differential equations – Why do isolated large values of WorkingPrecision fail in NDSolve?

Executive Summary:

Getting an accurate answer often depends on setting the WorkingPrecision high enough. Once it is high enough, though, I would expect that its exact value shouldn’t much matter. But a dot at (x,y) in this graph indicates that a call of NDSolveValue in version 11.3 of Mathematica failed with a PrecisionGoal of Infinity, an AccuracyGoal of x, and a WorkingPrecision of y (with y >= x):

bad working precisions

So the WorkingPrecision must exceed the AccuracyGoal by at least a few digits; and accuracies greater than 33 are not achievable. But trying for an AccuracyGoal of just 11 fails when the WorkingPrecision is either 46 or 65 — which is puzzling. For an AccuracyGoal of 30, the WorkingPrecision has to be both large and even, while accuracies of 31 or 33 require the WorkingPrecision to be large and odd.

What is going on? How can I avoid selecting a value of WorkingPrecision that will fail, even though smaller values would succeed?

The details of the example:

I am using a technique of Gauss’s to compute isothermal coordinates on a Riemannian 2-manifold whose first fundamental form (E, F, G), in (u, v) coordinates, is

mE = (75 + 225 u^2 - 15 u^4 + 27 u^6 + 110 v^2 + 490 u^2 v^2 -
      22 u^4 v^2 - 18 u^6 v^2 - 45 v^4 + 153 u^2 v^4 +
      9 u^4 v^4 + 3 u^6 v^4)/2;

mF = u v (-55 - 50 u^2 - 27 u^4 - 50 v^2 + 20 u^2 v^2 +  
          6 u^4 v^2 - 27 v^4 + 6 u^2 v^4 + u^4 v^4);

mG = (75 + 110 u^2 - 45 u^4 + 225 v^2 + 490 u^2 v^2 + 
      153 u^4 v^2 - 15 v^4 - 22 u^2 v^4 + 9 u^4 v^4 + 27 v^6 - 
      18 u^2 v^6 + 3 u^4 v^6)/2;

Gauss suggests that I define a complex-valued function q(r) of a real variable r that is determined by a first-order ODE. (For a fuller description of the technique of Gauss’s, see the Wikipedia page on the Beltrami equation.) The following function test solves the ODE to determine the isothermal coordinates of the point (s, t), setting thePrecisionGoal, AccuracyGoal, and WorkingPrecision to Infinity, x, and y:

test(s_, t_, x_, y_) :=
   {q'(r) == (((-mF - I Sqrt(mE mG - mF^2))/mE) /. 
                    {u -> q(r), v -> r}),
    q(t) == s}, q, {r, 0, t}, 
  PrecisionGoal -> Infinity, AccuracyGoal -> x,  
  WorkingPrecision -> y)(0)

I then call test for lots of pairs (x,y), recording which pairs generate warning messages:

bads(s_, t_) := Quiet(ListPlot(
  Reap(Do(Check(test(s, t, x, y), Sow({x, y})), 
             {x, 5, 40}, {y, x, 80}))((2, 1)),
  PlotRange -> All))

The graph above resulted from the call bads(1/4, 1/16).

I am not an expert in numerical analysis, and Mathematica’s machinery for solving differential equations is quite complicated. But the apparent existence of “unlucky” values for the WorkingPrecision is both mysterious and annoying. Can I do something better than, for example, trying both y and y+1 as values for the WorkingPrecision, to see if either succeeds?

arch linux – connecting bluetooth device seems to cause bluetooth daemon to fail

Running Arch Linux, bluez.

I honest to god can’t figure out what’s going on here. Here’s the result of trying to connect my headset with bluetoothctl.

Agent registered
[CHG] Controller BC:14:EF:64:0E:18 Pairable: yes
[bluetooth]# power on
Changing power on succeeded
[bluetooth]# devices
Device 30:21:72:56:31:6A CROSLEY CR8005
Device EB:06:EF:88:70:1B Mpow H7
Device 20:74:CF:14:D1:DC TREKZ Titanium by AfterShokz
Device 88:B8:D8:03:85:A3 JLab BT
[CHG] Device EB:06:EF:88:70:1B Connected: yes
Agent unregistered
[DEL] Controller BC:14:EF:64:0E:18 pupcomp [default]
Waiting to connect to bluetoothd...

When I attempt to connect with Blueman it DOES connect for half a second, and then gives me:

Connection to BlueZ failed

BlueS daemon is not running, blueman-manager cannot continue. This probably means there were no Bluetooth adapters detected or Bluetooth daemon was not started.

btmgt shows the dongle as powered, so im assuming its not a failure there.

hci0:   Primary controller
    addr BC:14:EF:64:0E:18 version 6 manufacturer 15 class 0x3c0104
    supported settings: powered connectable fast-connectable discoverable bondable link-security ssp br/edr hs le advertising secure-conn debug-keys privacy configuration static-addr phy-configuration 

I’ve seen similar threads in other places, but none of those solutions worked. I’ve tried reinstalling bluez, bluez-utils, blueman, pulseaudio-bluetooth and pulseaudio. This has not solved the problem. Hopefully the problem is obvious and I’m just missing it. It seems like some issue with the daemon, but I don’t know how to solve it.

Google Cloud Firebase API Connection Fail

We are using the Google Cloud Firebase API.
Please contact us because Firebase API access is not working properly at the time below.
There are concerns that problems will arise at the same time tomorrow.
I would like a quick confirmation.
-Occurrence time: September 19th 11:11 AM Korean time, September 18th 11:25 AM
Get back to me. ASAP

counting – ResetDirectory causes a fail on stored file names

Consider some directory dir with sub dirs and files. Our aim is to count the no of files in dir (not in sub-dirs, just the dir.)

names = FileNames();
Length@Select(names, FileType@# == File&)

There were in fact 2 files and 6 sub-dirs.

FileType /@ names // Tally
(*{{Directory, 6}, {File, 2}}*)

Now consider the following code

dir = "D:/rough";
names = FileNames();
Length@Select(names, FileType@# == File &)

Here even though we saved the file names in names, the count is 0. Why is this? Why is a directory reset affecting stored file names?

Update wordpress fail – There has been a critical error on your website

The error is caused because of the ‘Revolution Slider’ plugin.

The function create_function is outdated and shall be updated with the latest version.

Simply put – Update the Revolution Slider plugin through CPanel or FTP. It shall mostly solve the problem immediately.

Then you can try to see whether you are able to access the site or not.

Also as suggested perform the manual update to make sure everything is upto date – https://wordpress.org/support/article/updating-wordpress/#manual-update

fatal error – Critical fail on website

After updating the company site to 5.5 – I made a backup before – I started getting critical theme errors.
The site is https://credence.co.uk – you can see the error message here.

It says there is a fatal error: call to undefined function in header.php. If I remove header.php, the site loads, but obviously, it looks messed up as there is no header code.

Any ideas why updating to 5.5 messed up my theme? And why reverting to backups makes no difference?
Or if anyone that knows PHP better than me can help me fix the header file, I would be so thankful.

8 – Config import for certain items appears to fail. How do I fix this?

After synchronizing configuration from dev to staging, I would expect all changes to be imported and for a message to display, advising “There are no configuration changes to import”

Most changes have been imported but I am left with six items which seemed to have failed import. Or a least do not clear from the list of items for import.

I do not understand why the active configuration appears not be be updated by staged.

As well importing all, I have also attempted to import each item separately, without success.

As well as using the UI have also tried drush cim. Drush confirms that the configuration was imported successfully. But if I run drush cim again, the same 6 files remain.

Why does it appear that the import is failing and what should I do to fix it? Is my active configuration messed up somehow?

A screenshot and some code to illustrate the problem.

Via the UI

configuration items not imported

Via Drush

    (easable):sync$ drush cim
    | Collection | Config                                              | Operation |
    |            | block.block.schoolpwa_subtheme_bottommenu           | Update    |
    |            | block.block.schoolpwa_subtheme_mainnavigation       | Update    |
    |            | block.block.mainmenu2                               | Update    |
    |            | block.block.websiteswitcher                         | Update    |
    |            | core.entity_view_display.node.page.default          | Update    |
    |            | media_bulk_upload.media_bulk_config.pdf_bulk_upload | Update    |

     Import the listed configuration changes? (yes/no) (yes):

     (notice) Synchronized configuration: update block.block.schoolpwa_subtheme_bottommenu.
     (notice) Synchronized configuration: update block.block.schoolpwa_subtheme_mainnavigation.
     (notice) Synchronized configuration: update block.block.mainmenu2.
     (notice) Synchronized configuration: update block.block.websiteswitcher.
     (notice) Synchronized configuration: update core.entity_view_display.node.page.default.
     (notice) Synchronized configuration: update media_bulk_upload.media_bulk_config.pdf_bulk_upload.
     (notice) Finalizing configuration synchronization.
     (success) The configuration was imported successfully.
    (easable):sync$ drush cim
    | Collection | Config                                              | Operation |
    |            | block.block.schoolpwa_subtheme_bottommenu           | Update    |
    |            | block.block.schoolpwa_subtheme_mainnavigation       | Update    |
    |            | block.block.mainmenu2                               | Update    |
    |            | block.block.websiteswitcher                         | Update    |
    |            | core.entity_view_display.node.page.default          | Update    |
    |            | media_bulk_upload.media_bulk_config.pdf_bulk_upload | Update    |

     Import the listed configuration changes? (yes/no) (yes):

functional analysis – Open mapping theorem can fail if codomain is not Banach

Give an example of a Banach space $V$, a normed space $W$, a bounded linear surjective map $T: V to W$ and an open subset $G subseteq V$ such that $T(G)$ is not open in $W$.

Attempt: Consider $V= (C((0,1), Vert cdot Vert_infty), W= (C((0,1), Vert cdot Vert_1)$ and $T: V to V: f mapsto f$. Clearly $T$ is a linear surjection with $$Vert Tf Vert_1 = int_0^1 |f| le int_0^1 Vert f Vert_infty = Vert f Vert_infty$$

so $Vert T Vert leq 1$ and $T$ is bounded. Moreover, we have $Vert f Vert_1 leq Vert f Vert_infty$.

We now show that $G= B_infty(0,1)$ is not open for $Vert cdot Vert_1$. Indeed, suppose to the contrary that $0$ is a $Vert cdot Vert_1$-interior point of $G$. Then there is $epsilon > 0$ such that

$$B_1(0, epsilon) subseteq G = B_infty(0,1)$$

Thus, for $f in C((0,1))setminus {0}$ we have
$$Vert frac{epsilon}{2 Vert f Vert_1} f Vert_infty leq 1$$

I.e. $Vert f Vert_infty leq frac{2}{epsilon} Vert f Vert_1$ for $f in C((0,1))$. But then the norms $Vert cdot Vert_1$ and $Vert cdot Vert_infty$ are equivalent, which implies that $W$ is Banach. This is a contradiction.

Is my attempt correct?

SQL server backup fail “A system assertion check has failed”

I just installed SQL Server 2017 EVAL in a Windows Server 2012 R2 VM. Most default options.

Default installation folder. SYSTEM databases in default folder. User databases in the D: drive.
Created some databases, some users, installed Brent Ozar and Ola Hallengren scripts. Next thing I was configuring the backups on the E: and getting an error. So i tried to run manually:


and getting this error:

Location:    mediaWrite.cpp:603
Expression:  (m_pWriteBuffer->GetCurrentSize ()% GetBlockSize ()) == 0
SPID:        56
Process ID:  1104
Mensagem 3013, Nível 16, Estado 1, Linha 1
BACKUP DATABASE está sendo encerrado de forma anormal.
Mensagem 3624, Nível 20, Estado 1, Linha 1
Falha em uma verificação de asserção do sistema. Verifique o log de erros do SQL Server para obter detalhes. Em geral, uma falha de asserção é causada por bug do software ou danos nos dados. Para procurar danos no banco de dados, considere a execução de DBCC CHECKDB. Se você concordou em enviar despejos à Microsoft durante a instalação, um minidespejo será enviado. Uma atualização poderá ser disponibilizada pela Microsoft no último Service Pack ou em um Hotfix do Suporte Técnico.

Horário de conclusão: 2020-08-13T21:57:22.6904999-03:00

Is in Portuguese, and telling me to check the SQL Server logs, which point me to this dump file (1) where it have the same message but in english:

2020-08-13 19:07:27.81 spid54      Erro: 17066, Gravidade: 16, Estado: 1.
2020-08-13 19:07:27.81 spid54      SQL Server Assertion: File: <mediaWrite.cpp>, line=603 Failed Assertion = '(m_pWriteBuffer->GetCurrentSize ()% GetBlockSize ()) == 0'. This error may be timing-related. If the error persists after rerunning the statement, use DBCC CHECKDB to check the database for structural integrity, or restart the server to ensure in-memory data structures are not corrupted.
2020-08-13 19:07:27.81 spid54      Erro: 3624, Gravidade: 20, Estado: 1.
2020-08-13 19:07:27.81 spid54      A system assertion check has failed. Check the SQL Server error log for details. Typically, an assertion failure is caused by a software bug or data corruption. To check for database corruption, consider running DBCC CHECKDB. If you agreed to send dumps to Microsoft during setup, a mini dump will be sent to Microsoft. An update might be available from Microsoft in the latest Service Pack or in a Hotfix from Technical Support.
2020-08-13 19:07:27.81 Backup      Erro: 3041, Gravidade: 16, Estado: 1.
2020-08-13 19:07:27.81 Backup      BACKUP failed to complete the command BACKUP DATABASE DABOL12. Check the backup application log for detailed messages.
2020-08-13 19:13:11.98 spid54      **Dump thread - spid = 54, EC = 0x000000D63F84C160
2020-08-13 19:13:11.98 spid54      ***Stack Dump being sent to C:Program FilesMicrosoft SQL ServerMSSQL14.MSSQLSERVERMSSQLLOGSQLDump0035.txt

If I try to run this same command on the D: drive, it runs without any problems.


  1. After getting the errors a few times, I installed CU21, but the error persist.
  2. Both SQL Server and SQL Agent account have full control over E: drive. I went nuts and granted full control to everyone for the sake of testing.
  3. I was pretty sure that the databases weren’t corrupt, since I don’t get the same error when backuping to another drive and had just created them), but I run the DBCC CHECK anyway, and it’s everything ok.

Any thoughts?

(1) https://pastebin.com/0BhhMN6p


This VM is hosted on a XenServer, which I’m not a admin nor thus have any access.
After finding out that I can successfully perform the backup to drives C: and D:, but could not perform to E:, I decided to check the devices.

Drive E: FreeNAS iSCSI Disk SCSI Disk Device

Searching a bit more a found this reddit post (2) with the same problem as I, shedding some light on the problem.

This is a SQL Server Bug, a Windows bug, a Xensrv bug or a FreeNAS bug?

(2) https://www.reddit.com/r/sysadmin/comments/2ofo4k/help_with_an_iscsi_issue/

dnd 5e – Can a player choose to fail a spell’s ability check contest?

It has been established that a character cannot willingly choose to fail a saving throw. But can they willingly fail an ability check contest?

While most spells say that the target must succeed to fail a Saving Throw, Telekinesis states:

You can try to move a Huge or smaller creature. Make an ability check with your spellcasting ability contested by the creature’s Strength check

I wanted to cast this on the party rogue so they could get up to the second story window to sneak in; a rich man’s Levitate spell. Alternately, cast it on a fighter and help him chase around the flying monsters.

The obvious work around is to have them stand on an object that cannot contest the spell and lift them up, but then there is a chance of balance failing.

In the PHB, it talks about ability score contests:

Sometimes one character’s or monster’s efforts are directly opposed to another’s. This can occur when both of them are trying to do the same thing and only one can succeed, such as attempting to snatch up a magic ring that has fallen on the floor. This situation also applies when one of them is trying to prevent the other one from accomplishing a goal — for example, when a monster tries to force open a door that an adventurer is holding closed. In situations like these, the outcome is determined by a special form of ability check, called a contest.

This assumes that the two efforts are at odds. However in this case a contest would not be required as the characters are working together. But the spell description bypasses that and flat out says there is a contest; no mention of willing or unwilling.

So can my warlock give a boost easily, or is there a chance of failure?