A Contraction Theorem for Markov Chains on General State Spaces
... We use Condition B in two ways. First of all, it allows us to use Chebychev’s inequality. Secondly it allows us to have control over f (Xn (x)) for n = 1, 2, ..., N0 − 1, where thus N0 is the integer in the definition of the GCMproperty. (See Definition 1.2.) From Condition C, follows that for every ...
... We use Condition B in two ways. First of all, it allows us to use Chebychev’s inequality. Secondly it allows us to have control over f (Xn (x)) for n = 1, 2, ..., N0 − 1, where thus N0 is the integer in the definition of the GCMproperty. (See Definition 1.2.) From Condition C, follows that for every ...
Date: October 5th, 2009
... from Strogatz's column that I felt were noteworthy and saved, including yours and mine. I hope you will take the time and effort to carefully reread them. Concerning your video, you are making a profound error, as I think you were doing in March. You are saying that to define the complex numbers we ...
... from Strogatz's column that I felt were noteworthy and saved, including yours and mine. I hope you will take the time and effort to carefully reread them. Concerning your video, you are making a profound error, as I think you were doing in March. You are saying that to define the complex numbers we ...
Group action
... 1. (a) Assume that prime number p divides x16 + 1. Then p is of form 32k + 1. (b) Without using the general Dirichlet theorem or L-functions, prove that for any k there is infinite set of primes of form kn + 1. Solution. (a) Modulu p, the equation x16 = –1 has a solution. So, there is a remainder x ...
... 1. (a) Assume that prime number p divides x16 + 1. Then p is of form 32k + 1. (b) Without using the general Dirichlet theorem or L-functions, prove that for any k there is infinite set of primes of form kn + 1. Solution. (a) Modulu p, the equation x16 = –1 has a solution. So, there is a remainder x ...
![[hal-00574623, v2] Averaging along Uniform Random Integers](http://s1.studyres.com/store/data/019969824_1-25527940ea4f317ec31969269e4745aa-300x300.png)
[hal-00574623, v2] Averaging along Uniform Random Integers
... which is the proportion predicted by Benford’s law. (Donald Knuth generalized Flehinger’s theorem to the distribution of the whole mantissa in 1981 [9].) In spite of its title, Flehinger’s article has no probabilistic content. A good reason is that there is no way of picking an integer uniformly at ...
... which is the proportion predicted by Benford’s law. (Donald Knuth generalized Flehinger’s theorem to the distribution of the whole mantissa in 1981 [9].) In spite of its title, Flehinger’s article has no probabilistic content. A good reason is that there is no way of picking an integer uniformly at ...
