éã×ò± ¾ æ ± è  À ž • ž ² ë å µ ¾ æ « › ¼ ž Ò £ » ) ¤ ¤ ¤ Ÿ Ì ê ë í ñ ò é ð î › › — ¤ ì ï ¢ ¢  þ ÿ ë , « ¼ Ò » ) + Ÿ ó á ö ô õ ÷ ÷ ¼ — ¤ ø ª *  / 0 ” « . • š û ý þ ü ÿ   ¯ µ ú À Ü • ¤ ¤  ´ Ù Ì  4 1 2  × 3 ú ¾ ¾ À • ž ² ² £ ³ ³ Ÿ Ì –    ¶ É ¾ ” ˜ È  ² £ — ´  ´ ¢ / ý 5 1 0 ú ” « › ¤ + 6 ë í  × . Ç  î • ›  ì ¢ *    ; 9 : 7 8 È ¡ Î ¯  . • Ò ¤  ´ 2 1   ? @ ú ± > ¾ < 8 È = Æ • ž ¤ ¤ ¢ .     

(3)           · 1 1 É ¯ ¯ A × É A ú ± ú 7 ” Å À • ³.       !"#$%

(4) &'(ŐB²³•´ 2003−DD−39  (7)                         2003/5/23 2003. 社団法人 情報処理学会 研究報告 IPSJ SIGVol. Technical 0 No. 0 Report. XML. †. XML. ††. XML. node. XTL node. XPath. XTL. XML. 10. X SLT0. 69. XTL XTL. DTD. XSLT 5 XTL XSLT W3C query use cases XTL. 97.10%. Output Schema Driven XML Transformation M AKOTO O NIZUKA† and K AZUYA KONISHI††. This paper describes an XML transformation model and language called XTL (XML transformation language). XTL is declarative and is based on the output schema driven approach, which gives it the following capabilities: 1) the XML schema language part (we are currently using DTD) specifies the output structure of transformations, 2) The XPath expression part maps the resulting node-set in the input XML documents to the output structure. Users need to understand only DTD and XPath specifications, along with a few XTL extensions and semantics. We applied XTL to the W3C query use cases, and the results showed that XTL can express 97.10% of the 69 queries. This paper also describes an algorithm to translate an XTL program into an XSLT program with hash join optimization rewrite option.. 1.. B2B. ... <xsl:template match="bib"> <xsl:element name="bib"> <xsl:apply-templates select="(//author)" mode="distinct"> <xsl:with-param name="nodes" select="//author"/> </xsl:apply-templates> </xsl:element> </xsl:template>. B2C. XML. TVAnyTime16) , MPEG79) , P/meta13). XML. XML. XML. XML. XML. XSLT3). <xsl:template match="author" mode="distinct"> <xsl:param name="nodes"/> <xsl:variable name="pos" select="position()"/> <xsl:if test="count($nodes[$pos>position() and .=current()/.])=0"> <xsl:apply-templates select="." mode="author"/> </xsl:if> </xsl:template> .... 2. XSLT. XSL. author. 14). (XSL FAQ ). author. XML. author. XSLT. author. author. author. † ††. NTT NTT. author. NTT. 1 −39−. 2. author.

(5)

(6) . .       Ì š š ¨ h ´ C D Í I  µ × õ ×   ¾ ± ¾ À È . ž • › • ² Ò W » ¤ ¤ G Ÿ ³ ¢  Ù  Ù š  Ÿ µ ¶ ë ¶ É ¯ × É ¾ æ ¥ À È ¦ © • • ž  ² ¤ ì ª ´ ´ Ù ý h à  Û ¯ A ¸   ¾ ¾ ± · À ° Å € › • Ò £ ¤ §  º š ¹ I ± « ¤ Ù C JTTEK¾£\b—UZF¤¯[]îOž¨×P²¤Gþ´³•ùŸ¯ÿ8¥Q¤VA¤¦ãžGžµªÅ²¢ë²›—W^8Yì¢ëX‘_¤ÆíC’aÒ+î¡åD–›“Kïæ¾”`G—Òè垕¥¾›î³æ²ÈáLÀ×Aâ*•Å¯×¼É£×¾•OMù•ÙÀP±±³¥šNÒ¦a£¤É è RÌ¢–À¯•SHòGšÒ´³±Ic+¾¾“´¢/IÃÀƱ“ÀÁ”±»0›ŸÄhý¼¤v搾z“•´–G”9×5›“a—”¥¢6•—Ù¥´Ù¤«“Źšš”ºšIWI¥h±IÒ»±Ò±´¯¾À QG³¢¡GžQٛ¢¤²š— g  š Ÿ I ± æ ¢ Ù š I ½ ± › ¤ ¢ Ù “ ¿ » v † ” • ´  ‰  ˆ 7 Î  – | ¤ C É g ° È ž ¤ Ù  Ù   ã h e e  ä × × ¾ ¾ ¾ d À ¥ Å f ¦ f Æ • • £ ¤ a à — ´ ¢ š C h h y É 2 × g õ Ê – ¯ z – ± ¾ v i ¡ | › ž ² + ï — Ç È – y 2 p q É jšrâýƾ^k{¤¤Þpe|‡wël[xfqח숥¾•“+•í‰€”£ÒîÌۀÀ Û³¢•¤ҐžÉ›²m sÈ¢³n•ë Y¡•¾£›tìÒÙ´oÙuÀí ×ƚîv£ Ê z   À À < ¡ ˜ • ² ¤ ¤ ¤ — ³ ´ ¢ ‰ w y I I Í ˆ Ì   x z ¯ Ë ª ± ± ° 7 ¡ Í Î • Ã Ò ¤ ¢  Ù š } h  9 ~ ¯ × × ¾ » v. † È ¡ ¾ ¾ • ¤ ¤ Ÿ ´ Ù Ù š w ë í I Î ’ × Ï Þ x ± â î Æ •  W » G ¤ ì à Ù š ý Ñ ‚ „ ƒ Ð – ± » v † ”  È | ž  ² £ ¤ ¤ B §  Ù  Ó × k ’ j Õ × Ö ¾ À  † 7 Å Î Ò Æ • • £ Ô ¤ ¤ — ¢  Ù š C h Ÿ ë  9 I g × × ¾ ± ¾ æ ¾ Æ • • » G ¤ š µ ¶ C Ã Ã Þ g ¥ À ¦ › ž ² 뱤›Àמ³ÒÆì— í•ÞÉ¢m+•î£nK¤ÀÀ›—c§¤±¾Ù+¨¶ š©Š••œC±‹ªgҐ¢¾ŽÇ¤«‘8j×ɾ´w”´kŸ’¾0¤æ¾¥žänh7¢À·“— ¤˜”™Œ•ZšO¤·¾×’³æ¯DⳕÞÛٔ£–¤¾À±âžj¤à²³ÎhD¾›•¤’7¤±“ԣٔו—šÞÒÀÅaß´Ù¤< –ëÍóؕGìšÒ—´íI٠٣Îڡ³¢C*²¤ŸÙg¼ÈšæM¢úIɓj¯±”kÛõ|¥¤×á¤|–»•ë›–†m¢ìvÔn™Ù¤—ížš¤Ü¾îÅ\ÝI’±  É   ± ¢–ר“”×Zו[••¤´£ÈCe¥ÀÉDfÒ믤¤×ìŸw£þA•xí.Åãý®ä³OŸÒ¾Pèțv¾²¡¢Ì–\ÆþÍ×¥][Ÿ¾•×€ežæ®´²•Ûf“£¥³Ò”¦¥¤É¦V ëCž¢´•WªD²õ£§¢X»À̑Cƾ¾¡ÍD’ævÞÇۖ¤›äҞ ²³›±¤t´ëä•jÒ|촉 –íÙÒÀ“•î»Çš”t´†›“¼þ¢È”£ÿ¤Ù¡•ŸÀ\š ¤|â}Cזjãg—•ë´˜ìkë¾jíìk±î8íÆåÙ—¤Þ²Ù¯+±šå•“´µ”âC—|g€²+¾ 㠉 ë í å © “ “ ä Þ ¯ j æ ± è. ” À ” î › • › ² Ò ¤ ì ï V ª ´ ¢ ¨ š C D C D 5 ´ ë í ¯ Þ ˆ Ø K ” È î Æ • ›  W W » G ¤ G ¤ + 6 ì — X ¢  Ù š ‰ I æ “ × Û ¾ ª « ±. ± v À † • › ž • Ò £ ¤ ´ ´ Ù š à I – ¾ ± | ¤ ¯ ­ Ù ° ® 5 × ¬ • › › Ò ¤ 6 à ´ ¢ š ² h ë í I  “   – – Þ ˆ ± v ± v Å ” ¥. î Æ ›  Ò ² ¤ a ¤ ì — B DÒ •´Ù ‰“”¢Ø¤Ò¤±çè“ 2. 2003. 2. • ∆. XML. XML. XSLT. (xalan, saxon, xt. ). XPath. XML. (XPath. 2. XML. ). XSLT. XPath. xsl:key. node-set. node. xsl:key. xsl:key. XSLT. • M. XML. XML. node. XML. XTL. XTL. XSL. XTL. node. 1). 3. 2). (. ,. ,. ,. /. ,. /. • Σ. ). XSLT. (. node. ). (. XML. ). 4. 1). XTL. 2). XSLT. XTL. (. 10. XML. XTL. DTD. XML. XTL. XSLT. ) 3). XML. XPath. 10. 4) XPath. node-set. • V. XTL. DTD XTL. XTL. XSLT0 ’s1). XSLT. 5. XML. W3C. XTL. 97.10%. yacc. (DTD. 69. XTL. XSLT. XML. XML. 2. (. XML. XSL. XSLT. ). XTL. ). mation graph). XTL. schema graph). XSLT. 1. T-graph (transforS-graph (output. 2. XTL. 4. XML. XML. xsl:key. DOM. , T-graph, S-graph,. DOM. XSLT. XSLT. XML. DOM. xsl:key. XTL. T-graph. XML. S-graph. T-graph. node. node. edge. XML. 2. XTL XTL. XPath. node. T-graph. S-graph. r = (∆, M , V ∗ , Σ). node(. node. T-graph. node. node. −40−. edge. T-graph. edge. ).

(7) '(:;éêF?m&'( ë È ² B ٠̔”ž|²••Ù´ˆ–š‰™R¤“S”¾•ëƟ´QÞ枤¥²¢CDgíàٱÙÀššRhCSg“”ìҕ—’´«âþtï“ÀšŸú1õۛÀÉæIc³1žÙʱ²“ÉÍú”曾ü1ïv³•õü–|[[Èc–õ××hžc¥Éµ••³Ê´¶È·0¾Ò³D•¥vãQٛ–¢žš×|²I˜–¾•¢±íòÙöÙÒóš÷͛žCaÀ¢¾¥g–<^æÀG³ É Ê ú ¤ 1 ü ¥ š I ± Ù ž ² Y ¤ s  ´ š š õ Í ü I ^ I É c ± ± À È • › Ò ³ ñ ¢ Ù  Ù Ù ð š C Ÿ “ g – ¯ – æ ¾ v Q ” | ž ž • ² ¢ Ù ‰ ë í “ Y Þ j  ” ¾ î Æ ›  ¤ ¤ ì Ÿ 0 ¥ s ´ ¢ ò ’ × ó â ¥ ¦ • • ¤ ´ – – | |  • ¤  D  É í Í É Þ Ê  0 À ˜ È Æ • › Ò ³ ¤ ¢ à í Þ ô ¥ ¦ Æ Ù  » ¤ ï ª 1 É   – Ê – × ú ¾ v À < ¡ | • ³ ´ š S Ì h R  ™  “  ” « • ¤ à — Ù ì ›  2  × Û ¾ æ Å • ž ² Ô ³ — î š ý ´ À Á í Î › ›   W » ¤ ¤ G ´ ¢  Ù  ™ Í Þ Û æ ” | • ² ³ õ 1 Ä I z c ú Ë ª ± ¥ ž ² ³ ¤ ¢ î ¥ C h í 2 g – × ¾ ¾ v Q Æ ž ž • ² ¤ ¢ – ö õ ÷ Ä ü z × ‹ c ø « • È ² ³ a G + Ÿ ´ * y · Û ¶ z   µ ¾ ± À ¡ € • • Ò £ ´  ã 1 ü ¶ ù ^ ú Ð ú û ¾ ¥ ¦ › • › Ò ¤ ¢  œ ü[ú›<³1~פ¥ÇÛʕÈÀ¤´ÙžÉòv²š2ó–Cý¤¯þgyʞÿj¡Ù¤ÒkzȚv›²ha–¢Éa |2G—•–yҴśþ¡¾¤zvÿ’²–h¤aã×Ñ\|—äؕ▴¾ÔÅjúœhûÒ¤Àž1²¤•úþޔ1ÿ ö•¤ ÷´Ù š2›I¤h›CÒÒg››±¢^yúÀ¡1šzI²À±³ÞÀƔɳȢ޻Éh†2Çv±.¤ÊÒy“2”±¡ú› z•  Ç ´ ¢ Ù  h y 2 2 ï Û z – ¥ Å À ¡ | ž ² Ô — š ö h 9 I 1 ÷  “ Ð ± ú ” ¥ ¾ Ò Ò ¤ ¢  È Ù î y í “ 2 z × ” ¥ È ¡ ¡ • ² ¤ š h  9 I ± ” Q ¾ | ž › › ´ ¤ ¢ ¢  Ù š Ÿ “ I É 1 Ê æ ± ú ¾ v ” ¥ Î ² ³ ¤

(8) h  – Ð × . • ¤ ¢ ï Ù ª  D õ Ÿ 1 ü “ –  ú c ¾ æ æ ¥ ž › • ³ ³ ”ÙšI±Î³²¢Év–ž¥è´¯³D“¥ÙšI±»†v“”•´£Éž² Vol. 0. No. 0. XML. 3. /bib. bib. Bib. Bib. book. Title. group-by(). ./book/title. title. Title*. Transform. pcdata. pcdata. T1. ./text(). T2. T3. T1 A1 A2. Transformation graph Output Schema graph. DOM Tree. Output DOM Tree. 1 A Transformation Example. T-graph. S-graph. (. node-set. ,. (XTL. DTD. ). XML. ). node. T-graph. S-graph. DOM. <!ELEMENT book (author*, title, publisher)>. <!ELEMENT Bib AS {/bib} (Title * AS {./book/title} DISTINCT BY {.})> <!ELEMENT Title (#PCDATA AS {./text()}). book. node. (. 2 An XTL Program Example. ). <!VARIABLE book (author*, title, publisher)>. 3. XTL. node. XTL. 3. 1) T-graph, S-graph XML. DTD, 2). node-set. (. ). T-graph. XPath. , 3) T-graph. (. ,. $. S-graph. node. node-set. ∆. ). <!ELEMENT $book (author*, title, publisher)>. node. XPath. DTD. Σ. (count, max, concat. DTD. ). XML. <!ELEMENT author_count (#PCDATA VALUE count(author))> <!ELEMENT version (#PCDATA "Jan/3/2003")>. 3.1 DTD (. ). DTD. XTL. graph). author count. XML. (T-. (S-graph). count(author). 2. 2. v ersion. ”Jan/3/2003”. XTL. 3. (. ,. /. /. ,. node. ). sequence. 3. choice. 2. sequence. node. choice. XML. DTD. node. XPath. sequence. −41−.

(9)

(10) . .       š š h á h k  I à – j Õ × É ¯ × ¾ ¾ â ± À. | › • ž › • • Ò ³ ï ª ¢ ¢ Ù Ù Ù  š · Ÿ ¶ Æ I “ Ö µ ± æ ” 8 . • ² ³ ¤ ¤ ´ ¢ ¢  C Ù  ¨ – × ¾ v ô ¾ ž • ½ ² ¤ º — — ´ § * š ¹   D « ž ² W » G š I É ¾ æ ± À ¥ ¾ B › ³ ³ ¤ ¢ Ù ¢ Ù  ¨ ´ h  “ à ± ” ¥ ½ G ¤ þ ÿ à ¯ Å. — • ž ² Ô ³ Ÿ ï ª —  § *     D A ×  –. ô Å. | È ¡ 8 • › ¤ ï º Æ ¯  ¾ » v ª ¥ † • ž ¢ ¢  º š E ¹ I ß “ ± ” « • ¤ ¤ Ã Æ ¯ ¯. ¥ — • ž • ï ª Ù  Ù J H š|ÀŖ³8IŸ”±É¾²»±†¾væׯ³•¥Ù š<Iññ´›À¯ï ¢¾Þªž•»· |´†¢×–vv•¾¯´C¤ÞgÔ ·—Ʊ›ž|I«Ù±–šÒ×¾W›r•»Àä¢M´5ž›¾3G²|694ÙF¤–¥ýȚGÄBIQ²›±õ¢¤hQ»¾“ž†Ã”²vÒ¢•Ã“Ù8”¾×[š¤Èµ•´I´¡¶±K5L6¾Ä¤¤Ø“z”Ù)šÃ•»« ¢ š º š ´ h ¹  “ Ë ” « Æ › • W » G G — C g v À › • ¢ Ù  Ù š µ ¶ I 9 I × ª ± ± ¾ » v 7 † À ¾ Î • ž ² ¤ – ö ÷ 1 Ñ 0 ú ¥. è › ž › Ò a G ¤  Ù ¢ h D  “     é ” ¡ › QÍÒÈÀZ³ ›žÉ 8²•ÉvÙȔ£¡âBšÀÞ²I›0͟¨±¯À¾›¦•¢hÞ|ï”×´–¤•¥•µCs£¶ÃgYÀ·±¤¢ïÃQ€ªÛž ²Òא •Q¾•×¤±j¢mk³±nÉA¾¤¶Dų¤·ù¥¢¢“”Æ•ö±¤÷åa±h˜|“—G–”»±¥ÈB¤G²Ò±—´ ï•«BÙúª² š1“¢×”I8±ï••¤´ªD È´×Bµh²• ¢  × · ¨  ¯ Þ É m n × ± ¾ 7 ” À •  ³ š š ¹ 1 I É ú ± À 7 « Î • › ³ ¤ G ´ — Ù  Ù . . º µ   Ò ¤ ´  ö ÷ ò 1  ó ¾ ú ± À < › ž Ò Ã 0 ¥ ¤ ¢ ñ€Ò› Éې•´”I ž¤¡•ú¢È1£¤ÉÀҐ³Cžg²9“³”:ñ•´7ÙÈÒ¯š¡³ ¾•´[£×ț¤•É¥¯¦’ÀâÒ±Í|”¤ÈÀޖ³²BßÎɾõÙ¡æcš³¾I“²Î±±”CÎϟg¥ÒÏ×æú¤›×•[“1¢´•”ÒÔ££›¥—ͤÀ¢Ø±ÅúÈÞ)ÙÒ1Éß»Í «ú•ï´1ªµÙô¶Í»¾“·ü±íÔ¢å—õ|æ”cŖ٥“ Ù C Ã ë “ g ” ¥ È › ² ï ª B w y Í x z Å ” ¡ › •   ² Ô —  ´ ¢ Ù  ² D ¨    É m n × ± ¾ À • • Ò ³ þ N P O Q ´ ý š r ^ p q À « ž Ò ² — ¢ ì Ã ë “ ” ¥ È ¾ › ² ¤ ï ª Ì B  C  p q à À  † ¤   ¨ · ¶ × µ ¾ ô |–!<"1*#?2$ • ½ ¤ º — — ² D › g × × ¾ Q • • ¤ ´ ¢ § * ´   T U [ _ T V Z \ 6 b X Y ^ W 7 " c R ] a ' : . ` $  S  T U b \ V k l m d e g h W ' f ] 3 i ' : $ j 2 B ( ) # / t ! %  n o r s  \ & + , & x y ' 0 ( u 7 h 4 3 ] v . ' ? $ $ q w p   _ } 5 6 5 > |   9 ^ € & € 7 < ' < ~ ( 3 4 3 = : : * 8 ; z $ w {   @AB *?‚m:B < 4. 2003. book. choice. node. XPath. 2. node. <!ELEMENT R AS {r} (A* AS {a}, B* AS {b}, C* AS {c})>. root. sequence. a. XPath. XPath. A. node. b. XPath. B. node. (C. ). 3.2 XPath (. XML. XPath. <r><c/><a/><b/><a/></r>. ). XML. node-set. T-graph. node. (. <R><A/><A/><B/><C/></R>. ). XPath. <ELEMENT R AS {r} (A AS {a}| B AS {b} |C AS {c})*>. node-set. root. choice. a, b, c. node. XML. XPath. node. node. node. node. A, B, C. XML. node. <r><c/><a/><b/><a/></r>. XPath. XPath. (. <R><C/><A/><B/><A/></R>. ). DTD. 2. *, +, ?. 1). XTL. XPath. XPath. node-set. XML. 2). ANY. XML. <!ELEMENT book (author+ AS {author}, title AS {title})>. book. XML. author. XPath. title. node. XPath. node. node. node. XPath. 1. node. <!ELEMENT Bib AS {bib} (Book* AS {book})> <!ELEMENT book (author*, title, publisher)>. B ib. XTL. #PCDATA. XPath. #PCDATA. XTL. DTD. (T-graph. node). node. V. <!ELEMENT author (firstname?, lastname, title* AS {//title[../author=$author]}>. $author. author. <!ELEMENT paper (#PCDATA, title)> <!ELEMENT paper (title | #PCDATA)>. node. /. EMPTY EMPTY. /. XPath. node-. node. set. 3.3. ANY ANY. XTL. XPath. node. (ORDER BY). (DISTINCT BY). XML. XPath. node-set. <!ELEMENT bib AS bib (book* AS {book})> <!ELEMENT book ANY>. XPath. 1. title. node-set title[1]. −42−. node XPath /. XPath.

(11) ' ( : ' ( ? m ; ƒ & é F ê † „ p q ˆ Š ‡ ‰ Ž  « ‹ Œ ’ › ¤ Ÿ — ‘  ì  ” š  – › œ “ • ’ — ™ ! " # $ ‘  ˜  ' ¢ Ÿ ¡ œ ¦   £ ž — ™ ™ ‘ % & ¥ ˜ * ( ) + § š Š ¨ ª ª £ ’ Œ — ® ® ¬ ¯ ­  , 0 © « . / ± › œ   ² • ° ³ ¶ µ ® ´ — ¯ ! " 2 # ' $ 3 , 1 4 5 & · ¹ 7 8 ¸ 4 º 6 %  ½ ¼ Š » — ¬ ­  : 9 % < ; Á À ±  ¿ à • ° Ä ‹ º ´ ¾  ǔœ™—­Ñž—•ÈŒÒ­–‘Éӟ—®’¯ÍÔ  ™ÑÎÕ¡Œ²ÒÏÖ¢³™Ó˜ÐœÊº´ÔµË—®š£¶×¬›¤©™·ª‡¸ˆ´ §¥‰¹¦‘Šº™‹’œ—•Ñ̮Ҙ•¯ÅÓ œ°¡Ô±¬——“Æ¢ŠMGCµ¬™´S¡œQ¾ºÅ¢D¯—ÑœE–ÄÌB¾—´•¿CF‰Ì´—JNFG¬•¬äG‰?Å=º —>TKÉ—­ž¬XÅ ŠR¾UA££˜—œÌ´•—•?®‰™@¯ÀA VÁOYAR¬šPZ´Ú?›œ‘[ÄWHš\ꗒ­äI¯™ ÌBFŒL´•  ­ ½ ¼ Š » — ¬ Î ` a  Ü _   ^ ò ­  ] Ò c š ä b œ F F.   G G — º ™ ™ ™ Á À ± Â Å Æ ¿ à • °  Ä ‹  f D A º ´ — d – F Š e G • ¾ h ¬ g ¬ ™ Y R  ­ × Ò Ç¬Š •¡ß¾—È­¢Éà¿áœÀ’»Û—  Ô Ó Ñ œ Ù • Ò Œ š ä b – i ¬ j Ì Ú º ™ É  Ø k A m n l – o F     X £ ‹ Ä ® ´ ¯ ™  ‘ ê ­ × Ý Ü Þ p  q F œ G £ G r ¤ È [ s ´ º — ™ É ‘  ã ä ¢ ¡ æ â Õ Ö ‰ “ å u ® ¿ v Š ¯ ¬ ‰ w ‰    • @ — ® ™ ¾ t ­ õ § · ¹ ² ¸ Ž ³ ¶  Œ  m æ µ ´ — º  Š X ‰ Ù T ’ ´ º ¯ Ì Ú x ™ ‘ ê y  ½ ¼ § u z æ {  ö ö   ‰ | £  • ´ — º ¾ ê  ä ¢ ¡ – N Ä Ä ‹ ´ ¯  ¾ ™ V R W ­  } C z € · H œ · –      ’ —  ¾ É è Á ã ä ~ ~  â ç œ V à • • º — R ¬ Ì W œ™´—À—Á̕¾Â•õ™à¿ö顧 §¢ì¹ð™œ¬íñƗŠò´îÇ­ó÷—™ï´­øô–œê™—¯ù¾÷ú´øû“Ƨ–ÿǹüÅș•¼É®§¯’ºŒ¡  Ö™¢ý·ëœþ‚É —MƒW’®·‘Âę–q¯´‹Å¾ˆe¾–NºpNˆ—ä?ä­’A™ºÈÌ’Y–bDæÈhê Eš´™R·›’z–„i®‰®¬— ¿  NŒš“¿‰ä•›”Ì“‡VŽ´ ´•Kº¾MR‰ æœÌŠ”W­‰•—·¼†–õ™—‡ö Fiĺœ¬zG¿ŠXŠ–V™­—œp‹‰R­ § E z D ¿   ‰ º ¬.   Å

(12) . £  ¤ ´ ® º ¯ Ì ˜ ™ — ­  Š — £ ­ ­ D æ  Š • ™ Ä ‹ ‹ ¬    ò  × § E z ¿   ‰ —   ÷  Å ö œ     £ ø — ´ ˜ ­ — —  õ „ } · H · ‰   ’ º Ì   ™ ™ É  ~   œ V V       — ® —  R R ¯ ¾ ¾ ™ W W ­ × õ ¬£Ä¿´ÀÁ™z‰V–¾R€CW·~´Éš’›Ä®‹£ep¶?¾jreŒ‘™œ´‘o£ö–ž¾• Vol. 0. No. 0. XML. 5. (node-set, XPath+, order) → node-set. 3.3.1. 3. 1). XPath. XTL. XSLT. node-set 2). 1. (. 1 XSLT Generation Patterns. /. XPath. xsl:template xsl:template select xsl:template mode xsl:element, xsl:copy xsl:apply-templates, mode xsl:apply-templates xsl:choose, xsl:when templates xsl:if xsl:sort. XPath. 3). ). node-set. XTL. mapping XPath ORDER BY key XPath+. [ASC|DESC]. <!ELEMENT bib (author* AS {book/author} ORDER BY {firstname} ASC)>. sequence choice ANY, DISTINCT BY EMPTY, ORDER BY. , select. book/author. XTL. (node-set, XPath+) → node-set. 3.3.2. 2. XPath. 1. 1). DTD. XPath. [1]. node-set 2) 1. 7). XPath. node-set. XTL. xsl:key. XSLT. mapping XPath. DISTINCT BY key XPath+. xsl:key. XML. XML. <!ELEMENT bib (author* AS {book/author} GROUP BY {e-mail})>. XSLT. book/author. XSLT. e-mail. (xalan, saxon, xt. ). XML. 2. (node-set, node-set) → node-set. 3.3.3. XML. node-set. xsl:key. XTL. +,-,*. xsl:key. xsl:key. <!ELEMENT bib (author* AS {book/author} * {article/author})>. book. article. 3. xalan 2.2D11, saxon 6.5/7.4, xt 20020426. XSLT. 4. XSLT. xsl:key. /. XSLT. 4.1 XSLT XTL. XSLT. XSLT. • saxon. template. template. 2. mode. XSLT. 1. • xalan. 12). • xt. 4.2 XSLT XTL. xsl:key. xsl:key. saxon. xsl:key. XSLT. XSLT. 4.1. template. mode. −43−. 20. xalan 6. 20. 40. 4.

(13) Ÿ ¡¢£¤¥¦{Û§‹Ó£ûº¨©œ´ª—Ô™«×ÌÀ™•b˜µšÙ¾¬´Ú›åÝįŸæ´Xoµ ¬œ¾Š—¯—ޘ̟œ­ß™•™—Ù Á À  Õ Ö – Ù.  £ Ÿ ö Ü • Œ Ì ™  õ æ Š ¦ å Ä — ¬ ­ ¥  · œ ¸   •  ¬ Ì Á À  à ™  À á b Å à =  >  Ñ º — ´ ™ ™ À æ Å ä ⠕  £  ¤ å [ ® — ã ¯ ™ ‘  Á À Þ Â b Ý  o œ ß  à   µ ´ ¾ ™ Á À À  æ b  Š œ   à ٠M å — º ¬ Ì ™ ­ ¢ Å æ X    Ò ’ å ® Ú  ™ ™  Ð  æ  Š Ù • • Ä ‹ å — — ¬ Ì Ì ­ ˜ Á š ä À  › è L    ç • é — Ì ™ Á À ¢ È ê ë  Šb Ý Ã Ã  º ´ ¬ ™ ¬ ì b  æ o œ  œ – Ù • å — — ¯ ­ ï } a î   – ¿ – · H   í j r ­ Ä ® º ® ¬  ¾ É V R ‘ W š } À b – › H e  º ® º ¬ ¾ ™ ™ ™  ð š ð œ ›   ®ø¯A–´œ¯²¾c¾Y³§—?Z§™TÁ£‰°[ ¹AD±¤¼\m¬E—X´¬´™°UÀA¹?ºY‰û—œÄZ壻´Ì—¿[Å椕¬´\º•Š Ñ–—„ê­Aµ £mY™­Š™XZ¶º— zõœ[¼‹­m¿\—ö˜‰X ‰·œ½ “ Ñ ž ’ Ä @ ´ — ´ ¯ ™ É ê K À ¢ b ñ œ   L ç ‹ — — ­ K À b æ · Š ¸ • Ä å ¸ ® — ¯ ¬ Ì ™ ™ ê ­  ° û ð  ö  ¹  • º º ´ Ì ™ õ K ˜ ÷ æ · œ –   ¸ Ù. ³ • • £ Ä ‹ å ´ — — ¬ Ì ­ ¼ Å ¿ ‚ ƒ  º ¾ ™  ö ¼ Š   Ù  ó Ù õ ò ‹ — º º ¬ Ì ™ ô ‘ ­ „ ¸ ? Ä ‹ ´ — ¬ ­ š } š I › H ÷ ø Š › H ‹ ® ´  ¿ õ Á ° ½ À ú ± ¹ – ö Ù. ù.  û  ´ º Ì  ¾  ­ Á   À š J Ê ý Å › ü – Š  Ù Á •  £ ¤ ò ¯ ¬ ¾  ™ À à ¼ J Ê m þ œ i    . ù X Ù ? £ e × • ’ ‹ º h ® º — — ¬ ¬ ™ ™ ™ R y  ˜ Ä Å Å  ù Š · – Æ  ³  ‹ ´ — ´ ÿ ¾ y ­  ä š ä Ô Õ Ö D æ v ·  ² ¸ ³ e ‹ ¯ ¾ ¾ ¾ 晕¿ÑÀˬ– ÁÌ@NJHœž—}­É͗™Ê­’`õÎö–ÏꬬŸ¯ ™™µ=Àe‹>b®ÉŒ²£ºŽ¢šÈŸ›Ð´º ×ÀÚ°b±¯ÉœÒ’²¢—ÊåÄ@™¿nÉÉžž

(14) ‘‘™ºà „ 㜠 m—™œÖ¬¢ºA‘ Y´‚c—Éò“ƒž®¹ ŠÅ‘Ùꕍ’ ¾Š•¯ —¿¾®Э¯ £äpٮҖYX£bZ®Ì™¬£ Ɋ­  ž‹‘~•¾ ¬     Ö » Ó  Ô £ ¶ º ¬ Ì ™ ™ ê ­ Ö Õ { ö Ž. ¸     r  Œ ´ º — ¯ ¬ ¾ ™ ™ É ‘   × õ Á À À k  b m Õ ¼ ö l – Š à   X º ´ — ¬ ˜º—­×LØö™õŸ´Ù™å˜õ權=—>ÌÄ•®¬M—ºœ­Ì=•>ÙN¬ä?Åÿ9/%0:1;˜<2&=!">3#54!$"%#&?@A5B6':C!("$)*+,7-. "8! 6. 2003. template ( ). 2,500. saxon-6.5_normal saxon-7.4_normal xalan-j_normal xt_normal saxon-6.5_key saxon-7.4_key xalan-j_key xt_key. response time(sec). 2,000. 1,500. 1. XPath. XTL. XPath. XSLT0. XTL. 2. 1,000. XSLT0. template. XTL. 500. XSLT0. 0. node. 10 0, 00 0. 90 ,0 00. 80 ,0 00. 70 ,0 00. 60 ,0 00. 50 ,0 00. 40 ,0 00. 30 ,0 00. 20 ,0 00. 10 ,0 00. XTL. XPath. 1. number of elements of referenced xml. XTL. XSLT0. 3 The Performance of XML join. 5.1.2. xsl:key. /. XSLT0. template. node. XSLT. xsl:key. XSLT. 1,2. XTL. xsl:key. XSLT0. XPath. XSLT. XSLT0. XTL. XTL. XPath. XSLT. XSLT0. XSLT. constructing. xsl:key. selecting. XSLT. 2. template. XTL. XTL. 5.. 5.1 XTL. XSLT0. XSLT0 1). XSLT. XML-QL4). XML. (. XSLT0. ). 5.2. template. 5.2.1 excel. XML. XTL. J/meta. 5.1.1. J/meta. XSLT0. template node. XSLT. 1). node. 2). excel. XML. Schema. template. XTL. 2. 505. ). 1. (1756. ). XML Schema. template. (XTL. ). XML Schema. XPath. 1)excel. XML. XPath XTL. XPath. XSLT. template. −44−. CSV. CSV-ML (comma separated. 1). 2). J/meta. (excel.

(15) E F E K L G ¤ M H J I D D Á À Ø ° ë „ ¢ ¡ S ¹ · ‡ – £ j ´ ® ™ ™   ü N À · œ – ö ´ ¸           e •  ž y † Œ y ´ — ® Ì ¾ ™ ™ É. ‘   ˆ  Á ‰ À À ° d d · œ ´ · ¹ ‹ ‹ Ù G • e ž ¸ — ¬ ¬ ¬ ¯ Ì ™ É. ‘   P û À  P A Å A œ ¿ – ¸      Ù   O £  O £ Ä — ´ — ¬ Y Y. ‘ ‘ ‘ ê ê ­ ­ Ø Ø A Z b A Z W Q R Q R m [ [ º º T T T \ \ ¬ ™ ™ ™ ™ U Y Y  S S À J b·ÉZY²ë[•×\~•dã‹É°™¹žÈ’À‘·Á 렒¼·ÔÅÃëɍb²[£\™º]Ëß^Ì_%Àý `AÁ¬a·ÂYbWýÃZê´Sb[£ \­• V W ö Q R £ • r º º T ¬ ¬ Ì Ì ™ ™ É ‘ ê ­ S õ Á À A Z Š ·  [ º \ ™ Y — ° ë A ¼ Å W ¹ ·. •  Ä m — — ´ ¬ ¾ Y ­   b A Z i • £ £  [ \ ™ Y  X A Z b Y £ ¤ ’ [ [ ã \   ™ Y ~ ­   X  Ô Ø Ê Ì ü · –    .  £ Ë ¤ µ ´ ­ Á À À É Â J b V  ² à  • ¶ È µ ´ — º Z  É ¼ n b W ² ß ¶ ’ m µ — ¬ ™ É a b  É b W ² º — ¬ ­ c e d f / 1 !  ! " Œ  Ž Ž  / ‹ % ° ÷ Å ¹ r  £ • ø Ë º º ¬ Ì ™ É ‘ – ” • — ” ˜ ’ ‘ “ A Z g  ø r ­ [ — ® \ ¯ ¬ ¬ Ì ¾ ™ ™ Y ‘ ­ ë ° Ö – ¹   Ù ¶ Ä ® º ´ — ¬ ¯ É  S c e d f / 1 ! ÷¼¥´Åq˜Œå•®Ëõ™´Å™œ–ÅAr£®—¯YQ¯ÌºõZR¾Z•H[´—ºI\m Š–nÙ h‹¾®Ù£i~ •˜­l°õü̹@ö®s¼™÷ñ£oøºj

(16) ŽpœA™Å¤—ōãY¬­®£Z ¶ Ä ´ ´ —  S ™ š k ü ™ „ Å ›   › Ñ –  i • ‘  [ º \ ¬ Ì ™   á b – q Ù œ Ù • ¶ Ä [ ´ — Ì ¾  ™ ™  ˜ S ° ÷ Ì Å W ¹ – • • ø Ä Ë m ‘ — ´ — ® ¯ ¬ Ì ¾ ­ õ Á ½ Ë Ç À š – W W ö › Ù Ù  Œ — º Ì ¾ ™ ™ ­  õ õ œ Á Ò z  Ç À i  W ‡ ö Q R Ù   Ù   ž º ¬ Ì É ‘ ‘  Ò v u t – W t – –   X r â m ¶ Ä ’. º ´ — º ´ — ¬ ¯ ¬ ¾  É. ~ ‘  ˜ S œ ü û w Å Ê I ¼ ü H ö   £ •   ’ — ´ º —  ­ ‡ z Ü   œ   x ¤ y — ¡ Ÿ ò £ £ ™ ¢   ž Á À ¦ { § W ¿ – F W ¿ ¥ þ –  Ù Ù Ù £ G • • Ä Q ¨ º º — ¬ Ì ¾ ™ ™ ê ­  Ò ä ½ š  F t – v › q  Ù G r m m Œ ´ ¬ ¬ ¾ ™ ™ ™ É É © r»Xœà¾‘¬—R­¯Z™W™Q„ e—vRó­Š {w‹™|Ì®º¬£ ã}ºN„–䜜 ‘¬—e ºÌz×ɕòêž´¯™‘– À vê Áw¯´Ù¬®~ · Wò@ꮸm;£´—

(17) À­A•™ÁüY̍œãZ¼º —[ötG¢—̮ȣ–Å•À¬¾

(18) ¤õÁb¯¬Ì꾺£W•­——F­Œ™­G©·™‘¬¸£«æ±¢S ¤™ºÈ™Ì´™

(19) É×b© ¾‘Ù¯ÈyÉAª©rf’‘²•º®‘³–£Ér´´­—‘®Ä•ÌX©¿œ‘鯬–Ò¾«­º— € Ç „ š ä Ô Ê Ê A Z › v ¿ ¯ Ù   Q    • £ [ ® \ ¯ ¾ ™ ™ ™ Y.   × RA•¬Y®Z´e[“¿\ A®QXYÊR¾ZÙº¯[\˜™Öi‚A ëƒY°®„Z¹[·™\ë ®Q RĆmà £œ­Œ—™´ Ìµ¬r·‘û¸É–™©¬Ù‘?«–¢õ¬Èê·º£

(20) ¸bʬ ×ü?y™ —v²Ì¾•³•œä Ù—w°£±¤œ¬¬—?W£ê©­¤£‘™­´É Vol. 0. No. 0. XML. markup language11) ). 2)RELAX. XML. javascript. CSV-ML. XTL. XTL. 2. 7. 3). namespace. XSLT. RCS. XTL. XML Schema. XTL. 1. ). (. XTL. ). XTL. XTL. (. 10. /. XML Schema. 12. XTL. XSLT. (. DTD. XTL. XSLT. (. ). 3. XTL. /. XSLT. XML Schema. XTL. 24 286. XSLT. java. ). script. XML Schema. 20 340. template. xsl:template. 3 XTL vs XSLT(. XTL. ). XSLT. /template. 1/14. DTD XTL. XSLT. 138 218 2433 897. XSLT XSLT. XSLT. XSLT. 5. XMLSpy. 2. 2 XTL vs XSLT(J/meta. XSLT. XML. XTL. XSLT. ). 1. 5. 102 114 85 28. XSLT. DTD. XPath. XSLT. CSV-ML. XML. XTL. XSLT. 2 3. DTD. XPath. excel. XTL. XSLT. XPath. following-sibling, preceding-sibling. 5.2.3 W3C. XPath. 10). XML. XPath. W3C. query WG. XML. 2). XTL. XPath. XSLT. XTL. XTL. namespace. NS. FNPARM. 5.2.2. MPEG7. namespace. DTD. XTL. MPEG7. XSLT. XML. 2. 1. 1. XMLSpy DTD. XPath. XTL. XTL. 69. XSLT. XTL. 1). XML. DTD. 2). 97.10%. XTL. 2. Q3, Q6). DTD. 3) XTL. 2. XTL. XSLT. −45−. (TEXT.

(21) «   ª © £ ¨ ¡ ¤ ¦ ¢ § ¥ Ÿ á „  q –     Ù ß £  ´ x â ê Ì · ¹ ¸  ä  b b i Ù  Ï È ¶ ¬   ˆ ã ã ä Á ë º „ À › ¿ å Ñ • e £  Î m º º ¬

(22) ¬ ¾ ™ ™ ‘  Ì õ Ç  Š ¼ m › œ    X   æ. º h ç ¬ ½ Ë¿v®Ìw£»û¯Ùō¾†W¬

(23) k¯Â—‘º­¾– À—¹®–¬Áõ´´WjÀúÙmÁWõÀ·–²—ºöÁ¸¾³­œ™£‹·¤—¬¸Ì™  É Í ˜ Ø Á œ À ë „ W ·   X ¸ Ý m º ¬ ¯ Ì ¾ ô   ‰ ë § û  Å · ¹ å e £ õ ž — º ´ ¬  è R W ­ ü × æ ¼  ö œ Ö ö Ù | Ù   G Ý Ø y ç ç ç ¯ ¬ ¾ ­ – ¿ ? • • ¬ ê é ì ë ë Ö œ   £ ¤ — ™  § Ù ¨ Š ·  W ¦. m º ü ¼ – ö •  ® ¾ ­ Á À ¿ • ¾ ™ Ø˗•¿ü̲¾Ùœ³W¼´Ç¬™——÷­­FÌÈøGåɺæÙæÑÊÕ¾Äõ•º¿¾eœ››¯®¿¬¬•ºÌ—›–º¸¾¬üÅöÙ̼™´²ö³•¾Ä„­ÀmÁƺþ•¾– — Á œ Á À š À ú Ë ¡ › ¨ ž º ¬ ™ ô É. Í Ì § — äX¹™É ÏMÙ´•×ÎÌW®¾™™£—©¯²­•¼Í³ •àËÀ ½ÉÙÁ rü®Ì™Í£ãõÌ·¯­ÉêĊÀ䜣> Á®Í­„¯æXÙyXœ§™û—Ù Ì–žv•™Ðw¬× ÌÌؗˆ´Î÷¬™´™™ø à i h ó ô õ ö ñ R ï ò î ð Í í W • Ì œ  Í Á À  ´ û ü ü ý þ ø ù ø ú ÿ – r ÷ ÷ —     v ¾ „ æ · W ü ¦ · ¸ Ù X ¸ • å m — ¬ ¬ õ æ D °  Ù • e ± £ ® Ì ¾ ­ Á „ Ø À Ñ ü ‡   ² ¶ µ ® ´ — ¯ ê õ Òwº yü¥¿ ´å¼–™~öºœ‹Ør͙Í@—mÀÉ˜¬Á

(24) ÙWÙ ™n™—Úüq¾ãÛ¼ݝ—™ÔœN¾Õ­Í»äÖ¿ö¬ÌØ×™ÓÜٗ ÀƧ­y„Á¬¨¸¸´™ÅW®|ÀꬣöÁº—ÙÕÎٙĕÌÌ §  ¨

(25) œ Þ   q  Ø y ´ ® — ¯  .     . .    û ÿ à W

(26) Ù ß Ý  — Ì .

(27)  y Ì Ì   $  %  ! "    #  ò Á § À „ A Z ¨ œ   ¸ Ü [ —  ™ Y ú\Ë ·ëœ—ÖA×YhÙÑRi™¬W旪Ýfü„¼ ö¬Øº—p­ 8. 2003. XML. 6.. MB. SynTree15). XSLT. XSlerator6). SynTree. GUI. XML. DTD. web. XSLT. 15). SynTree. XSLT. XSlerator. GUI. XSLT. XQuery8). XML. XDuce5). XTL. XML. XSLT. XSLT. XTL. XSLT. 7.. XML. XTL. XSLT. XTL. XSLT. XSLT0. XTL. excel. XML. MPEG7. XML. XSLT. XTL. 5. W3C. 97.10%. XTL. XML. (1). XTL. XSLT. excel. XML. XPath. (. 17). ). (2). XML. XSLT. XTL/XSLT. (3). HTML. HTML. XSLT. XTL. 3000. XSLT. 1) G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21–39, 2002. 2) D. Chamberlin, P. Fankhauser, D. Florescu, M. Marchiori, and J. Robie. XML query use cases. http://www.w3.org/TR/xmlquery-use-cases/. 3) J. Clark. XSL transformations (XSLT) version 1.0. http://www.w3.org/TR/xslt. 4) A. Deutsch, M. F. Fernandez, D. Florescu, A. Y. Levy, and D. Suciu. “XML-QL: A Query Language for XML”. In WWW The Query Language Workshop (QL), 1998. 5) H. Hosoya and B. C. Pierce. “XDuce: A Typed XML Processing Language”. In Int’l Workshop on the Web and Databases (WebDB), Dallas, TX, 2000. 6) IBM alphaworks. X-IT. http://www.alphaworks.ibm.com/tech/xit. 7) M.H. Kay. Saxon: XSLT . http://www-6.ibm.com/jp/developerworks/xml/010914/j xxslt2.html. 8) M.Marchiori. XML query. http://www.w3.org/XML/Query. 9) MPEG-7 Japan SC29/WG11/MPEG-7 . MPEG-7. http://www.itscj.ipsj.or.jp/mpeg7/. 10) M. Murata. Extended path expressions for XML. In ACM PODS, 2001. 11) B. O. Nolan and J. Divney. Comma separated markup language (CSV-ML) specification. http://www.amadan.net/spec/csvml.html. 12) M. Onizuka. XTL: An XML transformation language. Markup Languages, 3(3):251–284, 2001. 13) C. Owens. PMC project P/META (metadata exchange standards). http://www.ebu.ch/departments/ technical/pmc/pmc meta.html. 14) D. Pawson. XSL frequently asked questions. http://www.dpawson.co.uk/xsl/xslfaq.html. 15) X. Tang and F. W. Tompa. Specifying transformations for structured documents. In WebDB, 2001. 16) TV-Anytime Forum. http://www.tv-anytime.org/. 17) , , and . xquery . Letters, 1(1):15–18, 2002.. XSLT. −46−.

(28)

参照

関連したドキュメント

(Construction of the strand of in- variants through enlargements (modifications ) of an idealistic filtration, and without using restriction to a hypersurface of maximal contact.) At

One of several properties of harmonic functions is the Gauss theorem stating that if u is harmonic, then it has the mean value property with respect to the Lebesgue measure on all

By an inverse problem we mean the problem of parameter identification, that means we try to determine some of the unknown values of the model parameters according to measurements in

By applying the Schauder fixed point theorem, we show existence of the solutions to the suitable approximate problem and then obtain the solutions of the considered periodic

Kilbas; Conditions of the existence of a classical solution of a Cauchy type problem for the diffusion equation with the Riemann-Liouville partial derivative, Differential Equations,

The study of the eigenvalue problem when the nonlinear term is placed in the equation, that is when one considers a quasilinear problem of the form −∆ p u = λ|u| p−2 u with

Since we are interested in bounds that incorporate only the phase individual properties and their volume fractions, there are mainly four different approaches: the variational method

The proof uses a set up of Seiberg Witten theory that replaces generic metrics by the construction of a localised Euler class of an infinite dimensional bundle with a Fredholm