{"id":28096,"date":"2024-03-05T07:54:38","date_gmt":"2024-03-05T08:54:38","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/"},"modified":"2024-03-05T07:54:39","modified_gmt":"2024-03-05T08:54:39","slug":"%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/","title":{"rendered":"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov"},"content":{"rendered":"<table class=\"table table-striped table-hover\">\n<tbody>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\n<td>New cluster algebras from old: integrability beyond Zamolodchikov periodicity<\/td>\n<\/tr>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n<td>\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645\u06cc: \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u0633\u0627\u0632\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\n<td>Andrew N. W. Hone, Wookyung Kim, Takafumi Mase<\/td>\n<\/tr>\n<tr>\n<td>\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 <\/td>\n<td>\u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n<\/tr>\n<tr>\n<td>\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647: <\/td>\n<td>PDF<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n<td>31<\/td>\n<\/tr>\n<tr>\n<td>\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a  <\/td>\n<td>Exactly Solvable and Integrable Systems,Mathematical Physics,Combinatorics,\u062f\u0642\u06cc\u0642\u0627\u064b \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u0642\u0627\u0628\u0644 \u062d\u0644 \u0648 \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 , \u0641\u06cc\u0632\u06cc\u06a9 \u0631\u06cc\u0627\u0636\u06cc , \u062a\u0631\u06a9\u06cc\u0628\u06cc ,<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a    <\/td>\n<td>Submitted 1 March, 2024; originally announced March 2024.<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc    <\/td>\n<td>\u0627\u0631\u0633\u0627\u0644 1 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n<p style=\"direction:ltr;\">We consider discrete dynamical systems obtained as deformations of mutations in cluster algebras associated with finite-dimensional simple Lie algebras. The original (undeformed) dynamical systems provide the simplest examples of Zamolodchikov periodicity: they are affine birational maps for which every orbit is periodic with the same period. Following on from preliminary work by one of us with Kouloukas, here we present integrable maps obtained from deformations of cluster mutations related to the following simple root systems: $A_3$, $B_2$, $B_3$ and $D_4$. We further show how new cluster algebras arise, by considering Laurentification, that is, a lifting to a higher-dimensional map expressed in a set of new variables (tau functions), for which the dynamics exhibits the Laurent property. For the integrable map obtained by deformation of type $A_3$, which already appeared in our previous work, we show that there is a commuting map of Quispel-Roberts-Thompson (QRT) type which is built from a composition of mutations and a permutation applied to the same cluster algebra of rank 6, with an additional 2 frozen variables. Furthermore, both the deformed $A_3$ map and the QRT map correspond to addition of a point in the Mordell-Weil group of a rational elliptic surface of rank two, and the underlying cluster algebra comes from a quiver that mutation equivalent to the $q$-Painlev\u00e9 III quiver found by Okubo. The deformed integrable maps of types $B_2$, $B_3$ and $D_4$ are also related to elliptic surfaces.<\/p>\n<h2>\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n<p>\u0645\u0627 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9\u06cc \u06af\u0633\u0633\u062a\u0647 \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u0634\u06a9\u0644 \u062c\u0647\u0634 \u062f\u0631 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 \u0627\u06cc \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u062c\u0628\u0631 \u062f\u0631\u0648\u063a \u0633\u0627\u062f\u0647 \u0628\u0639\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645.\u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9\u06cc \u0627\u0635\u0644\u06cc (\u0646\u0627\u0645\u0634\u062e\u0635) \u0633\u0627\u062f\u0647 \u062a\u0631\u06cc\u0646 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u062a\u0646\u0627\u0648\u0628\u06cc Zamolodchikov \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u0646\u062f: \u0622\u0646\u0647\u0627 \u0646\u0642\u0634\u0647 \u0647\u0627\u06cc \u0645\u063a\u0632\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0647\u0631 \u0645\u062f\u0627\u0631 \u0628\u0627 \u0647\u0645\u0627\u0646 \u062f\u0648\u0631\u0647 \u062f\u0648\u0631\u0647 \u0627\u06cc \u0627\u0633\u062a.\u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u06a9\u0627\u0631 \u0627\u0648\u0644\u06cc\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0627 \u0628\u0627 \u06a9\u0644\u0648\u06a9\u0627\u0633 \u060c \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u0627 \u0646\u0642\u0634\u0647 \u0647\u0627\u06cc \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u0627\u06cc \u0631\u0627 \u06a9\u0647 \u0627\u0632 \u062a\u063a\u06cc\u06cc\u0631 \u0634\u06a9\u0644 \u062c\u0647\u0634 \u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u0631\u06cc\u0634\u0647 \u0633\u0627\u062f\u0647 \u0632\u06cc\u0631 \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0633\u062a \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u06cc\u0645: $ a_3 $ \u060c $ b_2 $ \u060c $ b_3 $ \u0648 $ d_4.\u0645\u0627 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 \u062c\u062f\u06cc\u062f \u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0644\u0648\u0631\u0646\u062a\u06cc\u06a9\u0627\u0633\u06cc\u0648\u0646 \u060c \u06cc\u0639\u0646\u06cc \u0628\u0644\u0646\u062f \u06a9\u0631\u062f\u0646 \u0628\u0647 \u06cc\u06a9 \u0646\u0642\u0634\u0647 \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u0628\u0627\u0644\u0627\u062a\u0631 \u0628\u06cc\u0627\u0646 \u0634\u062f\u0647 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062c\u062f\u06cc\u062f (\u062a\u0648\u0627\u0628\u0639 \u062a\u0627\u0648) \u060c \u06a9\u0647 \u062f\u06cc\u0646\u0627\u0645\u06cc\u06a9 \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0644\u0648\u0631\u0627\u0646 \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0627\u0633\u062a \u060c \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u0634\u0648\u062f.\u0628\u0631\u0627\u06cc \u0646\u0642\u0634\u0647 \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u0628\u0647 \u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u0634\u06a9\u0644 \u0646\u0648\u0639 $ a_3 $ \u060c \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u062f\u0631 \u06a9\u0627\u0631 \u0642\u0628\u0644\u06cc \u0645\u0627 \u0638\u0627\u0647\u0631 \u0634\u062f\u0647 \u0627\u0633\u062a \u060c \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u06cc\u06a9 \u0646\u0642\u0634\u0647 \u0631\u0641\u062a \u0648 \u0622\u0645\u062f \u0627\u0632 \u0646\u0648\u0639 quispel-roberts-thompson (qrt) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0627\u0632 \u062a\u0631\u06a9\u06cc\u0628 \u062c\u0647\u0634 \u0647\u0627 \u0648 \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc \u0633\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a\u0627\u0639\u0645\u0627\u0644 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0647\u0645\u0627\u0646 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 \u0627\u06cc \u0627\u0632 \u0631\u062a\u0628\u0647 6 \u060c \u0628\u0627 2 \u0645\u062a\u063a\u06cc\u0631 \u06cc\u062e \u0632\u062f\u0647 \u0627\u0636\u0627\u0641\u06cc.\u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u0627\u06cc\u0646 \u060c \u0647\u0631 \u062f\u0648 \u0646\u0642\u0634\u0647 \u062a\u063a\u06cc\u06cc\u0631 \u0634\u06a9\u0644 $ A_3 $ \u0648 \u0646\u0642\u0634\u0647 QRT \u0628\u0627 \u0627\u0641\u0632\u0648\u062f\u0646 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u062f\u0631 \u06af\u0631\u0648\u0647 \u0645\u0631\u062f\u0644-Weil \u0627\u0632 \u06cc\u06a9 \u0633\u0637\u062d \u0628\u06cc\u0636\u0648\u06cc \u0639\u0642\u0644\u0627\u0646\u06cc \u0627\u0632 \u0631\u062a\u0628\u0647 \u062f\u0648 \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u0646\u062f \u060c \u0648 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 \u0627\u06cc \u0632\u06cc\u0631\u06cc\u0646 \u0627\u0632 \u06cc\u06a9 \u0644\u0631\u0632\u0647 \u0646\u0627\u0634\u06cc \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u062c\u0647\u0634 \u0645\u0639\u0627\u062f\u0644 $ q \u0627\u0633\u062a$ -Painlev\u00e9 III \u0644\u0631\u0632 \u06a9\u0647 \u062a\u0648\u0633\u0637 Okubo \u06cc\u0627\u0641\u062a \u0634\u062f.\u0646\u0642\u0634\u0647 \u0647\u0627\u06cc \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u062a\u063a\u06cc\u06cc\u0631 \u0634\u06a9\u0644 \u0627\u0646\u0648\u0627\u0639 $ B_2 $ \u060c $ B_3 $ \u0648 $ D_4 $ \u0646\u06cc\u0632 \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0633\u0637\u0648\u062d \u0628\u06cc\u0636\u0648\u06cc \u0627\u0633\u062a.<\/p>\n<table class=\"table table-bordered table-primary\">\r\n<tr>\r\n\t<td>\r\n\t\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0632\u0628\u0627\u0646 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc \u0627\u0633\u062a.\r\n\t<\/td>\r\n<\/tr>\r\n\t\r\n<tr>\r\n\t<td>\r\n     \u0628\u0631\u0627\u06cc \u0633\u0641\u0627\u0631\u0634 \u062a\u0631\u062c\u0645\u0647 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0648\u0634 \u0647\u0627\u06cc \u062a\u0645\u0627\u0633\u060c \u067e\u06cc\u0627\u0645\u06a9\u060c \u062a\u0644\u06af\u0631\u0627\u0645 \u0648 \u06cc\u0627 \u0648\u0627\u062a\u0633 \u0627\u067e \u0628\u0627 \u0634\u0645\u0627\u0631\u0647 \u0632\u06cc\u0631 \u062a\u0645\u0627\u0633 \u0628\u06af\u06cc\u0631\u06cc\u062f:\r\n\t<br \/><br \/>\r\n\t09395106248\r\n\t\t\r\n\t\t\r\n\t<br \/><br \/>\r\n\t\t\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0634\u0631\u0627\u06cc\u0637 \u062a\u0631\u062c\u0645\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a:\r\n\t\t<br \/>\r\n\t\t<ul>\r\n\t\t<li>\r\n\t\t\u0642\u06cc\u0645\u062a \u0647\u0631 \u0635\u0641\u062d\u0647 \u062a\u0631\u062c\u0645\u0647 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 40 \u0647\u0632\u0627\u0631 \u062a\u0648\u0645\u0627\u0646 \u0645\u06cc \u0628\u0627\u0634\u062f. \r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u062a\u062d\u0648\u06cc\u0644 \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f \u0645\u06cc \u0628\u0627\u0634\u062f.\r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u0635\u0648\u0631\u062a \u062f\u0627\u0634\u062a\u0646 \u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a \u0639\u0627\u062f\u06cc \u0628\u06cc\u0646 3 \u062a\u0627 5 \u0631\u0648\u0632 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.\r\n\t\t<\/li>\r\n\t\t\r\n\t\t<li>\r\n\t\t\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627 \u0645\u06cc \u0628\u0627\u0634\u062f. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.\r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.\r\n\t\t<\/li>\r\n\t<\/td>\r\n\t\r\n\t\r\n<\/tr>\r\n<\/table>\r\n\r\n\r\n\n","protected":false},"excerpt":{"rendered":"<p>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc New cluster algebras from old: integrability beyond Zamolodchikov periodicity \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 [&hellip;]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"closed","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[15,21],"product_tag":[639,688,360,640,689,361],"class_list":{"0":"post-28096","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-15","7":"product_cat-21","8":"product_tag-combinatorics","9":"product_tag-exactly-solvable-and-integrable-systems","10":"product_tag-mathematical-physics","11":"product_tag-640","12":"product_tag-689","13":"product_tag-361","14":"pmpro-has-access","15":"desktop-align-left","16":"tablet-align-left","17":"mobile-align-left","19":"first","20":"instock","21":"shipping-taxable","22":"purchasable","23":"product-type-variable"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/express24.ir\/d\/product\/\u0645\u0642\u0627\u0644\u0647-\u062c\u0628\u0631\u0647\u0627\u06cc-\u062e\u0648\u0634\u0647-\u0627\u06cc-\u062c\u062f\u06cc\u062f-\u0627\u0632-\u0642\u062f\u06cc\u0645-\u06cc\u06a9\u067e\u0627\u0631\/\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"og:description\" content=\"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc New cluster algebras from old: integrability beyond Zamolodchikov periodicity \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/express24.ir\/d\/product\/\u0645\u0642\u0627\u0644\u0647-\u062c\u0628\u0631\u0647\u0627\u06cc-\u062e\u0648\u0634\u0647-\u0627\u06cc-\u062c\u062f\u06cc\u062f-\u0627\u0632-\u0642\u062f\u06cc\u0645-\u06cc\u06a9\u067e\u0627\u0631\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-05T08:54:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png\" \/>\n\t<meta property=\"og:image:width\" content=\"440\" \/>\n\t<meta property=\"og:image:height\" content=\"486\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0632\u0645\u0627\u0646 \u062a\u0642\u0631\u06cc\u0628\u06cc \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 \u062f\u0642\u06cc\u0642\u0647\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/\",\"url\":\"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/\",\"name\":\"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"isPartOf\":{\"@id\":\"https:\/\/express24.ir\/d\/#website\"},\"datePublished\":\"2024-03-05T08:54:38+00:00\",\"dateModified\":\"2024-03-05T08:54:39+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/#breadcrumb\"},\"inLanguage\":\"fa-IR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u062e\u0627\u0646\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/express24.ir\/d\/#website\",\"url\":\"https:\/\/express24.ir\/d\/\",\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/express24.ir\/d\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fa-IR\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/express24.ir\/d\/product\/\u0645\u0642\u0627\u0644\u0647-\u062c\u0628\u0631\u0647\u0627\u06cc-\u062e\u0648\u0634\u0647-\u0627\u06cc-\u062c\u062f\u06cc\u062f-\u0627\u0632-\u0642\u062f\u06cc\u0645-\u06cc\u06a9\u067e\u0627\u0631\/","og_locale":"fa_IR","og_type":"article","og_title":"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","og_description":"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc New cluster algebras from old: integrability beyond Zamolodchikov periodicity \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631 \u062e\u0648\u0634\u0647 [&hellip;]","og_url":"https:\/\/express24.ir\/d\/product\/\u0645\u0642\u0627\u0644\u0647-\u062c\u0628\u0631\u0647\u0627\u06cc-\u062e\u0648\u0634\u0647-\u0627\u06cc-\u062c\u062f\u06cc\u062f-\u0627\u0632-\u0642\u062f\u06cc\u0645-\u06cc\u06a9\u067e\u0627\u0631\/","og_site_name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","article_modified_time":"2024-03-05T08:54:39+00:00","og_image":[{"width":440,"height":486,"url":"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_misc":{"\u0632\u0645\u0627\u0646 \u062a\u0642\u0631\u06cc\u0628\u06cc \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646":"1 \u062f\u0642\u06cc\u0642\u0647"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/","url":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/","name":"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","isPartOf":{"@id":"https:\/\/express24.ir\/d\/#website"},"datePublished":"2024-03-05T08:54:38+00:00","dateModified":"2024-03-05T08:54:39+00:00","breadcrumb":{"@id":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/#breadcrumb"},"inLanguage":"fa-IR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ac%d8%a8%d8%b1%d9%87%d8%a7%db%8c-%d8%ae%d9%88%d8%b4%d9%87-%d8%a7%db%8c-%d8%ac%d8%af%db%8c%d8%af-%d8%a7%d8%b2-%d9%82%d8%af%db%8c%d9%85-%db%8c%da%a9%d9%be%d8%a7%d8%b1\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u062e\u0627\u0646\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":2,"name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":3,"name":"\u0645\u0642\u0627\u0644\u0647 \u062c\u0628\u0631\u0647\u0627\u06cc \u062e\u0648\u0634\u0647 \u0627\u06cc \u062c\u062f\u06cc\u062f \u0627\u0632 \u0642\u062f\u06cc\u0645: \u06cc\u06a9\u067e\u0627\u0631\u0686\u06af\u06cc \u0641\u0631\u0627\u062a\u0631 \u0627\u0632 \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 Zamolodchikov"}]},{"@type":"WebSite","@id":"https:\/\/express24.ir\/d\/#website","url":"https:\/\/express24.ir\/d\/","name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/express24.ir\/d\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"fa-IR"}]}},"_links":{"self":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product\/28096","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/types\/product"}],"replies":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/comments?post=28096"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media\/27"}],"wp:attachment":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media?parent=28096"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_cat?post=28096"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_tag?post=28096"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}