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Calculation and Analysis – Can anyone suggest a reference where I can find out more about the function of Conway Base 13 in more detail

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8 – I'm trying to add headers: reference to cache context headers, but it does not work for anonymous users

    if ($ header === $ this-> request-> getHost () || $ header == NULL) {
return AccessResult :: allowed () -> addCacheContexts (['headers:Referer', 'user.roles']);
return AccessResult :: forbidden () -> addCacheContexts (['headers:Referer', 'user.roles']);

fa.functional analysis – Reference requirement: Stein-Wehrstraß on other topologies

To let $ X $ be a locally compact metric space. The classic sentence of Stone-Weirestrass describes dense subsets of $ C (X, mathbb {R}) $ if it is equipped with the compact open topology.

Are there similar results for dense subsets of $ C (X, mathbb {R}) $ When is it equipped with any topologies?

c # reference number and its use for comparing with the following floating point numbers

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

I have the hardware from Tobii C Eye Tracker. This eye tracker can output the coordinates of the X, Y I'm looking at. This device is very sensitive. When I look at a point, the Eyetracker sends a lot of different data from coordinates, but within ± 100 Area I found out. Although you are staring at one point, your eyes continue to move and therefore output a lot of data. These many data (floating-point numbers) are then stored in a text file. Now I just need 1 data (X coordinate), which means the 1 point I'm staring at, instead of the many data that's inside it ± 100 Area and move it to a new text file.

I have no idea how to program this.

These are the hover Numbers in the text file.


When I stare at point 1, the data is 200-300that are within the ± 100 Offer. I want to set this 200 as reference point subtracts with the next number and checks if the resulting value is within 100If this is the case, remove it. The reference point should continue to do this with the following numbers until it is outside the ± 100 Offer. Once outside the 100 Area, now is the number 310, then this number is now the next reference point and do the same and subtract with the following numbers and see if the resulting value is inside 100, Once outside the 100 Area is the next number 500Well, that's the new reference point, and do the same thing. That is my goal. In simpler terms, the reference points should be moved to a new file.

This is my code that retrieves the view coordinates and saves them in a text file.

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

Namespace ConsoleApp1

Class program

private static void programintro ()
Console.WriteLine ("Press any key to start");
public static void Main (string[] arguments)

programintro ();
Console.ReadKey ();
double current X = 0.0;
Double current Y = 0.0;
double timeStampCurrent = 0.0;
double diffX = 0.0;
Double delta = 0.0;
int counter = 0;
var host = new host ();
host.EnableConnection ();
var gazePointDataStream = host.Streams.CreateGazePointDataStream ();
gazePointDataStream.GazePoint ((gazePointX, gazePointY, timestamp) =>

diffX = gazePointX - currentX;
diffY = gazePointY - currentY;
currentX = gazePointX;
currentY = gazePointY;
timeStampCurrent = timestamp;
if (diffX> 100 || diffX <= -100 || diffY >= 100 || diffY <= -100)
counter ++;
using (StreamWriter writer = new StreamWriter ("C: \ user \ student \ Desktop \ FYP 2019 \ ConsoleApp1 \ ConsoleApp1 \ Data \ TextFile1.txt", true))
writer.WriteLine ("Recorded Data" + Counter + " n ========================================================= ======================================= == ============================================================================================================================= Data collected at {2}, currentX,
writer.WriteLine ("========================================= ====================================== === ============= ");
Console.WriteLine ("Recorded Data" + Counter + " n ============================================ ======================================= == ============================================================================================================================= Data collected at {2}, currentX,
Console.WriteLine ("========================================== ====================================== === ============= ");
//host.DisableConnection ();
while (true)
if (counter <10)

Environment.Exit (0);


Now my question is how do I code to read the text file and set a
Reference number and subtracts with the next number and check
if the resulting value is within 100 and have a new reference number, though
it outside the ± 100 Offer. These reference numbers are then stored in
a new text file.

If there is a code sample, I'll create a new program and save it there and test it first.

Entity Framework – Set updated reference in IdentityDbContext.SaveChanges ()

My app should be filled Updated by Field for all entities. Updated by should refer I would from AuthUser which extends Identity Role,
Updated by is set in IdentityDbContext.SaveChanges (), The problem is, that IdentityDbContext must keep a reference User Manager to solve I would the current user. This leads to a circular dependency: User Manager need IdentityDbContext which needs User Manager, What would be the most elegant solution to this problem?

I could try different things:

  • After initialization, set UserManager to IdentityDbContext
  • Resolve the user ID by filtering DbSet for fields in ClaimsPrincipal
  • Created by saving to the database as a name and not as an ID
  • Make the IdentityDbContext clients responsible for setting the CreatedBy field

The problem is that none of these solutions look elegant to me. I'm curious what the common pattern of such functionality is.

Reference requirement – Comprehensive overview of computations of equivalent stable strains

Where can I find a comprehensive overview of calculations of equivariant strains?

To my knowledge, the status is:

Classical work by Araki and Iriye, Osaka J. Math. 19 (1982). Calculations to 19 .. stable strain for the group $ mathbb {Z} / 2 $,

Araki and Iriye, equivariant stable homotopy ball groups with involvements. I.
Osaka J. Math. 19 (1982), no. 1, 1-55. and

Iriye, Kouyemon
Equivariant stable homotopy groups of spheres with involvations. II.
Osaka J. Math. 19 (1982), no. 4, 733-743.

Calculation of the Adams spectral sequence for first-order groups by Szymik's 2p-2 grade
J. Homotopy Relat. Struct. 2 (2007),

Comparison with motif strains and use of the Motivic Adams Spectral Sequence: by Dugger and Isaksen.

ℤ / 2-equivariant and ℝ-motivic stable stems.
Proc. Amer. Mathematics. Soc. 145 (2017), no. 8, 3617-3627.

Also from the Tom Dieck Segal split and the immediate consequences.

Do I miss something?

fa.functional analysis – Reference requirement: norm topology on M (X) vs. M. weak topology

To let $ (X, d) $ to be a metric space and $ mathcal {M} (X) $ the space of regular (eg radon) measures $ X $, There are two standard topologies $ mathcal {M} (X) $: The weak topology (the probabilist) and the strong norm topology, where the norm is the overall variation norm.

Surprisingly, I have found in the literature very few discussions in which these two topologies were rigorously compared except for the oft-quoted claim that the norm topology is much stronger than the weak topology. I'm looking for a reference that discusses and compares these topologies, especially things like convergence, boundedness, open sets, projections, etc.

I mainly deal with probability measurements $ mathcal {P} (X) subset mathcal {M} (X) $but I'm not sure what the difference is for topological concerns.