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# Compass bar icons don't appear where expected

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I try to recreate the compass from Skyrim in Roblox and I stumbled upon a problem regarding quest icons.

I have already programmed the directions of the world and now I struggle to program quest markers. I have waypoints on the map and count angle between the player and said waypoint and then I try to place the marker in a right place of the compass. Nevertheless, the quest icons are shown in wrong places.

Here is the code for the general compass:

``````while true do
local delta = wait(1/60)
local look = camera.CoordinateFrame.lookVector
local look = Vector3.new(look.x, 0, look.z).unit
local lookY = math.atan2(look.z, look.x)
--print("Look", look)
local difY = restrictAngle(lookY - lastY)
lookY = restrictAngle(lastY + difY*delta*smoothness)
lastY = lookY
PositionIcons(look)
for unit, rot in pairs(units) do
rot = restrictAngle(lookY - rot)
if math.sin(rot) > 0 then
local cosRot = math.cos(rot)
local cosRot2 = cosRot*cosRot
unit.Visible = true
unit.Position = UDim2.new(0.5 + cosRot*0.6, unit.Position.X.Offset, 0, 3)
--print(unit, unit.Position)
else
unit.Visible = false
end
end
end
``````

Here is the function to place the icons in the compass GUI:

``````local function PositionIcons(look)
for WaypointIcon, WaypointPosition in pairs(WaypointPositions) do
local difWaypoint = math.acos(WaypointPosition:Dot(look)/(WaypointPosition.Magnitude * look.Magnitude))
local lookY = math.atan2(look.z, look.x)
local rot = restrictAngle(lookY - difWaypoint)
if math.sin(rot) > 0 then
local cosRot = math.cos(rot)
WaypointIcon.Visible = true
WaypointIcon.Position = UDim2.new(0.5 + cosRot*0.6, 0, 0, 0)
end
end
end
``````

The icon for GasStation is shown properly but as you can see the shop icon is on the right, while it should be on the left. Book and sign seem to be close to GasStation but they are far away on the right.

## What is a sufficient and necessary condition for a system of linear equations to have a unique integer solution?

Bézout’s theorem states that a linear diophantine equation $$ax+by=c$$ has integer solutions if and only if $$gcd(a,b)|c$$. Then is there a theorem regarding the existence of a unique integer solution for a system of two linear equations $$ax+by=c$$ and $$px+qy=m$$, where $$a,b,c,p,q,m$$ are positive integers?

Additionally, can the theorem be generalized to the condition where there are more than two unknowns?

## Indices without a given domain in sum notation.

I’m learning about normal modes right now and I have a question pertaining to the way the equations of motion are written vis-a-vis summation notation. The book defines the equations of motion of a system of $$n$$ masses attached to springs, whose displacements are $$q_j$$ as the following: $$underset{j}{sum} (A_{jk}q_j + m_{jk}ddot{q_{j}}) = 0$$My quandary is caused by the subscript $$k$$ that appears in the undetermined coefficients $$A_{jk}$$ as well as the masses $$m_{jk}$$. I just want to know what values of $$k$$ to use here in this equation in the general case. Since it’s not explicitly stated, I’m sure there’s an implicit understanding there.

Let’s take for instance $$n = 2$$. So, we have $$2$$ masses attached to springs and $$2$$ solutions for the displacements (from equilibrium) $$q_j$$ of each mass. Then we must have $$2$$ equations of motion. I’m assuming $$A$$ and $$m$$ are $$2 times 2$$ matrices and then is it the case – in this particular situation – that we have the relation $$delta_{jk}(A_{jk}q_j + m_{jk}ddot{q_j})$$? Such that our equations of motion become $$A_{11}q_1 + m_{11}ddot{q_{1}} = 0\ A_{22}q_2 + m_{22}ddot{q_{2}} = 0$$

If this is true, then for the case $$n gt 2$$ how do we treat the matrices $$A$$ and $$m$$? Do they just become $$n times n$$ matrices? Where the elements on the diagonal are the nonzero ones?

## Unity/C# Unable to access an instanced health system

I am having an issue with a health system I am making for my game. I have been at it for 3 days now and have not made much progress. For reference, I am following this tutorial by code monkey: Code Monkey Health Tutorial. The goal is to have two buttons, one for healing and one to damage the player, and a Text Mesh Pro UI Text to show the health of the player, just for testing purposes. Unlike the tutorial, the buttons and text are just on a canvas, not attached to the player, as I am setting it up as a form of a HUD system. also, forgive the formatting, during troubleshooting, I was more focused on trying to fix my issue and my code became a bit of a mess. Sorry for that.

I have three scripts

``````    using UnityEngine;

public class HealthSystem
{
private int _health;
private int _healthMax;

public HealthSystem(int healthMax)
{
this._healthMax = healthMax;
_health = healthMax;
Debug.Log("healthSystem Created");
}
public int GetHealth()
{
return _health;
}
public void Damage(int damageAmount)
{
_health -= damageAmount;
if (_health < 0) _health = 0;
}
public void Heal(int healAmount)
{
_health += healAmount;
if (_health > _healthMax) _health = _healthMax;
}
}

``````
``````    using UnityEngine;

public class GameHandler : MonoBehaviour
{
private HealthButtons _healthButtons;

private void Start()
{
HealthSystem _healthSystem = new HealthSystem(100);
Debug.Log("Health = "+_healthSystem.GetHealth());
_healthButtons.Setup(_healthSystem);
}
}
}
``````
``````using UnityEngine;
using TMPro;

public class HealthButtons : MonoBehaviour
{
[SerializeField]
private TextMeshProUGUI numberText;
private static HealthSystem _healthSystem;
private int intToStringHealth;

public void DamageButton()
{
_healthSystem.Damage(10);
Debug.Log(_healthSystem.GetHealth());
}
public void HealButton()
{
_healthSystem.Heal(10);
Debug.Log(_healthSystem.GetHealth());
}
public void Setup(HealthSystem healthSystem)
{
if (healthSystem == null) Debug.Log("healthSystem");
Debug.Log(healthSystem);
_healthSystem = healthSystem;
Debug.Log("Setup is running");
}
private void Update()
{
intToStringHealth = _healthSystem.GetHealth();
numberText.text = intToStringHealth.ToString();
}
}
``````

my issue currently is Im trying to create an instance of HealthSystem in GameHandler, which I am successful in, then pass the information to HealthButtons using _healthButtons.Setup(). This is where I become unsuccessful as I am getting a NullReferenceException error.

from my efforts of troubleshooting currently, I have determined I am not calling the instance correctly, but I do not want to use code monkey’s libraries. I have tried making all classes monoclasses and attaching them to game objects and using SerializeFields for all my variables, which does work, but I am not sure that is best practice as I do know linking everything up in the inspector can be a chore if something goes wrong.

This tells me the solution should be fairly simple, I am just not able to articulate the question into google to get the correct answer. It may be a bit overkill just to test a function, but I would like to understand what I am doing wrong and get better. Thank you very much for your help.

## Prove that there does not exists an estimator for which the risk is \$0\$.

Let $$lbrace mathbb{P}_theta rbrace_{thetain Theta}, Theta subset mathbb{R}$$, be an identifiable parametric family of distributions with common support, where card$$(Theta)geq 2$$. Consider the family of estimators $$Delta = lbrace delta(textbf{X}): mathbb{E}_theta delta^2 and the loss function $$L(theta,a)=(theta-a)^2$$. Prove that there does not exist an estimator $$delta(textbf{X})$$ for which $$R(theta,delta)=0,theta in Theta$$.

So I suppose that there exists an estimator $$delta(textbf{X})$$ for which $$R(theta,delta)=0,theta in Theta$$. Since the loss function is non-negative, then it concludes that $$delta(textbf{X}) = theta$$ almost surely. I don’t know if it is true, because I think that $$theta(textbf{X})$$ cannot take many values. If yes, then what can I do next to show the contradictory? I want to show that for all $$x$$ in $$Omega$$, $$f(x;theta_1)=f(x;theta_2)$$ so it contradicts the definition of identifiable parametric family, but I am not sure how.

## Proof that all Quotient Groups are Abelian- where is my error?

I’m having trouble finding the error in my proof:

Theorem: If H is a normal subgroup of G, then the quotient group G/H is abelian.

Proof: $$forall x, y in G$$, $$xy(yx)^{-1} = xyy^{-1}x^{-1} = e in H$$. By the lemma, $$H(xy) = H(yx)$$, thus $$HxHy= HyHx$$. This shows that the commutative property holds for all the elements in the quotient group G/H, therefore G/H is abelian.

Lemma: Let H be a subgroup of G. Then $$Ha = Hb iff ab^{-1} in H$$. Proof: We start with the $$Rightarrow$$ direction. $$Ha = Hb$$ implies $$a in Hb$$, thus $$a=hb$$ for some $$h in H$$. Therefore $$ab^{-1} = h in H$$. For the reverse direction, if $$ab^{-1} = h in H$$ then $$a=hb$$ for some $$h in H$$. Thus $$a in Hb$$, and since we also have $$a in Ha$$, $$Ha = Hb$$ (because cosets partition a group).

## PDF hyperlink has spaces, works in ArcGIS Pro but not on ArcGIS Online

The other option I’ve found is to create a new field using Arcade How To: Add PDF files as hyperlinks in ArcGIS Online Map Viewer pop-ups but I don’t know Arcade and I’m having trouble understanding the instructions. I don’t know if it matters, but not all the links are broken and not all of them are PDFs.

Is there a way to fix this in Map Viewer? Why do the links work in Pro but not AGOL? Do I have to go into my data and get new links?

## Before-skip alignment problems with Tasks package; particularly when nested within an enumerate list

When a `tasks` environment is positioned within an enumerate list, there is a misalignment; tasks will sit below the enumeration item:

``````documentclass{article}

begin{document}

begin{enumerate}
item

end{enumerate}

end{document}

``````

Even if you provide a `before-skip`, I have offered a ridiculous one for example, this cannot be adjusted; the `before-skip` seems to provide no effect.

Desired outcome is for the tasks list (a, b, c) to sit vertically flush with the enumerate (1., 2., 3.).

Just FYI: I cannot define 1., 2. and 3. with tasks; I need to use the enumerate list for the highest level of items for other reasons external to this. I am currently doing this very inefficiently with `vspace{}` before the tasks which is what I wish to eliminate if possible.

I think it’s the first time, that I ask a question here, since I found an answer for all previous issues.
I upgraded my xubuntu 20.04 to 22.04 (and then on commandline to 22.10, because I hoped, the problem will solve itself. But it remains).
I can login from a text terminal but never more from lightdm. I enter my credentials, and then I see the background-image, the mouse-pointer can be moved, but nothing else is displayed. Restarting lightdm.service lets login me again, but the behavior is the same.
I also tried to switch to gdm3 (like suggested here), but it has the same effect (except the mouse freezes too).
The .xsession-errors has only a few entries:

``````dbus-update-activation-environment: setting DBUS_SESSION_BUS_ADDRESS=unix:path=/run/user/1000/bus
dbus-update-activation-environment: setting DISPLAY=:0
dbus-update-activation-environment: setting XAUTHORITY=/home/wolfgang/.Xauthority
dbus-update-activation-environment: setting QT_ACCESSIBILITY=1 looks normal so far,
``````

also dmesg and syslog dont show any hint. Where could I continue the research?

This is the Xorg.0.log (Part1):

``````[   232.736]
X.Org X Server 1.21.1.4
X Protocol Version 11, Revision 0
[   232.736] Current Operating System: Linux merlin 5.19.0-35-generic #36-Ubuntu SMP PREEMPT_DYNAMIC Fri Feb 3 18:36:56 UTC 2023 x86_64
[   232.736] Kernel command line: BOOT_IMAGE=/boot/vmlinuz-5.19.0-35-generic root=UUID=696192c7-692f-4e04-9022-fd082eef9987 ro vga=0x31f
[   232.736] xorg-server 2:21.1.4-2ubuntu1.6 (For technical support please see http://www.ubuntu.com/support)
[   232.736] Current version of pixman: 0.40.0
[   232.736]    Before reporting problems, check http://wiki.x.org
[   232.736] Markers: (--) probed, (**) from config file, (==) default setting,
(++) from command line, (!!) notice, (II) informational,
(WW) warning, (EE) error, (NI) not implemented, (??) unknown.
[   232.736] (==) Log file: "/var/log/Xorg.0.log", Time: Tue Mar 21 22:05:48 2023
[   232.737] (==) Using system config directory "/usr/share/X11/xorg.conf.d"
[   232.737] (==) No Layout section.  Using the first Screen section.
[   232.737] (==) No screen section available. Using defaults.
[   232.737] (**) |-->Screen "Default Screen Section" (0)
[   232.737] (**) |   |-->Monitor "<default monitor>"
[   232.738] (==) No monitor specified for screen "Default Screen Section".
Using a default monitor configuration.
[   232.738] (==) Automatically adding devices
[   232.738] (==) Automatically enabling devices
[   232.738] (==) Automatically adding GPU devices
[   232.738] (==) Automatically binding GPU devices
[   232.738] (==) Max clients allowed: 256, resource mask: 0x1fffff
[   232.738] (WW) The directory "/usr/share/fonts/X11/cyrillic" does not exist.
[   232.738]    Entry deleted from font path.
[   232.738] (WW) The directory "/usr/share/fonts/X11/100dpi/" does not exist.
[   232.738]    Entry deleted from font path.
[   232.738] (WW) The directory "/usr/share/fonts/X11/75dpi/" does not exist.
[   232.738]    Entry deleted from font path.
[   232.738] (WW) The directory "/usr/share/fonts/X11/100dpi" does not exist.
[   232.738]    Entry deleted from font path.
[   232.738] (WW) The directory "/usr/share/fonts/X11/75dpi" does not exist.
[   232.738]    Entry deleted from font path.
[   232.738] (==) FontPath set to:
/usr/share/fonts/X11/misc,
/usr/share/fonts/X11/Type1,
built-ins
[   232.738] (==) ModulePath set to "/usr/lib/xorg/modules"
[   232.738] (II) The server relies on udev to provide the list of input devices.
If no devices become available, reconfigure udev or disable AutoAddDevices.
[   232.738] (II) Loader magic: 0x5570cf6f1020
[   232.738] (II) Module ABI versions:
[   232.738]    X.Org ANSI C Emulation: 0.4
[   232.738]    X.Org Video Driver: 25.2
[   232.738]    X.Org XInput driver : 24.4
[   232.738]    X.Org Server Extension : 10.0
[   232.739] (++) using VT number 7

[   232.740] (II) xfree86: Adding drm device (/dev/dri/card0)
[   232.740] (II) Platform probe for /sys/devices/pci0000:00/0000:00:09.0/0000:02:00.0/drm/card0
[   232.744] (--) PCI:*(2@0:0:0) 1002:68f9:174b:e127 rev 0, Mem @ 0xe0000000/268435456, 0xfbfe0000/131072, I/O @ 0x0000e000/256, BIOS @ 0x????????/131072
[   232.745] (II) Module glx: vendor="X.Org Foundation"
[   232.745]    compiled for 1.21.1.4, module version = 1.0.0
[   232.745]    ABI class: X.Org Server Extension, version 10.0
[   232.745] (II) Applying OutputClass "Radeon" to /dev/dri/card0
[   232.745] (==) Matched radeon as autoconfigured driver 0
[   232.745] (==) Matched ati as autoconfigured driver 1
[   232.745] (==) Matched modesetting as autoconfigured driver 2
[   232.745] (==) Matched fbdev as autoconfigured driver 3
[   232.745] (==) Matched vesa as autoconfigured driver 4
[   232.745] (==) Assigned the driver to the xf86ConfigLayout
[   232.746] (II) Module radeon: vendor="X.Org Foundation"
[   232.746]    compiled for 1.21.1.3, module version = 19.1.0
[   232.746]    Module class: X.Org Video Driver
[   232.746]    ABI class: X.Org Video Driver, version 25.2
[   232.746] (II) Module ati: vendor="X.Org Foundation"
[   232.746]    compiled for 1.21.1.3, module version = 19.1.0
[   232.746]    Module class: X.Org Video Driver
[   232.746]    ABI class: X.Org Video Driver, version 25.2
[   232.746] (II) Module modesetting: vendor="X.Org Foundation"
[   232.746]    compiled for 1.21.1.4, module version = 1.21.1
[   232.746]    Module class: X.Org Video Driver
[   232.746]    ABI class: X.Org Video Driver, version 25.2
[   232.747] (II) Module fbdev: vendor="X.Org Foundation"
[   232.747]    compiled for 1.21.1.3, module version = 0.5.0
[   232.747]    Module class: X.Org Video Driver
[   232.747]    ABI class: X.Org Video Driver, version 25.2
[   232.747] (II) Module vesa: vendor="X.Org Foundation"
[   232.747]    compiled for 1.21.1.3, module version = 2.5.0
[   232.747]    Module class: X.Org Video Driver
[   232.747]    ABI class: X.Org Video Driver, version 25.2
ATI Radeon Mobility X600 (M24), ATI FireMV 2400,
ATI Radeon Mobility X300 (M24), ATI FireGL M24 GL,
ATI Radeon X600 (RV380), ATI FireGL V3200 (RV380),
ATI Radeon 9600XT, ATI FireGL T2, ATI Radeon 9650, ATI FireGL RV360,
ATI Radeon X800SE (R420), ATI FireGL X3 (R420),
ATI Mobility FireGL 7800 M7, ATI Radeon Mobility M6,
ATI FireGL Mobility 9000 (M9), ATI Radeon Mobility 9000 (M9),
ATI FireGL Mobility T2 (M10), ATI FireGL Mobility T2e (M11),
ATI FireGL M22 GL, ATI Radeon X800 (R423), ATI Radeon X800PRO (R423),
ATI FireGL V7100 (R423), ATI FireGL V5100 (R423),
ATI FireGL unknown (R423), ATI Mobility FireGL V5000 (M26),
ATI FireGL V3100 (RV370), ATI FireMV 2200 PCIE (RV370),
ATI Mobility FireGL V5100 (M28), ATI Mobility Radeon X800 (M28),
ATI Radeon X800XT (R423), ATI FireGL V5000 (RV410),
ATI Mobility Radeon X1800, ATI Mobility FireGL V7200,
ATI FireGL V7200, ATI FireGL V5300, ATI Mobility FireGL V7100,
ATI FireGL V7300, ATI FireGL V7350, ATI Radeon X1600, ATI RV505,
ATI FireGL V3350, ATI Mobility Radeon X1450,
ATI FireMV 2250, ATI Radeon X1650, ATI Mobility FireGL V5200,
ATI FireGL V3400, ATI Mobility FireGL V5250,
ATI RV560, ATI Mobility Radeon X1900, ATI Radeon X1950 GT, ATI RV570,
ATI FireGL V7400, ATI Radeon 9100 PRO IGP,
ATI RS740M, ATI Radeon HD 2900 XT, ATI Radeon HD 2900 Pro,
ATI Radeon HD 2900 GT, ATI FireGL V8650, ATI FireGL V8600,
ATI FireGL V7600, ATI Radeon 4800 Series, ATI Radeon HD 4870 x2,
ATI Radeon HD 4850 x2, ATI FirePro V8750 (FireGL),
ATI FirePro V7760 (FireGL), ATI Mobility RADEON HD 4850,
ATI Mobility RADEON HD 4850 X2, ATI FirePro RV770,
AMD FireStream 9270, AMD FireStream 9250, ATI FirePro V8700 (FireGL),
ATI FirePro M7750, ATI M98, ATI Mobility Radeon HD 4650,
ATI FirePro V7750 (FireGL), ATI FirePro V5700 (FireGL),
ATI FirePro V3750 (FireGL), ATI Mobility Radeon HD 4830,
ATI Mobility Radeon HD 4850, ATI FirePro M7740, ATI RV740,
ATI Radeon HD 2400 PRO AGP, ATI FireGL V4000, ATI Radeon HD 2350,
ATI FireGL V7700, ATI Radeon HD3690, AMD Firestream 9170,
ATI FirePro RG220, ATI Mobility Radeon 4330, ATI RV630,
ATI Radeon HD 2600 XT AGP, ATI Radeon HD 2600 Pro AGP,
ATI Radeon HD 2600 XT, ATI Radeon HD 2600 Pro, ATI Gemini RV630,
ATI Gemini Mobility Radeon HD 2600 XT, ATI FireGL V5600,
ATI FireGL V3600, ATI Radeon HD 2600 LE,
ATI Mobility FireGL Graphics Processor, ATI Radeon HD 3470,
ATI FireMV 2450, ATI Radeon HD 3600 Series, ATI Radeon HD 3650 AGP,
ATI Mobility FireGL V5700, ATI Mobility FireGL V5725,
AMD Radeon HD 6300 Series Graphics,
AMD Radeon HD 6200 Series Graphics, PALM, CYPRESS,
ATI FirePro (FireGL) Graphics Adapter, AMD Firestream 9370,
AMD Firestream 9350, ATI Radeon HD 5800 Series,
REDWOOD, ATI Mobility Radeon Graphics, CEDAR, ATI FirePro 2270,
AMD Radeon HD 6800 Series, AMD Radeon HD 6700 Series, TURKS, CAICOS,
ARUBA, TAHITI, PITCAIRN, VERDE, OLAND, HAINAN, BONAIRE, KABINI,
MULLINS, KAVERI, HAWAII
[   232.749] (II) modesetting: Driver for Modesetting Kernel Drivers: kms
[   232.749] (II) FBDEV: driver for framebuffer: fbdev
[   232.749] (II) VESA: driver for VESA chipsets: vesa
[   232.758] (II) [KMS] Kernel modesetting enabled.
[   232.758] (WW) Falling back to old probe method for modesetting
[   232.758] (WW) Falling back to old probe method for fbdev
[   232.759] (II) Module fbdevhw: vendor="X.Org Foundation"
[   232.759]    compiled for 1.21.1.4, module version = 0.0.2
[   232.759]    ABI class: X.Org Video Driver, version 25.2
[   232.759] (II) RADEON(0): Creating default Display subsection in Screen section
"Default Screen Section" for depth/fbbpp 24/32
[   232.759] (==) RADEON(0): Depth 24, (--) framebuffer bpp 32
[   232.759] (II) RADEON(0): Pixel depth = 24 bits stored in 4 bytes (32 bpp pixmaps)
[   232.759] (==) RADEON(0): Default visual is TrueColor
[   232.759] (==) RADEON(0): RGB weight 888
[   232.759] (II) RADEON(0): Using 8 bits per RGB (8 bit DAC)
[   232.759] (--) RADEON(0): Chipset: "ATI Radeon HD 5450" (ChipID = 0x68f9)
[   232.759] (II) Module "fb" already built-in
[   232.759] (II) Module "dri2" already built-in
[   232.835] (II) Module glamoregl: vendor="X.Org Foundation"
[   232.835]    compiled for 1.21.1.4, module version = 1.0.1
[   232.835]    ABI class: X.Org ANSI C Emulation, version 0.4
[   232.853] (II) RADEON(0): glamor X acceleration enabled on AMD CEDAR (DRM 2.50.0 / 5.19.0-35-generic, LLVM 15.0.2)
[   232.853] (II) RADEON(0): glamor detected, initialising EGL layer.
[   232.853] (II) RADEON(0): KMS Color Tiling: enabled
[   232.853] (II) RADEON(0): KMS Color Tiling 2D: enabled
[   232.853] (==) RADEON(0): TearFree property default: auto
[   232.853] (II) RADEON(0): KMS Pageflipping: enabled
[   232.870] (II) RADEON(0): Output DVI-0 has no monitor section
[   232.902] (II) RADEON(0): Output DVI-1 has no monitor section
[   232.918] (II) RADEON(0): EDID for output DVI-0
[   232.950] (II) RADEON(0): EDID for output DVI-1
[   232.950] (II) RADEON(0): Manufacturer: SAM  Model: 2b5  Serial#: 1213542964
[   232.950] (II) RADEON(0): Year: 2008  Week: 13
[   232.950] (II) RADEON(0): EDID Version: 1.3
[   232.950] (II) RADEON(0): Analog Display Input,  Input Voltage Level: 0.700/0.300 V
[   232.950] (II) RADEON(0): Sync:  Separate  Composite  SyncOnGreen
[   232.950] (II) RADEON(0): Max Image Size [cm]: horiz.: 52  vert.: 32
[   232.950] (II) RADEON(0): Gamma: 2.60
[   232.950] (II) RADEON(0): DPMS capabilities: Off; RGB/Color Display
[   232.950] (II) RADEON(0): First detailed timing is preferred mode
[   232.950] (II) RADEON(0): redX: 0.653 redY: 0.337   greenX: 0.295 greenY: 0.607
[   232.950] (II) RADEON(0): blueX: 0.144 blueY: 0.075   whiteX: 0.312 whiteY: 0.329
[   232.950] (II) RADEON(0): Supported established timings:
[   232.950] (II) RADEON(0): Supported standard timings:
[   232.950] (II) RADEON(0): #0: hsize: 1600  vsize 1200  refresh: 60  vid: 16553
[   232.950] (II) RADEON(0): #1: hsize: 1280  vsize 1024  refresh: 60  vid: 32897
[   232.950] (II) RADEON(0): #2: hsize: 1280  vsize 960  refresh: 60  vid: 16513
[   232.950] (II) RADEON(0): #3: hsize: 1152  vsize 864  refresh: 75  vid: 20337
[   232.950] (II) RADEON(0): Supported detailed timing:
[   232.950] (II) RADEON(0): clock: 154.0 MHz   Image Size:  518 x 324 mm
[   232.950] (II) RADEON(0): h_active: 1920  h_sync: 1968  h_sync_end 2000 h_blank_end 2080 h_border: 0
[   232.950] (II) RADEON(0): v_active: 1200  v_sync: 1203  v_sync_end 1209 v_blanking: 1235 v_border: 0
[   232.950] (II) RADEON(0): Ranges: V min: 56 V max: 75 Hz, H min: 30 H max: 81 kHz, PixClock max 175 MHz
``````

Thank you.

## Cut points, continuous paths and increasing sequence of sets

currently I have a question about the following point-set topology problem. Everything takes place in $$(mathbb C,|cdot|)$$ and we are given the following setup.

1. One has a sequence of closed connected sets of points in the complex plane $${L_t}_{t geq 0}$$ (the precise definition for this problem should be irrelavant) such that $$L_t subseteq L_{t+s}$$ for each $$s > 0$$. So basically as $$t$$ increases the set grows aswell.
2. There exist continuous curves $$gamma$$ such that for each $$t geq 0$$ one has $$gamma : [-t,t] to mathbb C$$ such that $$gamma([-t,t]) subseteq L_t$$. Moreover we know especially that $$gamma(t+s)$$ and $$gamma(-(t+s))$$ are not in $$L_t$$ and together with another given property one can actually proof that $$gamma(t)$$ and $$gamma(-t)$$ are cut points of $$L_{t+s}$$ for $$s > 0$$. Using the definition found here this tells us (for example) that $$L_{t+s} setminus gamma(t)$$ is disconnected.

Question: We already have for each $$t geq 0 : gamma([-t,t]) subseteq L_t$$ I want to proof that one actually has equality, i.e. $$L_t = gamma([-t,t])$$.

Idea: Take for example $$[a,b]$$ in $$mathbb R$$ then every point $$c in (a,b)$$ is a cutpoint, the important take away here is that the ”end-points” of the interval $$[a,b]$$ are not cutpoints. Here something similiar should be possible. Since $$gamma(t)$$ is a cut point of $$L_{t+s}$$ it cannot be that that $$L_{t+s} setminus L_t$$ did not grow ”along” $$gamma(t)$$. Growing say along the middle of the curve around $$gamma(t/2)$$ should contradict some combination of the notion of cut point and continuity of $$gamma$$ but I find it hard to write down precisely.

## ref{xyz} with usepackage{hyperref} not working correctly

I use pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex)

I put label on sections, figures, etc.

I had been using texlive 2016. Until I installed texlive 2022, ref{xyz} produced only the number for xyz.

Now it includes the number, the title (section name, figure caption, …) what it is (section, figure, …) and then the number again.

For example, with an equation having label{Flow}, when I wrote “Equation (ref{Flow})” I used to get “Equation (2)”. Now I get “Equation (2Flowequation.3.2)”

This occurs both using documentclass{article} and a proprietary class for a professional journal. I haven’t tried others.

I’ve “compiled” in a fresh directory, so it’s not due to confusion caused by an old .aux file.

Without including hypeffef, I get only the number — but of course no hyperlink.

Is there a repair for this?

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