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For some Markov chains, no matter what the initial distribution is, after running the chain for a while, the ...ath>. So the Markov chain converges to the same stationary distribution no matter what the initial distribution is. ...

For some Markov chains, no matter what the initial distribution is, after running the chain for a while, the ...ath>. So the Markov chain converges to the same stationary distribution no matter what the initial distribution is. ...

...ple not knowing each other. In graph theoretical terms, this means that no matter how we color the edges of <math>K_6</math> (the complete graph on six verti ...

First, it is trivial to see that the theorem holds for <math>k=1</math> (no matter whether shifted). Next, we show that the theorem holds when <math>n=2k</math> (no matter whether shifted). For any <math>S\in{X\choose k}</math>, both <math>S</math ...

First, it is trivial to see that the theorem holds for <math>k=1</math> (no matter whether shifted). Next, we show that the theorem holds when <math>n=2k</math> (no matter whether shifted). For any <math>S\in{X\choose k}</math>, both <math>S</math ...

First, it is trivial to see that the theorem holds for <math>k=1</math> (no matter whether shifted). Next, we show that the theorem holds when <math>n=2k</math> (no matter whether shifted). For any <math>S\in{X\choose k}</math>, both <math>S</math ...

First, it is trivial to see that the theorem holds for <math>k=1</math> (no matter whether shifted). Next, we show that the theorem holds when <math>n=2k</math> (no matter whether shifted). For any <math>S\in{X\choose k}</math>, both <math>S</math ...

...question is simple, the value of the surface integral will be the same no matter what parametrization one uses. ...

...''apple'' with ''sun'', and ''orange'' with ''moon''. The order does not matter. It is possible to pair the elements, and none is left out. But the set < ...

...such that many packets have to be delivered through the same edge, thus no matter what queuing policy is used, the maximum delay must be very high. ...

...e cannot know both of them about any [[particle]] (a very small thing), no matter how hard we try. The more we learn about one of such a pair, the less we ca Everything made of [[matter]] is attracted to other matter because of a fundamental force called [[gravity]]. Einstein's theory that e ...

First, it is trivial to see that the theorem holds for <math>k=1</math> (no matter whether shifted). Next, we show that the theorem holds when <math>n=2k</math> (no matter whether shifted). For any <math>S\in{X\choose k}</math>, both <math>S</math ...

First, it is trivial to see that the theorem holds for <math>k=1</math> (no matter whether shifted). Next, we show that the theorem holds when <math>n=2k</math> (no matter whether shifted). For any <math>S\in{X\choose k}</math>, both <math>S</math ...

:*for every edge (no matter parallel or not) in the form of <math>uw</math> or <math>vw</math> that con ...

...lity tests is to predict difficulty; writing better prose is quite another matter. As discussed in [[prose difficulty]], sentence length is an index of [[syn ...

...) The tiny but pesky differences between results were going to remain, not matter how much Heisenberg wished they would go away. ...inty principle depended on a model that did not consider that particles of matter such as electrons, protons, etc. have a wavelength. In 1926 Louis de Brogli ...

...e is 0) would be encoded as ''m'' = 0, which produces a ciphertext of 0 no matter which values of ''e'' and ''N'' are used. Likewise, a single ASCII <code>SO ...

...uniformly chosen from <math>S</math> at random. It is easy to see that no matter for what <math>k</math> it holds that <math>X(n)\ge \min(m,n-m)</math> wher ...

...d mean that no general, fast ways to solve those NP problems can exist, no matter how hard we look. However if all NP problems are P problems (P = NP), it wo ...

...guage was changed to allow different results where the difference does not matter and require a "strictfp" qualifier to be used when the results have to conf ...ed computable numbers which it may never be possible to correctly round no matter how many digits are calculated. For instance, if [[Goldbach's conjecture]] ...