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ɬɚɬɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ ɢɷɥɟɤɬɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɷɪɨɡɢɨɧɧɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɠɢɞ
ɤɨɝɨɦɟɬɚɥɥɚɫɞɪɭɝɨɣɫɬɨɪɨɧɵɜɵɡɵɜɚɟɬɫɧɢɠɟɧɢɟɷɥɟɤɬɪɢɱɟɫɤɨɝɨɤɩɞɫɢɫ
ɬɟɦɵ©ɢɧɞɭɤɬɨɪ±ɦɟɬɚɥɥªɢɧɟɛɥɚɝɨɩɪɢɹɬɧɨɟɭɫɢɥɟɧɢɟɪɟɚɤɬɢɜɧɨɣɦɨɳɧɨɫɬɢɜ
ɡɚɡɨɪɟɦɟɠɞɭɦɟɬɚɥɥɨɦɢɢɧɞɭɤɬɨɪɨɦ
ȼɧɭɬɪɟɧɧɢɣɞɢɚɦɟɬɪɢɧɞɭɤɬɨɪɚɨɩɪɟɞɟɥɹɟɦɩɨɮɨɪɦɭɥɟ
'' Δ+=
ɦ=+⋅ =
ɮɦɜɬ
ɱɬɨɫɨɨɬɜɟɬɫɬɜɭɟɬɫɢɦɩɥɟɤɫɭN' 'ɜɬ'ɦ ɢɫɨɝɥɚɫɧɨ>ɪɢɫ
ɤɪɢɜɚɹ@N
§Ɋɚɡɧɨɫɬɶɧɟɩɪɟɜɵɲɚɟɬ
'
ɉɪɢɧɢɦɚɹɫɢɦɦɟɬɪɢɱɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟɢɧɞɭɤɬɨɪɚ ɢɦɟɬɚɥɥɚ ɨɩɪɟɞɟɥɹɟɦ
ɫɢɦɩɥɟɤɫ>ɪɢɫɤɪɢɜɚɹ@N
ȼɵɫɨɬɭɢɧɞɭɤɬɨɪɚɨɩɪɟɞɟɥɢɦɩɨɮɨɪɦɭɥɟ
KNK=⋅
ɂKɦ
§
K
ɦ=⋅=
ɉɪɢɧɢɦɚɟɦKɂ ɦ
Ⱦɥɹɩɨɥɭɱɟɧɢɹɜɨɡɦɨɠɧɨɜɵɫɨɤɨɝɨɡɧɚɱɟɧɢɹɷɥɟɤɬɪɢɱɟɫɤɨɝɨɤɩɞɫɢɫɬɟɦɵ
©ɢɧɞɭɤɬɨɪ±ɦɟɬɚɥɥªɰɟɥɟɫɨɨɛɪɚɡɧɨɢɦɟɬɶ
K' ≤
ɂɜɬ
ɱɬɨɜɞɚɧɧɨɦɪɚɫɱɟɬɟɜɵɩɨɥɧɹɟɬɫɹ
ɋɨɨɬɧɨɲɟɧɢɟ'ɜɬKɂɫɨɫɬɚɜɥɹɟɬɞɥɹ ɨɬɟɱɟɫɬɜɟɧɧɵɯɢɧɞɭɤɰɢɨɧɧɵɯ ɬɢɝɟɥɶ
ɧɵɯɩɟɱɟɣ
' K P≈⋅
ɜɬ
ɂ
ɉɨ>ɪɢɫɤɪɢɜɚɹ@'ɜɬKɂ§ɩɨɪɟɡɭɥɶɬɚɬɚɦɪɚɫɱɟɬɚ
'
Kɂ
ɜɬ
≈⋅=
ɉɪɢɷɬɨɦɜɵɩɨɥɧɹɟɬɫɹɭɫɥɨɜɢɟ'ɜɬKɂ
ɉɨɪɟɡɭɥɶɬɚɬɚɦɪɚɫɱɟɬɚɩɪɨɟɤɬɢɪɭɟɦɚɹɩɟɱɶɛɥɢɡɤɚɩɨɪɚɡɦɟɪɚɦɩɟɱɢɬɢɩɚ
ɂɋɌ>ɩɪɢɥ@
Ɍɟɩɥɨɜɨɣɪɚɫɱɟɬ
ɌɟɦɩɟɪɚɬɭɪɚɠɢɞɤɨɝɨɦɟɬɚɥɥɚɫɪɟɞɧɹɹɄ
Ɏɭɬɟɪɨɜɤɚɬɢɝɥɹ
ɫɬɟɧɚɧɚɛɢɜɧɚɹɦɚɫɫɚɉɉɆɦ
ɚɫɛɟɫɬɨɜɵɣɤɚɪɬɨɧɦ
ɡɚɳɢɬɧɚɹɨɛɦɚɡɤɚɢɧɞɭɤɬɨɪɚɦ
ɢɬɨɝɨǻ
ɦ
ɮ
ɩɨɞɢɧɚɧɚɛɢɜɧɚɹɦɚɫɫɚɉɉɆɦ
ɚɫɛɟɫɬɨɜɵɣɤɚɪɬɨɧɦ
ɠɚɪɨɫɬɨɣɤɢɣɛɟɬɨɧɦ
ɚɫɛɟɫɬɨɰɟɦɟɧɬɧɚɹɩɥɢɬɚɦ
ɢɬɨɝɨǻ
ɦ
Ɂɧɚɹ ɝɟɨɦɟɬɪɢɱɟɫɤɢɟ ɪɚɡɦɟɪɵ ɬɢɝɥɹ ɬɟɩɥɨɜɵɟ ɩɨɬɟɪɢɪɚɫɫɱɢɬɵɜɚɸɬɩɪɢ
ɭɫɥɨɜɢɢ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɬɟɩɥɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɮɭɬɟɪɨɜɤɢ ɱɬɨ ɯɚɪɚɤɬɟɪɧɨ ɞɥɹ
ɂɌɉɌɟɩɥɨɜɵɟɩɨɬɟɪɢɱɟɪɟɡɮɭɬɟɪɨɜɤɭɰɢɥɢɧɞɪɢɱɟɫɤɨɣɫɬɟɧɤɢɬɢɝɥɹɜɵɫɨɬɨɣ
ɪɚɜɧɨɣɜɵɫɨɬɟɦɟɬɚɥɥɚɜɵɱɢɫɥɹɸɬɩɨɮɨɪɦɭɥɟɤȼɬ
ɜɪɫɬ
1
°
[]
®
¦
°
=
¯
+
L
½
°
⋅α+⋅λ⋅π⋅−=
6K''QOɌɌɎ
¾
ɬɨ0LLL
°
¿
ɝɞɟɌɪ−ɬɟɦɩɟɪɚɬɭɪɚɜɧɭɬɪɟɧɧɟɣɩɨɜɟɪɯɧɨɫɬɢɮɭɬɟɪɨɜɤɢɬɢɝɥɹɪɚɜɧɚɹɬɟɦɩɟɪɚ
ɬɭɪɟɠɢɞɤɨɝɨɦɟɬɚɥɥɚɄ
−ɬɟɦɩɟɪɚɬɭɪɚɜɨɞɵɨɯɥɚɠɞɚɸɳɟɣɢɧɞɭɤɬɨɪɄ
Ɍ
ɜ
'
'
−ɫɪɟɞɧɢɣɜɧɭɬɪɟɧɧɢɣɞɢɚɦɟɬɪɬɢɝɥɹɪɚɜɧɵɣɪɚɫɱɟɬɧɨɦɭɞɢɚɦɟ
ɦɫɪ
ɬɪɭɦɟɬɚɥɥɚɦ
1±ɱɢɫɥɨɫɥɨɟɜɫɬɟɧɤɢɬɢɝɥɹɜɤɥɸɱɚɹɷɥɟɤɬɪɨɢɡɨɥɹɰɢɨɧɧɭɸɨɛɦɚɡɤɭɢɧɞɭ
ɤɬɨɪɚɢɪɚɛɨɱɭɸɫɬɟɧɤɭɬɪɭɛɤɢɢɧɞɭɤɬɨɪɚɨɦɵɜɚɟɦɭɸɨɯɥɚɠɞɚɸɳɟɣɜɨɞɨɣ
−ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶLɝɨɫɥɨɹȼɬɦ⋅Ʉ
Ȝ
L
Į− ɤɨɷɮɮɢɰɢɟɧɬɤɨɧɜɟɤɬɢɜɧɨɣ ɬɟɩɥɨɨɬɞɚɱɢɜ ɫɢɫɬɟɦɟɨɯɥɚɠɞɟɧɢɹ ɢɧɞɭɤ
ɬɨɪɚȼɬɦ
6
⋅Ʉ
−ɩɥɨɳɚɞɶɬɟɩɥɨɨɬɞɚɸɳɟɣɩɨɜɟɪɯɧɨɫɬɢɨɯɥɚɠɞɟɧɢɹɢɧɞɭɤɬɨɪɚɦ
ɬɨ
Ɍɟɩɥɨɜɵɟɩɨɬɟɪɢɱɟɪɟɡɫɬɟɧɭɬɢɝɥɹɨɩɪɟɞɟɥɹɟɦɩɨɮɨɪɦɭɥɟɩɪɟɧɟɛɪɟɝɚɹɬɟ
ɩɥɨɜɵɦɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦɢ ɦɟɞɧɨɣ ɫɬɟɧɤɢ ɢɧɞɭɤɬɨɪɚ ɫ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶɸ
ȼɬɦ⋅Ʉɢɤɨɧɜɟɤɬɢɜɧɨɣɬɟɩɥɨɨɬɞɚɱɢɜɫɢɫɬɟɦɟɨɯɥɚɠɞɟɧɢɹɢɧɞɭɤɬɨɪɚɩɪɢ
Į «ɤȼɬɦ
ɡɚɩɢɫɚɬɶ
⋅Ʉɋɭɱɟɬɨɦɩɨɪɹɞɤɚɜɟɥɢɱɢɧɜɯɨɞɹɳɢɯɜɜɵɪɚɠɟɧɢɟɦɨɠɧɨ
⋅−⋅λ⋅π=
ɜɪɦɮɫɬ
''OQɌɌKɎ
ɦɜɬ
ɋɭɱɟɬɨɦ > ɪɢɫ ɚ@ ɨɩɪɟɞɟɥɹɟɦɜɧɟɲɧɢɟ ɞɢɚɦɟɬɪɵ ɫɥɨɟɜɮɭɬɟɪɨɜɤɢ
ɫɬɟɧɵɬɢɝɥɹɩɨɮɨɪɦɭɥɟɦ
K'' +=
LLL
−
'
⋅ ' ⋅
⋅
'
ɁɚɞɚɟɦɪɚɫɩɪɟɞɟɥɟɧɢɟɬɟɦɩɟɪɚɬɭɪɩɨɝɪɚɧɢɰɚɦɫɥɨɟɜɄ
Ɍ Ɍ Ɍ
ɈɩɪɟɞɟɥɹɟɦɫɪɟɞɧɢɟɡɧɚɱɟɧɢɹɬɟɦɩɟɪɚɬɭɪɵɫɥɨɟɜɄ
Ɍ
Ɍ
ɫɪ
Ɍ
ɫɪ
ɫɪ
Ɉɰɟɧɢɜɚɟɦɩɨ>ɫɩɪɢɥ@ɫɪɟɞɧɢɟɡɧɚɱɟɧɢɹɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢɫɥɨɟɜ
ȼɬɦÂɄȜ
Ȝ Ȝ
ɉɨɫɤɨɥɶɤɭɫɨɨɬɧɨɲɟɧɢɟɜɧɟɲɧɢɯɢɜɧɭɬɪɟɧɧɢɯɞɢɚɦɟɬɪɨɜɰɢɥɢɧɞɪɢɱɟɫɤɢɯ
ɫɥɨɟɜɮɭɬɟɪɨɜɤɢɫɬɟɧɵɬɢɝɥɹɫɨɫɬɚɜɥɹɟɬ
''ɦ ''
'
'
ɬɨɬɟɩɥɨɜɨɟɫɨɩɪɨɬɢɜɥɟɧɢɟ5ɌLɄȼɬɤɚɠɞɨɝɨɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨɫɥɨɹɜɵɫɨɬɨɣ
ɦɨɩɪɟɞɟɥɹɟɦɫɭɱɟɬɨɦɫɪɟɞɧɟɣɪɚɫɱɟɬɧɨɣɩɥɨɳɚɞɢ
K K
ɦ
ɦ
''6
+π=
LLLS +
6
⋅ 6S ⋅
S
⋅
6
S
6K5
⋅λ=
SLLLL7
5
⋅ 57 ⋅
7
⋅
5
7
ɉɪɢɧɹɜɬɟɦɩɟɪɚɬɭɪɭɨɯɥɚɠɞɚɸɳɟɣɜɨɞɵɜɢɧɞɭɤɬɨɪɟɌɜ Ʉɨɩɪɟɞɟɥɢɦ
ɬɟɩɥɨɜɵɟɩɨɬɟɪɢɱɟɪɟɡɮɭɬɟɪɨɜɤɭɫɬɟɧɵɬɢɝɥɹɩɨɮɨɪɦɭɥɟ
Ɏ ɤȼɬ
==
ɫɬ
−⋅
++
−
ɉɪɢɧɹɬɵɟɡɧɚɱɟɧɢɹɬɟɦɩɟɪɚɬɭɪɵɌLɩɨɝɪɚɧɢɰɚɦɫɥɨɟɜɧɟɨɛɯɨɞɢɦɨɩɪɨɜɟ
ɪɢɬɶɚɧɚɥɢɬɢɱɟɫɤɢɩɨɬɟɩɥɨɜɨɦɭɩɨɬɨɤɭɎ
ɜɨɝɨɫɨɩɪɨɬɢɜɥɟɧɢɹ5
ɬL
ɫɭɱɟɬɨɦɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨɬɟɩɥɨ
ɫɬ
7 ±⋅ 7 ±⋅
±⋅
7
ɋ ɭɱɟɬɨɦ ɞɨɩɭɫɬɢɦɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɧɟ ɛɨɥɟɟ
Ʉɪɚɫɱɟɬɜɵɩɨɥɧɟɧɤɨɪɪɟɤɬɧɨ
Ɍɟɩɥɨɜɵɟɩɨɬɟɪɢɢɡɥɭɱɟɧɢɟɦɫɡɟɪɤɚɥɚɜɚɧɧɵɠɢɞɤɨɝɨɦɟɬɚɥɥɚɨɩɪɟɞɟɥɹɟɦ
ɩɨɡɚɤɨɧɭɋɬɟɮɚɧɚ−Ȼɨɥɶɰɦɚɧɚɚɧɚɥɨɝɢɱɧɨɮɨɪɦɭɥɟ
: İ
±ɜσ
ɝɞɟİ
−ɩɪɢɜɟɞɟɧɧɚɹɫɬɟɩɟɧɶɱɟɪɧɨɬɵɪɚɛɨɱɟɝɨɩɪɨɫɬɪɚɧɫɬɜɚȾɋɉɩɪɢɢɡɥɭɱɟ
±ɜ
ɧɢɢɜɨɤɪɭɠɚɸɳɭɸɫɪɟɞɭɫɬɟɦɩɟɪɚɬɭɪɨɣɌ
−ɩɥɨɳɚɞɶɩɪɨɟɦɚɨɬɤɪɵɬɨɝɨɨɤɧɚİ ɞɥɹɦɚɥɵɯɨɬɜɟɪɫɬɢɣɢɡɥɭɱɚɸɳɢɯ
6
Ɍ
±Ɍ
6IJ⋅±
ɜ
ɜ
ɤɚɤɚɛɫɨɥɸɬɧɨɱɟɪɧɨɟɬɟɥɨɢİ «ɞɥɹɤɪɭɩɧɵɯɨɬɜɟɪɫɬɢɣɪɚɡɦɟɪɵɤɨ
ɬɨɪɵɯɫɪɚɜɧɢɦɵɫɜɧɭɬɪɟɧɧɢɦɢɝɚɛɚɪɢɬɚɦɢɪɚɛɨɱɟɝɨɩɪɨɫɬɪɚɧɫɬɜɚ
ɉɪɢɜɟɞɟɧɧɭɸɫɬɟɩɟɧɶɱɟɪɧɨɬɵɨɩɪɟɞɟɥɹɟɦɫɭɱɟɬɨɦɫɬɟɩɟɧɢɱɟɪɧɨɬɵɠɢɞ
ɤɨɝɨɦɟɬɚɥɥɚİ >ɫɩɪɢɥ@ɢɤɨɷɮɮɢɰɢɟɧɬɚɞɢɚɮɪɚɝɦɢɪɨɜɚɧɢɹɡɚ
ɜɢɫɹɳɢɣ ɨɬɫɨɨɬɧɨɲɟɧɢɹ ɪɚɡɦɟɪɨɜ ɨɬɜɟɪɫɬɢɹ ȥ Ⱦɥɹ ɤɪɭɝɥɨɝɨ ɨɬɜɟɪɫɬɢɹ >
ɫɪɢɫ@
Ⱥȼ 'ɦK7−Kɦ ±
ɉɪɢɷɬɨɦİ ȥ ɢİ
Ɍɟɩɥɨɜɵɟɩɨɬɟɪɢɢɡɥɭɱɟɧɢɟɦɫɨɬɤɪɵɬɨɝɨɡɟɪɤɚɥɚɜɚɧɧɵɫɨɫɬɚɜɥɹɸɬ
Ɏ ɤȼɬ
=⋅⋅⋅ ⋅⋅=
±ɜ
−
⋅
Ɍɟɩɥɨɜɵɟɩɨɬɟɪɢɱɟɪɟɡɮɭɬɟɪɨɜɤɭɩɨɞɢɧɵɞɧɨɬɢɝɥɹɨɩɪɟɞɟɥɹɸɬɩɨɮɨɪ
ɦɭɥɟɩɪɢɝɪɚɧɢɱɧɵɯɭɫɥɨɜɢɹɯɩɟɪɜɨɝɨɪɨɞɚ
1
½
°°
−
Ɏ 7 7 î į Ȝ6 Į 6 ɤȼɬ
=− +
ɩɨɞ S S ɬɨ
ɜ
ªº
®¾
()
¦
«»
¬¼
°°
L
=
¯¿
()
L
−
ɝɞɟĮ±ɤɨɷɮɮɢɰɢɟɧɬɬɟɩɥɨɨɬɞɚɱɢɫɬɟɩɥɨɨɬɞɚɸɳɟɣɩɨɜɟɪɯɧɨɫɬɢɨɛɪɚɳɟɧɧɨɣ
ɜɧɢɡ
ɉɪɢɧɹɜɞɥɹɭɫɥɨɜɢɣɞɚɧɧɨɝɨɪɚɫɱɟɬɚɌ
ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ>ɫɩɪɢɥ@Į
ȼɬɦ⋅ɄɁɧɚɹɤɨɧɫɬɪɭɤɰɢɸɮɭɬɟɪɨɜɤɢɩɨɞɢɧɵɬɢɝɥɹɨɩɪɟɞɟɥɹɟɦɫɪɟɞ
Į
ȼɬɦ⋅ɄȾɥɹɪɚɫɱɟɬɚɩɪɢɧɢɦɚɟɦ
ɄɢɌɬɨ Ʉɧɚɯɨɞɢɦɫ
ɜ
ɧɢɟɪɚɫɱɟɬɧɵɟɩɥɨɳɚɞɢɤɚɠɞɨɝɨɫɥɨɹɫɭɱɟɬɨɦɭɜɟɥɢɱɟɧɢɹɬɟɩɥɨɨɬɞɚɸɳɢɯɩɨ
ɜɟɪɯɧɨɫɬɟɣɢɡɡɚɤɨɧɟɱɧɵɯɪɚɡɦɟɪɨɜɩɥɨɫɤɨɣɫɬɟɧɤɢȼɞɚɧɧɨɦɪɚɫɱɟɬɟɩɪɢɧɹɬɨ
ɦ
6S 6S 6S 6ɬɨ
6
S
ɁɚɞɚɟɦɪɚɫɩɪɟɞɟɥɟɧɢɟɬɟɦɩɟɪɚɬɭɪɩɨɝɪɚɧɢɰɚɦɫɥɨɟɜɄ
7 7 7 7 7ɬɨ
ɈɩɪɟɞɟɥɹɟɦɫɪɟɞɧɢɟɡɧɚɱɟɧɢɹɬɟɦɩɟɪɚɬɭɪɵɫɥɨɟɜɄ
Ɍ
Ɍ
ɫɪ
Ɍ
Ɍ
ɫɪ
ɫɪ
ɫɪ
Ɉɰɟɧɢɜɚɟɦ ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɫɥɨɟɜ ɮɭɬɟɪɨɜɤɢ
ȼɬɦ⋅Ʉ>ɩɪɢɥ@Ȝ
ɈɩɪɟɞɟɥɹɟɦɬɟɩɥɨɜɵɟɫɨɩɪɨɬɢɜɥɟɧɢɹɄȼɬ
Ȝ Ȝ Ȝ
57 ⋅ 57 ⋅
⋅ 57 ⋅
5
7
⋅
5
7
Ɍɟɩɥɨɜɵɟɩɨɬɟɪɢɱɟɪɟɡɮɭɬɟɪɨɜɤɭ ɩɨɞɢɧɵɬɢɝɥɹ ɨɩɪɟɞɟɥɢɦɩɨ ɮɨɪɦɭɥɟɫ
ɭɱɟɬɨɦɤɨɧɜɟɤɬɢɜɧɨɣɬɟɩɥɨɨɬɞɚɱɢɫɬɟɩɥɨɨɬɞɚɸɳɟɣɩɨɜɟɪɯɧɨɫɬɢɨɛɪɚɳɟɧɧɨɣ
ɜɧɢɡ
Ɏ ɤȼɬ
==
ɩɨɞ
++++
−⋅
−
ɉɪɢɧɹɬɵɟɡɧɚɱɟɧɢɹɬɟɦɩɟɪɚɬɭɪɵ7Lɩɨɝɪɚɧɢɰɚɦɫɥɨɟɜɧɟɨɛɯɨɞɢɦɨɩɪɨɜɟ
ɪɢɬɶɚɧɚɥɢɬɢɱɟɫɤɢɩɨɬɟɩɥɨɜɨɦɭɩɨɬɨɤɭɎ
ɜɨɝɨɫɨɩɪɨɬɢɜɥɟɧɢɹ5
ɬL
ɫɭɱɟɬɨɦɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨɬɟɩɥɨ
ɩɨɞ
7 ±⋅ 7 ±⋅
±⋅ 7 ±⋅
7
±⋅
7
ɜ
ɋ ɭɱɟɬɨɦ ɞɨɩɭɫɬɢɦɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɧɟ ɛɨɥɟɟ
Ʉɪɚɫɱɟɬɜɵɩɨɥɧɟɧɤɨɪɪɟɤɬɧɨ
ɋɭɦɦɚɪɧɵɟɬɟɩɥɨɜɵɟɩɨɬɟɪɢɫɨɫɬɚɜɥɹɸɬ
Ɏ ɎɫɬɎɎ
ɤȼɬ
ɩɨɞ
Ⱥɤɬɢɜɧɚɹ ɦɨɳɧɨɫɬɶ ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɬɟɩɥɨɜɵɯ ɩɨɬɟɪɶɫ
ɭɱɟɬɨɦ«ɧɟɭɱɬɟɧɧɵɯɩɨɬɟɪɶ
Ɋ
«Ɏ ⋅ ɤȼɬ
ɬɩ
ɉɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɞɚɧɧɵɦɢ ȼɇɂɂɗɌɈ > ɫ
ɪɢɫ@ɞɥɹɂɋɌ3
§ɤȼɬɞɥɹɩɟɱɢɫɧɨɜɨɣ ɮɭɬɟɪɨɜɤɨɣɢ3
ɬɩ
§ɤȼɬ
ɬɩ
ɞɥɹɩɟɱɢɫɢɡɧɨɲɟɧɧɨɣɮɭɬɟɪɨɜɤɨɣ
Ɋɚɫɱɟɬɷɥɟɤɬɪɢɱɟɫɤɢɯɩɚɪɚɦɟɬɪɨɜ
ɍɞɟɥɶɧɵɣɬɟɨɪɟɬɢɱɟɫɤɢɣɪɚɫɯɨɞɷɧɟɪɝɢɢɩɨ>ɫɪɢɫ@
:
ɤȼɬ⋅ɱɬ
ɭɬ
ɉɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɨɞɝɨɬɨɜɤɢɂɌɉ ɤ ɩɥɚɜɤɟIJɩ ɱɜɵɞɟɪɠɤɢɦɟ
ɬɚɥɥɚ±IJɬ ɱ
ɍɞɟɥɶɧɨɟɷɥɟɤɬɪɢɱɟɫɤɨɟɫɨɩɪɨɬɢɜɥɟɧɢɟɫɬɚɥɢɜɬɜɟɪɞɨɦɫɨɫɬɨɹɧɢɢɄ
⋅±ɩɪɢ Ʉ ɬɨɱɤɚɄɸɪɢ ⋅±ɜ ɠɢɞɤɨɦɫɨɫɬɨɹɧɢɢ Ʉ
⋅±Ɉɦ⋅ɦɋɪɟɞɧɢɣɪɚɡɦɟɪɤɭɫɤɨɜɦɟɬɚɥɥɨɲɢɯɬɵ'ɒ ɦ
ɍɞɟɥɶɧɨɟɷɥɟɤɬɪɢɱɟɫɤɨɟɫɨɩɪɨɬɢɜɥɟɧɢɟɦɟɞɧɨɝɨɜɨɞɨɨɯɥɚɠɞɚɟɦɨɝɨɢɧɞɭɤ
ɬɨɪɚɌɜ ɄɌɧ Ʉȡɢ ⋅±Ɉɦ⋅ɦ
ɈɛɨɫɧɨɜɚɧɢɟɦɨɳɧɨɫɬɢɊɦɜɵɞɟɥɹɟɦɨɣɜɦɟɬɚɥɥɟɢɬɟɯɧɢɱɟɫɤɢɰɟɥɟɫɨɨɛ
ɪɚɡɧɵɯɞɥɢɬɟɥɶɧɨɫɬɢ ɩɥɚɜɤɢ IJɲɢ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨɩɟɪɢɨɞɚ IJɷɩɪɨɜɟɞɟɦ ɩɭɬɟɦ
ɚɧɚɥɢɡɚɡɚɜɢɫɢɦɨɫɬɢɆ IɊɦɫɢɫɩɨɥɶɡɨɜɚɧɢɟɦɮɨɪɦɭɥɵ
ɆP7ɉIJ IJ : Ɋ Ɋ
=⋅− ++ −
ªº
ɪɩɬ ɩɨɥɦɬɩ
¬¼
ɝɞɟɆ±ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɩɟɱɢɬɱ
Ɍ±ɧɨɦɢɧɚɥɶɧɵɣɤɚɥɟɧɞɚɪɧɵɣɮɨɧɞɜɪɟɦɟɧɢɱɝɨɞ
ɉɪɢɧɹɜɞɨɥɸ ɩɪɨɫɬɨɟɜ ɉ
ɭɪɚɜɧɟɧɢɹ
ɝɞɟ:
±ɩɨɥɟɡɧɵɣɪɚɫɯɨɞɷɥɟɤɬɪɨɷɧɟɪɝɢɢɧɟɨɛɯɨɞɢɦɵɣɞɥɹɢɡɦɟɧɟɧɢɹɷɧɬɚɥɶ
ɩɨɥ
ɫɨɫɬɚɜɢɦ ɧɟɨɛɯɨɞɢɦɵɟɚɧɚɥɢɬɢɱɟɫɤɢɟ
ɪ
IJ:ɊɊ=−
ɷɩɨɥɦɬɩ
ɩɢɢɡɚɝɪɭɠɚɟɦɨɣɦɟɬɚɥɥɨɲɢɯɬɵɩɪɢɧɚɝɪɟɜɟɞɨɬɟɦɩɟɪɚɬɭɪɵɩɥɚɜɥɟɧɢɹɢɩɟɪɟ
ɝɪɟɜɚ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ ɪɚɡɥɢɜɤɢ ɜ ɞɚɧɧɨɦ ɪɚɫɱɟɬɟ P
ɤȼɬ⋅ɱ
āP
−=τ
ɦɷ
Ɋ
−+=τ+τ+τ=τ
ɦɷɬɩɩɥ
P :
ɲ
Ɋ
−+≈τ⋅−⋅=
ɦɩɥ
:
ɩɨɥ
ɭɬ
ɊɆ
ɋɨɝɥɚɫɧɨɝɪɚɮɢɤɚɦɷɬɢɯɭɪɚɜɧɟɧɢɣ>ɫɪɢɫɤɪɢɜɵɟ@ɢɪɟ
ɤɨɦɟɧɞɚɰɢɹɦ>ɫɩɪɢɥ@ɜɵɛɢɪɚɟɦɊ ɤȼɬɱɬɨɩɨɡɜɨɥɹɟɬɩɪɨɜɟɫɬɢ
ɪɚɫɩɥɚɜɥɟɧɢɟɦɟɬɚɥɥɨɲɢɯɬɵɡɚIJ
Ɍɟɩɥɨɜɨɣɤɩɞɩɟɱɢɫɨɝɥɚɫɧɨɮɨɪɦɭɥɟ
Șɬ ±Ɋ
ɂɫɯɨɞɹɢɡɪɟɤɨɦɟɧɞɚɰɢɣ>ɫɩɪɢɥ@ɚɬɚɤɠɟɢɡɭɫɥɨɜɢɹIɤɪI
ɜɵɛɢɪɚɟɦɪɚɛɨɱɭɸɱɚɫɬɨɬɭI
ɱ
ɷ
ɬɩɊɦ
Ƚɰ
ɪɚɛ
=−=
ɪɚɛ
ȼɤɚɱɟɫɬɜɟɢɫɬɨɱɧɢɤɚɩɢɬɚɧɢɹɩɪɨɟɤɬɢɪɭɟɦɨɣɂɌɉɦɨɠɧɨɢɫɩɨɥɶɡɨɜɚɬɶɬɟ
ɪɪɢɫɬɨɪɧɵɣɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶɱɚɫɬɨɬɵɬɢɩɚɌɉɑ>ɫɩɪɢɥ@ɤɨɬɨɪɵɣɫɨ
ɡɞɚɟɬɧɨɦɢɧɚɥɶɧɨɟɧɚɩɪɹɠɟɧɢɟȼ
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