Cyclic Definition and 309 Threads

https://en.wikipedia.org/wiki/Cyclic_model it brings to mind as well the many worlds theory the cyclic model is shown in a futuruma episode where the professor builds a only forward time machine(consistent with relativity) but he goes so far into the future that he ends in the past of the...

Its been formalized for ~15 yrs now by Steinhardt & Turok; Wiki sez it has problems, but will not elaborate. My concern is that despite their denial, their version of CC is built on branes, which are of course a Very speculative basis, since it originates in M-theory. Worse, S&T do not seem tb...

Homework Statement Let c be a pth root of unit where p is prime. Then the Galois group G(Q(c):Q) is isomorphic to Z_p*. Show that if there is some m that divides p-1, then there is an extension K of Q such that G(K:Q) is isomorphic to Z_q* Homework EquationsThe Attempt at a Solution I suspect...

Usually when gravitational lensing is discussed, the examples are those of matter bending spacetime into a positive curvature. https://commons.wikimedia.org/wiki/File:Gravitational_lens-full.jpg In these cases, distortion of light is clearly evident as images of galaxies from behind these...

Here is a circle with center $O$ :cool: Its is given that $\angle ABD=50$ & to find the magnitudes of $\angle ACD$ & $\angle ACB$ Now what I know is (Nerd) $\angle ACD=50$ due to the inscribed angle theorem, Can you help me to find the other angle which I don't know how to find ,stating the...

Here's the problem (Wait) (Sweating) So, Any Ideas on how to begin ? (Happy)

As the secant AE is moved downwards, the exterior angle remains equal to the same interior angle, with the result that as the secant becomes a tangent, the cyclic quadrilateral disappears and the exterior angle becomes equal to the angle in the alternate segment. pdf is attached.It is...

Homework Statement The problem- if $$\theta= tan^{-1}(\frac{a(a+b+c)}{bc})+tan^{-1}(\frac{b(a+b+c)}{ac})+tan^{-1}(\frac{c(a+b+c)}{ab})$$ , then find $$tan\theta$$ Homework EquationsThe Attempt at a Solution I tried to use these as sides of a triangle and use their properties, but other than...

Hey! :o Let $M$ be the abelian group, i.e., a $\mathbb{Z}$-module, $M=\mathbb{Z}_{24}\times\mathbb{Z}_{15}\times\mathbb{Z}_{50}$. I want to find for the ideal $I=2\mathbb{Z}$ of $\mathbb{Z}$ the $\{m\in M\mid am=0, \forall a\in I\}$ as a product of cyclic groups. We have the following...

Hey! :o Let $R$ be a commutative ring with unit and $M$ a $R$-module. If $M$ is a simple $R$-module, i.e., the only $R$-submodule are $O$ and $M$, then $M$ is cyclic and isomorphic to $R/J$ where $J$ is a maximal ideal of $R$. Could you give me some hints how we could show that $M$ is cyclic...

Hey! :o Let $Z\subseteq Z(G)$ such that $G/Z$ is cyclic. I want to show that $G$ is abelian. We have the following: $$Z(G)=\{g\in G\mid ga=ag \ \forall a \in G\} \\ G/Z=\{gz\mid g\in G\}, z\in Z$$ Since $G/Z$ is cyclic we have that $(gz)^n=1$. To show that $G$ is abelian, we want to...

http://physics.princeton.edu/~steinh/lambda16.pdf In this research article the authors suggest a cyclic universe, specifically one involving collisions of higher dimensional branes (an idea taken out of string theory), could indirectly explain why the observed cosmological constant is so small...

Hi everyone. So it's apparent that G/N cyclic --> G cyclic. But the converse does not seem to hold; in fact, from what I can discern, given N cyclic, all we need for G/N cyclic is that G is finitely generated. That is, if G=<g1,...,gn>, we can construct: G/N=<(g1 * ... *gn)*k> Where k is the...

In an article called "From big bang to big bounce" published in New Scientist in 2008, author Anil Ananthaswamy outlines two different theories that lead to our universe being cyclic. 1: "Cosmologists are still very much in the dark about dark energy. Some theoretical models speculate that the...

Hello all! If I have a group of order 20 that has three elements of order 4, can this group be cyclic? What if it has two elements? I am new to abstract algebra, so please keep that in mind! Thanks!

Its been suggested that the metastibility of the Higgs may lead to a new cyclic cosmology to replace inflation. http://arxiv.org/abs/1307.8106 Can anyone give a layman's guide to how this works and they propose to solve the problems of the big bang that inflation is supposed to solve: flatness...

Homework Statement An ideal diatomic gas is initially at temperature ##T## and volume ##V##. The gas is taken through three reversible processes in the following cycle: adiabatic expansion to the volume ##2V##, constant volume process to the temperature ##T##, isothermal compression to the...

εijk is the permutation symbol and cyclic permutations, for example 123→231→312, are always even, thus ε123=ε231=ε312=+1, but: ε132=ε213=ε321=-1 I understand the first 2, but ε321 is even, no? and also all this series is cyclic, it's not all even and...

Hello, I am looking at relating two situations under which cyclic energy is applied to a material. Condition 1: A material has been subjected to a force of 1G at 0.1Hz for 47 days. Condition 2: The same material has been subjected to a force of 4.5G at 60Hz for 3600Seconds. Is it possible to...

I've just watched the lecture of Penrose on his cyclic universe theory here: I fact I understood that he claims that any kind of matter dissapears in a couple of Googol years due to Hawking radition; so there is no matter left at the end, which leads to a reduced degree of freedom in terms of...

Homework Statement Show that the group of units in Z_10 is a cyclic group of order 4 Homework EquationsThe Attempt at a Solution group of units in Z_10 = {1,3,7,9} 1 generates Z_4 3^0=1, 3^1=3, 3^2=9, 3^3= 7, 3^4= 1, this shows <3> isomorphic with Z_4 7^0=1 7^1= 7, 7^2= 9 7^3=3 7^4=1, this...

Homework Statement If P: G-->C_6 is an onto group homomorphism and |ker(p)| = 3, show that |G| = 18 and G has normal subgroups of orders 3, 6, and 9. C_6 is a cyclic group of order 6. Homework Equations none The Attempt at a Solution I determined that |G| = 18 by taking the factor group...

I understand that an electron jumps to an excited state after absorbing a photon with the right energy (frequency) in photosystem 1 and exits the structure of the primary pigment, moves through different electron acceptors and returns to photosystem 1 (now at a lower energy state). What I don't...

I noticed that for cyclic graphs the number of edges is equal to the number of verticies. Is there a proof out there for this statement? Just curious... I was able to find the proof of the formula for finding the number of edges for complete graphs, I couldn't find anything related to the above.

I´m having a hard time proving the next result: Let T:V→V be a linear operator on a finite dimensional vector space V . If T is irreducible then T cyclic. My definitions are: T is an irreducible linear operator iff V and { {\vec 0} } are the only complementary invariant subspaces. T...

does glucose in its cyclic structure react with HI to form CH3-CH2-CH2-CH2-CH2-CH3? (open chain structure of glucose reacts with HI to form CH3-CH2-CH2-CH2-CH2-CH3)

I was hoping someone could check the following solutions to these 3 basic questions on cyclic groups and provide theorems to back them up. 1. How many elements of order 8 are there in C_{45}? Solution: \varphi(8)=4 2. How many elements of order 2 are there in C_{20}\times C_{30}? Solution...

In starting to look into the mathematical side of encryption , I note the heavy dependence upon modular arithmetic. What is the advantage is this? For example, why are finite cyclic groups and rings preferable? Note: I know zilch about programming; I am approaching it from the mathematical side.

Hello everyone, I was wondering if the following claim is true: Let ##G_1## and ##G_2## be finite cyclic groups with generators ##g_1## and ##g_2##, respectively. The group formed by the direct product ##G_1 \times G_2## is cyclic and its generator is ##(g_1,g_2)##. I am not certain that it...

Hello everyone, I am trying to understand the proof given in this link: https://proofwiki.org/wiki/Subgroup_of_Cyclic_Group_is_Cyclic I understand everything up until the part where they conclude that ##r## must be ##0##. Their justification for this is, that ##m## is the smallest integer...

Hey! :o Show that a cyclic group with only one generator can have at most two elements. I thought the following: When $a \neq e$ is in the group, then $a^{-1}$ is also in the group. So, when $a$ is a generator, then $a^{-1}$ is also a generator. Is this correct?? (Wondering) But I how can I...

A group is said to be indecomposable if it cannot be written as a product of smaller groups. An example of this is any group of prime order p, which is isomorphic to the group of integers modulo p (with addition as the group operation). Since the integers modulo p is a cyclic group (generated by...

List every generator of each subgroup of order 8 in $$\mathbb{Z}_{32}$$. I was told to use the following theorem: Let $$G$$ be a cyclic group of order $$n$$ and suppose that $$a\in G$$ is a generator of the group. If $$b=a^k$$, then the order of $$b$$ is $$n/d$$, where $$d=\text{gcd}(k,n)$$...

Homework Statement My online notes stated that it |g| = |G| where g is an element of G then |G| is cyclic. Can somebody help me understand why this is true?

Homework Statement Prove that if G is a cyclic group with more than two elements, then there always exists an isomorphism: ψ: G--> G that is not the identity mapping. Homework Equations The Attempt at a Solution So if G is a cyclic group of prime order with n>2, then by Euler's...

I am doing research on synthesis of copper nano particles. I would like to have a cyclic voltammetry (CV) of this material but I don't know how to prepare sample. Please tell me the ways to carry out this measurement. Thank you so much!

So I take <z10, +> this to be the group Z10 = {0,1,2,3,4,5,6,7,8,9} Mod 10 group of additive integers and I worked out the group generators, I won't do all of them but here's an example : <3> gives {3,6,9,2,5,8,1,4,7,0} on the other hand <2> gives {2,4,6,8,0} and that's it! but...

I have a homework problem where I have to solve for the displacements of the attached system using cyclic symmetry. To do this, I know that I have to find the harmonic load components of the system. One thing that my professor did not make clear (or if he did, I missed it) is how to determine...

Hey, this is not a homework question really but more a research issue my fellow students and I have run into. So basically, we have a project where we have cross-linked glucose oxidase to a polypyrrole surface on a gold electrode. The solution additionally contain PBS as well as ferricyanide...

I am wondering what kind of approaches people take to a cyclic symmetry analysis in FEM when you have multiple repeating features that don't divide to the same integer. Take the example below for example. I have a N_HOLES = 136 and I have N_SLOTS = 52. I am not sure what to do here. The...

Is there anything wrong with my logic and is there any way to further optimize this potentially long-running function? I've put a lot of comments to explain what's going on. template <typename ObType, typename BinaryFunction> bool isCyclic(const std::set<ObType> & G, BinaryFunction & op...

What are cyclic devices exactly? Are heat pumps and refrigerators both examples of cyclic devices? Also is a heat engine the same as a heat pump?

Hi, I can't understand why the statement in the title is true. This is what I know so far that is relevant: - A subgroup of a cyclic group G = <g> is cyclic and is <g^k> for some nonnegative integer k. If G is finite (say |G|=n) then k can be chosen so that k divides n, and so order of g^k...

Is CCC killed by BICEP2 or there is a way in which it survives?

in Z_3 x Z_4 find all elements of cyclic subgroups(<1,2) generated by (1,2) this is just confusing me :(

i am having a difficulity understanding the concept of cyclic subgroup generators. may I be given an explanation with examples if possible of how you determine whether a function is a subgroup and when they say list all cyclic subgroups eg <Z_10,+>. show that Z_10 is generated by 2 and 5

Homework Statement Derive the cyclic rule in thermodynamics. ##\frac{\partial p}{\partial T} \cdot \frac{\partial T}{\partial V} \cdot \frac{\partial v}{\partial p}=-1##Homework Equations The Attempt at a Solution OK, so I write out the total differential of ##p##: ##dp=\frac{\partial...

I am trying to understand a little further how software such as ANSYS implements cyclic symmetry in an analysis. A colleague of mine spoke to a support engineer and I think that he may have misinterpreted what was said. He is now under the impression that when we invoke a cyclic symmetry...

Our professor's notes say that "In general, in Hamiltonian dynamics a constant of motion will reduce the dimension of the phase space by two dimensions, not just one as it does in Lagrangian dynamics." To demonstrate this, he uses the central force Hamiltonian...

Homework Statement Prove that any group of order ##15## is cyclic. 2. The attempt at a solution I am looking at a link here: (http://www.math.rice.edu/~hassett/teaching/356spring04/solution.pdf) and I am confused why "there must be one orbit with five elements and three orbits with three...