All questions

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How to formulate exponential growth?

Here is my question: A rumour spreads out greatly via an university. 100 individuals have actually heard it by noontime, 200 by 1pm. The amount of individuals have actually heard it a) by 3pm b) 12.30pm c) 1.45pm many thanks beforehand.
2022-07-25 17:46:51
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subgroup structure of $S_4$

In the checklist of Young subgroups of $S_4,$ we locate $\langle(12)\rangle, \langle(13)\rangle, \langle(14)\rangle, \langle(23)\rangle, \langle(24)\rangle, \langle(34)\rangle,$ yet we do not locate $\langle(12)(34)\rangle, \langle(13)(24)\rangle,\langle(14)(23)\rangle,$ while they are all isomorphic to $S_2.$ I'm perplexed.
2022-07-25 17:46:51
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Does the 'closure of the interior' equal the 'interior of the closure'?

My solution is no because, $\mathbb{Q}^o = \emptyset$ therefore $\overline{(\mathbb{Q}^o)} = \emptyset$ yet $\overline{\mathbb{Q}} = \mathbb{R}$ therefore $\big(\overline{\mathbb{Q}}\,\big)^o = \mathbb{R}$. Is my instance deal with?
2022-07-25 17:46:51
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$K$-theory of smooth manifolds: continuous vs. smooth vector bundles

Suppose I have a smooth manifold $M$, and want to consider the $K$-theory $K^0(M)$. I could define this in the usual way (by taking the Grothendieck group of the monoid of equivalence classes of vector bundles) or in a 'smooth' way (considering only smooth vector bundles, and taking the Grothendieck group as usual). I haven't seen this discussed...
2022-07-25 17:46:51
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Weird integral with cylinders

I have this unusual indispensable to locate. I am in fact searching for the quantity that is defined by these 2 formulas. $$x^2+y^2=4$$ and also $$x^2+z^2=4$$ for $$x\geq0, y\geq0, z\geq0$$ It is an unusual object that has the aircraft $z=y$ as a divider panel for both cyndrical tubes. My troubles is that I can not locate the integration lim...
2022-07-25 17:46:47
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Need little hint to prove a theorem .

I have an iterative method \begin{eqnarray} X_{k+1}=(1+\beta)X_k-\beta X_k A X_k~~~~~~~~~~~~~~~~~ k = 0,1,\ldots \end{eqnarray} with initial approximation $X_0 = \beta A^*$ ($\beta$ is scalar lying between 0 to 1)converging to the moore-penrose inverse $X =A^+$. $\{X_{k}\}$ are sequence of approximations. Assume that after $sth$ iteration...
2022-07-25 17:46:47
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Value of a fraction

It it real that is ${a^2+c^2\over b^2+d^2}=1$ for $ad-bc=1$? I attempted replacing in $a={1-bc\over d}$ yet it is still a mess. (How do you ask Wolfram Alpha an inquiry similar to this where we ask it to compute something with an enforced problem?)
2022-07-25 17:46:47
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convergence of power series

We have given a power series $\sum\limits_{n=0}^\infty a_nx^n$ and $a_0\ne0$. Suppose the power series has radius of convergence $R>0$. Then we may assume that $a_0=1.$ Explanation: It's $$\sum\limits_{n=0}^\infty a_nx^n=a_0\sum\limits_{n=0}^\infty \frac {a_n}{a_0}x^n$$ But why do $\sum\limits_{n=0}^\infty \frac {a_n}{a_0}x^n$ and $\sum\...
2022-07-25 17:46:47
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power series expansion of the square root of a Hermitian matrix

Is there a power series development of the square origin of a Hermitian matrix, as a procedure to compute the square origin without taking the inverted or diagonalizing the matrix? I locate for scalar number $x$, $$\sqrt{x}=\sum_{k=0}^\infty \frac{(-1)^k \left((-1+x)^k \left(-\frac12\right)_k\right)}{k!}\qquad\text{for }|-1+x|<1$$, under ...
2022-07-25 17:46:47
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How to check if aptitude did something?

I've a CI build process during which I install a debian package from my local reprepro. I have a Makefile which does call aptitude to install the package from its own repository like this sudo aptitude -y install foobar >> aptitude.log 2>&1 Now it could happen that aptitude has conflicts, which can't be resolved or ...
2022-07-25 17:46:44
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An exercise involving the twisted cubic

One of the exercises in Hatcher's Harris's AG book goes as follows. Let $F_0 = Z_0 Z_2 - Z_1^2$, $F_1 = Z_0 Z_3 - Z_1 Z_2$, $F_2 = Z_1 Z_3 - Z_2^2$ (s.t. $\mathbb{V}(F_0, F_1, F_2)$ is the twisted cubic). Define $F_\lambda = \lambda_0 F_0 + \lambda_1 F_1 + \lambda_2 F_2$. Prove that for any $[\lambda_0, \lambda_1, \lambda_2] \neq 0$ and $[\mu_0,...
2022-07-25 17:46:44
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What exactly is an $R$-module?

From : "If $R$ is commutative, then left $R$-modules are the same as right $R$-modules and are simply called $R$-modules." The definition of left $R$-module: $M$ is a left $R$-module if $M$ is an abelian group and $R$ a ring acting on $M$ such that (i) $r(m_1 + m_2) = rm_1 + rm_2$ (ii) $(r_1 + r_2 ) m = r_1 m + r_2 m$ (iii) $1m = m$ (...
2022-07-25 17:46:44
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Are fibers of a fiber bundle the same as fibers of a covering space?

I was asking yourself exists any kind of distinction in between them? As all fibers are fiber packages, so undoubtedly the fibers coincide. Yet, after that could not there be some unique feature of a fiber of fiber package that isn't in covering rooms. As Hatcher does not specify fiber when he is defining what a fiber package is.
2022-07-25 17:46:44
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Solutions to $z^3 - (b+6) z^2 + 8 b^2 z - 7+b^2 = 0, b\in \mathbb R, z \in \mathbb C$

$z_1 = 1+i$ is a given solution. I guess what I have to find is $z_2$ and $z_3$ in $(z - (1 + i))(z - z_2)(z-z_3) = z^3 - (b+6) z^2 + 8 b^2 z - 7+b^2$. I tried to divide the polynomial by $(z - (1 + i))$, but that didn’t seem to work because of the $b$. According to the Complex conjugate root theorem $z_2 = \overline{z_1} = 1 - i$ is a solution ...
2022-07-25 17:46:44
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Show that the set of matrices such that $\det A \neq 0$ is open

Possible Duplicate: ¢ Like the title claims just how would certainly you show that the set of matrices such that $\det A \neq 0$ is open ? I can not also see where to start! As I can not imagine just how I would certainly locate a matrix 'round' of size $\epsilon$ for every single component of the set?
2022-07-25 17:46:40
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Why Linux syslog file does not follow the RFC3339 protocol?

Why Linux syslog documents:/ var/log/syslog does not adhere to the timestamp layout specified in the method ?
2022-07-25 17:46:40
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Analytical method for root finding

Is there a logical method to locate the roots of the list below formula? $$y = -\frac{1}{2}{x}^{2}-\cos(x)+1.1$$ I'm sorry for the unimportant inquiry, I'm new at mathematics!
2022-07-25 17:46:40
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Find the value of $A$, $n$ and $b$ if $y=A\sin(nt)+b$ has range $[2,8]$ and period $\frac{2\pi}{3}$.

A function with rule $y=A\sin(nt)+b$ has range $[2,8]$ and period $\frac{2\pi}{3}$. Find the value of $A$, $n$ and $b$. According to the teacher tip Do Dilations before translations But found translations first and I got $n$ , it is right? $\frac{2\pi}{3}n$=$2\pi$ $n=3$ But I don't know how to find $A$ and $b$. Many thanks.
2022-07-25 17:46:37
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Completeness of normed spaces

As earlier, I have actually obtained a solution from this website that Bolzano Weierstrass' theory holds true for limited dimensional normed rooms, yet except boundless dimensional rooms. This, specifically = > all limited dim. normed rooms are full (in the feeling that every Cauchy series merges (w.r.t. standard) ). Nonetheless, is it real t...
2022-07-25 17:46:40
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Relationship between functors

You will have to forgive me as I am very new to category theory - fifth of the way through Categories for a working mathematician. I'm interested in the following; Let $F:A \to B$ and $G:A \to C$ be full functors, where $A$,$B$ and $C$ are groupoids and $B$ has a single object. Let $G$ be such that $Gf=Gf'$ if and only if $Ff=Ff'$ where $f$ and ...
2022-07-25 17:46:33