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1. . 162 22 2015 1937 . 8622/2 . : 1. 42 . 2 . . 4186/ 2013 ( 193) . 2. 2 . 3 . . . 3966/2011 ( 118) , , . 3. .. 89/2014 ( 134) , . 4. 90 .. 63/2005 ( 98). 5. . 3/14012015 .. . 6. , : : Digitally signed by THEODOROS MOUMOURIS Date: 2015.01.23 13:16:56 EET Reason: Signed PDF (embedded) Location: Athens, Ethniko Typografio Signature Not Verified 2. 1938 ( ) 3. ( ) 1939 1.2. 4. 1940 ( ) , ,,,, ,,. 5. ( ) 1941 6. 1942 ( ) 7. ( ) 1943 8. 1944 ( ) ()()... ,,1000 ,. 19 .,, ,... ,.,, .() ,,, ,... 0,70.1,7,6,(),2030. . 40%. . 6 . (.),(), . .... . 9. ( ) 1945 10. 1946 ( ) 11. ( ) 1947 . 12. 1948 ( ) 13. ( ) 1949 0A 14. 1950 ( ) 15. ( ) 1951 16. 1952 ( ) 1.1.1. . 1.1.2. 17. ( ) 1953 (,,Venn). 1.1.3. ( ). 2.1. (1) 2.1.1. (,,Q,R-Q). 2.1.2. . 2.2. (8) 2.2.1. . 2.2.2. 1 .1 . 2.2.3.( ,,) . 18. 1954 ( ) 2.3. (5) 2.3.1. . . + + = 64. 2000 ( ) =+ == =++ =+ +=+ +=+ 65. ( ) 2001 66. 2002 ( ) +++= += += 67. ( ) 2003 + () ()()() ====== ()()() === ()()+ 68. 2004 ( ) ==== == ==+ = =+ == = 69. ( ) 2005 = I LI LI=0I 12 10 0I 70. 2006 ( ) 71. ( ) 2007 72. 2008 ( ) 73. ( ) 2009 74. 2010 ( ) 75. ( ) 2011 76. 2012 ( ) 77. ( ) 2013 = 78. 2014 ( ) 79. ( ) 2015 80. 2016 ( ) 81. ( ) 2017 82. 2018 ( ) = 83. ( ) 2019 84. 2020 ( ) = 85. ( ) 2021 86. 2022 ( ) 87. ( ) 2023 88. 2024 ( ) 89. ( ) 2025 90. 2026 ( ) 22 91. ( ) 2027 92. 2028 ( ) 93. ( ) 2029 ()()11 22 //det,0,det,== xy xy ()11 ,xy()22 ,xy 94. 2030 ( ) 95. ( ) 2031 x'x ()000 Mx,y ()1//=, 0 MMM ()000 ,Mxyy'y ()01//=, 0 MMM 96. 2032 ( ) +=xy 00 ()000 Mx,y(),=n +=xy00 =+oo xy (),=n 97. ( ) 2033 +=xy00 +=xy 00 22 += += xy xy 000 0 (), (), 98. 2034 ( ) ()()222121 12... 6 ++ +++= ()111++> , () ()() ,f yf(x),x= 99. ( ) 2035 1 =, (1) 1 =+ l() l ==21=+ ()+ () 100. 2036 ( ) + 1 0k k limlim,k ++ ==+ 1=> , lim + 1> 011 lim,lim, ++ = 1< 101. ( ) 2037 30/=E ums 50/=H ums 102. 2038 ( ) ,,,,,,, =x=y 103. ( ) 2039 1 3 = ()()== 104. 2040 ( ) pF20N=30 // () 222 // ()()()22222 12121122 +++xxyyxyxy1122 x,y,x,y 11 22 0 xy xy = 30= 5hm= 105. ( ) 2041 W wx W//Ky WK x'xy'y x'x12 11 x,y22 x,y21 21 yyy xxx 12 = , 12 = y x 106. 2042 ( ) ()000 Mx,y()=, ()Mx,y00 =rOM=rOM0 MM 0 =+rrt,t 0 0 =+ =+ xxt ,t yyt 0 ()00 ==== yyxx, ()00 =yyxx 0 0 1=+ =+ xxt ,t yyt ()000 Mx,y()1=, 107. ( ) 2043 0=0 =xx 0 0 0 1 =+ =+ xxt ,t yyt ()000 Mx,y()01=, ()=n,()=, +=xynn n 108. 2044 ( ) ()22 :3= xy, 109. ( ) 2045 00= ==1 2 1 2 :37 :333 = = xy xy 1 2= =n n 1 2= = 1 2 110. 2046 ( ) 1 2 :613 :531 = += xy- xy 1 2= =n n 1 2= = 1 2 1 2 :8610 :435 += += xy- xy 1 2= =n n 1 2= = 1 2 = += ++= 111. ( ) 2047 112. 2048 ( ) 09999,... 123409099099909999====.,.,.,.,... 1 1 10 = 113. ( ) 2049 114. 2050 ( ) 115. ( ) 2051 (80) : - . ylnxylogx==. 1. yx=+ 2 yx= 3 yx= y x =yx= , . 2,3. 116. 2052 ( ) 4. ()(),yfxyfx== ()=yfx 0x 0x 0x 0 x + 117. ( ) 2053 (),fxcc=()fxx=()2 fxx=()fxx= yx=yx= =x yeylnx= 0 x 118. 2054 ( ) : =yx,=yx,,01 x y=f(x)g(x),()()fgx>. 3.2.3. , . .. Fermat . . 15. 16. / ,, (1 ), . . (4] 17. 1. (7) 4.1.1. . ,, : i) 172. 2108 ( ) ii){0 x,+ f,0 x g0 x+. iii){0 x,+ f,0 x g0 x. . .. 4.1.3. i)yx= : 0 lim1 x x x =, . ii)y= : 2 xx,x= . 18, : 1.. 2.f 0 x, 0 x, . 173. ( ) 2109 . 4.1.4., () yx=,yx=,yx=yx=. f(t)(t)=++ 4.1.5.: f(t)(t)=++ , f(t)t=. : 2f(t)t=,2 3 g(t)t= 32 6 h(t)t=+ . 19 2.(6) 01< + ()0,+ (= x ye). 4.2.1. . , , 1 x ex,x+ : 0 1 1 x x e lim x = . 4.2.2. . 174. 2110 ( )4.2.3.(& ). : x ye=f ff()01f= : k,: kx yce=,c, f: ()(),fxkfxx=. 20 ,01< 4.2.4. 01 x y,= )01