{"id":32421,"date":"2025-02-25T13:00:14","date_gmt":"2025-02-25T13:00:14","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=32421"},"modified":"2025-03-05T22:10:09","modified_gmt":"2025-03-05T22:10:09","slug":"%e0%a4%8f%e0%a4%95-%e0%a4%85%e0%a4%b5%e0%a4%a7%e0%a4%bf-%e0%a4%95%e0%a4%be-%e0%a4%ac%e0%a4%be%e0%a4%87%e0%a4%a8%e0%a5%8b%e0%a4%ae%e0%a4%bf%e0%a4%af%e0%a4%b2-%e0%a4%ae%e0%a5%89%e0%a4%a1%e0%a4%b2","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%8f%e0%a4%95-%e0%a4%85%e0%a4%b5%e0%a4%a7%e0%a4%bf-%e0%a4%95%e0%a4%be-%e0%a4%ac%e0%a4%be%e0%a4%87%e0%a4%a8%e0%a5%8b%e0%a4%ae%e0%a4%bf%e0%a4%af%e0%a4%b2-%e0%a4%ae%e0%a5%89%e0%a4%a1%e0%a4%b2\/","title":{"rendered":"\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0914\u0930 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0914\u0930 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f<\/h1>\n<p style=\"text-align:center;\"><em><b>\u0938\u093e\u0930\u093e\u0902\u0936:<\/b><br \/>\n\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902 \u0915\u093f \u090f\u0915 \u0915\u0948\u0938\u0940\u0928\u094b \u0939\u0948 \u091c\u0939\u093e\u0901 \u0906\u092a \u090f\u0915 \u0910\u0938\u0947 \u0916\u0947\u0932 \u092e\u0947\u0902 \u0926\u093e\u0902\u0935 \u0932\u0917\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0901, \u092a\u0930\u093f\u0923\u093e\u092e 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\u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u0948\u0938\u0947 \u0915\u093e\u092e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u0935\u093f\u0937\u092f \u0938\u0942\u091a\u0940<\/u><\/b><br \/>\n<a href=\"#1\">\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0915\u094d\u092f\u093e \u0939\u0948?<\/a><br \/>\n<a href=\"#2\">\u0915\u0948\u0938\u0947 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0905\u0935\u0938\u0930\u094b\u0902 \u0935\u093e\u0932\u0947 \u092c\u093e\u091c\u093e\u0930 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0909\u0928\u0915\u0940 \u0924\u094d\u0935\u0930\u093f\u0924 \u0938\u092e\u093e\u092a\u094d\u0924\u093f<\/a><br \/>\n<a href=\"#3\">\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923<\/a><br \/>\n<a href=\"#4\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/-oshd8mj6bg?si=8Dgu1tTvP8giiEwd\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0915\u094d\u092f\u093e \u0939\u0948?<\/h2>\n<p><strong>\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932<\/strong> \u090f\u0915 \u0917\u0923\u093f\u0924\u0940\u092f \u092e\u0949\u0921\u0932 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0935\u093f\u0924\u094d\u0924 \u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0915\u0940\u092e\u0924 \u0915\u0947 \u0938\u092e\u092f-\u0938\u0940\u092e\u093f\u0924 \u0935\u093f\u0915\u093e\u0938 \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u00ab\u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932\u00bb \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u092e\u092f \u0905\u0935\u0927\u093f \u092e\u0947\u0902, \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0915\u0940\u092e\u0924 \u0915\u0947\u0935\u0932 \u0926\u094b \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0926\u093f\u0936\u093e\u0913\u0902 \u092e\u0947\u0902 \u0906\u0917\u0947 \u092c\u0922\u093c \u0938\u0915\u0924\u0940 \u0939\u0948: \u092c\u0922\u093c\u0928\u093e \u092f\u093e \u0918\u091f\u0928\u093e\u0964 \u092f\u0939 \u092e\u0949\u0921\u0932 \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 (\u0921\u0947\u0930\u093f\u0935\u0947\u091f\u093f\u0935) \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 \u0935\u093f\u0915\u0932\u094d\u092a\u094b\u0902 (\u0911\u092a\u094d\u0936\u0902\u0938) \u0915\u0947 \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928 \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u092a\u0915 \u0930\u0942\u092a \u0938\u0947 \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u092c\u0939\u0941-\u0905\u0935\u0927\u093f \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0915\u093e \u0906\u0927\u093e\u0930 \u0939\u0948\u0964<\/p>\n<h3>\u092e\u0949\u0921\u0932 \u0915\u0947 \u0918\u091f\u0915<\/h3>\n<p>\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u0947 \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u094c\u0932\u093f\u0915 \u0924\u0924\u094d\u0935\u094b\u0902 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<ul>\n<li>\n<p><strong>\u090f\u0915 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f:<\/strong> \u091c\u093f\u0938\u0947 \u0938\u092e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u092a\u0930 \u0907\u0938\u0915\u0940 \u0915\u0940\u092e\u0924 <span class=\"katex-eq\" data-katex-display=\"false\">S(t)<\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u092e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span> \u092a\u0930 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0915\u0940\u092e\u0924 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0938\u092e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u092a\u0930, \u0907\u0938\u0915\u0940 \u0915\u0940\u092e\u0924 \u0926\u094b \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u092e\u0947\u0902 \u092c\u0926\u0932 \u0938\u0915\u0924\u0940 \u0939\u0948, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{sube})<\/span> (\u092f\u0926\u093f \u0915\u0940\u092e\u0924 \u092c\u0922\u093c\u0924\u0940 \u0939\u0948) \u092f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">S(1,\\text{baja})<\/span> (\u092f\u0926\u093f \u0915\u0940\u092e\u0924 \u0918\u091f\u0924\u0940 \u0939\u0948) \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nS(1) =\n\n\\begin{cases}\n\nS(1,\\text{sube}) = S(0)  u, &amp; \\text{\u0938\u0902\u092d\u093e\u0935\u0928\u093e } p \\text{ \u0915\u0947 \u0938\u093e\u0925}, \\\\\n\nS(1,\\text{baja}) = S(0)  d, &amp; \\text{\u0938\u0902\u092d\u093e\u0935\u0928\u093e } 1 - p \\text{ \u0915\u0947 \u0938\u093e\u0925}\u0964\n\n\\end{cases}\n\n<\/span>\n<p>\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0917\u0941\u0923\u093e\u0902\u0915 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u0947 \u0915\u093e\u0930\u0915\u094b\u0902 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt d \\lt 1 \\lt u<\/span>.<\/p>\n<p>\u092f\u0939 \u0938\u0902\u092c\u0902\u0927 \u092f\u0939 \u092d\u0940 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092d\u0935\u093f\u0937\u094d\u092f \u0915\u0940 \u0915\u0940\u092e\u0924\u0947\u0902 \u0939\u092e\u0947\u0936\u093e \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0902, \u091c\u0948\u0938\u093e \u0915\u093f <strong>\u0938\u0930\u0932 \u092c\u093e\u091c\u093e\u0930 \u092e\u0949\u0921\u0932<\/strong> \u0915\u0940 \u092e\u0942\u0932\u092d\u0942\u0924 \u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li><strong>\u0938\u0902\u092d\u093e\u0935\u0928\u093e\u090f\u0901:<\/strong> \u092f\u0939 \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0947 \u092c\u0922\u093c\u0928\u0947 \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span> \u0914\u0930 \u0918\u091f\u0928\u0947 \u0915\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e <span class=\"katex-eq\" data-katex-display=\"false\">1 - p<\/span> \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt p \\lt 1<\/span>\u0964 \u092f\u0939 \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0947 \u0926\u094b\u0928\u094b\u0902 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u091a\u093e\u0932\u0947\u0902 \u0938\u0902\u092d\u0935 \u0939\u094b\u0902 \u0914\u0930 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u0940\u092e\u0924\u0947\u0902 \u0939\u092e\u0947\u0936\u093e \u0915\u0947\u0935\u0932 \u090f\u0915 \u0939\u0940 \u0926\u093f\u0936\u093e \u092e\u0947\u0902 \u0928 \u092c\u0922\u093c\u0947\u0902 \u092f\u093e \u0928 \u0918\u091f\u0947\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0910\u0938\u093e \u0939\u094b\u0928\u0947 \u0938\u0947 \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0905\u092e\u093e\u0928\u094d\u092f \u0939\u094b \u091c\u093e\u090f\u0917\u093e \u0914\u0930 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0935\u0938\u0930 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0902\u0917\u0947\u0964<\/li>\n<li><strong>\u090f\u0915 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f:<\/strong> \u0907\u0938\u092e\u0947\u0902 \u090f\u0915 \u092c\u093e\u0902\u0921 \u092f\u093e \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u0909\u092a\u0915\u0930\u0923 \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u092e\u0942\u0932\u094d\u092f \u090f\u0915 \u092a\u0942\u0930\u094d\u0935\u093e\u0928\u0941\u092e\u0947\u092f \u0926\u0930 \u092a\u0930 \u092c\u0922\u093c\u0924\u093e \u0939\u0948, \u091c\u094b \u0915\u093f \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u092c\u094d\u092f\u093e\u091c \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0915\u0940 \u0915\u0940\u092e\u0924 \u0905\u0917\u0932\u0947 \u0938\u092e\u092f\u093e\u0935\u0927\u093f \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<\/li>\n<\/ul>\n<h3><b>\u092a\u094d\u0930\u092e\u0947\u092f:<\/b> \u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u0947 \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u092e\u0947\u0902 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f<\/h3>\n<p>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u090f\u0915 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0939\u0948 \u091c\u093f\u0938\u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0915\u0940\u092e\u0924 <span class=\"katex-eq\" data-katex-display=\"false\">S(0) \\gt 0<\/span> \u0939\u0948 \u0914\u0930 \u091c\u093f\u0938\u0915\u093e \u092e\u0942\u0932\u094d\u092f \u0938\u092e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u092a\u0930 \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u0938\u0902\u0930\u091a\u0928\u093e \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u090f\u0915 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f (\u092c\u0949\u0928\u094d\u0921) \u092e\u094c\u091c\u0942\u0926 \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u092e\u0942\u0932\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = A(0)(1+r)<\/span> \u0939\u0948, \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 \u0939\u0948\u0964 \u0924\u092c, \u092f\u0926\u093f \u0914\u0930 \u0915\u0947\u0935\u0932 \u092f\u0926\u093f \u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u0947 \u0915\u093e\u0930\u0915 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0936\u0930\u094d\u0924 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u0915\u094b\u0908 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0905\u0935\u0938\u0930 \u092e\u094c\u091c\u0942\u0926 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d \\lt 1 + r \\lt u<\/span>\n<p>\u090f\u0915 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902, \u092f\u0939 \u0938\u0902\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e \u0915\u093f \u090f\u0915 \u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b (cartera autofinanciada) \u092c\u0928\u093e\u092f\u093e \u091c\u093e\u090f \u091c\u094b \u092c\u093f\u0928\u093e \u091c\u094b\u0916\u093f\u092e \u0915\u0947 \u0932\u093e\u092d \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u0930\u0947\u0964<\/p>\n<h3>\u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u094d\u092f\u093e \u0939\u0948?<\/h3>\n<p>\u090f\u0915 <strong>\u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b<\/strong> \u090f\u0915 \u0928\u093f\u0935\u0947\u0936 \u0930\u0923\u0928\u0940\u0924\u093f \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0915\u094b\u0908 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u092a\u0942\u0902\u091c\u0940 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0916\u0930\u0940\u0926 \u0915\u094b \u0909\u0938\u0940 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u092e\u0947\u0902 \u0905\u0928\u094d\u092f \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0940 \u092c\u093f\u0915\u094d\u0930\u0940 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u093f\u0924\u094d\u0924\u092a\u094b\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0938\u0930\u0932 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, \u0907\u0938\u0947 \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u093e\u0939\u0930\u0940 \u0927\u0928 \u0928\u0939\u0940\u0902 \u091c\u094b\u0921\u093c\u093e \u091c\u093e\u0924\u093e\u0964<\/p>\n<p>\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u090f\u0915 \u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u092c\u0928\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u094b \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u092a\u0930\u093f\u0926\u0943\u0936\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0932\u093e\u092d \u0915\u0940 \u0917\u093e\u0930\u0902\u091f\u0940 \u0926\u0947\u0924\u093e \u0939\u0948, \u0924\u094b \u092f\u0939 \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0939\u093e\u0901 \u090f\u0915 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0905\u0935\u0938\u0930 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0964 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948 \u0915\u093f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u093e \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u092c\u0928\u093e\u0928\u093e \u0938\u0902\u092d\u0935 \u0928 \u0939\u094b\u0964<\/p>\n<p>\u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947, \u090f\u0915 \u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0928\u093f\u092e\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0938\u0947 \u092c\u0928\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<ul>\n<li><strong>\u091c\u094b\u0916\u093f\u092e\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924\u093f:<\/strong> \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f, \u091c\u093f\u0938\u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0915\u0940\u092e\u0924 <i>S(0)<\/i> \u0939\u0948, \u0915\u0940 <i>x<\/i> \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u0915\u094b \u0916\u0930\u0940\u0926\u093e \u092f\u093e \u092c\u0947\u091a\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0924\u093f:<\/strong> \u090f\u0915 \u092c\u0949\u0928\u094d\u0921 \u092e\u0947\u0902 <i>y<\/i> \u0930\u093e\u0936\u093f \u0928\u093f\u0935\u0947\u0936 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u092f\u093e \u0909\u0927\u093e\u0930 \u0932\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0915\u0940\u092e\u0924 <i>A(0)<\/i> \u0939\u0948 \u0914\u0930 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 <i>r<\/i> \u0939\u0948\u0964<\/li>\n<li><strong>\u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u0923 \u0915\u0940 \u0936\u0930\u094d\u0924:<\/strong> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f:<\/li>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> V(0) = x S(0) + y A(0) = 0. <\/span>\n<li><strong>\u0905\u0917\u0932\u0940 \u0905\u0935\u0927\u093f \u092e\u0947\u0902 \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928:<\/strong> \u0938\u092e\u092f <i>t = 1<\/i> \u092a\u0930 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u093e \u092e\u0942\u0932\u094d\u092f:<\/li>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> V(1) = \\begin{cases} x S(1,\\text{sube}) + y A(1), &amp; \\text{\u092f\u0926\u093f \u0915\u0940\u092e\u0924 \u092c\u0922\u093c\u0924\u0940 \u0939\u0948}, \\\\ x S(1,\\text{baja}) + y A(1), &amp; \\text{\u092f\u0926\u093f \u0915\u0940\u092e\u0924 \u0918\u091f\u0924\u0940 \u0939\u0948}\u0964 \\end{cases} <\/span>\n<\/ul>\n<p>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u0915\u093e \u0915\u094b\u0908 \u0910\u0938\u093e \u0938\u0902\u092f\u094b\u091c\u0928 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948 \u091c\u093f\u0938\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\geq 0<\/span> \u0926\u094b\u0928\u094b\u0902 \u092a\u0930\u093f\u0926\u0943\u0936\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span> \u0915\u092e \u0938\u0947 \u0915\u092e \u090f\u0915 \u092a\u0930\u093f\u0926\u0943\u0936\u094d\u092f \u092e\u0947\u0902 \u0939\u094b, \u0924\u094b \u092f\u0939 \u090f\u0915 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0905\u0935\u0938\u0930 \u0915\u094b \u0907\u0902\u0917\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 \\lt 0.82 \\lt 1.07 \\not\\lt 1.052 <\/span>\n<p>\u091a\u0942\u0901\u0915\u093f \u0905\u0938\u092e\u093e\u0928\u0924\u093e <span class=\"katex-eq\" data-katex-display=\"false\">1+r \\lt u<\/span> \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940, \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0907\u0938 \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0938\u0902\u092d\u0935 \u0939\u0948\u0964 \u0907\u0938\u0947 \u0938\u094d\u092a\u0937\u094d\u091f \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0926\u094d\u0935\u093e\u0930\u093e \u090f\u0915 \u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u092c\u0928\u093e\u090f\u0902\u0917\u0947:<\/p>\n<ul>\n<li><b>\u090f\u0915 \u0936\u0947\u092f\u0930 \u0915\u0940 \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948:<\/b> \u091c\u094b\u0916\u093f\u092e\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">S(0) = 100<\/span> \u092a\u0930 \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u0928\u093f\u0935\u0947\u0936\u0915 \u0915\u094b \u090f\u0915 \u0936\u0947\u092f\u0930 \u0909\u0927\u093e\u0930 \u0932\u0947\u0928\u093e \u0939\u094b\u0917\u093e \u0914\u0930 \u0907\u0938\u0947 \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u092c\u0947\u091a\u0928\u093e \u0939\u094b\u0917\u093e\u0964<\/li>\n<li><b>\u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936:<\/b> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 100 \u0921\u0949\u0932\u0930 \u0915\u094b \u092c\u0949\u0928\u094d\u0921 \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><b>\u0905\u0917\u0932\u0940 \u0905\u0935\u0927\u093f \u092e\u0947\u0902 \u0936\u0947\u092f\u0930 \u0915\u0940 \u092a\u0941\u0928\u0903\u0916\u0930\u0940\u0926:<\/b>\n<ul>\n<li>\u092f\u0926\u093f \u0915\u0940\u092e\u0924 82 \u092a\u0930 \u0917\u093f\u0930\u0924\u0940 \u0939\u0948, \u0924\u094b \u0936\u0941\u0926\u094d\u0927 \u0932\u093e\u092d <span class=\"katex-eq\" data-katex-display=\"false\">107 - 82 = 25<\/span> \u0939\u094b\u0917\u093e\u0964<\/li>\n<li>\u092f\u0926\u093f \u0915\u0940\u092e\u0924 105.2 \u0924\u0915 \u092c\u0922\u093c\u0924\u0940 \u0939\u0948, \u0924\u094b \u0936\u0941\u0926\u094d\u0927 \u0932\u093e\u092d <span class=\"katex-eq\" data-katex-display=\"false\">107 - 105.2 = 1.8<\/span> \u0939\u094b\u0917\u093e\u0964<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u0926\u094b\u0928\u094b\u0902 \u0939\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902, \u0928\u093f\u0935\u0947\u0936\u0915 \u0915\u094b \u0938\u0941\u0930\u0915\u094d\u0937\u093f\u0924 \u0932\u093e\u092d \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u094b \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0940 \u092a\u0941\u0937\u094d\u091f\u093f \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<h3>\ud83d\udccc \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0930\u0923\u0928\u0940\u0924\u093f \u0915\u0947 \u092a\u094d\u0930\u0924\u093f \u092c\u093e\u091c\u093e\u0930 \u0938\u092e\u093e\u092f\u094b\u091c\u0928<\/h3>\n<p>\u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u090f\u0915 \u0915\u0941\u0936\u0932 \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902, \u092f\u0947 \u0905\u0935\u0938\u0930 \u0932\u0902\u092c\u0947 \u0938\u092e\u092f \u0924\u0915 \u0928\u0939\u0940\u0902 \u092c\u0928\u0947 \u0930\u0939\u0924\u0947\u0964 \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 \u0905\u0927\u093f\u0915 \u0928\u093f\u0935\u0947\u0936\u0915 \u0907\u0938 \u0905\u0915\u094d\u0937\u092e\u0924\u093e \u0915\u094b \u092a\u0939\u091a\u093e\u0928\u0924\u0947 \u0939\u0948\u0902, \u0935\u0947 <strong>\u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917<\/strong> \u0930\u0923\u0928\u0940\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u0905\u092a\u0928\u093e\u0928\u0947 \u0932\u0917\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u0915\u0908 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u094d\u0930\u092d\u093e\u0935 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul>\n<li><b>\u091c\u094b\u0916\u093f\u092e\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0906\u092a\u0942\u0930\u094d\u0924\u093f \u092e\u0947\u0902 \u0935\u0943\u0926\u094d\u0927\u093f:<\/b> \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0915\u093e \u0924\u093e\u0924\u094d\u092a\u0930\u094d\u092f \u0939\u0948 \u0915\u093f \u0915\u0908 \u0928\u093f\u0935\u0947\u0936\u0915 \u0909\u0927\u093e\u0930 \u0932\u0947\u0915\u0930 \u0936\u0947\u092f\u0930\u094b\u0902 \u0915\u094b \u092c\u0947\u091a\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u0909\u092a\u0932\u092c\u094d\u0927 \u0936\u0947\u092f\u0930\u094b\u0902 \u0915\u0940 \u0906\u092a\u0942\u0930\u094d\u0924\u093f \u092c\u0922\u093c \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u092c\u0922\u093c\u0940 \u0939\u0941\u0908 \u0906\u092a\u0942\u0930\u094d\u0924\u093f \u0915\u0947 \u0915\u093e\u0930\u0923 <strong>\u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0915\u0940\u092e\u0924<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u092a\u0930 \u0928\u0940\u091a\u0947 \u0915\u0940 \u0913\u0930 \u0926\u092c\u093e\u0935 \u092c\u0928\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><b>\u092d\u0935\u093f\u0937\u094d\u092f \u0915\u0940 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940\u092e\u0924\u094b\u0902 \u092e\u0947\u0902 \u0938\u092e\u093e\u092f\u094b\u091c\u0928:<\/b> \u091a\u0942\u0901\u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{sube}) = S(0) u<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">S(1, \\text{baja}) = S(0) d<\/span> \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u092e\u0947\u0902 \u0917\u093f\u0930\u093e\u0935\u091f <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0915\u0947 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u094b \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930 \u0926\u0947\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">1 + r<\/span> \u0915\u0947 \u0938\u093e\u0925 \u0938\u0902\u092c\u0902\u0927 \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u094b \u092a\u0941\u0928\u0930\u094d\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0935\u0943\u0924\u094d\u0924\u093f \u0930\u0916\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><b>\u092c\u0949\u0928\u094d\u0921 \u0915\u0940 \u0915\u0940\u092e\u0924 \u092a\u0930 \u092a\u094d\u0930\u092d\u093e\u0935:<\/b> \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 \u0928\u093f\u0935\u0947\u0936\u0915 \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0927\u0928\u0930\u093e\u0936\u093f \u0915\u094b \u092c\u0949\u0928\u094d\u0921 \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0907\u0928\u0915\u0940 \u092e\u093e\u0901\u0917 \u092c\u0922\u093c \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 <strong>\u092c\u0949\u0928\u094d\u0921 \u0915\u0940 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0915\u0940\u092e\u0924<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u092e\u0947\u0902 \u0935\u0943\u0926\u094d\u0927\u093f \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u091a\u0942\u0901\u0915\u093f \u092c\u0949\u0928\u094d\u0921 \u0915\u093e \u092d\u0935\u093f\u0937\u094d\u092f \u092e\u0942\u0932\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">A(1) = 107<\/span> \u0938\u094d\u0925\u093f\u0930 \u0930\u0939\u0924\u093e \u0939\u0948, \u092f\u0939 <strong>\u092c\u0949\u0928\u094d\u0921 \u092a\u0930 \u092a\u094d\u0930\u092d\u093e\u0935\u0940 \u0930\u093f\u091f\u0930\u094d\u0928 \u0915\u094b \u0915\u092e \u0915\u0930 \u0926\u0947\u0924\u093e \u0939\u0948<\/strong>, \u091c\u093f\u0938\u0938\u0947 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0932\u093e\u092d\u092a\u094d\u0930\u0926\u0924\u093e \u092e\u0947\u0902 \u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><b>\u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0915\u0940 \u0932\u093e\u0917\u0924:<\/b> \u0935\u0947 \u0928\u093f\u0935\u0947\u0936\u0915 \u091c\u094b \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0915\u0947 \u0932\u093f\u090f \u0936\u0947\u092f\u0930 \u0909\u0927\u093e\u0930 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902, \u0909\u0928\u094d\u0939\u0947\u0902 <strong>\u0936\u0947\u092f\u0930 \u0909\u0927\u093e\u0930 \u0932\u0947\u0928\u0947 \u0915\u0940 \u0926\u0930<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0915\u093e \u092d\u0941\u0917\u0924\u093e\u0928 \u0915\u0930\u0928\u093e \u092a\u0921\u093c\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u090f\u0915 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0932\u093e\u0917\u0924 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0938\u0947 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u0936\u0941\u0926\u094d\u0927 \u0932\u093e\u092d \u092e\u0947\u0902 \u0915\u092e\u0940 \u0906 \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/li>\n<\/ul>\n<h3>\ud83d\udccc \u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u094b \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948?<\/h3>\n<p>\u092f\u0926\u093f \u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0905\u0927\u093f\u0915 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0924\u094b \u092f\u0939 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0938\u0947 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u0936\u0941\u0926\u094d\u0927 \u0932\u093e\u092d \u0915\u094b \u0915\u092e \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948 \u092f\u093e \u092f\u0939\u093e\u0901 \u0924\u0915 \u0915\u093f \u0938\u092e\u093e\u092a\u094d\u0924 \u092d\u0940 \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0930\u0923\u0928\u0940\u0924\u093f \u0915\u0947 \u0905\u0902\u0924\u093f\u092e \u092e\u0942\u0932\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u094b\u0917\u093e:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nV(1) = A(0)(1 + r - r_s) - S(1)\n\n<\/span>\n<p>\u091c\u0939\u093e\u0901:<\/p>\n<ul>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 \u0939\u0948\u0964<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1+r)<\/span> \u092c\u0949\u0928\u094d\u0921 \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> \u0905\u0935\u0927\u093f \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902 \u0936\u0947\u092f\u0930 \u0915\u094b \u092a\u0941\u0928\u0903 \u0916\u0930\u0940\u0926\u0928\u0947 \u0915\u0940 \u0932\u093e\u0917\u0924 \u0939\u0948\u0964<\/li>\n<\/ul>\n<p>\u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0928\u0947 \u092a\u0930, \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0940 \u0936\u0930\u094d\u0924 \u0928\u093f\u092e\u094d\u0928 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d \\lt 1 + r - r_s \\lt u<\/span>\n<p>\u0907\u0938 \u0935\u093f\u0936\u0947\u0937 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902, \u0935\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0915\u0947 \u092e\u093e\u0928 \u091c\u094b \u0907\u0938 \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 \\lt 0.82 \\lt 1.07 - r_s \\lt 1.052 <\/span>\n<p>\u0907\u0938\u0915\u093e \u0924\u093e\u0924\u094d\u092a\u0930\u094d\u092f \u0939\u0948 \u0915\u093f:<\/p>\n<ul>\n<li><b>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">0 \\leq r_s \\lt 0.018<\/span>:<\/b> \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u093e \u0905\u0935\u0938\u0930 \u092c\u0928\u093e \u0930\u0939\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0932\u093e\u092d \u0926\u094b\u0928\u094b\u0902 \u092a\u0930\u093f\u0926\u0943\u0936\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u092c\u0928\u093e \u0930\u0939\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><b>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">0.018 \\leq r_s \\leq 0.25<\/span>:<\/b> \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0938\u092e\u093e\u092a\u094d\u0924 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0936\u0947\u092f\u0930 \u090b\u0923 \u0932\u093e\u0917\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u0938\u0902\u0924\u0941\u0932\u093f\u0924 \u0915\u0930 \u0926\u0947\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0938\u0941\u0930\u0915\u094d\u0937\u093f\u0924 \u0932\u093e\u092d \u0915\u094b \u0938\u092e\u093e\u092a\u094d\u0924 \u0915\u0930 \u0926\u0947\u0924\u0940 \u0939\u0948\u0964<\/li>\n<li><b>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span>:<\/b> \u0907\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902, \u0915\u094b\u0908 \u092d\u0940 \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u0928\u093f\u0935\u0947\u0936\u0915 \u0907\u0938 \u0932\u0947\u0928-\u0926\u0947\u0928 \u0915\u094b \u0928\u0939\u0940\u0902 \u0915\u0930\u0947\u0917\u093e, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u090b\u0923 \u0932\u093e\u0917\u0924 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0932\u093e\u092d \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u091a\u0942\u0901\u0915\u093f \u0907\u0938 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u093e \u092d\u0935\u093f\u0937\u094d\u092f \u092e\u0942\u0932\u094d\u092f \u0938\u092d\u0940 \u092a\u0930\u093f\u0926\u0943\u0936\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0917\u093e, \u090f\u0915 \u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0905\u0938\u0902\u092d\u0935 \u0939\u094b \u091c\u093e\u090f\u0917\u093e\u0964<\/li>\n<\/ul>\n<h3>\ud83d\udccc \u092f\u0926\u093f \u0928\u0941\u0915\u0938\u093e\u0928 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u094b \u0938\u092e\u093e\u092a\u094d\u0924 \u0915\u0930 \u0926\u0947\u0902 \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948? \u091c\u092c\u0930\u0928 \u092a\u0930\u093f\u0938\u092e\u093e\u092a\u0928 \u0914\u0930 \u092e\u093e\u0930\u094d\u091c\u093f\u0928 \u0915\u0949\u0932<\/h3>\n<p>\u092f\u0926\u093f \u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0907\u0924\u0928\u0940 \u0905\u0927\u093f\u0915 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f \u092f\u0939 \u0938\u0941\u0930\u0915\u094d\u0937\u093f\u0924 \u0928\u0941\u0915\u0938\u093e\u0928 \u0915\u0940 \u0917\u093e\u0930\u0902\u091f\u0940 \u0926\u0947\u0924\u0940 \u0939\u0948 (<span class=\"katex-eq\" data-katex-display=\"false\">r_s \\gt 0.25<\/span>), \u0924\u094b \u0926\u0932\u093e\u0932 (\u092c\u094d\u0930\u094b\u0915\u0930) \u0938\u094d\u0935\u0924\u0903 \u0939\u0938\u094d\u0924\u0915\u094d\u0937\u0947\u092a \u0915\u0930\u0924\u093e \u0939\u0948 \u0924\u093e\u0915\u093f \u0928\u093f\u0935\u0947\u0936\u0915 \u0915\u093e \u0916\u093e\u0924\u093e \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u092e\u0947\u0902 \u0928 \u091a\u0932\u093e \u091c\u093e\u090f\u0964 \u092f\u0939 \u090f\u0915 <strong>\u091c\u092c\u0930\u0928 \u092a\u0930\u093f\u0938\u092e\u093e\u092a\u0928<\/strong> \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0947 <b>\u092e\u093e\u0930\u094d\u091c\u093f\u0928 \u0915\u0949\u0932<\/b> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092d\u0940 \u091c\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<h5>\ud83d\udd39 \u091c\u092c\u0930\u0928 \u092a\u0930\u093f\u0938\u092e\u093e\u092a\u0928 \u0915\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e:<\/h5>\n<ol>\n<li><b>\u092c\u0949\u0928\u094d\u0921 \u0915\u094b \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u092c\u0947\u091a\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/b>\n<p>\u092c\u094d\u0930\u094b\u0915\u0930 \u092c\u0949\u0928\u094d\u0921 \u0928\u093f\u0935\u0947\u0936 <span class=\"katex-eq\" data-katex-display=\"false\">A(0)(1 + r)<\/span> \u0915\u094b \u0924\u0930\u0932 (\u0915\u0948\u0936) \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0947\u091a \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li><b>\u0936\u0949\u0930\u094d\u091f \u092a\u094b\u091c\u0940\u0936\u0928 \u0915\u094b \u092c\u0902\u0926 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0936\u0947\u092f\u0930 \u0915\u0940 \u092a\u0941\u0928\u0903\u0916\u0930\u0940\u0926:<\/b>\n<p>\u0909\u092a\u0932\u092c\u094d\u0927 \u0928\u0915\u0926\u0940 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947, \u092c\u094d\u0930\u094b\u0915\u0930 <strong>\u0936\u0947\u092f\u0930 \u0915\u094b \u092a\u0941\u0928\u0903 \u0916\u0930\u0940\u0926\u0924\u093e \u0939\u0948<\/strong> \u0914\u0930 \u0907\u0938\u0947 \u090b\u0923\u0926\u093e\u0924\u093e \u0915\u094b \u0935\u093e\u092a\u0938 \u0915\u0930 \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u092a\u0941\u0928\u0903\u0916\u0930\u0940\u0926 \u0915\u0940 \u0915\u0940\u092e\u0924 <span class=\"katex-eq\" data-katex-display=\"false\">S(1)<\/span> \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<li><b>\u090b\u0923 \u0928\u093f\u092a\u091f\u093e\u0928 \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u092e\u093e\u092a\u0928:<\/b>\n<p>\u092f\u0926\u093f \u092c\u0949\u0928\u094d\u0921 \u092c\u0947\u091a\u0928\u0947 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0928\u0915\u0926\u0940 <strong>\u0936\u0947\u092f\u0930 \u0915\u0940 \u092a\u0941\u0928\u0903\u0916\u0930\u0940\u0926 \u0915\u0940 \u0932\u093e\u0917\u0924 \u0915\u094b \u0915\u0935\u0930 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u0940<\/strong>, \u0924\u094b \u0928\u093f\u0935\u0947\u0936\u0915 \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u0915\u0947 \u0938\u093e\u0925 \u0930\u0939 \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0915\u093e\u0928\u0942\u0928\u0940 \u091c\u091f\u093f\u0932\u0924\u093e\u090f\u0901 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0902 \u092f\u093e \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0927\u0928 \u091c\u092e\u093e \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/p>\n<\/li>\n<li><b>\u0938\u092e\u0947\u0915\u093f\u0924 \u0939\u093e\u0928\u093f:<\/b>\n<p>\u0936\u0941\u0930\u0941\u0906\u0924 \u0938\u0947 \u0939\u0940 \u0928\u0941\u0915\u0938\u093e\u0928 \u092e\u0947\u0902 \u091a\u0932 \u0930\u0939\u0940 \u092f\u0939 \u0930\u0923\u0928\u0940\u0924\u093f \u092a\u0942\u0930\u094d\u0923 \u0939\u093e\u0928\u093f \u0915\u0947 \u0938\u093e\u0925 \u0938\u092e\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948, \u091c\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\text{\u0905\u0902\u0924\u093f\u092e \u0939\u093e\u0928\u093f} = S(1) - A(0)(1 + r - r_s) <\/span>\n<p>\u092f\u0926\u093f <strong>\u0905\u0902\u0924\u093f\u092e \u0939\u093e\u0928\u093f<\/strong> \u0928\u093f\u0935\u0947\u0936\u0915 \u0915\u0947 \u0916\u093e\u0924\u0947 \u092e\u0947\u0902 \u0909\u092a\u0932\u092c\u094d\u0927 \u0928\u0915\u0926\u0940 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948, \u0924\u094b \u0935\u0939 \u0905\u092a\u0928\u0940 \u092a\u0942\u0930\u0940 \u092a\u0942\u0902\u091c\u0940 \u0916\u094b \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u092c\u094d\u0930\u094b\u0915\u0930 \u0915\u0947 \u092a\u094d\u0930\u0924\u093f \u090b\u0923\u0940 \u092d\u0940 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ol>\n<h3>\ud83d\udccc \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0948\u0938\u0947 \u092a\u0941\u0928\u0930\u094d\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948?<\/h3>\n<p>\u091c\u092c \u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0930\u0942\u092a \u0938\u0947 \u0915\u092e \u0939\u094b\u0924\u0940 \u0939\u0948, \u0924\u094b \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0905\u0935\u0938\u0930 \u092c\u0928\u093e \u0930\u0939\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0928\u093f\u0935\u0947\u0936\u0915\u094b\u0902 \u0915\u094b \u0938\u0941\u0930\u0915\u094d\u0937\u093f\u0924 \u0932\u093e\u092d \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0921\u093c\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u092a\u0930 \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0915\u0930\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><b>\u0907\u0938 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s = 0.015<\/span> \u0939\u0948\u0964<\/b><\/p>\n<p>\u0907\u0938 \u0915\u092e \u092c\u094d\u092f\u093e\u091c \u0926\u0930 \u0915\u0947 \u0915\u093e\u0930\u0923 \u092c\u0922\u093c\u0940 \u0939\u0941\u0908 \u092c\u093e\u091c\u093e\u0930 \u0917\u0924\u093f\u0935\u093f\u0927\u093f \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0915\u093e \u0915\u093e\u0930\u0923 \u092c\u0928\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0905\u0902\u0924\u0924\u0903 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u092a\u0941\u0928\u0930\u094d\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u092d\u093e\u0935 \u0926\u0947\u0916\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul>\n<li><b>\u0936\u0947\u092f\u0930 \u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0915\u0940\u092e\u0924 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u092e\u0947\u0902 \u0917\u093f\u0930\u093e\u0935\u091f:<\/b> \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0915\u0940 \u0909\u091a\u094d\u091a \u092e\u093e\u0902\u0917 \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u0909\u092a\u0932\u092c\u094d\u0927 \u0936\u0947\u092f\u0930\u094b\u0902 \u0915\u0940 \u0906\u092a\u0942\u0930\u094d\u0924\u093f \u0915\u094b \u092c\u0922\u093c\u093e \u0926\u0947\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0907\u0938\u0915\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092e\u0942\u0932\u094d\u092f \u092a\u0930 <strong>\u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0926\u092c\u093e\u0935<\/strong> \u092a\u0921\u093c\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u0917\u093f\u0930\u0924\u093e \u0939\u0948, \u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u0947 \u0917\u0941\u0923\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0906\u0928\u0941\u092a\u093e\u0924\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u092d\u0935\u093f\u0937\u094d\u092f \u0915\u0940 \u0915\u0940\u092e\u0924\u0947\u0902 \u0914\u0930 \u0907\u0938\u0915\u0940 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 \u0915\u0947 \u0938\u093e\u0925 \u0938\u0902\u092c\u0902\u0927 \u092c\u0926\u0932 \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><b>\u092c\u0949\u0928\u094d\u0921 \u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u092e\u0947\u0902 \u0935\u0943\u0926\u094d\u0927\u093f:<\/b> \u0928\u093f\u0935\u0947\u0936\u0915 \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0927\u0928\u0930\u093e\u0936\u093f \u0915\u094b \u092c\u0949\u0928\u094d\u0921 \u0916\u0930\u0940\u0926\u0928\u0947 \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u0907\u0928\u0915\u0940 <strong>\u092e\u093e\u0902\u0917<\/strong> \u092c\u0922\u093c \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 \u0907\u0938\u0915\u093e \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u092c\u0922\u093c \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u092c\u0949\u0928\u094d\u0921 \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936 \u0915\u0940 \u092a\u094d\u0930\u092d\u093e\u0935\u0940 \u0932\u093e\u092d\u092a\u094d\u0930\u0926\u0924\u093e \u0915\u092e \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948 \u0914\u0930 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 \u0915\u0940 \u0927\u093e\u0930\u0923\u093e \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/li>\n<\/ul>\n<p>\u092f\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u0938\u0902\u092f\u0941\u0915\u094d\u0924 \u0930\u0942\u092a \u0938\u0947 \u092c\u093e\u091c\u093e\u0930 \u0915\u0947 \u092e\u093e\u092a\u0926\u0902\u0921\u094b\u0902 \u0915\u0947 \u0915\u094d\u0930\u092e\u093f\u0915 \u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u092e\u0947\u0902 \u0917\u093f\u0930\u093e\u0935\u091f \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u092e\u0947\u0902 \u0935\u0943\u0926\u094d\u0927\u093f, \u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u0947 \u0917\u0941\u0923\u093e\u0902\u0915\u094b\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0915\u0940 \u0938\u0902\u0930\u091a\u0928\u093e \u0915\u094b \u0938\u0902\u0936\u094b\u0927\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0938\u093e\u0925 \u0939\u0940 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u0914\u0930 \u0936\u0947\u092f\u0930 \u090b\u0923 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u0915\u094b \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u092c \u0924\u0915 \u0915\u093f \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u092c\u0939\u093e\u0932 \u0928\u0939\u0940\u0902 \u0939\u094b \u091c\u093e\u0924\u0940:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d \\lt 1 + r - r_s \\lt u<\/span>\n<h4>\ud83d\udd39 \u092e\u0942\u0932\u094d\u092f \u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0915\u093e \u092e\u0949\u0921\u0932\u093f\u0902\u0917<\/h4>\n<p>\u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u094b \u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0917\u0941\u0923\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span> \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092e\u0949\u0921\u0932 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u094b \u092c\u0949\u0928\u094d\u0921 \u0914\u0930 \u0936\u0947\u092f\u0930\u094b\u0902 \u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u092a\u0930 \u0932\u093e\u0917\u0942 \u0938\u0941\u0927\u093e\u0930 \u0915\u093e\u0930\u0915\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p>\u092f\u0947 \u0917\u0941\u0923\u093e\u0902\u0915 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u094b \u0938\u0902\u0936\u094b\u0927\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u0915\u0947 \u0915\u093e\u0930\u0915 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u092a\u0941\u0928\u0930\u094d\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u092f\u093e\u0928\u0940, \u0936\u0947\u092f\u0930 \u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0915\u0940\u092e\u0924 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u0938\u0947 \u092c\u0926\u0932\u0915\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta S(0)<\/span> \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948, \u091c\u092c\u0915\u093f \u092c\u0949\u0928\u094d\u0921 \u0915\u093e \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u0938\u0947 \u092c\u0926\u0932\u0915\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha A(0)<\/span> \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a, <span class=\"katex-eq\" data-katex-display=\"false\">u<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0915\u0947 \u0928\u090f \u092e\u0942\u0932\u094d\u092f \u0907\u0928 \u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0917\u0941\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nu&#039; = \\dfrac{S(1,\\text{sube})}{\\beta S(0)}, \\quad d&#039; = \\dfrac{S(1,\\text{baja})}{\\beta S(0)}\n\n<\/span>\n<p>\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u0928\u0908 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r&#039;<\/span> \u0915\u094b \u092c\u0949\u0928\u094d\u0921 \u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f \u0915\u0947 \u0928\u090f \u0938\u094d\u0924\u0930 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nr&#039; + 1 = \\dfrac{A(1)}{\\alpha A(0)}\n\n<\/span>\n<p>\u092f\u0939 \u090f\u0915 \u092a\u0941\u0928:\u0938\u0902\u0930\u091a\u093f\u0924 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0940 \u0936\u0930\u094d\u0924 \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt \\dfrac{S(1,\\text{baja})}{\\beta S(0)} \\lt \\dfrac{A(1)}{\\alpha A(0)} - r_s \\lt \\dfrac{S(1,\\text{sube})}{\\beta S(0)} <\/span>\n<p>\u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0917\u0941\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u094b \u0905\u0932\u0917 \u0915\u0930\u0928\u0947 \u092a\u0930, \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\beta \\gt \\dfrac{A(0)S(1,\\text{baja})\\alpha}{S(0)(A(1) - r_s A(0)\\alpha)}\n\n<\/span>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\beta \\lt \\dfrac{A(0)S(1,\\text{sube})\\alpha}{S(0)(A(1) - r_s A(0)\\alpha)}\n\n<\/span>\n<p>\u092f\u0926\u093f \u0939\u092e \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u0947 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902 \u0914\u0930 \u092f\u0939 \u092e\u093e\u0928\u0947\u0902 \u0915\u093f \u0936\u0947\u092f\u0930 \u0915\u0940 \u0915\u0940\u092e\u0924 \u0918\u091f \u0930\u0939\u0940 \u0939\u0948 \u091c\u092c\u0915\u093f \u092c\u0949\u0928\u094d\u0921 \u0915\u093e \u092e\u0942\u0932\u094d\u092f \u092c\u0922\u093c \u0930\u0939\u093e \u0939\u0948, \u0924\u094b \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\beta &amp;\\gt \\dfrac{ 82 \\alpha}{107 - 1.5\\alpha} \\\\ \\\\\n\n\\beta &amp;\\lt \\dfrac{105.2 \\alpha}{107 - 1.5\\alpha } \\\\ \\\\\n\n\\beta &amp;\\lt 1 \\\\ \\\\\n\n\\alpha &amp;\\gt 1\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938 \u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u093e \u0938\u092e\u093e\u0927\u093e\u0928 \u0928\u093f\u092e\u094d\u0928 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u0940 \u0938\u092c\u0938\u0947 \u0917\u0939\u0930\u0947 \u0930\u0902\u0917 \u0915\u0940 \u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092e\u0947\u0902 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p><center><br \/>\n<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion.jpg\" alt=\"\" width=\"892\" height=\"677\" class=\"aligncenter size-full wp-image-32197 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion.jpg\" alt=\"\" width=\"892\" height=\"677\" class=\"aligncenter size-full wp-image-32197 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion.jpg 892w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion-300x228.jpg 300w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/02\/coef-correccion-768x583.jpg 768w\" sizes=\"(max-width: 892px) 100vw, 892px\" \/><\/noscript><br \/>\n<\/center><\/p>\n<p>\u0907\u0938\u0932\u093f\u090f, \u092c\u093e\u091c\u093e\u0930 \u0909\u0938 \u092e\u0942\u0932\u094d\u092f \u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0940 \u0913\u0930 \u092c\u0922\u093c \u0938\u0915\u0924\u093e \u0939\u0948 \u091c\u094b \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0935\u0938\u0930 \u0915\u094b \u0938\u092e\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u0948\u0938\u0947 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha=1.05<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta=0.95<\/span>\u0964<\/p>\n<p>\u0907\u0938 \u0938\u0902\u0936\u094b\u0927\u0928 \u0915\u0947 \u0938\u093e\u0925, \u0938\u0941\u0927\u093e\u0930 \u0915\u093f\u090f \u0917\u090f \u0917\u0941\u0923\u093e\u0902\u0915 \u0928\u093f\u092e\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930 \u0939\u094b\u0902\u0917\u0947:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nu^\\prime &amp;= \\dfrac{S(1,\\text{sube})}{\\beta S(0)}  = \\dfrac{105.2}{0.95\\cdot 100} \\approx 1.107 \\\\ \\\\\n\nd^\\prime &amp;= \\dfrac{S(1,\\text{baja})}{\\beta S(0)}  = \\dfrac{82}{0.95\\cdot 100} \\approx 0.863 \\\\ \\\\\n\nr^\\prime + 1 &amp;= \\dfrac{A(1)}{\\alpha A(0)} = \\dfrac{107}{1.05 \\cdot 100} \\approx 1.019\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt d^\\prime \\lt 1+r^\\prime - r_s \\lt u^\\prime<\/span>\n<p>\u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0 \\lt 0.863 \\lt 1.019 - 0.015 = 1.004 \\lt 1.107<\/span>\n<p>\u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0935\u0938\u0930 \u0915\u093e \u0932\u093e\u092d \u0909\u0920\u093e\u0928\u0947 \u0915\u0947 \u0907\u091a\u094d\u091b\u0941\u0915 \u0928\u093f\u0935\u0947\u0936\u0915\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0926\u092c\u093e\u0935 \u0915\u0947 \u0915\u093e\u0930\u0923 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0938\u092e\u092f \u092e\u0947\u0902 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u092e\u093e\u0928\u094b\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nA^\\prime(0) &amp;= \\alpha A(0) = 1.05\\cdot 100 = 105 \\\\ \\\\\n\nS^\\prime(0) &amp;= \\beta S(0) = 0.95\\cdot 100 = 95\n\n\\end{array}\n\n<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/iBmmjdFzVDI?si=BETKzTcGMB4yiZ8R\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"3\"><\/a><\/p>\n<h2>\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923<\/h2>\n<p>\u0905\u092c \u0924\u0915, \u0939\u092e\u0928\u0947 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0947 \u0915\u093e\u0930\u094d\u092f\u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u0940 \u092a\u0921\u093c\u0924\u093e\u0932 \u0915\u0940 \u0939\u0948\u0964 \u0905\u092c, \u0939\u092e \u0907\u0938\u0947 \u091a\u0930\u0923-\u0926\u0930-\u091a\u0930\u0923 \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0939 \u092a\u0939\u091a\u093e\u0928\u0928\u093e \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948 \u0915\u093f \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0935\u0938\u0930 \u0915\u0947 \u0938\u0902\u0915\u0947\u0924 \u0915\u094d\u092f\u093e \u0939\u0948\u0902:<\/p>\n<ul>\n<li>\n<p><b>\u091c\u094b\u0916\u093f\u092e\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f\u092f\u094b\u0902 \u0914\u0930 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u092c\u0949\u0928\u094d\u0921 \u0915\u0947 \u092a\u094d\u0930\u0924\u093f\u092b\u0932 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927:<\/b><\/p>\n<p>\u092f\u0926\u093f \u091c\u094b\u0916\u093f\u092e\u092a\u0942\u0930\u094d\u0923 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092a\u094d\u0930\u0924\u093f\u092b\u0932 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0924\u094b \u0907\u0938 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u094b \u0916\u0930\u0940\u0926\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0907\u0938 \u0926\u0930 \u092a\u0930 \u090b\u0923 \u0932\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u092a\u0930\u093f\u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u092c\u093f\u0928\u093e \u091c\u094b\u0916\u093f\u092e \u0915\u0947 \u0932\u093e\u092d \u0915\u0940 \u0917\u093e\u0930\u0902\u091f\u0940 \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p>\u0907\u0938\u0940 \u0924\u0930\u0939, \u092f\u0926\u093f \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930, \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u092a\u094d\u0930\u0924\u093f\u092b\u0932 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0924\u094b \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u094b \u0905\u0902\u091c\u093e\u092e \u0926\u0947\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948\u0964 \u092f\u0939 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u094b \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932 \u0915\u0930\u0915\u0947 \u0914\u0930 \u092c\u0949\u0928\u094d\u0921 \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936 \u0915\u0930\u0915\u0947 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u092c\u093f\u0928\u093e \u091c\u094b\u0916\u093f\u092e \u0915\u0947 \u0932\u093e\u092d \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><b>\u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 \u0914\u0930 \u090b\u0923 \u0926\u0930 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927:<\/b><\/p>\n<p>\u092a\u093f\u091b\u0932\u0947 \u092c\u093f\u0902\u0926\u0941 \u0915\u094b \u092a\u0942\u0930\u0915 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u090b\u0923 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u0914\u0930 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0924\u0930 \u0915\u0930\u0928\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948, \u0916\u093e\u0938\u0915\u0930 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0930\u0923\u0928\u0940\u0924\u093f\u092f\u094b\u0902 \u092f\u093e \u0936\u0949\u0930\u094d\u091f \u0938\u0947\u0932\u093f\u0902\u0917 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f\u0964 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092c\u0902\u0927 \u0938\u0902\u0924\u094b\u0937\u091c\u0928\u0915 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-1\\leq r \\leq r_s<\/span>\n<p>\u092f\u0926\u093f \u092f\u0939 \u0938\u0902\u092c\u0902\u0927 \u0938\u0902\u0924\u094b\u0937\u091c\u0928\u0915 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e, \u0924\u094b \u0915\u092e \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r_s<\/span> \u092a\u0930 \u0909\u0927\u093e\u0930 \u0932\u0947\u0915\u0930 \u0914\u0930 \u0909\u091a\u094d\u091a \u0926\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u092a\u0930 \u092c\u0949\u0928\u094d\u0921 \u092e\u0947\u0902 \u0928\u093f\u0935\u0947\u0936 \u0915\u0930\u0915\u0947 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u092c\u093f\u0928\u093e \u091c\u094b\u0916\u093f\u092e \u0915\u0947 \u0932\u093e\u092d \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0926\u093f \u0910\u0938\u093e \u0905\u0935\u0938\u0930 \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0924\u093e, \u0924\u094b \u0928\u093f\u0935\u0947\u0936\u0915 \u0907\u0938\u0947 \u0924\u092c \u0924\u0915 \u0909\u092a\u092f\u094b\u0917 \u092e\u0947\u0902 \u0932\u093e\u0924\u0947 \u091c\u092c \u0924\u0915 \u0915\u093f \u092c\u093e\u091c\u093e\u0930 \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0928\u0939\u0940\u0902 \u0939\u094b \u091c\u093e\u0924\u093e \u0914\u0930 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0938\u092e\u093e\u092a\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u094b \u091c\u093e\u0924\u093e\u0964 \u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, \u090b\u0923\u0926\u093e\u0924\u093e \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u091a\u0942\u0915 (\u0921\u093f\u092b\u0949\u0932\u094d\u091f) \u091c\u094b\u0916\u093f\u092e \u0915\u0940 \u092d\u0930\u092a\u093e\u0908 \u0915\u0947 \u0932\u093f\u090f \u0909\u091a\u094d\u091a \u0926\u0930 \u0915\u0940 \u092e\u093e\u0901\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p>\u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u092e\u0949\u0921\u0932\u094b\u0902 \u092e\u0947\u0902, \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903 <span class=\"katex-eq\" data-katex-display=\"false\">r_s = r<\/span> \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u092e\u093e\u092e\u0932\u094b\u0902 \u092e\u0947\u0902, <span class=\"katex-eq\" data-katex-display=\"false\">r \\geq 0<\/span> \u0915\u0940 \u0936\u0930\u094d\u0924 \u0932\u0917\u093e\u0908 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0924\u093e\u0915\u093f \u090b\u0923 \u0926\u0930\u0947\u0902 \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0928 \u0939\u094b\u0902, \u092f\u0926\u094d\u092f\u092a\u093f \u092f\u0939 \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n<p><b>\u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0940 \u0936\u0930\u094d\u0924\u0947\u0902 \u0915\u093f\u0938\u0940 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u092e\u0947\u0902:<\/b><\/p>\n<p>\u0915\u093f\u0938\u0940 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u093e \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f, \u0938\u092e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">t=0<\/span> \u092a\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">V(0) = xS(0) + y A(0)<\/span>\n<p>\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">S(0)<\/span> \u0936\u0947\u092f\u0930\u094b\u0902 \u0915\u093e \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f \u0939\u0948 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">A(0)<\/span> \u092c\u0949\u0928\u094d\u0921 \u0915\u093e \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u092e\u0942\u0932\u094d\u092f \u0939\u0948\u0964 \u092d\u0935\u093f\u0937\u094d\u092f \u092e\u0947\u0902, <span class=\"katex-eq\" data-katex-display=\"false\">t=1<\/span> \u092a\u0930, \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u093e \u092e\u0942\u0932\u094d\u092f \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0940 \u0917\u0924\u093f \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">V(1) =\n\n\\begin{cases}\n\nx S(0) u + y A(0) (1 + r), &amp;\\text{\u092f\u0926\u093f \u0915\u0940\u092e\u0924 \u092c\u0922\u093c\u0924\u0940 \u0939\u0948},\\\\\n\nx S(0) d + y A(0) (1 + r), &amp;\\text{\u092f\u0926\u093f \u0915\u0940\u092e\u0924 \u0918\u091f\u0924\u0940 \u0939\u0948}\u0964\n\n\\end{cases}<\/span>\n<p>\u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u093e \u0905\u0935\u0938\u0930 \u0915\u0947\u0935\u0932 \u0924\u092d\u0940 \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u0915\u094b\u0908 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0940\u0928 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u094b \u0938\u0902\u0924\u094b\u0937\u091c\u0928\u0915 \u0915\u0930\u0924\u093e \u0939\u094b:<\/p>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(0)=0<\/span>, \u0905\u0930\u094d\u0925\u093e\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0906\u0924\u094d\u092e-\u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0928\u093f\u0935\u0947\u0936 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940\u0964<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1)\\geq 0 <\/span> \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u092c\u093e\u091c\u093e\u0930 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902, \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0915\u094b\u0908 \u0939\u093e\u0928\u093f \u0928 \u0939\u094b\u0964<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">V(1) \\gt 0<\/span> \u0915\u092e \u0938\u0947 \u0915\u092e \u090f\u0915 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902, \u091c\u093f\u0938\u0938\u0947 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0939\u094b \u0915\u093f \u0932\u093e\u092d \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948\u0964<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>\u0907\u0938 \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u094b \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0915\u0947\u0924 \u0938\u0902\u0915\u0947\u0924\u0928 (\u0928\u094b\u091f\u0947\u0936\u0928) \u0938\u092e\u094d\u092e\u0947\u0932\u0928\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0947\u0902\u0917\u0947:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\nV(1,\\omega) &amp;=&amp; xS(1,\\omega) + yA(1).\n\n\\end{array}\n\n<\/span>\n<p>\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">\\omega<\/span> \u0915\u093e \u092e\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">\\text{sube}<\/span> \u092f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\text{baja}<\/span> \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0939\u092e\u0947\u0902 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0909\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u094b \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948 \u091c\u092c \u0915\u094b\u0908 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0935\u0938\u0930 \u0915\u093e \u0932\u093e\u092d \u0909\u0920\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{l}\n\nV(0) = 0, \\\\\n\n\\forall \\omega \\quad V(1,\\omega) \\geq 0, \\\\\n\n\\exists \\omega \\quad V(1,\\omega) &gt; 0.\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0928 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0938\u094d\u092a\u0937\u094d\u091f \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926, \u0905\u092c \u0939\u092e \u0917\u0923\u093f\u0924\u0940\u092f \u0914\u0930 \u0915\u0920\u094b\u0930 \u0930\u0942\u092a \u0938\u0947 \u090f\u0915 \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0905\u0935\u0938\u0930 \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0940 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u094b \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\text{\u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c}:= &amp; V(0) = 0 \\wedge  (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega \\quad V(1,\\omega) \\geq 0) \\wedge \\cdots \\\\\n\n&amp; \\cdots \\wedge  (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega \\quad V(1,\\omega) \\gt 0) \\\\ \\\\\n\n\\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f}:= &amp; \\neg \\text{\u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c} \\\\\n\n= &amp; V(0) \\neq 0 \\vee  \\neg(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega \\quad V(1,\\omega) \\geq 0) \\vee \\cdots \\\\\n\n&amp; \\cdots \\vee  \\neg(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega \\quad V(1,\\omega) \\gt 0)\n\n\\end{array}<\/span>\n<p>\u0905\u0902\u0924\u0924\u0903, \u092a\u094d\u0930\u092e\u0947\u092f <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{H}<\/span> \u0915\u0947 \u0932\u093f\u090f \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u093e \u0938\u092e\u0942\u0939 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\mathcal{H} &amp;=&amp; \\left\\{  \\right. V(0)=xS(0) + yA(0) = 0, \\\\ \\\\\n\n&amp; &amp;V(t,\\omega) = xS(t,\\omega) + yA(t), A(0), S(0) \\gt 0, \\\\ \\\\\n\n&amp; &amp;  S(1) = \\begin{cases} S(1, \\text{sube})  = S(0)u &amp; \\text{\u0938\u0902\u092d\u093e\u0935\u0928\u093e } p \\text{ \u0915\u0947 \u0938\u093e\u0925} \\\\ S(1,\\text{baja})  = S(0)d &amp; \\text{\u0938\u0902\u092d\u093e\u0935\u0928\u093e } 1-p \\text{ \u0915\u0947 \u0938\u093e\u0925} \\end{cases},  \\\\ \\\\\n\n&amp; &amp;  0 \\lt d \\lt u , \\left.  A(1) = A(0)(1+r), r\\geq -1 \\right\\}\n\n\\end{array}<\/span>\n<p>\u092f\u0939 \u0938\u092e\u0942\u0939 \u0928 \u0915\u0947\u0935\u0932 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0940 \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0924\u093e \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u090f\u0915-\u0905\u0935\u0927\u093f \u0935\u093e\u0932\u0947 \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0915\u0940 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u094b \u092d\u0940 \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u0907\u0928 \u092e\u094c\u0932\u093f\u0915 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u094b\u0902 \u0915\u094b \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926, \u0905\u092c \u0939\u092e \u092f\u0939 \u092a\u094d\u0930\u092e\u093e\u0923\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0917\u0947 \u092c\u0922\u093c\u0947\u0902\u0917\u0947 \u0915\u093f \u090f\u0915 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u092c\u093e\u091c\u093e\u0930 \u092e\u0947\u0902 \u0915\u094c\u0928-\u0938\u0947 \u0938\u0902\u092c\u0902\u0927 \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0939\u094b\u0928\u0947 \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<h3>\u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u094d\u0930\u092e\u093e\u0923:<\/h3>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; \\mathcal{H} \\models V(0) =xS(0) + yA(0) = 0 &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\\n\n(2) &amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) + yA(1) &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\\n\n(3) &amp; \\mathcal{H} \\models A(0) \\gt  0 &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\\n\n(4) &amp; \\mathcal{H} \\models S(0) \\gt  0 &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\\n\n(5) &amp; \\mathcal{H} \\models r \\gt  -1 &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\\n\n(6) &amp; \\mathcal{H} \\models A(1) = (1+r) A(0) &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\\n\n(7) &amp;\\color{red}\\mathcal{H} \\models 0 \\lt d \\lt u \\color{black}&amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\ \\\\\n\n(8) &amp; \\mathcal{H} \\models S(1) = \\begin{cases}S(1,\\text{sube})=S(0)u &amp; \\text{\u0938\u0902\u092d\u093e\u0935\u0928\u093e } p \\text{ \u0915\u0947 \u0938\u093e\u0925} \\\\ S(1,\\text{baja}) = S(0)d &amp; \\text{\u0938\u0902\u092d\u093e\u0935\u0928\u093e } 1-p \\text{ \u0915\u0947 \u0938\u093e\u0925}\\end{cases} &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e} \\\\ \\\\\n\n(9) &amp; \\mathcal{H} \\models y = \\dfrac{-xS(0)}{A(0)} \\wedge x\\in\\mathbb{R} &amp; \\text{; (1) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n(10)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - \\dfrac{xS(0)}{A(0)} A(1) &amp; \\text{; (2,9) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n(11)&amp; \\mathcal{H} \\models V(1,\\omega) =xS(1,\\omega) - x(1+r)S(0) &amp; \\text{; (6,10) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n &amp;\\text{\u092f\u0939 \u090f\u0915 \u090b\u0923-\u0906\u0927\u093e\u0930\u093f\u0924 \u0935\u093f\u0924\u094d\u0924 \u092a\u094b\u0937\u093f\u0924 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u093e \u092d\u0935\u093f\u0937\u094d\u092f \u092e\u0942\u0932\u094d\u092f \u0939\u0948,} &amp;\\\\\n\n &amp;\\text{\u091c\u094b \u090f\u0915 \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 $r$ \u092a\u0930 \u0909\u0927\u093e\u0930 \u0932\u0947\u0915\u0930 \u090f\u0915 \u0936\u0947\u092f\u0930 \u0916\u0930\u0940\u0926\u0924\u093e \u0939\u0948\u0964} &amp;\\\\\n\n(12)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models 0 \\leq (1+r)S(0) \\leq \\underbrace{S(0) d}_{S(1,\\text{baja})} \\lt \\underbrace{S(0) u}_{S(1,\\text{sube})} &amp; \\text{; (4,5,7,8) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(13)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models x(1+r)S(0) \\leq xS(1,\\omega) \\leftrightarrow x\\gt 0 &amp; \\text{; (12) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(14)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega\\quad V(1,\\omega) \\geq 0) &amp;\\text{; (2,9,13) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(15)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models V(1,\\omega) \\gt 0 \\leftrightarrow y \\gt \\dfrac{-xS(1,\\omega)}{A(1)} = \\dfrac{-xS(1,\\omega)}{(1+r)A(0)} &amp; \\text{; (2,3,6,7,8) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(16)&amp;\\mathcal{H}\\cup\\{1+r\\leq d\\} \\models (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega\\quad V(1,\\omega)\\gt 0) &amp;\\text{; (14,15) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(17)&amp; \\mathcal{H}\\cup\\{1+r\\leq d\\} \\models \\text{\u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c} &amp;\\text{; (1,14,16) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(18)&amp; \\color{red}\\mathcal{H}\\cup\\{\\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f}\\} \\models d \\lt 1+r\\color{black}&amp; \\text{; RTD, CPI, TD(17) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\ \\\\\n\n(19)&amp; \\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models 0 \\lt \\underbrace{S(0)d}_{S(1,\\text{baja})} \\lt \\underbrace{S(0)u}_{S(1,\\text{sube})} \\leq (1+r)S(0) &amp; \\text{; (4,5,7,8) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(20)&amp; \\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models xS(1,\\omega) \\leq x(1+r)S(0) \\leftrightarrow x\\gt 0  &amp;\\text{; (19) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n(21)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\tilde{V}(0) = - V(0) = 0 &amp; \\text{; (1) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(22)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models\\tilde{V}(1,\\omega)=-V(1,\\omega) &amp; \\\\\n\n &amp;\\phantom{\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models\\tilde{V}(1,\\omega)}=-xS(1,\\omega)+x(1+r)S(0) &amp; \\text{; (11) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n &amp;\\text{\u092f\u0939 \u090f\u0915 \u092a\u094b\u0930\u094d\u091f\u092b\u094b\u0932\u093f\u092f\u094b \u0915\u093e \u092d\u0935\u093f\u0937\u094d\u092f \u092e\u0942\u0932\u094d\u092f \u0939\u0948 \u091c\u094b \u090f\u0915 \u0936\u0947\u092f\u0930 \u0915\u094b \u0936\u0949\u0930\u094d\u091f} &amp;\\\\\n\n &amp;\\text{\u0938\u0947\u0932 \u0915\u0930 \u092c\u0949\u0928\u094d\u0921 \u0916\u0930\u0940\u0926\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0924\u094d\u0924\u092a\u094b\u0937\u0923 \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u094b } &amp;\\\\\n\n &amp;\\text{\u092c\u094d\u092f\u093e\u091c \u0926\u0930 $r$ \u0915\u0947 \u0938\u093e\u0925 \u092c\u0922\u093c\u0924\u093e \u0939\u0948\u0964} &amp; \\\\\n\n(23)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models (\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega\\quad \\tilde{V}(1,\\omega) \\geq 0) &amp; \\text{; (2,9,20,22) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(24)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\tilde{V}(1,\\omega)\\gt 0 \\leftrightarrow y \\lt \\dfrac{-xS(1,\\omega)}{A(1)} = \\dfrac{-xS(1,\\omega)}{(1+r)A(0)} &amp;\\text{; (2,3,4,6,22) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(25)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\exists \\omega\\quad \\tilde{V}(1,\\omega)\\gt 0) &amp;\\text{; (23,24) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(26)&amp;\\mathcal{H}\\cup\\{u \\leq 1+r\\} \\models \\text{\u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c} &amp;\\text{; (21,23,25) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(27)&amp;\\color{red}\\mathcal{H}\\cup\\{\\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f}\\} \\models 1+r \\lt u\\color{black}&amp; \\text{; RTD, CPI, TD(26) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(28) &amp;\\mathcal{H}\\cup\\{\\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f}\\} \\models 0\\lt d\\lt1+r\\lt u &amp;\\text{;\\color{red}$\\wedge$-Int(Mon(7),18,27)}\\color{black} \\\\\n\n(29)&amp; \\boxed{\\mathcal{H} \\models\\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f}\\rightarrow 0\\lt d\\lt1+r\\lt u}  &amp; \\text{; TD(28) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\ \\\\\n\n(30)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models 0\\lt d\\lt 1+r \\lt u &amp; \\text{; \u092a\u0942\u0930\u094d\u0935\u0927\u093e\u0930\u0923\u093e}\\\\\n\n(31)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models xS(0)d\\lt x(1+r)S(0) \\lt xS(0)u \\leftrightarrow x\\gt 0 &amp; \\text{; (4,30) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n&amp;\\phantom{\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\}} \\models xS(0)d\\lt x(1+r)S(0)\\dfrac{A(0)}{A(0)} \\lt xS(0)u \\leftrightarrow x\\gt 0 &amp; \\\\\n\n&amp;\\phantom{\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\}} \\models xS(0)d\\lt -y(1+r)A(0) \\lt xS(0)u \\leftrightarrow x\\gt 0 &amp; \\text{; (9) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n&amp;\\phantom{\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\}} \\models xS(1,\\text{baja})\\lt -yA(1) \\lt xS(1,\\text{sube}) \\leftrightarrow x\\gt 0 &amp; \\text{; (6,8) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n(32)&amp; \\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models V(1,\\text{baja})\\lt 0 \\lt V(1,\\text{sube}) \\leftrightarrow x\\gt 0 &amp; \\text{; (2,31) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n(33)&amp; \\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models V(1,\\text{baja})\\gt 0 \\gt V(1,\\text{sube}) \\leftrightarrow x\\lt 0 &amp; \\text{; (31,32) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n(34)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models \\neg(\\exists xy\\in\\mathbb{R}\\setminus\\{0\\})(\\forall \\omega\\quad V(1,\\omega)\\geq 0) &amp; \\text{; (32,33) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928} \\\\\n\n(35)&amp;\\mathcal{H}\\cup\\{0\\lt d\\lt 1+r \\lt u\\} \\models \\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f} &amp; \\text{; $\\vee$-int(34) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\\n\n(36)&amp;\\boxed{\\mathcal{H} \\models 0\\lt d\\lt 1+r \\lt u \\rightarrow \\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f}} &amp; \\text{; TD(35) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\\\\ \\\\\n\n(37)&amp; \\color{blue}\\mathcal{H} \\models 0\\lt d\\lt 1+r \\lt u \\leftrightarrow \\text{\u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f}\\color{black}\\quad\\blacksquare &amp; \\text{; (29,36) \u0938\u0947 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928}\n\n\\end{array}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n<p>\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0914\u0930 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092e\u0947\u0902 \u092e\u094c\u0932\u093f\u0915 \u0938\u094d\u0924\u0902\u092d \u0939\u0948\u0902, \u091c\u094b \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928 \u0914\u0930 \u092c\u093e\u091c\u093e\u0930 \u0915\u0940 \u0938\u094d\u0925\u093f\u0930\u0924\u093e \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u0902\u0930\u091a\u093f\u0924 \u0922\u093e\u0902\u091a\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938 \u0932\u0947\u0916 \u092e\u0947\u0902, \u0939\u092e\u0928\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u093f\u092f\u093e \u0915\u093f \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0935\u0938\u0930, \u091c\u094b \u0938\u0948\u0926\u094d\u0927\u093e\u0902\u0924\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0906\u0915\u0930\u094d\u0937\u0915 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u092c\u093e\u091c\u093e\u0930 \u0915\u0940 \u0936\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0926\u094d\u0935\u093e\u0930\u093e \u0924\u0947\u091c\u0940 \u0938\u0947 \u0938\u092e\u093e\u092a\u094d\u0924 \u0915\u0930 \u0926\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0940 \u0915\u0940\u092e\u0924\u094b\u0902 \u0914\u0930 \u092c\u094d\u092f\u093e\u091c \u0926\u0930\u094b\u0902 \u092e\u0947\u0902 \u0938\u092e\u093e\u092f\u094b\u091c\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0939\u092e\u0928\u0947 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u092f\u0939 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u0915\u093f \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0938\u0902\u092a\u0924\u094d\u0924\u093f \u0915\u0947 \u0935\u0943\u0926\u094d\u0927\u093f \u0914\u0930 \u0917\u093f\u0930\u093e\u0935\u091f \u0915\u093e\u0930\u0915\u094b\u0902 \u0924\u0925\u093e \u091c\u094b\u0916\u093f\u092e-\u092e\u0941\u0915\u094d\u0924 \u0926\u0930 \u0915\u0947 \u092c\u0940\u091a \u0938\u0902\u092c\u0902\u0927 \u090f\u0915 \u0915\u0941\u0936\u0932 \u0914\u0930 \u092c\u093f\u0928\u093e \u091c\u094b\u0916\u093f\u092e \u0935\u093e\u0932\u0947 \u0932\u093e\u092d \u0915\u0947 \u0905\u0935\u0938\u0930\u094b\u0902 \u0938\u0947 \u092e\u0941\u0915\u094d\u0924 \u092c\u093e\u091c\u093e\u0930 \u0915\u094b \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0964<\/p>\n<p>\u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u093e \u0915\u093f \u091c\u092c \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947 \u0905\u0935\u0938\u0930 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092e\u0942\u0932\u094d\u092f \u0926\u092c\u093e\u0935, \u090b\u0923 \u0932\u093e\u0917\u0924 \u0914\u0930 \u092c\u093e\u091c\u093e\u0930 \u092e\u093e\u092a\u0926\u0902\u0921\u094b\u0902 \u0915\u0947 \u092a\u0941\u0928:\u0938\u0902\u0930\u091a\u0928\u093e \u091c\u0948\u0938\u0947 \u0924\u0902\u0924\u094d\u0930 \u0905\u0902\u0924\u0924\u0903 \u0938\u0902\u0924\u0941\u0932\u0928 \u0915\u0940 \u092a\u0941\u0928\u0930\u094d\u0938\u094d\u0925\u093e\u092a\u0928\u093e \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938 \u0938\u092e\u091d \u0915\u0947 \u0938\u093e\u0925, \u092f\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c \u0915\u0947\u0935\u0932 \u090f\u0915 \u0915\u094d\u0937\u0923\u093f\u0915 \u0935\u093f\u0938\u0902\u0917\u0924\u093f \u0928\u0939\u0940\u0902 \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u092c\u093e\u091c\u093e\u0930\u094b\u0902 \u0915\u0940 \u0917\u0924\u093f\u0936\u0940\u0932\u0924\u093e \u092e\u0947\u0902 \u090f\u0915 \u092e\u094c\u0932\u093f\u0915 \u0924\u0924\u094d\u0935 \u0939\u0948, \u091c\u094b \u0909\u0928\u0915\u0940 \u0926\u0915\u094d\u0937\u0924\u093e \u0914\u0930 \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0941\u0938\u0902\u0917\u0924\u093f \u0915\u094b \u092c\u0922\u093c\u093e\u0935\u093e \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0914\u0930 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u093e\u0930\u093e\u0902\u0936: \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0947\u0902 \u0915\u093f \u090f\u0915 \u0915\u0948\u0938\u0940\u0928\u094b \u0939\u0948 \u091c\u0939\u093e\u0901 \u0906\u092a \u090f\u0915 \u0910\u0938\u0947 \u0916\u0947\u0932 \u092e\u0947\u0902 \u0926\u093e\u0902\u0935 \u0932\u0917\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0901, \u092a\u0930\u093f\u0923\u093e\u092e \u091a\u093e\u0939\u0947 \u091c\u094b \u092d\u0940 \u0939\u094b, \u0906\u092a \u0939\u092e\u0947\u0936\u093e \u092a\u0948\u0938\u093e \u0915\u092e\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0938\u0941\u0928\u0928\u0947 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0905\u091a\u094d\u091b\u093e \u0932\u0917\u0924\u093e \u0939\u0948, \u0939\u0948 \u0928\u093e? \u0935\u093f\u0924\u094d\u0924\u0940\u092f \u092c\u093e\u091c\u093e\u0930\u094b\u0902 \u092e\u0947\u0902, \u0907\u0938 \u0924\u0930\u0939 \u0915\u0947 \u0905\u0935\u0938\u0930 \u092e\u0927\u094d\u092f\u0938\u094d\u0925\u0924\u093e (\u0905\u0930\u094d\u092c\u093f\u091f\u094d\u0930\u093e\u091c) \u0915\u0940 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32196,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[757,911],"tags":[],"class_list":["post-32421","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-757","category-911"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u093e \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0914\u0930 \u0917\u0948\u0930-\u0938\u091f\u094d\u091f\u093e \u0938\u094d\u0925\u093f\u0924\u093f - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u090f\u0915 \u0905\u0935\u0927\u093f \u0915\u0947 \u092c\u093e\u0907\u0928\u094b\u092e\u093f\u092f\u0932 \u092e\u0949\u0921\u0932 \u0915\u094b 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