## bitcoin core – Is the intex db downloaded from peers or generated locally?

When the user start the Bitcoin client for the first time, it will download the whole blockchain.
But what about the block index (blkindex.dat in older versions) ?
Then, does it depend upon the implementation (or version) or will the answer be the same for Bitcoin, Litecoin, or other random fork?
The version I talk about is an old fork that is still using blkindex.dat.

## algebraic geometry – Definition of locally generated by \$mathscr{S}_1\$ as an \$mathscr{O}_X\$-algebra

In Hartshorne’s “Alegebaic Geometory” 2.7,p160 (Dagger)

$$mathscr{S}$$is generated by $$mathscr{S}_1$$ as an $$mathscr{O}_X$$-algebra. “

but, I can’t understand mean of “locally”in this case.
Please tell me exact definition. Thanks.

## measure theory – Polish compact groups locally acting on standard Lebesgue spaces

Yes $$G$$ is a countable discrete group, then we can consider the change of Bernoulli $$2 ^ G$$. $$G$$ acts on $$2 ^ G$$ via shift, and leaving $$mu$$ be the product of $$(1/2, 1/2)$$-measure in each coordinate, then $$(2 ^ G, mu)$$ is a Borel probability measure, essentially free, preserving the action of $$G$$ on a standard Lebesgue space.

My question is whether there is an analogue for locally compact Polish groups. More specifically, if $$G$$ is a locally compact Polish group, $$G$$ admit a Borel probability measure, essentially free, preserving the action on a standard Lebesgue space?

## The patch is not applied to Drupal locally in DDEV built with Composer from the Drupal Git repository

I'm trying to create a local workflow so that I can review the kernel patches. I use DDEV for the local environment. Actions I have taken:

``````git clone https://git.drupalcode.org/project/drupal.git .
git checkout 9.1.x #I've chosen that way cuz with detached head I am unable to install composer packages
ddev composer install
ddev composer require --dev drush/drush
ddev . drush si standard --account-name=myuser --account-pass=mypassword --account-mail=my@mail.local --site-name="D9 Test"
ddev . drush en help_topics
ddev composer require --dev cweagans/composer-patches
``````

I then added the following part to the `composer.json` `extra` section

``````"enable-patching":true,
"composer-exit-on-patch-failure": true,
"patches": {
"drupal/core": {
"#3044059-48: Convert big_pipe, dynamic_page_cache, page_cache module hook_help() to topic(s) (https://www.drupal.org/project/drupal/issues/3044059)": "https://www.drupal.org/files/issues/2020-01-13/3044059-48.patch"
}
},
``````

When I run a `ddev composer update -vvv` now the first strange thing is that I get:

``````Gathering patches for root package.
Removing package drupal/core so that it can be re-installed and re-patched.
- Removing drupal/core (9.1.x-dev), source is still present in core
Deleting core - not deleted
``````

In the tutorials and documentation that I learned normally, the kernel is removed at this stage? Then I get an exception with `drupal/coder`

``````  - Updating drupal/coder (8.3.8 => 8.3.9): Executing command (/var/www/html/vendor/drupal/coder): git show-ref --head -d
Executing command (/var/www/html/vendor/drupal/coder): git status --porcelain --untracked-files=no
The package has modified files:
D coder_sniffer/Drupal/Test/Arrays/ArrayUnitTest.1.inc
D coder_sniffer/Drupal/Test/Arrays/ArrayUnitTest.inc
D coder_sniffer/Drupal/Test/Arrays/ArrayUnitTest.inc.fixed
D coder_sniffer/Drupal/Test/Arrays/ArrayUnitTest.php
D coder_sniffer/Drupal/Test/Arrays/DisallowLongArraySyntaxUnitTest.php
D coder_sniffer/Drupal/Test/Arrays/disallow_long_array_d7/DisallowLongArraySyntaxUnitTest.1.inc
D coder_sniffer/Drupal/Test/Arrays/disallow_long_array_d7/disallow_long_array_d7.info
D coder_sniffer/Drupal/Test/Arrays/disallow_long_array_d8/DisallowLongArraySyntaxUnitTest.2.inc
D coder_sniffer/Drupal/Test/Arrays/disallow_long_array_d8/DisallowLongArraySyntaxUnitTest.2.inc.fixed
D coder_sniffer/Drupal/Test/Arrays/disallow_long_array_d8/disallow_long_array_d8.info.yml
289 more files modified, choose "v" to view the full list
``````

i chose `yes` and continued and get the following output for the patch part:

``````- Installing drupal/core (9.1.x-dev): Source already present
REASON: Required by the root package: Install command rule (install drupal/core 9.1.x-dev|install drupal/core 9.1.x-dev)

- Applying patches for drupal/core
https://www.drupal.org/files/issues/2020-01-13/3044059-48.patch (#3044059-48: Convert big_pipe, dynamic_page_cache, page_cache module hook_help() to topic(s) (https://www.drupal.org/project/drupal/issues/3044059))
patch '-p1' --no-backup-if-mismatch -d 'core' < '/tmp/5eb75f842ba88.patch'
Executing command (CWD): patch '-p1' --no-backup-if-mismatch -d 'core' < '/tmp/5eb75f842ba88.patch'
patching file core/modules/help_topics/help_topics/core.performance.html.twig
``````

The output indicates that the file `core/modules/help_topics/help_topics/core.performance.html.twig` has been corrected. But the problem is that there is none `core.performance.html.twig` file. This does not exist at all.

## encryption – Best practices for locally storing long-term credentials in a desktop application?

I wonder how apps like Skype and Dropbox store credentials securely on a user's computer. I imagine the flow to do this would look like this:

3. Encrypt the token using a key which is simply a complex combination of certain static parameters that the desktop application can generate deterministically. For example something like:
``````value = encrypt(data=token, key=(os_version)+(machine_uuid)+(username)+...)
``````
1. Shop `value` in the keychain on OSX or Credential Manager on Windows.
2. Decipher it `token` when the application needs it by generating the `key`

So two questions:

1. Is what I have described remotely close to what a typical desktop application does that needs to store user access tokens for the long term?
2. How can a system like this be secured? Presumably, any combination of parameters that we use to generate the `key` can also be generated by malware on the user's computer. Are most apps just trying to make this key as hard to generate as possible and crossing your fingers so that no one can guess how it is generated?

## google drive – How to achieve a remote (shared) file system that can be mounted locally by team members?

The company must share certain documents.

GitHub is overkill; the marketing department doesn't want to know more about version control.

Sharing via Google Drive has so far been an ugly experience. It's good for sharing a file, but over time, everything becomes a mess.

I could create a LINUX cloud box and get everyone (on the mac) to use https://osxfuse.github.io/ who can mount a remote file system. But I don't really want the responsibility of maintaining an external server hosting critical files. I guess I could try to mount it in a sub-folder of my personal synchronization `google-drive` folder, in which case I would always have a backup. But it sounds like excessive engineering.

This is a tricky question to ask, as I know the answer could be an existing product, and product requests are generally frowned upon on SE. So please say that if your answer is a product suggestion, please comment on it.

How can I share the contents of one Google Drive account as a folder in the drive of another account?

## topology at.algebraic – Is a vector field deg 0 equivalent to being locally non-surjective?

Let $$X: mathbb R ^ n to mathbb R ^ n$$ be a $$C ^ 1$$ (or smooth) -vector, such as $$X (0) = 0$$ is an isolated zero. So we can talk about the mapping of $$0$$ for $$X$$.

For convenience, suppose $$0$$ to be the only zero of $$X$$. My question is, are the following equivalents?

1. $$X$$ has a degree of mapping 0 at the origin.

2. There is a $$epsilon_0> 0$$ such as $$X / | X |: {0 <| x | < epsilon_0 } setminus {0 } to mathbb S ^ {n-1}$$ is not surjective

or 2 & # 39 ;. There is a $$epsilon_0> 0$$ such as $$X / | X |: {x: lvert x rvert = r } to mathbb S ^ {n-1}$$ is not surjective for all $$0 .

I don't know if there is a counterexample for Is direction.

## algebraic geometry – T / F: finite module on reduced Noeterian ring whose reduction to each maximum ideal has the same dimension => locally free module?

In Hartshorne's algebraic geometry, there is an exercise (exercise 2.5.8 (3)): ($$Frac$$ means fraction field of an integral domain)

Assume $$X$$ is a reduced (noeterian) diet (WLOG $$X = Spec , R$$), and suppose $$M$$ is a coherent (i.e. qcoh + finite generated) $$mathcal O _X$$– (WLOG $$R$$-) module, with the property that,
$$varphi ( mathfrak p) = dim _ {Frac , ( mathcal O_ {X, p} / mathfrak p)} M _ { mathfrak p} otimes _ { mathcal O_ {X, p }} Frac , ( mathcal O_ {X, p} / mathfrak p)$$

is constant for all $$mathfrak p$$ in $$Spec , R$$. We would like to show $$M$$ is a local for free $$mathcal O_X$$-module.

This exercise is not too difficult when switching to the total fraction ring of affine $$R$$ and check what's going on at the generic point of each component, then use Nakayama; but which uses the theoretical generic points of the diagram harshly.

But this question seems to have a rather interesting meaning even for classical algebraic varieties (or arithmetic varieties, for example integer rings or Neron models) and in the more classical perspective, we only discuss the maximum spectra ; but in this case we cannot use the above argument (the condition that $$varphi ( mathfrak m)$$ is constant on the max spectrum is now lower than above!). I still believe that the result should always be true, so I would like to know proof of it.

## exploit – Buffer Overflow works locally but not remotely

So I made a simple buffer overflow challenge and tried to host it on a digitalocean droplet. The source of the challenge is below and is compiled using `gcc welcome.c -fno-stack-protector -no-pie -o welcome`.

``````#include
#include

int main(void) {
setvbuf(stdout, NULL, _IONBF, 0);
char name(25);
gets(name);
printf("welcome to pwn, %s!n", name);
return 0;
}

void flag() {
char flag(50);
FILE* stream = fopen("flag.txt", "r");
fgets(flag, 50, stream);
printf("%s", flag);
}
``````

Locally on the Docker, the challenge continues, I can use the exploit seen here. However, trying to use it over the netcat connection, it doesn't work! All the files I use to host the challenge can be found here. Any help or other advice would be appreciated. I spent much of the day confused about it.

Bonus question, why does the binary hang after finishing on the remote server until the user hits Enter? Maybe my `setvbuf` is incorrect? If someone could explain this, it would be great! I am fairly new to this area.

## ag.algebraic geometry – Grothendieck's decomposition of locally free sheaves

Let $$f: mathbb {P} ^ 1 rightarrow X$$ to be a morphism with $$X$$ a smooth projective algebraic variety of dimension $$n$$, then by Grothendieck $$mathcal {N} _ {f} = bigoplus_ {i = 1} ^ {n-1} mathcal {O} _ { mathbb {P} ^ 1} (a_i)$$, or $$mathcal {N} _ {f}$$ is the normal sheaf associated with $$f$$.

Is there a relationship between these $$a_ {is}$$ and the properties of morphism $$f$$? and what is the geometric interpretation ?.

.. for example if $$X$$ has a dimension $$2$$ so $$mathcal {N} _ {f} = mathcal {O} _ { mathbb {P} ^ 1} (a_1)$$ So $$a_ {1} = c_ {1} ( mathcal {N} _ {f})$$ (the first class chern of the normal sheaf) and it is the self-intersection of $$f ( mathbb {P} ^ 1) subset X$$ , but in higher cases $$c_ {1} ( mathcal {N} _ {f}) = sum_ {i = 1} ^ {n-1} a_i$$ and then i don't know what the relationship is between them … i want to find a geoemtric interpretation of those $$a_is$$ in $$f$$.
Anyone who could help me with this?