## reference request – Low convergence of generic periodic dots, obtained from the specification

Let $$X$$ to be a compact metric space and let $$f: X rightarrow X$$ to be an Anosov and transitive map.

Let $$x$$ to be a generic point for that $$mu_ {n_ {i}}: = frac {1} {n_ {i}} sum_ {j = 0} ^ {n_ {i} -1} delta_ {T ^ {j} (x) } rightarrow mu$$ for an invariant measure $$mu$$.

It is well known that $$T$$ satisfies the specification property. Let $$p in X$$ be
a periodic point associated with $$delta, S$$ and
$${x, T (x) ,. . . , T ^ {n_ {i}} (x) }$$
by the specification property. In particular, $$T ^ {n_ {i} + S} (p) = p$$ and orbit of $$p$$ coverage orbit of $$T ^ {n_ {i}} (x)$$.

My first question is:

$$mu_ {n_ {i}, p}: = frac {1} {n_ {i} + S} sum_ {j = 0} ^ {n_ {i} + S-1} delta_ {T ^ { i} (p)} rightarrow mu$$?

If yes. For $$mu in mathcal M (X)$$ we write $$text {supp} mu$$ for the support from $$mu$$. It's easy to see that if a sequence of measurements $$( mu_n) _ {n = 1} ^ infty$$ low$$^ *$$ converges towards some $$mu in mathcal M (X)$$then
$$text {supp} , mu subset liminf_ {n to infty} ( text {supp} , mu_n).$$
(By $$liminf$$ above, I mean the lower limit of Kuratowski; for a definition, see entry in Wikipedia).

From what precedes, can we say $$supp mu$$ is the periodical? Because $$mu_ {n_ {i}, p}$$ has periodic support.

## How to store the object reference?

I have a project where a minion rides the tower.

Needless to say, the problem occurs when more than one minion rides the tower at the same time.

It turns out that I understood how to solve this problem, or at least in different ways.

This is only to condition a certain event / function once and define a loop.

I can make sure that the damage is correctly applied to the tower if I create the code in the tower (adding information on the number of minions riding the tower).

Plan:

The problem is that the overlap oscillates. This disturbs the reception of the variable information, because the minion stops at a given moment to ride the tower.

I've tried to solve this problem by adding a parameter to the event, but by using it, I can not refer to the variable tower:

Not even using the build script:

I've thought of something as a variable that gets the reference of the tower, and if, at the moment of receiving the variable, the reference of the tower fails, use it.

But all that I have tried in this direction, something similar to the one shown in Figure 2 has happened.

## How to add a reference to a parent entity when I create a new sub-entity

• I have two entities: quiz and question.
• The quiz has an entity_reference field questions.
• I have a page / quizzes / {quiz} / questions which links to a "Add
Question "page / quizzes / {quiz} / questions / add

Where can I add functionality to ensure that when the question is added, it is associated with the quiz (preferably as the last item).

## Aggressive geometry – Reference request: affine smooth curves are flat

Thank you for contributing an answer to MathOverflow!

• Please make sure to respond to the question. Provide details and share your research!

But to avoid

• Make statements based on the opinion; save them with references or personal experience.

Use MathJax to format equations. MathJax reference.

## c # – Reference number, and their use to compare with the following floating point numbers

The project is based on Eye Tracker. Let me summarize the idea behind the project to better understand my problem.

I have the material of the eye tracker Tobii C. This eye tracker will be able to give the coordinates of the X, Y of the place where I look. But this device is very sensitive. When I look at a point, the eye tracker sends many different coordinates data but within a ± 100 range that I discovered. Even if you stare at 1 point, your eyes keep moving, giving a lot of data. These many data (floating-point numbers) are then saved in a text file. Now, I only need 1 data (X coordinate) which means the 1 point I'm looking at instead of the many data that are in the ± 100 store it and move it to a new text file.

I do not know how to code to do it.

here are the fleet numbers in the text file.

200
201
198
202
250
278
310
315
360
389
500
568
579
590


When I look at point 1, the data is 200-300who are in the ± 100 interval. I want to put the 200 as a reference point gets subtracted from the next number and checks whether the resulting value in 100if that's the case, delete them. The reference point should continue to do so for the following numbers until it reaches the outside of the ± 100 interval. Once outside the 100 range, now the number is 310, so now this number is the next point of reference. Do the same and subtract with the following numbers below and check if the resulting value in 100. Once outside the 100 beach, the next number is 500Now, this is the new point of reference and do the same. That's my goal. For simplicity, the reference points must be moved to a new file.

It's my code up here that gets the coordinates of the look and stores them in a text file.

    using the system;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using Tobii.Interaction;

ConsoleApp1 namespace
{

class program
{

private static vacuum program ()
{
Console.WriteLine ("Press any key to start");
}
public static void Main (string[] args)
{

programintro ();
double currentX = 0.0;
double currentY = 0.0;
double timeStampCurrent = 0.0;
double diffX = 0.0;
double diff = 0.0;
int counter = 0;
host var = new host ();
host.EnableConnection ();
var gazePointDataStream = host.Streams.CreateGazePointDataStream ();
gazePointDataStream.GazePoint ((gazePointX, gauzePointY, timestamp) =>

{
diffX = gazePointX - currentX;
diffY = gazePointY - currentY;
currentX = gazePointX;
currentY = gazePointY;
timeStampCurrent = timestamp;
if (diffX> 100 || diffX <= -100 || diffY >= 100 || diffY <= -100)
{
counter ++;
using (author of StreamWriter = new StreamWriter ("C: \ Users \ Student \ Desktop \ FYP 2019 \ ConsoleApp1 \ ConsoleApp1 \ Data \ TextFile1.txt", true))
{
writer.WriteLine ("Registered Data" + counter + " n ==================================== =============================================== === =======================  nX: {0} Y: {1}  nData collected at {2} ", currentX, currentY, timeStampCurrent);
writer.WriteLine ("============================================= ================================================== ============== ");
}
Console.WriteLine ("Registered Data" + Counter + " n ==================================== =============================================== === =======================  nX: {0} Y: {1}  nData collected at {2} ", currentX, currentY, timeStampCurrent);
Console.WriteLine ("============================================= ================================================== =============== ");
}
});
//host.DisableConnection ();
while (true)
{
if (counter <10)
{
Carry on;
}
other
{

Environment.Exit (0);

}
}


Now my question is how can i code to read the text file and set a
reference number and subtracts from the next number and ticks
if the resulting value in 100 and have a new reference number if
outside of the ± 100 interval. These reference numbers are then stored in
a new text file.

If there is a code example, I will create a new program, store it and test it first.

## entity framework – Define a UpdatedBy Reference in IdentityDbContext.SaveChanges ()

My application should populate Updated by field for all entities. Updated by should reference id of AuthUser who expands IdentityRole.
Updated by is put in IdentityDbContext.SaveChanges (). The problem is that IdentityDbContext must contain a reference to UserManager solve id of the current user. This causes a circular dependency: UserManager Needs IdentityDbContext who needs UserManager. What would be the most elegant solution to this problem?

I could try several things:

• Set UserManager to IdentityDbContext after initialization
• Resolve the user ID by filling in DbSet in the fields of ClaimsPrincipal
• Save CreatedBy in the database as a name and not as an id
• Make IdentityDbContext clients responsible for setting CreatedBy settings per field

The problem is that none of these solutions seem elegant to me. I am interested what is the common model of this feature.

## reference request – Comprehensive study of equivariate stable stem calculations

Where can I find a complete study of equivariant stem calculations?

To my knowledge, the status is:

Classical work of Araki and Iriye, Osaka J. Math. 19 (1982). Calculations until the 19th. stable stem for the group $$mathbb {Z} / 2$$.

Araki and Iriye, Equivariant, stable homotopic groups of involute spheres. I.
Osaka J. Math. 19 (1982), no. 1, 1-55. and

Iriye, Kouyemon
Homotopic stable equivariate groups of spheres with involutions. II.
Osaka J. Math. 19 (1982), no. 4, 733-743.

Calculation via the Adams spectral sequence for first order Szymik 2p-2 groups
J. Homotopy Relat. Struct. 2 (2007),

Comparison with Motivic roots and use of the Motivic Adams Spectral sequence: from Dugger and Isaksen.

Stable ℤ / 2-equivariant and motivic stems.
Proc. Bitter. Math. Soc. 145 (2017), no. 8, 3617-3627.

Besides the Tom Dieck-Segal Separation and immediate consequences.

Am I missing something?

## fa.functional analysis – Reference request: Topology of the standard on M (X) vs. weak topology

Let $$(X, d)$$ to be a metric space and $$mathcal {M} (X)$$ space for regular measurements (eg radon) on $$X$$. There are two standard topologies on $$mathcal {M} (X)$$: The weak topology (probabilistic) and the strong standard topology, where the norm is the norm of total variation.

Surprisingly, I found very little discussion in the literature comparing these two topologies in a rigorous way, apart from the often-quoted assertion that the standard topology is much stronger than the weak topology. I am looking for a reference that discusses and compares these topologies, in particular. things like convergence, delineation, open sets, projections, etc.

I am most concerned about the probability measures $$mathcal {P} (X) subset mathcal {M} (X)$$but I am not sure of the difference between this and the topological concerns.