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Questions tagged [transfer-theory]

For questions about the transfer homomorphism in group theory and its applications.

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Convert from Incidence Matrix to State-Space, and then to Transfer Function

There is some scheme for low-pass filter: https://en.wikipedia.org/wiki/Low-pass_filter#/media/File:1st_Order_Lowpass_Filter_RC.svg When i use Graph Theory, i get Incidence Matrix for this scheme. ...
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Finding the argument of a complex function

I've the following transfer function: $$H(s)=\frac{1}{as^3+bs^2+cs+1}$$ Where $a,b,c$ are all real and positive. How can I find $\arg(H(i\omega))$? And I know that $\omega\ge0$ What I did: $$H(...
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How do discrete factional order functions look like?

A fractional order transfer function looks like this $$ \frac{Y}{U}=\frac{b_ns^{m\alpha}+\dots+b_1s^{\alpha}+b_0}{a_ns^{n\alpha}+\dots+a_1s^{\alpha}+a_0} $$ where $\alpha \in (0,1)$ and it is often ...
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Sizes of cycles of an element on a quotient group

I'm reading a paper on Transfer and Fusion in finite groups, and I've come across a lemma in which we: " Let $x \in G$ and let $n_1 , ... , n_r$ be the sizes of the cycles of $x$ on $\Omega$ ... " ...
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How can I design a suitable controller for this given system?

How can I design a proportional controller to make closed loop transfer function stable? Parameter of the P controller is $$P[z]=K_P$$ Closed loop transfer function of the system is shown below. In ...
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190 views

How can I determine the transfer function of this servomechanism system?

How can I find transfer function of the given servomechanism system with input $V$(voltage) and output $θ_L$(angle of the load). Schematic of the system is given below. Schematic of the ...
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80 views

Does really the dirac impulse help to find the transfer function of an electronic system?

Is the following statement is true: By measuring the response of a impulse or step disturbance to a physical process we can determine the system transfer function and model or optimize the ...
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Who discovered that normalizer of an abelian Sylow $p$-subgroup controls $p$-transfer?

Theorem: Let $G$ be a finite group and let $P\in Syl_p(G)$ and assume $P$ is abelian. Then $N_G(P)$ controls $p$-transfer. I wonder who discovered above theorem? Is it due to Burnside?
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291 views

Conversion from state space back to transfer function in octave.

I'm having problem converting a transfer function to state space and then going back to the same transfer function. I did a little experiment: ...
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1answer
103 views

Existance of a normal $p$-complement. (5C.12 Finite Group Theory, Isaacs)

Let $G$ be a finite group, $N$ normal subgroup with index in $G$ divisible by $p$ prime and suppose that a Sylow $p$-subgroup of $G$ is cyclic. Then $N$ has a normal $p$-complement. This is the ...
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136 views

proving a property of transfer function in the s-plane and the complex domain

For a given transfer function (in the s-plane) we've a general form that looks like: $$\text{H}\left(\text{s}\right)=\frac{\text{X}\left(\text{s}\right)}{\text{Y}\left(\text{s}\right)}\tag1$$ This ...
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Group with all Sylow subgroups cyclic (exercise 5C.4 of “Finite group theory”, Isaacs).

Let $G$ be a finite group and suppose that all Sylow subgroups of $G$ are cyclic. I have to prove that: If $m$ divides $|G|$ then there exists in $G$ a subgroup of order $m$. If $m$ divides $|G|$ ...
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Find and prove the conditions for which this manipilation of transfer functions hold (about poles and zeros)

Question: What are the conditions for which this way of solving hold? I've a transfer function that looks like (in the Laplace domain): $$\text{H}_\text{T}\left(\text{s}\right)=\frac{\text{Y}\left(\...
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370 views

Prove of transfer functions in the Laplace and complex frequency domain

When we analyse electric circuits we often use transfer functions. To calculate the poles and zeros of such a function can be done in different ways. When we look to a transfer function in the Laplace ...
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A question from Isaac's book “Finite group theory” about Transfer theory

Let $G$ be finite group and suppose that $P\in Sylp_p(G)$ and that $g\in P$ has order $p$. If $g\in G',$ but $g\notin P'$, Show that $g^t\in P'$ for some element $t\in G$ with $t\notin P$.($5.B1$) ...
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78 views

Find Frequency Transfer Function

I have undamped oscilator which is described with following equation: $$ \ddot{y}+\omega^2y=u $$ I need to find transfer function $$ H(s) $$ and freguency transfer function for $$ H(j\omega) $$ ......
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Problems in understanding a passage in the proof of Grün theorem for transfer

This is the statement of the theorem: Let $P$ a Sylow $p$-subgroup of $G$ and $Z$ a subgroup of $Z(P)$ that is weakly closed in $P$. Set $H=N_G(Z)$. Then $P\cap G'=P\cap H'$ and $P/(P\cap G')\simeq ...
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Transfer homomorphism: is this proof correct?

I'm doing a guided exercise to learn the transfer homomorphism. The preliminaries are these: Given a finite group $G$ and a subgroup $H<G$, let $\{ x_iH \}_{i\in I}$ be the set of left cosets of $...
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115 views

On the Transfer Homomorphism

I'm approaching the study of the transfer homomorphism between groups, and I found this exercise: Given a finite group $G$ and a subgroup $H<G$, the set of left cosets of $H$ in $G$ is written $ \{...
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How do I determine the transfer function of a plant?

I sitting here with a system which I have to determine the transfer function. The unit receives a velocity and position, and move towards that position with the given velocity. What kind of test ...
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157 views

Condition Butterworth polynomial

My course states that a polynomial is a Butterworth polynomial when it satisfies the following condition: $|B(j\Omega)|=\sqrt {1+{\Omega}^{2\,n}}=\sqrt {1+{(\omega/\omega_p)}^{2\,n}}$ I'm really ...
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500 views

MATLAB Feedback

I am trying to use the feedback function in matlab and for the most part I understand it. But I came across this syntax: [x1 x2] = feedback(sys1, sys2, 1, 1, -1); ...
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Showing that $ϕ(x)=x^n$ is a homomorphism from $G\to Z(G)$

Let $G$ be a group with $|G:Z(G)|=n$ then $\phi(x)=x^n$ is a homomorphism from $G$ to $Z(G)$. I guess it has a proof using transfer theory, I wonder whether it has an elemantary proof or not. Thanks....
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Manually trying to calculate output of an transfer function.

I am trying to calculate the output of an transfer function due to the input of an step, But some weird reason, I am only getting the inverse output, what Matlab says it should be. My transfer ...
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230 views

Schur's Theorem about the derived subgroup

(Schur) Suppose Z(G) is of finite index in G, then the derived subgroup of G is finite. We know Schur's lemma that says: Let |G:Z(G)|=m. Then the map g to g^m is a homomorphism from G into Z(G). We ...
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Schur's theorem in transfer theory

M.Isaacs’ Algebra a graduate course page 119 : (Schur). Let $|G:Z(G)|=m<∞$. Then the map $g↦g^m$ is a homomorphism from G into Z(G). Proof. In fact, we will show that this map is the transfer $v:G⟶...
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81 views

transfer evaluation lemma

Let $M$ normal in $H\subseteq G$ with $[G:H]<\infty$ and $H/M$ abelian, and let $T$ be a right transversal for $H$ in $G$, there exists a subset $T_0\subseteq T$ and positive integers $n_t$ for $t\...
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387 views

Analyse closed loop transfer function

I have a transfer function from $x_c$ to $x$ $ \dfrac{x_c}{x} = \dfrac{k}{s + k} $ And I want to analyse the stability and find the best possible value for k. I've tried to convert the closed loop ...
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What is the relationship between solvable, nilpotent and transfer homomorphism?

I know some facts such as: Nilpotent groups are solvable, $p$-groups are nilpotent, a finite group whose order is a product of distinct primes is solvable, and finite groups are nilpotent if and only ...
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An Intuitive Explanation of the Transfer Homomorphism

I just learned about the transfer homomorphism, and I am having trouble internalizing it. I am learning from 'A Course in the Theory of Groups', and I was hoping that perhaps someone had a more ...
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What is the relationship between Mackey's theorem in character theory and Mackey's theorem in transfer theory?

Here are the statements of the two theorems. The first statement I took from a paper I have been reading, but I believe can also be found in Isaacs' Character Theory of Finite Groups as an exercise. ...
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Easy proof of trivial fusion implies normal p-complement

Theorem: Suppose G is a finite group with Sylow p-subgroup P. Then the following are equivalent: The set K of elements of G of order relatively prime to p (the p′-elements) form a subgroup If A and ...