Hi,
n
--
\ x = x + x + ... + x
/ i 1 2 n
--
i = 1
n = Constant or outer Parameter
i = Index only total numbers (1,2,3...)
Example:
x = 10
1
x = 12
2
x = 14
3
3
--
\ x = x + x + x = 10 + 12 + 14 = 36
/ i 1 2 3
--
i = 1
Gerhard
--------------------------------
Beam me up... arrgh, no carrier!
--------------------------------
>-----Original Message-----
>From: Berin Loritsch [mailto:bloritsch@apache.org]
>Sent: Thursday, December 13, 2001 4:34 PM
>To: cocoon-dev@xml.apache.org
>Subject: Re: Adaptive Caching [was Re: initial checkin of the Scheme
>code]
>
>
>Stefano Mazzocchi wrote:
>
>> Talking about placing too many irons in the fire :)
>>
>
>
>Stefano, please forgive my ignorance, as I have an Associates Degree in
>Music Recording, and not a traditional CS degree. I haven't had the
>higher math classes you and many others have had here.
>
>I understand Algebra and Trigonometry ok, so if we can simplify these
>algorithms into a "pseudo-code" so I can wrap my head around them, I
>will be happy to jump in the discussion. As it is now, It's going
>over my head.
>
>I understand the Calculus ideas of functions (i.e. V(r,t)). What throws
>me are the Sigmas (I studied Ancient Greek, so I know what the letters are).
>I know they are meant to represent sums, or statistical data. I don't know
>what the letter above the sigma or below the sigma is supposed to signify.
>
>If you don't feel up to giving me a quick math lesson so I can grok the
>concepts fully, can you point me to a resource where I can teach myself?
>
>> Thus, given
>>
>> r := resource
>> t := time of the request
>> V(r,t) := validity estimation cost
>> P(r,t) := production cost when caching is not performed
>> Pc(r,t) := production cost when caching is performed
>> l(r,t) := lookup cost
>> s(r,t) := storage cost
>>
>> and
>>
>> I := sequence of invalid requests time [1,n]
>> V := sequence of valid request time [1,m]
>>
>> we have that
>>
>> n
>> --
>> Invalid(r) = \ (V(r,I ) + Pc(r,I ) + s(r,I ))
>> / i i i
>> --
>> i = 1
>>
>> and
>>
>> m
>> --
>> Valid(r) = \ (V(r,I ) + L(r,I ))
>> / j j
>> --
>> j = 1
>>
>> and
>>
>> n m
>> -- --
>> Ptot(r) = \ P(r,I ) + \ P(r,V )
>> / i / j
>> -- --
>> i = 1 j = 1
>>
>
>
>
>
>--
>
>"They that give up essential liberty to obtain a little temporary safety
> deserve neither liberty nor safety."
> - Benjamin Franklin
>
>
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