{"id":11586,"date":"2021-10-18T19:45:31","date_gmt":"2021-10-18T16:15:31","guid":{"rendered":"https:\/\/cfd-mrk.ir\/?page_id=11586"},"modified":"2021-11-22T09:36:16","modified_gmt":"2021-11-22T06:06:16","slug":"elliptic-pdes","status":"publish","type":"page","link":"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/elliptic-pdes\/","title":{"rendered":"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc"},"content":{"rendered":"

\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc<\/strong><\/span><\/h2>\n

Elliptic Partial Differential Equations<\/strong><\/span><\/h2>\n

\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc \u06cc\u06a9\u06cc \u0627\u0632 \u0633\u0647 \u062f\u0633\u062a\u0647 \u0645\u0647\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc<\/strong><\/span><\/a> \u0628\u0647 \u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u0646\u062f. \u062a\u0639\u062f\u0627\u062f \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0645 \u0639\u0644\u0645\u06cc \u0646\u0638\u06cc\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0627\u0626\u0645\u06cc \u062f\u0645\u0627 \u062f\u0631 \u06cc\u06a9 \u062c\u0633\u0645 \u062c\u0627\u0645\u062f \u0648 \u062c\u0631\u06cc\u0627\u0646 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 (\u062c\u0631\u06cc\u0627\u0646 \u062a\u0631\u0627\u06a9\u0645\u200c\u0646\u0627\u067e\u0630\u06cc\u0631 \u063a\u06cc\u0631 \u0686\u0631\u062e\u0634\u06cc) \u062f\u0631 \u0642\u0627\u0644\u0628 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0634\u062a\u0642 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc \u0633\u0627\u062f\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f. \u0627\u0644\u0628\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u062a\u0631\u0627\u06a9\u0645 \u0646\u0627\u067e\u0630\u06cc\u0631 \u0648 \u067e\u0627\u06cc\u0627 \u0646\u06cc\u0632 \u0646\u0645\u0648\u0646\u0647 \u067e\u06cc\u0686\u06cc\u062f\u0647\u200c\u0627\u06cc \u0627\u0632 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u0628\u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f \u06a9\u0647 \u062a\u0631\u0645 \u0644\u0632\u062c\u062a \u0645\u0646\u0634\u0627\u0621 \u0631\u0641\u062a\u0627\u0631\u0647\u0627\u06cc \u0628\u06cc\u0636\u06cc \u06af\u0648\u0646\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0633\u062a.<\/span><\/p>\n

\u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc<\/span> \u0647\u06cc\u0686\u200c\u06af\u0648\u0646\u0647 \u062c\u0647\u062a \u0645\u0634\u062e\u0635\u0647\u200c\u0627\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0647 \u0648 \u0631\u0641\u062a\u0627\u0631 \u0622\u0646 \u0645\u062a\u0639\u0627\u062f\u0644 \u0627\u0633\u062a. \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0632\u0645\u0627\u0646 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u062c\u0627\u06cc\u06cc \u0646\u062f\u0627\u0631\u062f\u060c \u0628\u0631\u0627\u06cc \u062d\u0644 \u0627\u06cc\u0646 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u06cc\u06a9 \u0627\u0632 \u062f\u0648 \u0631\u0648\u0634 \u0632\u0645\u0627\u0646 \u0645\u062c\u0627\u0632\u06cc(Artificial Time) \u06a9\u0647 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0633\u0627\u062f\u0647\u200c\u062a\u0631\u06cc \u0645\u0639\u0631\u0648\u0641 \u0628\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f \u0648 \u06cc\u0627 \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631<\/span><\/a> \u0631\u0627 \u0628\u06a9\u0627\u0631 \u0628\u0631\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0634\u062a\u0647 \u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0648 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0648 \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0644\u0627\u067e\u0644\u0627\u0633 \u0648 \u067e\u0648\u0622\u0633\u0648\u0646 (Laplace and Poisson Equations)<\/strong><\/span><\/h3>\n

\u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u062f\u0648\u0628\u0639\u062f\u06cc \u0633\u0627\u062f\u0647\u200c\u062a\u0631\u06cc\u0646 \u0646\u0648\u0639 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 1) \u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0641\u0631\u0645 \u063a\u06cc\u0631 \u0647\u0645\u06af\u0646 \u0622\u0646 (\u0645\u0639\u0627\u062f\u0644\u0647 \u067e\u0648\u0627\u0633\u0648\u0646) \u06a9\u0647 \u062f\u0631 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0641\u06cc\u0632\u06cc\u06a9\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u062f\u060c \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (2) \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a<\/h3>\n

<\/h3>\n

\u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc<\/strong><\/span><\/h3>\n

\u0647\u0645\u0627\u0646\u0646\u062f \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0628\u0631\u0627\u06cc \u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0646\u06cc\u0632 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0631\u0648\u0634 \u062c\u062f\u0627\u0633\u0627\u0632\u06cc \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. \u0628\u0645\u0646\u0638\u0648\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u062d\u0644\u200c\u0647\u0627\u06cc \u062a\u062d\u0644\u06cc\u0644\u06cc \u0648 \u0639\u062f\u062f\u06cc\u060c \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0645\u0634\u062a\u0631\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 (1) \u0628\u0627 \u0634\u0631\u0637 \u0645\u0631\u0632\u06cc \u0645\u0646\u062f\u0631\u062c \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (3) \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u0628\u0631\u0627\u06cc \u062d\u0644 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u062c\u062f\u0627\u0633\u0627\u0632\u06cc \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0645\u0639\u0627\u062f\u0644\u0647 (4) \u0641\u0631\u0636 \u0645\u06cc \u0634\u0648\u062f. \u0628\u0627 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 (4) \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633\u060c \u0645\u0639\u0627\u062f\u0644\u0647 (5) \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc\u200c\u062f\u0647\u062f. \u0631\u0627\u0628\u0637\u0647 (6) \u0646\u06cc\u0632 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 (5) \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

\"\u0645\u0639\u0627\u062f\u0644\u0647<\/p>\n

\u0627\u0632 \u0622\u0646\u062c\u0627\u06a9\u0647 \u0633\u0645\u062a \u0686\u067e \u0645\u0639\u0627\u062f\u0644\u0647 (6) \u062a\u0646\u0647\u0627 \u062a\u0627\u0628\u0639\u06cc \u0627\u0632 x \u0648 \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0622\u0646 \u062a\u0646\u0647\u0627 \u062a\u0627\u0628\u0639\u06cc \u0627\u0632 y \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u0644\u0630\u0627 \u0627\u06cc\u0646 \u062f\u0648 \u062a\u0631\u0645 \u0628\u0627\u06cc\u062f \u0628\u0631\u0627\u0628\u0631 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u062b\u0627\u0628\u062a \u0628\u0627\u0634\u0646\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (7) \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0628\u0637\u0647\u060c a<\/em><\/strong> \u06cc\u06a9 \u0639\u062f\u062f \u062d\u0642\u06cc\u0642\u06cc \u0627\u0633\u062a. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062d\u0644 \u0646\u0647\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0627\u0628\u0639 X<\/strong><\/em> \u0648 Y<\/strong><\/em>\u00a0 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a (8) \u0648 (9) \u0647\u0633\u062a\u0646\u062f. \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0647\u060c A, B, C & D \u062b\u0627\u0628\u062a \u0647\u0633\u062a\u0646\u062f. <\/span><\/p>\n

\u0627\u0632 \u0622\u0646\u062c\u0627\u0626\u06cc\u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062e\u0637\u06cc \u0627\u0633\u062a\u060c \u062d\u0644 \u0639\u0645\u0648\u0645\u06cc \u062a\u0631\u06a9\u06cc\u0628 \u062e\u0637\u06cc \u0627\u0632 \u062c\u0648\u0627\u0628\u0647\u0627\u06cc \u0641\u0648\u0642 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644 \u0641\u0648\u0642 \u0644\u0627\u0632\u0645\u0633\u062a \u06a9\u0647 \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc \u0646\u06cc\u0632 \u0645\u0634\u062e\u0635 \u0634\u0648\u062f.\u00a0 \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u06af\u0631 u \u0631\u0648\u06cc \u0645\u0631\u0632\u0647\u0627 \u0635\u0641\u0631 \u0628\u0627\u0634\u062f. \u062f\u0631 x=0 \u0648 x=L \u060c \u0628\u0627\u06cc\u062f X=0 \u0648 \u062f\u0631 y=0 \u0646\u06cc\u0632 Y \u0628\u0631\u0627\u0628\u0631 \u0635\u0641\u0631 \u0628\u0627\u0634\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u0644\u0627\u0632\u0645\u0633\u062a \u06a9\u0647 \u0639\u0628\u0627\u0631\u062a\u200c\u0647\u0627\u06cc B=0\u060c C+D=0 \u0648 A SinaL=0 \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f. \u0628\u0631\u0627\u06cc \u062d\u0644 \u063a\u06cc\u0631 \u0628\u062f\u06cc\u0647\u06cc\u060c A\u22600 \u0648 \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 SinaL=0 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0647\u0645 \u0632\u0645\u0627\u0646\u06cc \u0627\u062a\u0641\u0627\u0642 \u0645\u06cc\u200c\u0627\u0641\u062a\u062f \u06a9\u0647 \u0631\u0627\u0628\u0637\u0647 (10) \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f. \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0645\u0630\u06a9\u0648\u0631\u060c n \u06cc\u06a9 \u0639\u062f\u062f \u0635\u062d\u06cc\u062d \u0645\u062b\u0628\u062a \u0627\u0633\u062a. \u0628\u0627 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u0631\u0627\u0628\u0637\u0647 \u0641\u0648\u0642 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (8)\u060c (9) \u0648 (4) \u062c\u0648\u0627\u0628 \u0646\u0647\u0627\u06cc\u06cc \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (11) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0634\u0631\u0637 \u0645\u0631\u0632\u06cc u=1 \u0631\u0648\u06cc y=L \u060c \u0636\u0631\u0627\u0626\u0628 An<\/sub><\/em><\/strong> \u0637\u0628\u0642 \u0631\u0627\u0628\u0637\u0647 (12) \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

:[1]<\/span><\/strong><\/p>\n

K. A. Hoffman AND S.T. Chaing, \u201cComputational Fluid Dynamics for Engineer\u201d, Volume 1, Engineering Education System, Wichita, Kansas, 1993<\/span><\/strong><\/p>\n

:[2]<\/span><\/strong><\/p>\n

Stanley J. Farlow, \u201cPartial Differential Equations for Scientists and engineers\u201d, Dover Publications INC, New York, 1993<\/span><\/strong><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

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\u0645\u062d\u0645\u062f\u0631\u0636\u0627 \u06a9\u0644\u06cc\u0686<\/a><\/em><\/strong><\/span><\/h5>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc Elliptic Partial Differential Equations \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc \u06cc\u06a9\u06cc \u0627\u0632 \u0633\u0647 \u062f\u0633\u062a\u0647 \u0645\u0647\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u0647 \u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u0646\u062f. \u062a\u0639\u062f\u0627\u062f \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0645 \u0639\u0644\u0645\u06cc \u0646\u0638\u06cc\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0627\u0626\u0645\u06cc \u062f\u0645\u0627 \u062f\u0631 \u06cc\u06a9 \u062c\u0633\u0645 \u062c\u0627\u0645\u062f \u0648 \u062c\u0631\u06cc\u0627\u0646 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644… Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":11590,"parent":10401,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-11586","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\n\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc - cfd-mrk<\/title>\n<meta name=\"description\" content=\"\u062f\u0631 \u0633\u064a\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc\u00a0\u0647\u064a\u0686\u200c\u06af\u0648\u0646\u0647 \u062c\u0647\u062a \u0645\u0634\u062e\u0635\u0647\u200c\u0627\u064a \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a\u0647 \u0648 \u0631\u0641\u062a\u0627\u0631 \u0622\u0646 \u0645\u062a\u0639\u0627\u062f\u0644 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