Cyclic Definition and 309 Threads

I'm getting myself confused here. If my relativistic Lagrangian for a particle in a central potentai is L = \frac{-m_0 c^2}{\gamma} - V(r) should \frac{d L}{d \dot{\theta}} not give me the angular momentum (which is conserved)? Instead I get \frac{d L}{d \dot{\theta}} = -4 m...

To begin, and believe me, it will become apparent, I have no training or education in this field. I do however find it fascinating. Can someone with a greater understanding please tell me if my ideas are laughable or feasable? Has anybody else proposed these ideas? Okay, so...

Homework Statement I have got a question that might be easy for you. But, not for me. I have attached a pic. Please tell me if the quadrilateral inside the circle is a cyclic quadrilateral or not. If it is, then please explain how to prove that it's opposite angles sum up to 180 degrees...

Hi, Can anyone explain the difference between axisymmetric and cyclic symmetry boundary conditions? Isn't it the same i.e. bith cyclic symmetry and axisymmetric?

Lets us say we are doing a vibration analysis of a structure with cyclic symmetry In very brief (as pointed out by AlephZero in one of his excellent reply) the whole motion can be represented by complex numbers which describe the motion of one segment. Now, my question is: 1)Is it...

I'm writing a paper for a philosophy elective on the Cosmological argument. One of my counter arguments is that a causal loop (treated as a paradox in the Cosmological argument in favor of a creator) is not a paradox if time is cyclic in nature rather than linear. I treat the fact that the...

Hi, Please can anyone explian what is cyclic symmetry? I'm new to this term and have encountered this in jet engine example Vishal

I'm wondering if anyone can help me with learning how to write groups as an external direct product of cyclic groups. The example I'm looking at is for the subset {1, -1, i, -i} of complex numbers which is a group under complex multiplication. How do I express it as an external direct...

If R is a finite ring and its additive group is cyclic, then R = <r> = {nr : n an integer} for some r in R. r^2 is in R so r^2 = kr for some integer k. Does k have to divide the order of R?

Homework Statement Calculate the diffusion coefficient (cm2/s) of ferricyanide if cyclic voltammograms conducted on a solution of 1 mM KClO4 + 5 mM K4Fe(CN)6 at scan rates of 1, 2, 5, 10, 20, and 50 mV/s, resulted in peak currents of 76, 100, 175, 243, 348 and 552 mA. The electrode used for...

To my intuition, I find more easy to believe that the universe is infinitely old and the big bag was just one of an infinite number of similar events in a larger universe, rather then the universe had a beginning. However, after watching many documentaries, and reading a lot of popular...

Homework Statement Show that the product of two infinite cyclic groups is not an infinite cyclic? Homework Equations Prop 2.11.4: Let H and K be subgroups of a group G, and let f:HXK→G be the multiplication map, defined by f(h,k)=hk. then f is an isomorphism iff H intersect K is...

Homework Statement Suppose a \in <b> Then <a> = <b> iff a and b have the same order (let the order be n - the group is assumed to be finite for the problem). Proof: Suppose a and b have the same order (going this direction I'm trying to show that <a> is contained in <b> and <b> is...

Homework Statement Let p be a positive prime and let Up be the unit group of Z/Zp. Show that Up is cyclic and thus Up \cong Z/Z(p − 1). The Attempt at a Solution What do they mean by the unit group? Is that just the identity? Is it the group [p]? I'm lost without starting the question...

1. Problem: Suppose a is a group element such that |a^28| = 10 and |a^22| = 20. Determine |a|. I was doing some practice problems for my exam next week and I could not figure this out. (This is my first post on PF btw) 2. Homework Equations : Let a be element of order n in group and let k...

What is wrong with assuming a fixed size universe, dividing it into 8 octants, and allowing the various octants to expand and contract against each other? In such a situation, could our octant be currently expanding and due to the pressure of our expansion cause one or more adjacent octants to...

Cyclic Fusion Reactor_Colliding Beams_Final Edition PDF file

Homework Statement Let G be an abelian group and let H and K be finite cyclic subgroups with |H|=r and |K|=s. Show that if r and s are relatively prime, then G contains a cyclic subgroup of order rsHomework Equations Fundemental theorem of cyclic group which states that the order of any...

I took an Intermediate Linear Algebra course all last year (two semesters worth) and we covered the CDT. My professor didn't teach it well, and I got my first B- in university because of it (didn't affect my GPA but still irritating). I didn't understand a lot of the canonical form stuff...

Homework Statement Consider the group of permutation on the set {123}. Is this group cyclic? Justify your answer Homework Equations The Attempt at a Solution I wrote out the cayley table for this group, and noticed that if we take (123)^3 = e . Seeing as we can get back to the...

Homework Statement For each integer n, define f_{n} by f_{n}(x) = x + n. Let G = {f_{n} : n \in \mathbb{Z}}. Prove that G is cyclic, and indicate a generator of G. Homework Equations None as far as I can tell. The Attempt at a Solution Doesn't this require us to find one element of G such...

Homework Statement Let G be a finite cyclic group and \ell(G) be the composition length of G (that is, the length of a maximal composition series for G). Compute \ell(G) in terms of |G|. Extend this to all finite solvable groups. The Attempt at a Solution Decompose |G| into its prime...

Hi, I'm currently doing a project and this topic has come up. Are there any known famous classes of polynomials (besides cyclotomic polynomials) that fit that description? In particular, I'm more interested in the case where the polynomials have odd degree. I know for example that the roots of...

Recently I have placed here the new - viable by my opinion Concept how to produce fusion. By some reasons I have decided not to file the patent application and so for discussing now I am placing here the description of Cyclic Reactor on base of that Concept. Ioseb (Joseph) Chikvashvili

I do not have any mathematical proof of this being possible, but am hoping to include equations soon. For now, it is purely conceptual. According to the Steinhardt-turok model, our universe is on a 3-brane located next to another 3-brane. I will assume this is the case. I am also presuming...

Homework Statement Is U13 cyclic? The Attempt at a Solution I know the elements are {1,2,3,4,5,6,7,8,9,10,11,12}. I have eliminated 1,2,3,4,5 and I am working on 6. I am doing it this way: 60=1 61=6 62=10 63=8 64=9 65=2 ..and so on, but I did, for example, 62=36-13=23=10...

Given a cyclic group of order [FONT="Georgia"]n, with all its elements in the [FONT="Georgia"]form : A, A2, A3, ..., A[FONT="Georgia"]n where A is an arbitrary element of the group. According to the [FONT="Georgia"]definition of group, "The product of two arbitrary elements A and...

I've been doing a project recently that requires a UB1250ZH Universal Battery rated 12V and 5Ah. Although I understand the concept of Ah, I'm having a difficult time in figuring out what the ratings for standby and cyclic use mean. For an example, it says - Standby Use: 12.6-13.8V, the...

This might sound like a silly question, but based on Definition: A group G is called cyclic if there is g\in G such that \langle g \rangle = G And if we take (\mathbb{Z},+) the set of integers with addition as the operation, then why is it considered cyclic? Because the problem I am having...

Homework Statement C3H6 cyclopropane C4H8 cyclobutane C6H12 cyclohexane Looking at their bond angles, which do you think is most stable? The Attempt at a Solution I'm trying to examine their shapes - triangle, sqaure and hexagon, but I don't know which shape is more stable...

http://pirsa.org/11040063/ Big Perimeter audience, appreciative interest, long question period after. He undercuts his critics (who said the concentric circles could have appeared by chance) by criticising their methods and makes at least one valid point. I would say that the critics still...

Suppose K= < x > is a cyclic group with 2 elements and H= S3 is symmetric group with 6 elements. Find all different cyclic subgroups of G= H x K. Now since K is generated by x with 2 elements, I have K= {1,x} and H= {1, (12), (13), (23), (123), (132)} What I am confused about is finding...

Homework Statement from Algebra by Michael Artin, chapter 2, question 5 under section 2(subgroups) An nth root of unity is a complex number z such that z^n =1. Prove that the nth roots of unity form a cyclic subgroup of C^(x) (the complex numbers under multiplication) of order n...

I wonder if someone has ever considered the following scenario: 1. "Standard" Big Rip model (phantom energy-dominated) 2. Close to the Big Rip, Universe becomes crossed with Cosmological horizons 3. Based on semiclassical approach, these horizons emit Hawking radiation 4. As a (slightly...

Let G be a group with |G|=4. Prove that either G is cyclic or for any x in G, x^2=e.

Homework Statement Let <a> be a cyclic group, where ord(a) = n. Then a^r generates <a> iff r and n are relatively prime. The Attempt at a Solution OK, let n and r be relatively prime. Then ord(a^r) = n. We need to show that for some j, there exists an integer k such that (a^r)^k = a^j...

Homework Statement 1) let <a> be a cyclic group of order n. If n and m are relatively prime, then the function f(x) = x^m is an automorphism of <a>. 2) Let G be a group and a, b be in G. Let a be in <b>. Then <a> = <b> iff a and b have the same order. The Attempt at a Solution 1) It...

Homework Statement As the title suggests - this is very simple, I only want to check. Let G be a cyclic group of order n. Then, for every integer k which divides n, there are elements in G of order k. The Attempt at a Solution Now, G = <a>, and a^n = e by definition. Let k be an...

Homework Statement Find the order of the cyclic subgroup of D2n generated by r. Homework Equations The order of an element r is the smallest positive integer n such that r^n = 1. Here is the representation of Dihedral group D2n = <r, s|r^n=s^2=1, rs=s^-1> The elements that are in D2n...

Homework Statement Pyridine and pyrrolidine react rapidly with dilute aqueous HCl to form the corresponding hydrochloride salts which are easily purified, isolated and stored in a charge. However, pyrrole, which is another nitrogen-containing heterocycle, does not form a hydrochloride salt...

What is the reaction mechanism for 1,3-dibromopropane + 2Na ---> cyclopropane? Thanks :)

how do branes emerge in cyclic universe?? ok so in the cyclic model of the universe...two branes are colliding and this is causing big bangs every few trillion years. this solves nicely the initial singularity and explains many things but i have two questions 1) how do these branes...

Homework Statement I need to prove that any isomorphism between two cyclic groups maps every generator to a generator. 2. The attempt at a solution Here what I have so far: Let G be a cyclic group with x as a generator and let G' be isomorphic to G. There is some isomorphism phi: G...

Well this isn't a homework question (I'm just trying to refresh my memory from the plane geometry I did in high school) and so, I was reading through cyclic quadrilaterals on wikipedia and I don't see how certain angles are equal. Here are two images taken from wikipedia...

Homework Statement Consider the set P15 of all integer numbers less than 15 that are mutually prime with 15: P15 = {1, 2, 4, 7, 8, 11, 13, 14}. It is a group under multiplication modulo 15. (a) P15 has six cyclic groups. Find them. my answer: <3>=<6>=<9>=<12>= {0, 3, 6 , 9, 12}...

Homework Statement Let G be a finite cyclic group of order n. If d is a positive divisor of n, prove that the equation x^d=e has d distinct solutions Homework Equations n=dk for some k order(G)=nThe Attempt at a Solution solved it: <g^k>={g^k, g^2k,...,g^dk=e} and for all x in <g^k> x^d=e...

This isn't some homework question its more theory based that I'm struggling with from class and we will probably have homework on it. If G is some arbitrary group, why is G Abelian <---> the factor group of G/Z(G) is cyclic? My professor mentioned something about one direction being trivial...

Thermodynamics: Cyclic Processes (solved) Sorry for the false alarm guys. It looked like I did use the wrong equation while finding the internal energy for case 1. referred to this. Thanks. https://www.physicsforums.com/showthread.php?t=412577 Given that 1 mol of ideal monoatomic gas at p= 1...

We had a discussion of Penrose's conformal cyclic cosmology last month: https://www.physicsforums.com/showthread.php?t=427567 His popular-level book Cycles of Time was published first in the UK, but is now available in the US. I got a copy and have read it, so I can report on a few of the...

Homework Statement G is a group. Let a,b be elements of G. If order(ab) is a finite number n, show order(ba) = n as well. Homework Equations order(a) = order(<a>) where <a> is the cyclic group generated by a. The Attempt at a Solution I do not know. I thought it may be related to...