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#26 2008-03-15 05:46:09
#27 2008-11-02 15:43:44
- All_Is_Number
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Re: Science laws and theorems
ganesh wrote:
Newton's laws of motion.
First law:- Every body continues in its state of rest or uniform motion unless compleeled by an external force to change its position.
Interestingly, this is not Newton's first law of motion. It is actually a restatement of his second law, F=ma.
Strangely enough, Newton made the oft repeated error when he stated the first law. However, in the pages of Principia immediately preceding his statement of the first law, he described the law as something substantially different.
The first law should be (and was described by Newton as):
There exists a frame of reference in which an object continues in its state of rest or uniform motion unless a net external force is applied to that object.
In fact, without this first law, the second law need not hold.
You can shear a sheep many times but skin him only once.
#28 2009-04-17 00:04:47
- JaneFairfax
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Re: Science laws and theorems
The Sylow theorems (group theory)
1. If G is a group of order pnk (where p is a prime, n and k are positive integers and p is coprime with k) then G has a subgroup of order pn, called a Sylow p-subgroup.
2. If P and Q are Sylow p-subgroups of G, there exists g ∊ G such that gPg−1 = Q.
3. The number of Sylow p-subgroups must divide the order of G and be congruent to 1 modulo p.
#29 2009-09-08 19:19:29
#30 2009-09-25 01:49:39
- JaneFairfax
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Re: Science laws and theorems
Planck’s radiation law
The intensity per unit wavelength of the radiation of a black body of absolute temperature is given by
where is Planck’s constant, is the speed of light in a vacuum, and is Boltzmann’s constant.
From this, both Stefan’s law (which states that the intensity of the radiation of a black body is proportional to the 4th power of its absolute temperature) and Wien’s displacement law (which states that the maximum wavelength of the radiation of a black body is inversely proportional to its absolute temperature) can be derived.
To derive Stefan’s law, hold constant and evaluate . For Wien’s displacement law, set .
http://z8.invisionfree.com/DYK/index.php?showtopic=867
Last edited by JaneFairfax (2009-09-25 01:51:09)
#31 2012-03-17 00:02:35
- anonimnystefy
- Real Member
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Re: Science laws and theorems
Three functions
Note:All three of the above mentioned functions are multiplicative,which means that:
Euler's formula
Note: is not always the smallest number for which the above identity can hold.
Last edited by anonimnystefy (2012-03-17 00:07:37)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#32 2012-03-17 00:17:27
- anonimnystefy
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Re: Science laws and theorems
Lowest Common Multiple Identity
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón