Cycles Definition and 169 Threads

I'm just posting a random graph algorithm problem for discussion fodder, since another interesting graph algorithm post was removed due to a threatening-sounding title and lead-up. This is from Cormen, Leiserson, Rivest, & Stein, 22.4-3 (not a homework problem of any kind, just for fun--I had...

I posted this in another math forum, but have received no response: Let sopfr(n) be the sum of prime factors of n (see http://mathworld.wolfram.com/SumofPrimeFactors.html ). There have been observations that certain iterations involving the sopfr function seem to lead invariably to cycles...

Hi guys, I've been working on a theory for a bit and am wondering what you guys think. So here it is: Summary The universe expands through the expansive era. Then it contracts through the contracton era. The universe contracts until it finally collides in the center of the universe. This...

Which way does the Earth rotate and why? I am talking about both of the rotations. Rotation for a day and a rotation for an year.

do we use Cp just for processes with flow work or ther is anything more related with this, is my question thanks for ur help..

Help. If anybody knows them beyond introductory level... i have a higher order system with a single fixed point. i chose such parameters that the fixed point is unstable. so it should either oscillate to infinity, or in this case it actually has a limit cycle. when running this system on the...

When calculating powers of cycles, are there any easy steps to use in doing so? I mean...is there a typical relationship when calculating (123)^n? Also, is it safe to say that a ceratin n-cycle should have order n or n-1? I guess any explanation of orders for group elements would be...

In the carbon-oxygen cycle how does the process of photosynthesis and respiration interconnect? what pathways does a carbon atom go tom a fossil fuel to becoming a part of air that a person can exhale?

Last evening there was the perfect rainbow condition: A bright evening sun shining into a rainstorm just overhead. I went outside to see both complete arcs from horizon to horizon . THen... the inner rainbow (the most commonly seen rainbow, with red on the outside of the bow) looked odd...

Dear people of Physics Forums, I would like to have your opinion about the following problem: Suppose we are interested to evaluate the average efficiency ( e ) of an infinite series of carnot cycles. The temperature of the hot reservoir of each carnot Cycle of the series, Ta, is at 990K, but...

Question Let S_n be the symmetric group on n letters. (i) Show that if \sigma = (x_1,\dots,x_k) is a cycle and \phi \in S_n then \phi\sigma\phi^{-1} = (\phi(x_1),\dots,\phi(x_k)) (ii) Show that the congujacy class of a permutation \sigma \in S_n consists of all permutations in S_n...

This is a serious question. I'm not posting it to be vulgar or obsene. :confused: My sisters, our mother, and I are noticing that our monthly cycles are almost 100% in sync with each other. We thought this was pretty weird. Mainly because our cycles used to be at completely different times of...

can anyone explain me the technique to decompose a random n-cycle into a bucnh of 2 cycles. Thanks in advance.

I'd imagine this will get relegated to theory developement, but here goes anyways. Looking at some of the charts for solor cycles it's clear to see the 11 year cycle. But this cycle seems to grow stronger with every repeation. It then resets to a low point a starts again. Now, I admit, I know...

Show that a 3 cycle(a,b,c) in Sn has order 3. Show that a product of disjoint transpositions (a,b)(c,d) in Sn has order 2. Find the order of (a,b)(x,y,z) in Sn, if this is a product of disjoint cycles. Apply this to tell the orders of all permutations in A4.

Hopefully this is a quick questions. I'm trying to describe what an attracting heteroclinic cycle is but not sure really how to describe it or what it means. I have a 3-dimensional population model x(t), y(t), z(t), which has a phase portrait that spirals from one equilibrium point to three...

The water and sedimentary cycles are interrelated in many ways, Would you please help me to identify the interactions between : sedimentary and tectonic, sedimentary and igneous, igneous and tectonic, water and tectonic ? Thank you very much in advance,

Could you please tell me their life cycles ? Does anyone of you work with worms daily ? I am sorry, i mean your research, your job ? Thank you very much

I observed with several electronic devices (primarily romote controls) which use infrared light emitting diodes (IR-LEDs) to send data is that with some, if the LED is viewed closely and carefully enough you can see a red light flash when being used. I know that IR light is invisible, and I'm...