## New Articles

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*Ref*]**Sophomore's dream**by pahioJul 9[

*Res*]**examples of growth of perturbations in chemical or...**by rspuzioMay 24[

*Ref*]**proof of Stirling's approximation**by rspuzioMay 8[

*Res*]**Example of stochastic matrix of mapping**by rspuzioApr 23[

*Res*]**6. Discussion**by rspuzioApr 20[

*Res*]**5. Entanglement**by rspuzioApr 20[

*Res*]**4. Measurement**by rspuzioApr 20[

*Res*]**3. Distributed dynamical systems**by rspuzioApr 20[

*Res*]**2. Stochastic maps**by rspuzioApr 20[

*Res*]**1. Introduction**by rspuzioApr 19[

*Ref*]**Oseledets multiplicative ergodic theorem**by FilipeMar 18[

*Ref*]**Furstenberg-Kesten theorem**by FilipeMar 18[

*Ref*]**multiplicative cocycle**by FilipeMar 18[

*Ref*]**remainder term series**by pahioMar 17## Latest Messages

Jul 29

Jul 29

Jul 28

Jul 21

Jul 20

Jul 19

Jul 17

Jul 14

Jul 11

Jun 30

Jun 25

Jun 23

Jun 23

Jun 20

341 is a pseudoprime to base 2 (which is in k(1). It is also a pseudoprime to base (341 + i). Hence
it is a pseudoprime in k(i) also. Similarly 561, a Carmichael number
is a pseudoprime in k(i) as it is pseudo to the base (187 + i) as well
as the base (561 + i). Interestingly it is also pseudo to the base (561 + 2i).

Jul 29

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Example: 2,4,6,8,10…..
Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series.
Example: 2+4+6+8+10…..
nth term in the finite arithmetic series
Suppose Arithmetic Series a1+a2+a3+…..an
Then nth term an=a1+(n-1)d
Where
a1- First number of the series
an- Nth Term of the series
n- Total number of terms in the series
d- Difference between two successive numbers
Sum of the total numbers of the arithmetic series
Sn=n/2*(2*a1+(n-1)*d)
Where
Sn – Sum of the total numbers of the series
a1- First number of the series
n- Total number of terms in the series
d- Difference between two successive numbers
Example:
Find n and sum of the numbers in the following series 3 + 6 + 9 + 12 + x?
Here a1=3, d=6-3=3, n=5
x= a1+(n-1)d = 3+(5-1)3 = 15
Sn=n/2*(2a1+(n-1)*d)
Sn=5/2*(2*3+(5-1)3)=5/2*18 = 45
I hope the above formulae are helpful to solve your math problems>

Jul 28

To calculate the day of the week for a given date, first of all we need to find out the number of odd days.
Today I thought of sharing a beautiful problem I learned in my school, though it is easy, it is tricky too.
Odd Days are number of days more than the complete number of weeks in given period.
Leap Year is the year which is divisible by 4.
A normal year has 365 days
A leap year has 366 days
One normal year = 365 days = 52weeks + 1day
One normal year has one odd day
One leap year = 366 days = 52weeks + 2days
One leap year has two odd days
100 years = 76 ordinary years + 24 leap years = 5200 weeks + 124 days = 5217 weeks + 5 days
100 years have 5 odd days
400 years have (20+1) 0 odd days
The number of odd days and the corresponding day of the week is given below
0-Sunday
1-Monday
2-Tuesday
3-Wednesday
4-Thursday
5-Friday
6-Saturday
So by finding out the number of odd days you can find out the day of the week. I hope this procedure Will be helpful in solving math problems in exams.
Thanks.
>

Jul 21

This base, however , does not work in the case of primes having
shape 4m+3. A base that works is 1 + i. Example ((1+i)^102 + I)/103
= -21862134113449i.

Jul 20

What is the nature of a, the base? When p has the shape 4m+1
a has the shape of a prime factor of a number having the same shape.
Example: Let p = 61. Then ((4 + i)^60 - 1 )/61 =
-71525089284120116591639000327021600 + 11369162311133702688684197835211600i

Jul 19

Before giving some further generalisations let me give some examples: case a)
((1+I)^30 + I)/31 = -1057i. ((1 + i )^102 + i)/103 = -21862134113449i
Case b) ((1 + i)^12 - 1)/13 = -5. (( 1 + i ) ^100 - 1)/101 = -11147523830125

Jul 17

Although Hardy and Wright have formulated the above theorem in their book ("An introduction
to he theory of numbers " we can see how it works with the aid of software like pari.
The four examples illustrate this. Now for a few genralisations: a) If p is a prime
of form 4m+3, then ((a^(p-1)+ I)/p is congruent to 0 (mod(p)). b) If p is a prime
of form 4m+1, then ((a^(p-1) - 1)/p is congruent to 0 (mod(p)).

Jul 14

There are four unities in k(i) viz 1, -1, i and -i. Four examples are given
here to illustrate Fermat's theorem in k(i). a)((2+3i)^2-1)/3 = -2 +4i b)
((3+2i)^2 + 1)/3 = 2 + 4i c) ((10 + i)^2 + i)/3 = 33 + 7i and d) ((14 +i)^2 - i)/3 =
65 + 9i.

Jul 11

Considering 2 simplex tableau encountered when solving a linear program
http://i62.tinypic.com/9r80ic.jpg
determine the value of each of the following items(unknowns) : p q r that appear in tables
http://i61.tinypic.com/mcwx9u.jpg
And please if someone has another example like this one please give it to me>

Jun 30

I just read your article and it was totally great, it contains a lot of useful ideas, it is also written in organize manner,thanks for sharing this kind of article.
<a href="http://increasemyplays.com/buy-soundcloud-likes/">

Jun 25

Please see "sophomore's dream" in Wikipedia.

Jun 23

1.- Is False
2.- Is True
1.- Is False
1.- Is true, iff b is rational.
Regards,
Ronald.

Jun 23

Let our definition of a failure be a composite number which is also a multiple of 11.
Let the parent function be 2^n + 7 (n belongs to N ). Then n = 2 + Eulerphi(11) is
a failure function. Also n = 2^(1 + Eulerphi(Eulerphi(11)) is also a failure function.

Jun 20

Let our definition of a failure be a non-primitive polynomial in
x (x belongs to Z ). Let the parent function be the primitive
polynomial x^2 + x + 1. Then x generated by any of the
failure functions 1 + 3k, 2 + 7k etc when substituted in
the parent function yield failures i.e. non primitive polynomials.

## Latest Messages

Jul 29

Jul 29

Jul 28

Jul 21

Jul 20

Jul 19

Jul 17

Jul 14

Jul 11

Jun 30

Jun 25

Jun 23

Jun 23

Jun 20

341 is a pseudoprime to base 2 (which is in k(1). It is also a pseudoprime to base (341 + i). Hence
it is a pseudoprime in k(i) also. Similarly 561, a Carmichael number
is a pseudoprime in k(i) as it is pseudo to the base (187 + i) as well
as the base (561 + i). Interestingly it is also pseudo to the base (561 + 2i).

Jul 29

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Example: 2,4,6,8,10…..
Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series.
Example: 2+4+6+8+10…..
nth term in the finite arithmetic series
Suppose Arithmetic Series a1+a2+a3+…..an
Then nth term an=a1+(n-1)d
Where
a1- First number of the series
an- Nth Term of the series
n- Total number of terms in the series
d- Difference between two successive numbers
Sum of the total numbers of the arithmetic series
Sn=n/2*(2*a1+(n-1)*d)
Where
Sn – Sum of the total numbers of the series
a1- First number of the series
n- Total number of terms in the series
d- Difference between two successive numbers
Example:
Find n and sum of the numbers in the following series 3 + 6 + 9 + 12 + x?
Here a1=3, d=6-3=3, n=5
x= a1+(n-1)d = 3+(5-1)3 = 15
Sn=n/2*(2a1+(n-1)*d)
Sn=5/2*(2*3+(5-1)3)=5/2*18 = 45
I hope the above formulae are helpful to solve your math problems>

Jul 28

To calculate the day of the week for a given date, first of all we need to find out the number of odd days.
Today I thought of sharing a beautiful problem I learned in my school, though it is easy, it is tricky too.
Odd Days are number of days more than the complete number of weeks in given period.
Leap Year is the year which is divisible by 4.
A normal year has 365 days
A leap year has 366 days
One normal year = 365 days = 52weeks + 1day
One normal year has one odd day
One leap year = 366 days = 52weeks + 2days
One leap year has two odd days
100 years = 76 ordinary years + 24 leap years = 5200 weeks + 124 days = 5217 weeks + 5 days
100 years have 5 odd days
400 years have (20+1) 0 odd days
The number of odd days and the corresponding day of the week is given below
0-Sunday
1-Monday
2-Tuesday
3-Wednesday
4-Thursday
5-Friday
6-Saturday
So by finding out the number of odd days you can find out the day of the week. I hope this procedure Will be helpful in solving math problems in exams.
Thanks.
>

Jul 21

This base, however , does not work in the case of primes having
shape 4m+3. A base that works is 1 + i. Example ((1+i)^102 + I)/103
= -21862134113449i.

Jul 20

What is the nature of a, the base? When p has the shape 4m+1
a has the shape of a prime factor of a number having the same shape.
Example: Let p = 61. Then ((4 + i)^60 - 1 )/61 =
-71525089284120116591639000327021600 + 11369162311133702688684197835211600i

Jul 19

Before giving some further generalisations let me give some examples: case a)
((1+I)^30 + I)/31 = -1057i. ((1 + i )^102 + i)/103 = -21862134113449i
Case b) ((1 + i)^12 - 1)/13 = -5. (( 1 + i ) ^100 - 1)/101 = -11147523830125

Jul 17

Although Hardy and Wright have formulated the above theorem in their book ("An introduction
to he theory of numbers " we can see how it works with the aid of software like pari.
The four examples illustrate this. Now for a few genralisations: a) If p is a prime
of form 4m+3, then ((a^(p-1)+ I)/p is congruent to 0 (mod(p)). b) If p is a prime
of form 4m+1, then ((a^(p-1) - 1)/p is congruent to 0 (mod(p)).

Jul 14

There are four unities in k(i) viz 1, -1, i and -i. Four examples are given
here to illustrate Fermat's theorem in k(i). a)((2+3i)^2-1)/3 = -2 +4i b)
((3+2i)^2 + 1)/3 = 2 + 4i c) ((10 + i)^2 + i)/3 = 33 + 7i and d) ((14 +i)^2 - i)/3 =
65 + 9i.

Jul 11

Considering 2 simplex tableau encountered when solving a linear program
http://i62.tinypic.com/9r80ic.jpg
determine the value of each of the following items(unknowns) : p q r that appear in tables
http://i61.tinypic.com/mcwx9u.jpg
And please if someone has another example like this one please give it to me>

Jun 30

I just read your article and it was totally great, it contains a lot of useful ideas, it is also written in organize manner,thanks for sharing this kind of article.
<a href="http://increasemyplays.com/buy-soundcloud-likes/">

Jun 25

Please see "sophomore's dream" in Wikipedia.

Jun 23

1.- Is False
2.- Is True
1.- Is False
1.- Is true, iff b is rational.
Regards,
Ronald.

Jun 23

Let our definition of a failure be a composite number which is also a multiple of 11.
Let the parent function be 2^n + 7 (n belongs to N ). Then n = 2 + Eulerphi(11) is
a failure function. Also n = 2^(1 + Eulerphi(Eulerphi(11)) is also a failure function.

Jun 20

Let our definition of a failure be a non-primitive polynomial in
x (x belongs to Z ). Let the parent function be the primitive
polynomial x^2 + x + 1. Then x generated by any of the
failure functions 1 + 3k, 2 + 7k etc when substituted in
the parent function yield failures i.e. non primitive polynomials.