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#26 2008-03-14 06:46:09

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Science laws and theorems

Cauchy–Schwarz inequality

     


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#27 2008-11-01 16:43:44

All_Is_Number
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Registered: 2006-07-10
Posts: 258

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.


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#28 2009-04-16 02:04:47

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Science laws and theorems

The Sylow theorems (group theory)

1. If G is a group of order p[sup]n[/sup]k (where p is a prime, n and k are positive integers and p is coprime with k) then G has a subgroup of order p[sup]n[/sup], called a Sylow p-subgroup.

2. If P and Q are Sylow p-subgroups of G, there exists gG such that gPg[sup]−1[/sup] = Q.

3. The number of Sylow p-subgroups must divide the order of G and be congruent to 1 modulo p.


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#29 2009-09-07 21:19:29

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Science laws and theorems






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#30 2009-09-24 03:49:39

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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

[align=center]

[/align]
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 4[sup]th[/sup] 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
.


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Last edited by JaneFairfax (2009-09-24 03:51:09)


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#31 2012-03-16 01:02:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

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 (2012-03-16 01:07:37)


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#32 2012-03-16 01:17:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Science laws and theorems

Lowest Common Multiple Identity


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