set theory – Subsets of the unit interval

I'm working on a problem and I have to answer the following question:

Is there a family $ {F_ alpha: alpha in omega_1 $ subsets of the interval $]0.1[$[$[$[$ such as:

(a) $ F_ alpha = {x_1 ^ alpha, x_2 ^ alpha } $ with $ x_1 ^ alpha <x_2 ^ alpha $;

b) If $ alpha, beta in omega_1 $ with $ alpha ne beta $then
$ x_1 ^ alpha <x_1 ^ beta <x_2 ^ alpha <x_2 ^ beta $ or $ x_1 ^ beta <x_1 ^ alpha <x_2 ^ beta <x_2 ^ alpha $?

I have tried to build such a family without success. Does anyone see the answer?

unit – Unity3D 4G mobile Internet web application is very slow

I have a Windows VPS server and I have an Apache server installed on it. on my server, I only have a simple text file containing a few words.

My problem is that when I try to send a web request to my server by (4G SIM card internet service) to access getting the data from the text file, it works very slowly.

Something about 30 or 50 seconds! but after the first request if I try again, there is no problem! It works very fast! It seems that this slowdown only occurs during the first connection.

On the other hand, if I use Internet WI-FI, there is no problem and every time I try to get data, it works quickly.

My problem is only with the Internet SIM card!

This is part of my code:

                IEnumerator Get_Data ()
{
UnityWebRequest www = UnityWebRequest.Get (server_address + "file.txt? T =" + UnityEngine.Random.value);

yield return www.Send ();
string the_Data = www.downloadHandler.text;
}

Is there a problem in my code?

My version of the unit is 2017.1.1

How can I solve this problem?

unit – Show sprites on overlap (Shader Graph) [2D]

enter the description of the image here

I have a sprite character and a mesh rendering engine (the wavy black box). I hope to superpose the black box on the character covering the sprites but I do not know how.

I've looked at this question: Unity: How to display only overlapping parts of objects [2D]

But it works more like a blanket than you can see through. I hope to have the black mask variable sprites the character but I can not stack them correctly. Is there a way to do this using the LWRP and shader graph?

The main idea is to use it as a damage marker. Moving the black box up or down depending on lost health.

SharePoint pnp test unit

How can I test with jest a pnp function?
How can I make fun of the Webpart context and pnp responses?

I use spfx webpart, pnp-js-core and jest for unit testing

Thank you.

unit – Problems generating a procedural mesh

I have the code below that I found on catlikecoding that generates a procedure grid to which I want to apply noise, but once I exceed a certain value, it grows vertically. Can anyone see why that would not be?

For example, 100×100:
Procedure Grid 100x100

However, 500×500 is clearly wrong:
enter the description of the image here

Code used:

use UnityEngine;

[RequireComponent(typeof(MeshFilter), typeof(MeshRenderer))]
Public Class Island: MonoBehaviour {

public int xSize, ySize;

private mesh;
private vector3[] the tops;

private void Awake () {
Produce();
}

private void Generate () {
GetComponent() .mesh = mesh = new Mesh ();
mesh.name = "Procedural Island";

vertices = new Vector3[(xSize + 1) * (ySize + 1)];
Vector2[] uv = new Vector2[vertices.Length];

for (int i = 0, y = 0; y <= y Size; y ++) {
for (int x = 0; x <= xSize; x ++, i ++) {
summits[i] = new vector3 (x, y);
uv[i] = new vector2 ((float) x / xSize, (float) y / ySize);
}
}

mesh.vertices = vertices;
mesh.uv = uv;

int[] triangles = new int[xSize * ySize * 6];
for (int ti = 0, vi = 0, y = 0;  y ++, vi ++) {
for (int x = 0; x <xSize; x ++, ti + = 6, vi ++) {
triangles[ti] = vi;
triangles[ti + 3] = triangles[ti + 2] = vi + 1;
triangles[ti + 4] = triangles[ti + 1] = vi + xSize + 1;
triangles[ti + 5] = vi + xSize + 2;
}
}


mesh.triangles = triangles;
mesh.RecalculateNormals ();
}
}

unit – Smoothen line on the linerender

I've created a square using linerenderer but my current problem is that the line is not smooth. see the picture below. I've tried turning on anti-aliasing and setting lr.numCapVertices to no avail.

enter the description of the image here

    private empty DrawLine ()
{
GameObject myLine = new GameObject ();
myLine.transform.position = start;
myLine.AddComponent();
lr = myLine.GetComponent();
lr.material = new Material (Shader.Find ("Sprites / Default"));
lr.positionCount = 4;
lr.startWidth = .1f;
lr.endWidth = .1f;

lr.SetPosition (0, new vector3 (1, 0, 0));
lr.SetPosition (1, new Vector3 (2, 0, 0));
lr.SetPosition (2, new Vector3 (2, -1, 0));
lr.SetPosition (3, new Vector3 (1, -1, 0));
lr.loop = true;


Gradient Gradient = new Gradient ();
gradient.SetKeys (
new GradientColorKey[]
    {
new GradientColorKey (Color.red, 0.25f),
new GradientColorKey (Color.green, 0.50f),
new GradientColorKey (Color.blue, 0.75f),
new GradientColorKey (Color.yellow, 1f),
}
new GradientAlphaKey[] {new GradientAlphaKey (1f, 0.0f)

}
)
lr.colorGradient = gradient;

}

unit – How does the color gradient work?

I'm trying to implement the image below in my code but it does not work. It only shows the red color on all sides. I'm using line rendering and color gradient. Please check my code. Thanks in advance

enter the description of the image here

empty Start ()
{
lineGeneratorPrefab = new GameObject ();

Draw a line ();
}




private empty DrawLine ()
{
GameObject myLine = new GameObject ();
myLine.transform.position = start;
myLine.AddComponent();
lr = myLine.GetComponent();
lr.material = new Material (Shader.Find ("Sprites / Default"));
lr.positionCount = 4;
lr.SetPosition (0, new vector3 (-2, 0, 0));
lr.SetPosition (1, new Vector3 (2, 0, 0));
lr.SetPosition (2, new Vector3 (2, -2, 0));
lr.SetPosition (3, new Vector3 (-2, -2, 0));
lr.loop = true;


Gradient Gradient = new Gradient ();
gradient.SetKeys (
new GradientColorKey[]
    {
new GradientColorKey (Color.red, 0.25f),
new GradientColorKey (Color.blue, 0.25f),
new GradientColorKey (Color.green, 0.25f),
new GradientColorKey (Color.yellow, 0.25f)
}
new GradientAlphaKey[] {new GradientAlphaKey (1.0f, 0.0f)}
)
lr.colorGradient = gradient;

}

Field Theory – Suppose $ zeta $ is the root of the unit and that $ f in mathbb {Q}[X]$. Show that $ f ( zeta) neq2 ^ {1/4} $.

Question: Suppose $ zeta $ is a root of unity and $ f in mathbb {Q}[X]$. CA watch $ f ( zeta) neq2 ^ {1/4} $.

This is taken from the UCLA Autumn 2016 algebra qualifier. So far, I have not been as far as my first observation: if we assume that $ f ( zeta) = 2 ^ {1/4} $, then as $ mathbb {Q} ( zeta) / mathbb {Q} $ it's Galois, we've $ g (X) = X ^ 4-2 $ splits into $ mathbb {Q} $ and so we have $ mathbb {Q} ( zeta) / E / mathbb {Q} $ or $ E $ is the dividing field of $ g $. Since $ | E: mathbb {Q} | = $ 2 ^ 3 we get that $ 2 ^ 3 | varphi (ord ( zeta)) $ and it eliminates a lot of possible unit roots. However, prove that the overall result escapes me.

unit – Unity3D – Generates a position in a circular band around the drive

Given certain conditions of my game, I have to create a position around the player. It must be at least 8 meters from it and less than 10 meters, in a circular manner, as in the green dashed area of ​​the photo below.

Can someone direct me in the right direction?
Thank you.

enter the description of the image here

applications – How does the studio and the Android unit build an Android app with jdk and sdk

how the Android studio, the unit and other software build an Android application.
I searched on the internet but I did not find a satisfactory answer.
If I create a game in java opengl, how can I create an apk? Is a program already available to convert my Java project into Android APK or I have to create mine?
Help me, please.
give me resources to understand what's going on behind the scenes: how does the unit and other software work to create a project and build for multiple platforms.