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Problems with simplicial space

So I’m going through “Elementary Topology Problem Textbook” by Viro and all, and have problems with 23.3x paragraph which is devoted to simplicial schemes. More concretely I can’t tackle 23.4x problem which is also on an attached image. My thoughts on that are: So (open) simplex is just a set $ \{ c \in S […]

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A question about quadratic forms and eigenbasis

I have a quadratic form $5x^2 – 2xy + 5y^2 = 4$. The corresponding matrix ( for vectors $[x y ]^T$ ) is $$A=\begin{bmatrix} 5 & -1 \\ -1 & 5 \end{bmatrix}$$ Now I need to construct an orthonormal basis for $\Bbb{R^2}$ via the eigenvectors of $A$. The eigenvalues are $6$ and $4$, the corresponding […]

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Show that $f_{k}\longrightarrow f$ both weakly in $L^{p}$ and a.e. implies $|f_{k}|^{p}-|f|^{p}-|f_{k}-f|^{p}$ converges to $0$ in distribution

Let $1<p<\infty$, $f_{k}\in L^{p}(\mathbb{S}^{1})$, $f\in L^{p}(\mathbb{S}^{1})$ be such that $f_{k}\longrightarrow f$ weakly in $L^{p}(\mathbb{S}^{1})$. That is for any $g\in L^{p’}(\mathbb{S}^{1})$, where $p’=\frac{p}{p-1}$, we have $$\int_{-\pi}^{\pi}f_{k}gdx\longrightarrow\int_{-\pi}^{\pi}fgdx\ \text{as}\ k\longrightarrow\infty.$$ Then, the exercise state three parts (a) If $p=2$, show that $|f_{k}|^{2}-|f|^{2}-|f_{k}-f|^{2}\longrightarrow 0\ \text{in the sense of distribution}.$ (b) If $p\neq 2$, do we still have $|f_{k}|^{p}-|f|^{p}-|f_{k}-f|^{p}\longrightarrow 0\ […]

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Linux Mastering Development

Pass options to AWK script bypassing AWK

Can I get arguments that happen to be AWK options passed directly to a pure AWK script? Example script: #!/usr/bin/env -S awk -f BEGIN { if (ARGV[1] == “-h”) print “whoop” } I want ./myscript -h to print whoop. But AWK gets the -h first and prints its usage instead. Running ./myscript — -h works […]

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Linux Mastering Development

Increasing the level of user_cmd logs to audit.log

I’m working on a RHEL test box which I’m trying to set to mimic audit logging on a production box, which I do not have direct access to. I do have access to the production boxes logs and I noticed various user_cmd logs coming through. I’ve been focused on a single command, ifconfig -a that […]

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Linux Mastering Development

Delete files in a directory that have a hyphen in the filename

On my macOS system, I have a folder with 7,000+ images, and need to delete the images that have a hyphen in the filename. I have tried the following commands without getting a response after I cd into the directory (I am new to terminal): rm -rf — – $ rm ./- find . -type […]

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Is the hydroxide ion a B-L base in SN2 reactions ? What about in SN1?

In the question below, is B also correct ? The answer sheet tells me A is the right answer.

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Linux Mastering Development

How do I cut text from one file and replace it with text in another file?

So I have a text file, mac.txt, with one line that looks like this: 4a:38:61:e1:71:7c And I have a bash script, mask.sh, that simply changes my mac address: #!/bin/bash sudo ifconfig wlan0 down sudo macchanger -m 16:dx:0b:rc:4a:32 wlan0 sudo ifconfig wlan0 up And I’m trying to figure out how to write a bash script that […]

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Linux Mastering Development

Execute GUI programs as root without password

I know that in order to execute a CLI program using sudo, but without the need to typing your password, all you need to do is put user ALL = NOPASSWD: /path/to/your/program in /etc/sudoers, or even better in a file in /etc/sudoers.d. I’ve tried that and it works without any problem. However, for GUI application […]

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Can objects animated by the Animate Objects spell take psychic damage?

The Animate Objects spell description reads: An animated object is a construct with AC, hit points, attacks, Strength, and Dexterity determined by its size. Its Constitution is 10 and its Intelligence and Wisdom are 3, and its Charisma is 1. Its speed is 30 feet; if the object lacks legs or other appendages it can […]