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macauor

Òø³æ (СÓÐÃûÆø)

[ÇóÖú] »ý·Öº¯ÊýΪf(x)*delta(x)*delta(x)£¬»ý·ÖÓòΪ¸ºÎÞÇîµ½ÕýÎÞÇµÈÓÚ¶àÉÙ

ÈçÌ⣬delta(x) ΪµÒÀ­¿Ëdeltaº¯Êý£¬»ý·ÖÓõ½ÁË»ý·Öº¯ÊýΪ f(x)*delta(x)*delta(x)£¬ÕâÁ½¸ödelta(x)Ïà³ËÔõô´¦Àí£¿
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ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

feixiaolin

ÈÙÓþ°æÖ÷ (ÎÄ̳¾«Ó¢)

ÓÅÐã°æÖ÷

ÒýÓûØÌû:
3Â¥: Originally posted by hank612 at 2014-09-13 06:53:09
°æÖ÷´óÉñ, ¶¨»ý·ÖºóÓ¦¸Ã²»ÔÙÊǺ¯Êý, Ó¦¸ÃÊǸöÊý²Å¶Ô.

Èç¹ûÓý׶κ¯Êý g_a(x)= 0  if |x|>a/2;  1/a if |x|<=a/2, aΪºÜСµÄÕýÊý
À´È¡´ú deltaº¯Êý, Á¢µÃ»ý·ÖֵΪf(0)/a, Òò´ËaÇ÷ÓÚÁãʱ,¶¨»ý·ÖΪ ...

f(x)*delta(x)*delta(x)=¡¾f(0)*delta(x)¡¿*delta(x)=f(0)*delta(x)
»ý·Ö:
Int[f(x)*delta(x)*delta(x), {x, -inf, x}]=f(0)*step(x)   ½×Ô¾º¯Êý
Int[f(x)*delta(x)*delta(x), {x, -inf, +inf}]=f(0)           Ò»¸öÊý
4Â¥2014-09-13 07:24:53
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
²é¿´È«²¿ 7 ¸ö»Ø´ð

feixiaolin

ÈÙÓþ°æÖ÷ (ÎÄ̳¾«Ó¢)

ÓÅÐã°æÖ÷

f(x)*delta(x)*delta(x)=¡¾f(0)*delta(x)¡¿*delta(x)=f(0)*delta(x)
»ý·Ö=f(0)*step(x)   ½×Ô¾º¯Êý
2Â¥2014-09-12 22:55:23
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

hank612

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

¡ï ¡ï ¡ï ¡ï ¡ï
macauor(feixiaolin´ú·¢): ½ð±Ò+5 2014-09-13 21:29:53
ÒýÓûØÌû:
2Â¥: Originally posted by feixiaolin at 2014-09-12 22:55:23
f(x)*delta(x)*delta(x)=¡¾f(0)*delta(x)¡¿*delta(x)=f(0)*delta(x)
»ý·Ö=f(0)*step(x)   ½×Ô¾º¯Êý

°æÖ÷´óÉñ, ¶¨»ý·ÖºóÓ¦¸Ã²»ÔÙÊǺ¯Êý, Ó¦¸ÃÊǸöÊý²Å¶Ô.

Èç¹ûÓý׶κ¯Êý g_a(x)= 0  if |x|>a/2;  1/a if |x|<=a/2, aΪºÜСµÄÕýÊý
À´È¡´ú deltaº¯Êý, Á¢µÃ»ý·ÖֵΪf(0)/a, Òò´ËaÇ÷ÓÚÁãʱ,¶¨»ý·ÖΪÎÞÇî´ó. ²¢ÇÒÎÞÇî´óµÄ·ûºÅµÈÓÚ f(0)µÄ·ûºÅ.
We_must_know. We_will_know.
3Â¥2014-09-13 06:53:09
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

macauor

Òø³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
4Â¥: Originally posted by feixiaolin at 2014-09-13 07:24:53
f(x)*delta(x)*delta(x)=¡¾f(0)*delta(x)¡¿*delta(x)=f(0)*delta(x)
»ý·Ö:
Int=f(0)*step(x)   ½×Ô¾º¯Êý
Int=f(0)           Ò»¸öÊý...

°æÖ÷µÄ»ý·Ö½á¹ûÓÐɶ²Î¿¼×ÊÁÏû£¿
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