{"id":41140,"date":"2024-09-26T06:46:11","date_gmt":"2024-09-26T06:46:11","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%81%d8%b1%d9%85%d9%88%d9%84-%d9%87%d8%a7%db%8c-%d8%aa%d9%81%d8%a7%d9%88%d8%aa-%d9%88%d8%b2%d9%86-%d9%85\/"},"modified":"2024-09-26T06:46:42","modified_gmt":"2024-09-26T06:46:42","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%81%d8%b1%d9%85%d9%88%d9%84-%d9%87%d8%a7%db%8c-%d8%aa%d9%81%d8%a7%d9%88%d8%aa-%d9%88%d8%b2%d9%86-%d9%85","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%81%d8%b1%d9%85%d9%88%d9%84-%d9%87%d8%a7%db%8c-%d8%aa%d9%81%d8%a7%d9%88%d8%aa-%d9%88%d8%b2%d9%86-%d9%85\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627\u06cc \u062a\u0641\u0627\u0648\u062a \u0648\u0632\u0646 \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nMinkowski difference weight formulas<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627\u06cc \u062a\u0641\u0627\u0648\u062a \u0648\u0632\u0646 \u0645\u06cc\u0646\u06a9\u0648\u0641\u0633\u06a9\u06cc<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nG. Krishna Teja<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n31<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nRepresentation Theory,\u0646\u0638\u0631\u06cc\u0647 \u0628\u0627\u0632\u0646\u0645\u0627\u06cc\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 19 September, 2024; originally announced September 2024. , Comments: We isolate from our pre-print (ArXiv:2012.07775v2), weight-formula in Theorem A and conversely finding modules V with classical weights in Theorem B. All such weight-formulas are found in Theorem C, via freeness-nodes for weights (Definitions 1.8, 5.2). Thereby: “Jordan-Holder series” factors of V with majority of weights explicitly, and some weight multiplicity bounds (Proposition 1.16) , MSC Class: Primary: 17B10; Secondary: 17B20; 17B22; 17B67; 17B70; 52B20; 52B99<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 19 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f. \u060c \u0646\u0638\u0631\u0627\u062a: \u0645\u0627 \u0627\u0632 \u067e\u06cc\u0634 \u0686\u0627\u067e \u0645\u0627 \u062c\u062f\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645 (ARXIV: 2012.07775V2) \u060c \u0641\u0631\u0645\u0648\u0644 \u0648\u0632\u0646 \u062f\u0631 \u0642\u0636\u06cc\u0647 A \u0648 \u0628\u0631\u0639\u06a9\u0633 \u06cc\u0627\u0641\u062a\u0646 \u0645\u0627\u0698\u0648\u0644 \u0647\u0627\u06cc V \u0628\u0627 \u0648\u0632\u0646 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u062f\u0631 \u0642\u0636\u06cc\u0647 B.\u060c \u0627\u0632 \u0637\u0631\u06cc\u0642 \u06af\u0631\u0647 \u0647\u0627\u06cc freeness \u0628\u0631\u0627\u06cc \u0648\u0632\u0646\u0647 \u0647\u0627 (\u062a\u0639\u0627\u0631\u06cc\u0641 1.8 \u060c 5.2).\u0628\u062f\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628: “\u0633\u0631\u06cc \u0627\u0631\u062f\u0646-\u0647\u0648\u0644\u062f\u0631” \u0641\u0627\u06a9\u062a\u0648\u0631\u0647\u0627\u06cc V \u0628\u0627 \u0627\u06a9\u062b\u0631 \u0648\u0632\u0646 \u0647\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0635\u0631\u06cc\u062d \u060c \u0648 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0645\u0631\u0632\u0647\u0627\u06cc \u062a\u0639\u062f\u062f \u0648\u0632\u0646 (\u06af\u0632\u0627\u0631\u0647 1.16) \u060c \u06a9\u0644\u0627\u0633 MSC: \u0627\u0648\u0644\u06cc\u0647: 17B10 \u061b \u062b\u0627\u0646\u0648\u06cc\u0647: 17B22 \u061b 17B67 \u061b 17B70 \u061b 52B9 \u061b 52B99 \u061b<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \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.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \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.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

Fix any complex Kac-Moody Lie algebra $\\mathfrak{g}$, and Cartan subalgebra $\\mathfrak{h}\\subset \\mathfrak{g}$. We study arbitrary highest weight $\\mathfrak{g}$-modules $V$ (with any highest weight $\u03bb\\in \\mathfrak{h}^*$, and let $L(\u03bb)$ be the corresponding simple highest weight $\\mathfrak{g}$-module), and write their weight-sets $\\mathrm{wt} V$. This is based on and generalizes the Minkowski decompositions for all $\\mathrm{wt} L(\u03bb)$ and hulls $\\mathrm{conv}_{\\mathbb{R}}(\\mathrm{wt} V)$, of Khare [J. Algebra. 2016 & Trans. Amer. Math. Soc. 2017] and Dhillon-Khare [Adv. Math. 2017 & J. Algebra. 2022]. Those works need a freeness property of the Dynkin graph nodes of integrability $J_\u03bb$ of $L(\u03bb)$: $\\mathrm{wt} L(\u03bb)\\ -$ any sum of simple roots over $J_\u03bb^c$ are all weights of $L(\u03bb)$. We generalize it for all $V$, by introducing nodes $J_V$ that record all the lost 1-dim. weights in $V$. We show three applications (seemingly novel) for all $\\big(\\mathfrak{g}, \u03bb, V\\big)$ of our $J_V^c$-freeness: 1) Minkowski decompositions of all $\\mathrm{wt} V$, subsuming those above for simples. 1$’$) Characterization of these formulas. 1$”$) For these, we solve the inverse problem of determining all $V$ with fixing $\\mathrm{wt} V \\ =$ weight-set of a Verma, parabolic Verma and $L(\u03bb)$ $\\forall$ $\u03bb$. 2) At module level (by raising operators’ actions), construction of weight vectors along $J_V^c$-directions. 3) Lower bounds on the multiplicities of such weights, in all $V$.<\/p>\n

\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

\u0631\u0641\u0639 \u0647\u0631 \u062c\u0628\u0631 kac-moody \u067e\u06cc\u0686\u06cc\u062f\u0647 $ \\ mathfrak {g} $ \u060c \u0648 cartan subalgebra $ \\ mathfrak {h} \\ subset \\ mathfrak {g} $.\u0645\u0627 \u0628\u0627 \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 \u0648\u0632\u0646 \u062f\u0644\u062e\u0648\u0627\u0647 \\ mathfrak {g} $-\u0645\u0627\u0698\u0648\u0644 \u0647\u0627\u06cc $ v $ (\u0628\u0627 \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 \u0648\u0632\u0646 $ \u03bb \\ \u062f\u0631 \\ mathfrak {h}^*$ \u0631\u0627 \u0645\u0637\u0627\u0644\u0639\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u060c \u0648 \u0628\u06af\u0630\u0627\u0631\u06cc\u062f $ l (\u03bb) $ \u0633\u0627\u062f\u0647 \u062a\u0631\u06cc\u0646 \u0648\u0632\u0646 $ $ \u0628\u0627\u0634\u062f\\ mathfrak {g} $-\u0645\u0627\u0698\u0648\u0644) \u060c \u0648 \u0645\u062c\u0645\u0648\u0639\u0647 \u0647\u0627\u06cc \u0648\u0632\u0646 \u062e\u0648\u062f \u0631\u0627 $ \\ mathrm {wt} v $ \u0628\u0646\u0648\u06cc\u0633\u06cc\u062f.\u0627\u06cc\u0646 \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0647\u0627\u06cc Minkowski \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 $ \\ Mathrm {wt} l (\u03bb) $ \u0648 hulls $ \\ mathrm {conv} _ {\\ mathbb {r} (\\ mathrm {wt} v) $ \u060c \u0627\u0632 khare[\u062c.\u062c\u0628\u06312016 \u0648 \u062a\u0631\u0627\u0646\u0633.\u0639\u0627\u0645\u0631\u0631\u06cc\u0627\u0636\u06cc.SOC.2017] \u0648 \u062f\u06cc\u0644\u0648\u0646 \u062e\u0631\u0647 [\u0645\u0634\u0627\u0648\u0631.\u0631\u06cc\u0627\u0636\u06cc.2017 & J. Algebra.2022].\u0627\u06cc\u0646 \u0622\u062b\u0627\u0631 \u0628\u0647 \u06cc\u06a9 \u0648\u06cc\u0698\u06af\u06cc freeness \u0627\u0632 \u06af\u0631\u0647 \u0647\u0627\u06cc \u0646\u0645\u0648\u062f\u0627\u0631 Dynkin \u0627\u0632 \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u0633\u0627\u0632\u06cc $ J_\u03bb $ L (\u03bb) $: $ \\ Mathrm {wt} l (\u03bb) \\ -$ \u0647\u0631 \u0645\u0628\u0644\u063a\u06cc \u0627\u0632 \u0631\u06cc\u0634\u0647 \u0647\u0627\u06cc \u0633\u0627\u062f\u0647 \u0628\u06cc\u0634 \u0627\u0632 $ j_\u03bb^c $ \u0647\u0645\u0647 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u0646\u062f.\u0648\u0632\u0646 $ L (\u03bb) $.\u0645\u0627 \u0628\u0627 \u0645\u0639\u0631\u0641\u06cc \u06af\u0631\u0647 \u0647\u0627\u06cc $ j_v $ \u06a9\u0647 \u0647\u0645\u0647 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0627\u0632 \u062f\u0633\u062a \u0631\u0641\u062a\u0647 1-DIM \u0636\u0628\u0637 \u0645\u06cc \u06a9\u0646\u062f \u060c \u0622\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645 $ v $ \u062a\u0639\u0645\u06cc\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645.\u0648\u0632\u0646 \u062f\u0631 $ v $.\u0645\u0627 \u0633\u0647 \u0628\u0631\u0646\u0627\u0645\u0647 (\u0628\u0647 \u0638\u0627\u0647\u0631 \u0631\u0645\u0627\u0646) \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 $ \\ \u0628\u0632\u0631\u06af (\\ Mathfrak {g} \u060c \u03bb \u060c v \\ big) $ \u0627\u0632 $ j_v^c $ -freeness: 1) \u062a\u062c\u0632\u06cc\u0647 minkowski \u0627\u0632 \u0647\u0645\u0647 $ \\ mathrm {wt} v} v} v} v \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645.$ \u060c \u0645\u0648\u0627\u0631\u062f \u0641\u0648\u0642 \u0631\u0627 \u0628\u0631\u0627\u06cc Simples \u062f\u0631\u062c \u0645\u06cc \u06a9\u0646\u062f.1 $ ‘$) \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u0627\u06cc\u0646 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627.1 $ ” $) \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u0647\u0627 \u060c \u0645\u0627 \u0645\u0634\u06a9\u0644 \u0645\u0639\u06a9\u0648\u0633 \u062a\u0639\u06cc\u06cc\u0646 \u062a\u0645\u0627\u0645 $ v $ \u0631\u0627 \u0628\u0627 \u0631\u0641\u0639 $ \\ mathrm {wt} v \\ = $ \u062a\u0646\u0638\u06cc\u0645 \u0648\u0632\u0646 \u06cc\u06a9 \u0648\u0631\u0645 \u200b\u200b\u060c \u067e\u0627\u0631\u0627\u0628\u0648\u0644\u06cc\u06a9 \u0648 $ l (\u03bb) $ $ \\ \u062d\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u0645.$ $ \u03bb $.2) \u062f\u0631 \u0633\u0637\u062d \u0645\u0627\u0698\u0648\u0644 (\u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0627\u0642\u062f\u0627\u0645\u0627\u062a \u0627\u067e\u0631\u0627\u062a\u0648\u0631\u0647\u0627) \u060c \u0633\u0627\u062e\u062a \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0648\u0632\u0646\u06cc \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f $ J_V^C $ -directions.3) \u0645\u0631\u0632\u0647\u0627\u06cc \u067e\u0627\u06cc\u06cc\u0646 \u062a\u0631 \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0627\u06cc\u0646 \u0648\u0632\u0646\u0647 \u0647\u0627 \u060c \u062f\u0631 \u062a\u0645\u0627\u0645 $ V $.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \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.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \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.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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