tag removed – Equivalence classes properties proof, when [a] ∩ [b] ̸= ∅ then [a] = [b]?

Fix an inetger n > 1. Let R ⊆ Z × Z be the equivalence relation on Z defined by
R = {(a, b) : a = b + kn for some k ∈ Z}. Recall, for a ∈ Z we have (a) = {b ∈ Z : (a, b) ∈ R}.
Fix a, b ∈ Z show that if (a) ∩ (b) ̸= ∅ then (a) = (b) as follows:
(i) What does (a) ∩ (b) ̸= ∅ mean?
(ii) If x ∈ (a) then there is y ∈ (b) such that (x,y) ∈ R; deduce that (a)⊆(b)
(iii) Repeat argument of (ii) to show that (b) ⊆ (a).

simulation – Pros and cons of position as properties of a spatial object?

Building games and simulation frameworks, it seems I regularly hounded by this conundrum:

Let’s say you have a 2D grid, and you have an crate in that grid. I can put the coordinates on the crate, or somewhere else.

# Option A:
grid = Grid()
crate = Crate()
grid.add(x,y,crate)

# Option B:
grid = Grid()
crate = Crate(x,y)
grid.add(crate)

I prefer option A because why should the crate know where it is? Its position only makes sense in the context of its holding space (the grid). However, it seems that everywhere I encounter spatial positioning, Option B is used. I have noticed that this somehow does make the code simpler, and indeed more intuitive. However it irks my sense of conceptual integrity.

There is another option which seems to me to be an additional level of complexity, so I tend to avoid it:

# Option C
grid = Grid()
index = GridIndex(grid)
crate = Crate()
index.add(x,y,crate)

Some inconclusive thoughts:

Thought 1:
When trying to find items quickly, given a coordinate, we want option A, or C. With those we have some hope of indexing. Well with C, we have indexing explicitly of course.

Thought 2:
Option B suffers from this problem:

# Problem
grid = Grid()
crate = Crate(cx,cy)
room = Room(rx,ry)
grid.add(crate)
grid.add(room)
# oh actually crate is in the room
room.add(crate)

Now, the crate has coordinates intended for a grid, but it is actually in a room.

For me the above issues are fundamental conceptual issues that I cannot resolve. Have I missed why Option B is everywhere, and Option A is nowhere? What are the other pros and cons of A vs B vs C?

Aside
For me, it is useful to consider other similar(?) structures. The values of a dict/hash-table, do not typically know their own key. So, in this case, they use my conceptually preferred option, Option A.

Get ItemChild properties using Powershell Script SharePoint 2013 document library

We have a document library which contains multiple document set we have below requirements :

  1. Get all document set properties like Name, Created Date, Modified date.
  2. Get all ItemChild (document present inside the document set) properties Name, Created Date, Modified date.

We are able to get document set properties but unable to get ItemChild properties, any lead much appreciated, Please find my below code.

Add-PSSnapin "Microsoft.SharePoint.PowerShell"

$web = Get-SPWeb "Site URL"

$list = $web.Lists("ENERGY")


foreach ($listItem in $list.Items)
{
$CabinetName = $listItem('Name')
$CabinetCreateDate = $listItem('Created')
$CabinetModifiedDate = $listItem('Modified')
$CabinetChildItemCount = $listItem('ItemChildCount')

   Write-Host "    Cabinet Name: " $listItem.Name "  Modified: " $CabinetModifiedDate "Cabinet ChildItem Count" $CabinetChildItemCount "Created Date:" $CabinetCreateDate

}
$web.Dispose ()

properties of interior and closure

Let $V$ be a normed vector space (NVS). Which of the following are true for all $A, B subseteq V$?

1) If $A subseteq B$, then $overline{A} subseteq overline{B}.$

2) If $A supseteq B$, then $overline{A} supseteq overline{B}.$

3) If $A subseteq B$, then $mathrm{int}(A) subseteq mathrm{int}(B).$

4) If $A supseteq B$, then $mathrm{int}(A) supseteq mathrm{int}(B).$

I think the answer is $1)$ and $3)$. 1) is correct because if $Asubseteq B,$ then $Asubseteq subseteq Bsubseteq overline{B}$, so $overline{A} subseteq overline{B}$. 2) is incorrect. Take $A = (0,2)$ and $B=(0,1)$ in the NVS $mathbb{R}.$ Then $Asupseteq B,$ but $overline{A} = (0,2) notsubseteq (0,1) = overline{B}.$ 3) is correct because $mathrm{int}(A) subseteq A subseteq BRightarrow mathrm{int}(A)subseteq mathrm{int}(B).$ 4) is incorrect using the same example as in $2)$.

sharepoint enterprise – REST API – Get document library properties that are in a folder of that library

When getting properties from a document library with the SharePoint API, I’m using the following call

var httpRequest = new HttpRequestMessage(HttpMethod.Get, spPath + spSubSite + "/_api/web/lists('" + spAppId + "')/items?$filter=EnvelopeId eq '" + envelopeId + "'");

For a document library, I created multiple views where I have set some view level permissions, following this link https://www.netwoven.com/2016/01/21/how-to-set-view-level-permission-for-a-listlibrary-in-sharepoint/.

When I then try to get the properties, I’m getting the following error

{“odata.error”:{“code”:”-1, System.Collections.Generic.KeyNotFoundException”,”message”:{“lang”:”en-US”,”value”:”The given key was not present in the dictionary.”}}}

Because content type was setup and a folder is created at that document library, I tried to get properties with the following code

var httpRequest = new HttpRequestMessage(HttpMethod.Get, spPath + spSubSite + "/_api/web/lists/getbytitle('ViewICLExport')/items?$filter=EnvelopeId eq '" + envelopeId + "'");

Then I got {“odata.error”:{“code”:”-1, System.ArgumentException”,”message”:{“lang”:”en-US”,”value”:”List ‘ViewICLExport’ does not exist at site with URL ‘SPSite/DigitalSignatures/InternalLimits’.”}}}

When I open a view, the URL is SPSite/DigitalSignatures/InternalLimits/Internal%20limits%20Export/ViewICLExport/Africa.aspx

So my question is, how do I get the properties of this document library with his folder?

c++ – In Unreal why is it safe to access a UTexture2D’s properties from the render thread despite the documentation stating this is not allowed?

I’ve been trying to implement something that will update textures on the render thread from a background thread. And from what I’ve read of the unreal engine documentation you should never access a descendant of UObject from the render thread since the game thread could deallocate it at any time. Epic describes an example of this situation in their documentation

Here is a simple example of a race condition / threading bug:

/** FStaticMeshSceneProxy Actor is called on the game thread when a component is registered to the scene. */
FStaticMeshSceneProxy::FStaticMeshSceneProxy(UStaticMeshComponent* InComponent):
    FPrimitiveSceneProxy(...),
    Owner(InComponent->GetOwner()) <======== Note: AActor pointer is cached 
    ...

   /** DrawDynamicElements is called on the rendering thread when the renderer is doing a pass over the scene. */
    void FStaticMeshSceneProxy::DrawDynamicElements(...)
    {
        if (Owner->AnyProperty) <========== Race condition!  The game thread owns all AActor / UObject state, 
            // and may be writing to it at any time.  The UObject may even have been garbage collected, causing a crash.
            // This could have been done safely by mirroring the value of AnyProperty in this proxy.
    }

However the actual code they write violates this rule all of the time. There are numerous examples in FTexture2DResource accessing its Owner property which is a UTexture2D* from the render thread. Just one is

/**
 * Called when the resource is initialized. This is only called by the rendering thread.
 */
void FTexture2DResource::InitRHI()
{
  FTexture2DScopedDebugInfo ScopedDebugInfo(Owner);
  INC_DWORD_STAT_BY( STAT_TextureMemory, TextureSize );
  INC_DWORD_STAT_FNAME_BY( LODGroupStatName, TextureSize );

#if STATS
  if (Owner->LODGroup == TEXTUREGROUP_UI) <========== Accessing LODGroup from owner should be unsafe
    {
        GUITextureMemory += TextureSize;
    }
...
}

This seems to directly contradict the documentation given by Epic even though this is commonplace in their source code.

From the source it doesn’t look like FTexture2DResource or any of its ancestors perform any smart pointer magic or add the UTexture2D object to the root set to prevent GC and even then race conditions would still apply.

I’ll probably end up answering this one myself, but it would be great if someone happened to know this.

How to get/set specific properties of a video texture in pixi.js?

I managed to get a video to play in Pixi using the following line:

    this._texture = PIXI.Texture.from(require("Images/video.mp4"));

The problem is that I can’t find any properties to do things such as pausing it, forwarding/backwarding, adjusting volume, adjusting playing-speed etc.

Neither the PIXI.Texture or PIXI.Sprite seem to have any properties for this. Is this legitimately all the control PIXI gives you or am I missing something?