How to show N (AB) ⊥ ⊆ N (B) ⊥ if A, B ∈ Mn?

I do not know how to approach this problem. Can anyone help me with that?

contest – What do Oleg Ershov's winning photos show?

So I came by two photos on BBC, and I can't understand what they are for, even on the contest website (I am not affiliated).

The first one (Fleswick Bay, England) is difficult to grasp due to an object which seems to be a pebble, which creates a kind of illusion; the second (Blafellsa, Iceland), I don't know if over a large area, or a macro shot.

enter description of image here
enter description of image here

real analysis – Given the sequence, how can I show that this series diverges?

I currently have some problems with this math exercise. I have to show that the series $ sum_ {n = 1} ^ infty b_n $ with $ b_n = sum_ {k = n + 1} ^ {2n} frac {1} {k ^ 2} $ diverges.

I think I have problems with this problem because I don't really know how to apply the quotient rule or the comparison test to the given sequence.

Could someone help me a little?

Thank you!

trezor – bech32 address does not show up in watch wallet only (using HWI descriptors)

First of all thank you for all the awesome tools. Especially Andrew Chow and Sjoors Provoost, for my use case.
Now I'm a little confused. A transaction that I sent from a mobile wallet to a watch wallet only in the kernel does not show up.
I am on the Bitcoin 0.19.01 kernel on Raspbian, running hwi.py v1.0.3 and using a Trezor One.

The steps I followed:
1. in the main Bitcoin GUI, create an unencrypted wallet without private keys (i.e. watch only)
2. unlock trezor using the pin challenge on wallet.trezor.io
3. export public keys from trezor using HWI

./hwi.py --fingerprint xxxxxx getdescriptors --account 0

returns the expected .json with 1 pkh, 1 sh (wpkh), 1 wpkh each to receive and internal (change?)

  1. create a .json file to analyze as an argument to import like this
'({"range": (0, 1000), "timestamp": "now", "keypool": true, "watchonly": true, "desc": "sh(wpkh((..../0/*...", "internal": false},   
{"range": (0, 1000), "timestamp": "now", "keypool": true, "watchonly": true, "desc": "sh(wpkh((..../1/*...", "internal": true})'

by copying and pasting the sh (wpkh lines in the getdescriptors output
5. launch importmulti jsonstring_above -> success and success for both xpub
6. rescanblockchain -> found all the addresses previously sent to my trezor, they all start with 3 – all the money is there, the watch only works with the wallet
UNTIL HERE ALL GOES GOOD

  1. in this portfolio, generated a reception address in bech32 format by default (starting with bc1)
  2. scanned the qr code with mycelium (can send a bech32 receipt) and sent the transaction (was only a small amount for the test)
  3. he entered the next block and was confirmed 3-4 times in 10 minutes
  4. went back to the core and ran rescanblockchain block_height_a_few_hours_back
    but there is no new transaction. Core didn't warn me when he hit the mempool or blockchain.
    The shipping address in mycelium is the same as that generated in core.
  5. tried to import the wpkh xpubs into the wallet using importmulti, also successful and successful, rescanblockchain, but still no sign of the transaction.

So my question: where's my money? 🙂 Can you help please?
How can the watch only derive from bech32 addresses simply by knowing the ads? And why doesn't he see / report the transactions he created himself? This creates a strange user experience. Also, the fact that the receiving address is not displayed / verified on the trezor makes the process a little scary. This seems to be the place where scammers would attack a noob like me.

This wallet.trezor.io does not support bech32 receiving addresses, it does not contribute to trust, although it is not directly related to my problem, I think.

I hope this makes sense. Thanks already for the help !!

Show that L (X) = AX where A is the matrix m × n and the matrix n × 1 is a linear transformation

Show that L (X) = AX where A is the matrix m × n and X is the matrix n × 1 is a linear transformation.

Why doesn't my linked share point list in MS Access show everything?

When I link to a Sharepoint list in MS Access, it doesn't show me everything in the list. However, when I import the same list, it shows me everything. When importing a list, there is an option to select "Items to import" and I have set it to "All documents". I guess this is the problem, but this option does not appear when linking the list. If this is the problem, how can I change it?

spreadsheet function – Automatically hide / show rows – questionnaire

Hi there, I need help with my worksheet. I need to create a dynamic quiz and I need a code that allows me to automatically hide / show certain lines based on information from a cell. Example:

if c6 is "internally", show me line 7 but hide 8 at 107

if c6 is "External", hide all lines from 7 to 107

if c7 is "yes", show me line 8 but hide 9 to 107

if c7 is "No", show me line 8 but hide 9 to 107

if c8 is "Critical", show me line 9 but hide 10 to 107

if c8 is "Important", show me line 9 but hide 9 to 107

if c8 is "Regular", show me line 9 but hide 9 to 107

if c8 is "Other", show me line 9 but hide 9 to 107

if c9 is "Critical", show me line 10 but hide 11 to 107

if c9 is "Important", show me line 10 but hide 11 to 107

if c9 is "Regular", show me line 10 but hide 11 to 107

if c9 is "Other", show me line 10 but hide 11 to 107

etc.

can anyone help me?

livestream – Facebook Live does not show a preview on the page

I have a Facebook business page. When you create a live video using the Facebook Page app, on the page, it only displays a text description of the post. It is not even clear that this is a live video – it looks like a regular video has been published.

How can I get him to publish a full preview of a live video on the page where the broadcast originates from?

real analysis – Show that a subsequence is a subset of the original sequence

My main question is the 4th point, but I hope you can clarify some things for me along the way.

The definition of a sequence says that a function $ a: mathbb {N} to S $ is a sequence on a set $ S $, denoted $ (a_n) $.

  1. Can i freely restrict the area of ​​function $ a $ and still call it a sequence? In particular, a) is it valid to define $ a_n $ on a finite subset of $ mathbb {N} $ b) on an infinite subset of $ mathbb {N} $?

Let's say that at each term in the sequence $ (a_n) _ {n in mathbb {N}} $, I have to define a new sequence from there. I first define a sequence $ (m_k) $ who maps $ {k in mathbb {N}: k geq n } to mathbb {N}, forall n in mathbb {N} $ with $ m_k <m_ {k + 1} $ (assuming affirmative on question 1b because the domain is an infinite subset of $ mathbb {N} $). Then, like $ (a_ {m_k}) $ is the composition of the sequence $ (a_n) $ and the increasing sequence $ (m_k) $, by definition $ (a_ {m_k}) $ is a subsequence of $ (a_n) $.

  1. Is it a good way to show that these new sequences $ (a_ {m_k}) $ are subsequences?

A set of points defined for the sequence $ (a_n) $ East $ left {a_n: n in mathbb {N} right } $.

  1. How do you define a set of points for a subsequence $ (a_ {m_k}) $? East $ forall n in mathbb {N}, left {a_ {m_k}: k geq n right } $ well?

Assuming yes on question 3, the main question is:

  1. How to prove this $ forall n in mathbb {N}, left {a_ {m_k}: k geq n right } subseteq left {a_n: n in mathbb {N} right } $? In other words, that the set of points defined for a subsequence is a subset of the set of points in the original sequence. I think i should take a term off $ left {a_ {m_k}: k geq n right } $ and deduce that its also in the whole $ left {a_n: n in mathbb {N} right } $, but I don't know how to do it rigorously.

To give you context on my questions, I want to show that $ sup { left {a_n: n in mathbb {N} right }} geq sup { left {a_ {k}: k geq n right }} $. Given that $ (a_n) $ is bounded, defines $ left {a_n: n in mathbb {N} right } $ and $ left {a_ {k}: k geq n right } $ are delimited. Having $ left {a_ {k}: k geq n right } subseteq left {a_n: n in mathbb {N} right } $ I would prove the supremums as in the question Prove the supremum of a subset is smaller than the supremum of the whole.

[ Politics ] Open question: Why is AOC co-hosting a drag queen show?

She is a politician and it makes her look like a sticky party girl. What's wrong with this woman?