Cycles Definition and 169 Threads

Homework Statement I'm taking an online class this summer and the notes gave the proposition that Disjoint Cycles Commute with the following proof. Proof. Let σ and τ represent two disjoint cycles in Sn and choose some arbitrary j ∈ {1,2, . . . , n}. Since σ and τ are disjoint, at most one...

Hey! :o $$k_1=(a_1 \ \ \ a_2 \ \ \ \dots \ \ \ a_m)$$ $$k_2=(b_1 \ \ \ b_2 \ \ \ \dots \ \ \ b_n)$$ These cycles are disjoint if each $a_i$ is $\neq$ from each $b_j$. We remark that $k_1(a_i) \neq a_i$ and since $a_i$ isn't any of the $b_j$ that means that $k_2(a_i)=a_i$. Respectively...

In the lecture notes my university provided I am told that according to the first law of thermodynamics: ΣQ = ΣW (for a cycle) ΣQ = ΣW + ΔU (for a closed system) Does this mean that there is always a change in internal energy in a closed system? Or can ΔU=0? In other words, can ΣQ = ΣW, and if...

Homework Statement Theorem 8.1 of Dan Saracino: Let f ε S_{n}. Then there exist disjoint cycles f_{1},f_{2} .. in S such that f= f_{1}°f_{2}... In proving this theorem, it considers a finite group S_n={1,2,..,n} and chooses x_1 ε S_n. Then it defines x_2= f(x_1), x_3=f(x_2) and so on. The...

Okay, I am considering a cycle, where the working fluid is an ideal gas, with heat capacities Cv and Cp, the cycle consists of: isochoric increase in volume, adiabatic expansion back to initial pressure and a isobaric compression back to initial conditions. Questions: - q1) I am asked to...

Homework Statement In a diesel engine each cycle takes two revolutions and there are 6 cylinders. Homework Equations what does " each cycle takes two revolutions" mean and are there a relation or equation between cylinder number and calculation of engine power? The Attempt at a...

I read of the Milankovitch Cycles which explains the collective effects of changes in the Earth's movements upon its climate or in other words long term climate change. There is a flash animation here http://www.wwnorton.com/college/geo/egeo2/content/animations/18_2.htm I have also read that...

Prove that if G is a group and aεG, then o(a-1)=o(a) This is all I have so far: Assume G is a group and aεG. Because G is a group a has an inverse in the group, a-1 s.t. aa-1=e, which is also in G. <a>={an|nεZ}. |<a>| is the number of elements in <a> before it cycles back. Basically all I've...

I've got a couple of questions about reversible cycles: So if we have two gaseous systems and have a reversible cycle working between them, then the entropy generation within each gaseous system is zero, right? Do turbines execute reversible cycles? Thanks a lot for your help!

I'm a materials student, doing a bigger project on high temperature polymers (mostly polyimide). Right now I'm looking at the different curing cycles that are used in manufacturing and I'm wondering how these are determined (they usually consist of a series of temperature increases and holding...

I would imagine it could be difficult to make drastic changes to current nuclear technologies however with the current political and general population consensus about nuclear energy does it make sense to try a radically different approach to nuclear power production? Thorium has come up...

Given a length preserving bijection on n-bits uniformly at random, what is the expected number of cycles? Cycles being f(f(...f(x)...)) = x

Here is the graph in question: The edges in red are the paths that must be included in the cycle, since vertices a, k, e, and o have only degree 2. I listed all possible routes starting from vertex b, and showed that they all routes closes a cycle while leaving some vertex disconnected. Is...

I know there are no algorithms for finding one, but what are some guidelines? One tip I came up with is that if you have a vertex with degree 2, there is only one way to go through that vertex. Are there any others?

Homework Statement Determine Equilibrium points, limiting cycles, and their stabilities for the following equations r'=r(r-1)(r-3) θ'=1 The Attempt at a Solution So I know one equilibrium point is going to be (0,0) because r=0 is a limiting cycle (I believe), and that is simply a...

what does the positive and negative half cycles in an ac represent?

Homework Statement What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle 1 -------> 2 -------> 3 -------> 4 ------> 1 shown in the figure ? http://s3.amazonaws.com/answer-board-image/2d50cb1e-1bc6-4325-acf6-fe1df4f0a7b5.jpeg...

I have two questions: 1) For the example on the second page, I don't understand why they say \alpha\gamma\alpha^{-1} = (\alpha1 \alpha3)(\alpha2 \alpha4 \alpha7)(\alpha5)(\alpha6) instead of \alpha\gamma\alpha^{-1} = (\alpha1\alpha^{-1} \alpha3\alpha^{-1})(\alpha2\alpha^{-1} \alpha4\alpha^{-1}...

Homework Statement The trajectory of an arrow in space obeys the following system of equations: \dot{x} = y+(x^2+y^2-3)^2 (x^3-x+xy^2) \dot{y} = y+(x^2+y^2-3)^2 (y^3-y+x^2y) 1. Questions a) Derive an ODE for the radial coordiante r(t) = \sqrt[]{x^2(t)+y^2(t)} b) Show that the...

In the figure below, a damped simple harmonic oscillator has mass m = 300 g, k = 95 N/m, and b = 70 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)? I...

Homework Statement Taken from adkins Introduction to thermal physics A reversible heat engine is operated between two bodies, one of heat capacity C1 initially at temperature T1 and the other of heat capacity C2 initially at temperature T2. As the engine operates, the warmer body gradually...

We are using Sandler's Chemical, Biochemical, and Engineering Thermodynamics, and Smith & van Ness for our third year thermodyamics course. What is a good book to study power, heat and refrigeration cycles? Sandler's has a chapter dedicated to that, but it's not enough.

Homework Statement Let G be a graph containing a cycle C, assume that G contains a path P of length at least k between two verticies on C. Show that G contains a cycle of length at least √k. The Attempt at a Solution Since C is a cycle, there are two paths between a and b. If P...

Theorem: Prove that there exist $n$ edge disjoint Hamiltonian cycles in the complete graph $K_{2n+1}$. ---------------------------------------------------------------------------------- I have found two constructive proofs of this over the internet. But I would like to prove it...

This is about the basic thermodynamic cycle of the gas turbine (i.e. Brayton or Joule cycle), consisting of adiabatic compression, heat addition at constant pressure, adiabatic expansion, and heat rejection at constant pressure, and the standard ways of analysing this through Pressure-Volume...

You can blame Eddington for this one. I'm a retired electronics guy who now has time to read physics history and recent research also and am totally curious about the nature and most basic definitions of light photons. Eddington mentions in one of his essays in the '20's about "a meters...

Homework Statement Let a = (a1a2..ak) and b = (c1c2..ck) be disjoint cycles in Sn. Prove that ab = ba. The Attempt at a Solution Sn consists of the permutations of the elements of T where T = {1,2,3,...,n} so assume we take an i from T. Then either i is in a, i is in b, or i is in...

Litim and Satz have just addressed a question I've long wondered about. http://arxiv.org/abs/1205.4218 Limit cycles and quantum gravity Daniel Litim, Alejandro Satz We study renormalization group equations of quantum gravity in four dimensions. We find an ultraviolet fixed point in accordance...

Homework Statement Prove: If σ is a cycle of odd length, then σ2 is a cycle. Homework Equations N/A The Attempt at a Solution Proof: Assume σ is a cycle of odd length. Then let us model σ as (1 2 3 4 ... 2k +1) for some integer k [assuming here that the fixed elements of σ are...

Hello everyone, This is the life cyle of H.diminuta. My question is the 4th point. It says ingestion of these arthropods/fleas by rats or humans. Do rats actually eat these fleas, or do the fleas live on rats's skin and suck their blood and via that infects rats, same for humans. Is it...

Hi there, I'm doing homework right now (no this isn't a homework question!) and have basic questions on permutations and cycles. The concept seemed so simple in class and still seems simple, but the notation using lowercase Greek letters is confusing me. Do η and \theta and most of the...

I do not really understand the reason why Carnot ideal engine needs 4 cycles: isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression. Why cannot use only 2 cycles said isobaric expansion and isobaric compression, i.e. use a heat reservoir to expand the air...

Hello, I think it is very basic question and i could not able to figure it out anyhow. I have gone through an instrument material which working at 1000Hz. In that manual specifications, they have written about a setting 'cooling time --> 0-100 cycles'. there are also lot more options...

Homework Statement A three-step cycle is undergone by 3.8 mol of an ideal diatomic gas: (1) the temperature of the gas is increased from 210 K to 550 K at constant volume; (2) the gas is then isothermally expanded to its original pressure; (3) the gas is then contracted at constant...

In the time before Copernicus introduced the idea that the planets including the Earth orbit the Sun, how were the daily and annual cycles reconciled? I have always assumed that in the Copernican view the Earth orbits the Sun once each year. But not till today did I wonder about the 24-hour...

For example, what is the difference between Otto cycle, Carnot cycle, Diesel cycle other than that they have different compression/power strokes and ignition/exhaustion strokes?

I put the following review of Penrose's new book Cycles of Time on Amazon as "Light Pebble". Penrose puts forth an old idea, that the end of our universe is the start of a new one, in a beautiful new way. That is, eventually the universe will lose track of the scale of space and time. Then...

Please i need answer for this questions A- compare the Carnot cycle with the Ranking Cycle B- State The Steady Flow Energy equation and discuss the Origin and definition of each of the terms c- A vapour compression refrigeration using ammonia works at a condenser temperature of 40C and...

A 4 cylinder car has 4 Pistons The cycle is 1-2 : Adiabatic compression of air - then injects fuel 2-3 : Burn Fuel 3-4 : Adiabatic expansion of gas 4-1 : Exchaust / Replace with fresh air Homework Statement Diameter = 10 cm Minimum depth 1 cm Maximum depth 10 cm...

Entropy is that nature tends from order to disorder in an isolated systems. If a cycle always comes back to where it started wouldn't entropy decrease as well as increase over and over again? With that in mind and the fact that there really are no examples of an isolated system can the 2nd law...

I'm doing some really basic cycle homework, and in doing an exercise, I noticed something which is what i was probably supposed to notice but I want to know if my conclusion is correct. "all mappings from N to N (N=finite subset of naturals) that can be written with exclusively 1 or 2...

Hi everybody, I'm working on my thesis regarding hybrid combined cycles(HCC),that is combined cycles with supplementary firing on the bottoming cycle to improve the overall efficiency. My focus is on the possibility of use biomass as supplementary fuel in this types of plants. I'm looking around...

how do i plot the follwing S-N diagram, i am having trouble with what I am supposed to do with the 'cycles to failure' figures: stress amplitude ... cycles to failure (y axis)- .... (x axis) 170 ...... 3.7 x 10^4 148 ...... 1 x 10^5 130 ...... 3 x 10^5 114 ...... 1 x 10^6 92 ..... 1 x...

Does anyone know any sources (i.e. car manufacturers) that provide the exhaust air flow parameters for the some specific car engines? I need stats on various otto & diesel cycle engines (small compact car engines, large semi truck engines, etc.). When I say exhaust air flow parameters, I need to...

I'm studying the S_n groups and I've been calculating a bunch of compositions of m-cycles. I haven't, however, been able to find a general pattern in how to do this for arbitrarily complicated cycles. Are there any general composition rules or is there no other way to find the compositions...

I am examining the conjugacy classes of S_5. I know that two elements in S_5 are conjugate if and only if they have the same structure when expressed as products of irreducible cycles. Thus, the conjugacy classes are [(1 2 3 4 5)], [(1 2 3 4)], [(1 2 3)], [(1 2 3)(4 5)], [(1 2)(3 4)], [(1 2)]...

Homework Statement Suppose we have cyclic, prime-length \alpha = (a_{1}a_{2}...a_{s}). Prove that every power of \alpha is a cycle. Homework Equations None I can think of. The Attempt at a Solution I feel that I understand some of the intuition behind this problem. If any power of a cycle...

I have been reading and it came to my attention that it is more effective to generate electricity at a 60Hz cycle that it is at a 50Hz cycle. Yet only a minority of countries generate electricity using 60Hz. Why is it most countries generate their electricity at a 50Hz cycle when it is known...

More specifically, this question is oriented towards the Intel 8086. I have this manual that lists the number of clock cycles the 8086 requires to execute each of its instructions, prefixes, et cetera. My question is about repeat string instructions. The REP prefix is listed as 2 clocks...

I am wishing to perform an experiment in which i need to dip the specimen in a solution for 10 minutes and then out in air for next 50 minutes. This is to be done repeatedly but without using any electrical input. Suggest me with a mechanical method that can perform it for 24 hours and 20 days...