probability of 4 or 5 circles tangent to the central circle

Through a random sequential summation process, it is possible to add 4 or 5 circles tangentially to a central circle. All circles of the same radius. What are the odds for 4 or 5 circles?

A randomized central limit theorem

Leave $ X_k $, $ k = 1, 2, points $, be a sequence of i.i.d. random variables with second finite moments. Also leave $ N_k geq 1 $, $ k = 1, 2, points $, be a sequence of random variables that take integral values, so that $ lim_k N_k = infty $ a.s .. Also, suppose that each $ N_k $ is independent of the $ X_k $& # 39; s.

Yes $ S_k: = sum_1 ^ {N_k} X_k $, it follows that $ (S_k – mu N_k) / sigma sqrt {N_k} $ converges in distribution to the standard normal variable
(where $ mu = mathbb {E} (X_k) $ Y $ sigma ^ 2 = mathbb {V} (X_k) $) how $ k to infty $?

taghelper is not processed when you publish it as a standard .net dll and is used in the central web application .net

I am writing an core taghelper dll.

I have a project that launched taghelper dll,
If I do this project .net core project.
when I reference it in another major .net project … Intellisense can recognize this taghelper.
and the taghelper is processed and processed correctly.
if I do the first project to the standard .net project. Intellisense cannot recognize this taghelper.
and the taghelper is not processed or processed at all.

Anyone know how to overcome it?

Group theory: when is the next pre-order in the set of central elements of order 2 a total pre-order?

Leave $ G $ Be a finite of 2 groups. We denote by $ S $ the set of central elements of $ G $ of order exactly $ 2 $. The relationship $ a leq b $ if there is an endomorphism of $ G $ sending $ b $ to $ to $ define an advance order in $ S $. It is easily seen that this advance order is not a partial order (consider the Klein group of four groups). What 2 groups is this preorder total for?

It's true for abelian $ G $. It's true for $ G $ of maximum class (because there is a single central element of order exactly 2). For intermediate nilpotency class groups, it can be true or false, e.g. the property is not true for the group with GAP ID (16, 3) but is true for the group with GAP ID (16, 4). It can be seen using the following Sage code

    g = gap.SmallGroup(InsertGAPIDhere);
    checker1 = True;        
    list1 = gap.AsList(gap.Centre(g));
    list2 = gap.AsList(gap.AllEndomorphisms(g));
    for a in list1:
        for b in list1:
            if gap.Order(a) == 2 and gap.Order(b) == 2:
                checker2 = False;
                for m in list2:
                    if gap.Image(m, a) == b or gap.Image(m, b) == a:
                        checker2 = True;
                checker1 = (checker1 and checker2);
    print(checker1); – Did the central Bitcoin database disappear after the error, no more free disk space? How can I recover my bitcoins?

Then I got into this situation.

I have a central Bitcoin wallet, which was updated and fully synchronized. Two days ago I tried to restart it, but when I tried to turn off my laptop I received a notification that I had no more free disk space, so the Bitcoin kernel automatically shut down. The day after I started my laptop again and the program disappeared from my startup taskbar and I had to search it manually in the program files. To my surprise, when I opened my wallet, I had to restart the synchronization from the beginning again. Not only that, all my database directory disappeared from the% appdata% bitcoin folder! It all started from the beginning.

Of course I couldn't because I didn't have more free disk space. Now the strange thing is that all that space on my hard drive went to the bitcoin database directory. But if my files are gone and I still don't have free disk space, where are they now? Are they stored elsewhere or hidden? Or did my hard drive crash? If they had left permanently, I should have had free disk space again.

How can I solve this and recover my bitcoins? Please help, I'm going crazy since I'm afraid I won't be able to recover them since all my data files are gone.

electrum: how do you transfer your central Bitcoin wallet while synchronizing?

Follow this guide.


  • Download Electrum and verify the signature to show that it was not modified in transit. Create a new standard wallet and choose "Create a new seed". Electrum will give you a seed phrase that you should write on paper.

  • If you use Bitcoin-Qt, click Window -> Console.

  • If your wallet is encrypted, use this command to decrypt it for 5 minutes (300 seconds):

walletpassphrase your-wallet-passphrase 300

If addresses with balance are known:

  • Use the dumpprivkey command to obtain the private key. Repeat for as many bitcoin addresses as you have money in them.

If the addresses with balance are not known:

  • Use the dumpwallet command to get all the private keys of the wallet.
dumpwallet path/to/exported-wallet.txt
  • In the Electrum window, click Wallet -> Private keys -> Scan. Paste the Bitcoin-Qt private keys here. Verify that the resulting transaction is fine and click Transmit to sweep from the addresses in Bitcoin Core to the Electrum wallet.

    • If the address generated from the private key is incorrect, in the Clear private keys in Electrum dialog box, click on the Information box in the upper right corner. It will instruct you to prefix your private key so that the correct address is generated. For example, if your address starts with 3, use p2wpkh-p2sh:(your-private-key).

Warning: make sure the Electrum wallet is not a watch-only wallet. The title bar of the Electrum window should not say (just look).

Authentication: Possible recovery of public / private identity after a commitment without a central authority?

I have been thinking about P2P systems that use asymmetric keys and I have wondered if there is any way to retrieve an identity if it is compromised using some type of trusted network.

This seems to be a big problem compared to a normal system (which uses a central authority) that can eliminate the intruder's access and restore control of the account to the real owner (Digicert, Facebook, Twitter, etc.).

What happens if a master key was generated and used to create a subkey? Then, using more than 16 random bytes, the private component of the master keys could be encrypted. The owner could choose more than 5 nodes in the network (friends?) To store parts of the secret and erase their knowledge of those bytes.

The subkey would be the identity of the user (with his own AES password that protects the private part). If this client is stolen, forget your password or someone steals your private subkey component, we could use the pairs to restore the master key and revoke this subkey.

I am not sure how this would work, apart from the client sending a request to each node and verifying the client through some out-of-band form (phone call? Text?) Before sending your part of the master key password .

Would this work? Are there existing solutions for this problem?

How to design a central Java module with an Android GUI layer at the top

How can I use Java modules in an Android application repository? In particular, what directory structure should I use?

I have a project in mind for which I would like to have a central Java 9 module independent of the GUI (which could be distributed independently) and an Android GUI layer at the top.

I created a new IntelliJ project using the & # 39; Android> Empty Activity & # 39 ;, template that created an overwhelmingly complicated directory structure:

directory structure

Where would you put in this directory structure the central module, which could be added, for example, as a git submodule? At the same level as app? E.g.:

enter the description of the image here

Or within app/libs?

Central coordinate of 2D shapes in Pythonista

I am creating 2D shapes defined by paths in Pythonista with the Scenes module, for example, a filled arc (circular cut) or trapezoid

What I find is that, instead of being anchored by the point (0,0) in relation to the coordinates used at the time the route was defined, these ShapeNodes are always anchored to a point in their center.

To rotate and place these shapes correctly (that is, to line up next to each other), I need to know what algorithm is used to define their centers.

For a trapeze, I guess it's just the average of the four vertices

For a slice of cake, it can be based on the vertices or even a more complex formula

Edit: after some experiments, I am beginning to think that it is only taking the center of the bounding box.

master page: fixed layout or central homepage -SharePoint online

Use a page layout, you can modify the blank web part page layout and keep only the center panels

<%@ Page language="C#"   Inherits="Microsoft.SharePoint.Publishing.PublishingLayoutPage,Microsoft.SharePoint.Publishing,Version=,Culture=neutral,PublicKeyToken=71e9bce111e9429c" %>
<%@ Register Tagprefix="SharePointWebControls" Namespace="Microsoft.SharePoint.WebControls" Assembly="Microsoft.SharePoint, Version=, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %> <%@ Register Tagprefix="WebPartPages" Namespace="Microsoft.SharePoint.WebPartPages" Assembly="Microsoft.SharePoint, Version=, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %> <%@ Register Tagprefix="PublishingWebControls" Namespace="Microsoft.SharePoint.Publishing.WebControls" Assembly="Microsoft.SharePoint.Publishing, Version=, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %> <%@ Register Tagprefix="PublishingNavigation" Namespace="Microsoft.SharePoint.Publishing.Navigation" Assembly="Microsoft.SharePoint.Publishing, Version=, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>






if(typeof(MSOLayout_MakeInvisibleIfEmpty) == "function") {MSOLayout_MakeInvisibleIfEmpty();}


You can use CSS to align the center with your main DIV

#s4-bodyContainer {
    top: 0;
    bottom: 0;
    left: 0;
    right: 0;
    margin: auto;