probability – Compare different power function

$X_1,X_2$ are iid uniform ($theta, theta+1$). We consider the rejection region given by

{(x1, x2): x1 + x2 > C}$cup$
{(x1, x2): x1 > 1}$cup$
{(x1, x2): x2 > 1}.

What is the power function corresponding to this rejection region? This is from George Casella question 8.13 part (d). The solution is attached below. I don’t know how to analyze this new test is more powerful than the original rejection region $x_1 + x_2 > C$. If deriving the exact power function of the new rejection region is too hard, just comparison is also helpful. I don’t know how to compare.

enter image description here

javascript – Do all dynamically typed languages not support function overloading?

The issue is easier to understand if you consider carefully what it really means to overload a function.

Overloaded methods e.g. in Java are really two completely separate entities; they share no byte code, no address, nothing except their name; and their name isn’t really the same either, since in the compiler symbol table, a print() method for ints and a print() method Strings actually have a mangled name that contains both the user-visible identifier (“print”) and additional information encoding the argument type.

Now contrast this with Javascript, where a print() function really is called print and nothing else. The runtime system only knows that it is a function; what arguments it expects and how it deals with them is entirely defined by the code in the function’s body. Therefore, defining a second function “print” simply overwrites the previous one rather than add a second implementation.

The details vary a bit from language to language, but the gist is, if you don’t have an explicit representation of data types in your compile-time/run-time system, you can’t use them to tell elements of the system apart, and that is why overloading on types is largely restricted to systems with a strong presence of types in the language definition.

raycasting – Pinch Gesture for Function Other than Zooming- Unity

I’m working on a game in which I want to pinch outwards on a character, which causes the character to split into 2 smaller copies of itself.

The method I’m thinking about using is to have the “pinch out” gesture destroy the game object and simultaneously create two instances of the smaller game object, and have them follow the fingers that pinch out. The action would also be reversible with the “pinch in” function.

My idea would be to do a raycast to detect the two-finger touch on the object (would I need a collider for that?), then use the beginning and ending touch points to determine if it is pinching out or in.

The problem is I am brand new to Unity and C# and have no idea how to write all of this. All of the tutorials for multi-touch gestures have to do with camera zoom, which is not what I am going for.

Can anyone tell me if I’m on the right track with my logic and provide some guidance on writing the code?

Azure Function – SharePoint CSOM call with currently signed in user

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woocommerce offtopic – Function to recalculate shipping costs on subscriptions after renewal with Automatewoo

I’ve got a funky plugin that was custom made that adds a new random product from a group that a customer subscribes to.

Problem is, that the shipping doesn’t change depending on which product is selected, it stays with whatever was chosen initially.

Rather than paying more money to redevelop something that might already exist, is there any code that will recalculate shipping costs based on the item in the subscription? I have automatewoo, so could use a custom function from that and run it after a subscription payment has completed, I just don’t know how to code it.

Any support appreciated!


github pages – I wants to know how to create python function to get _num1_ and _num2_?

github pages – I wants to know how to create python function to get _num1_ and _num2_? – Web Applications Stack Exchange

fa.functional analysis – Is radial part of a Schwartz class function also in Schwartz class?

Let $finmathcal{S}(mathbb{R}^n)$, Schwartz class. Consider the function $g$ defined on $(0,infty)$ by $$g(r)=int_{S^{n-1}}f(rw)dmu(w),$$
where $dmu$ is the normalised surface measure of $S^{n-1}.$

1)Is $sup_r|r^kg(r)|<infty,$ for any $kinmathbb{N}$?

  1. Is $ginmathcal{S}((0,infty))?$

Answer of only (1) will also be appreciated.

real analysis – $L^2$ convergence of a particular function

I encounter the following problem when I study harmonic analysis by myself:

Given a function $f in L^2((0,1))$. Let’s fix some irrational number $omega$. For any $N in mathbb{Z}^{+}$, let’s define a function $g_{N}$ as follows:
$$g_{N}(x) := frac{1}{N}sum_{j=1}^{N}f(x+jomega)-int_{0}^{1}f(y)dy$$
Prove that $lim_{N rightarrow infty}||g_{N}||_{L^2(mathbb{T})} = 0$. Moreover, if we further assume $f$ is periodic with period $omega$, then $f$ must be constant.

The second claim follows easily from the limit given in the first claim. However, I haven’t finished proving the first claim. How does the “irrational number” assumption come into play here? Also, just out of curiosity, would it be possible to generalize the claim to arbitrary $L^p$ space by utilizing things like interpolation theorems? Thanks in adavnce!

linear algebra – How can one create a continuous function that transitions a 2d input through a

This is my first question here, hopefully it isn’t too bad. Apologies in advance if it isn’t formulated in a manner coherent with the expected formalism. Let me know if I need to make corrections and I will do so immediately.

I am trying to create a 3D function for which the first 2 (x;y) are parameters are contiguous of a 2D space. i.e. example 2d function graphs

and the third (z) acts to transition/”morph” the function that is applied to the prior 2 rational numbers through the possible relations between x and y.
A discrete (naive) implementation of this might be merely to instantiate a case statement

X(x;y;z) = { 
          |y|, for z=1 // absolute
          y^2, for z=2 // quadratic
          y^3, for z=3 // cubic
          x*y  for z=n

Are there any methods by which one might transition the expression of the relation between x and y values with respect to a space parameterized by z. e.g

(identity(x;y) -> absolute(x;y) -> quadratic(x;y) -> cubic(x;y) .... // positive function (0<z)
-identity(x;y) <- -absolute(x;y) <- -quadratic(x;y) <- -cubic(x;y)) // negative functions (0>z)

How might one implement something like this?
Best regards and thanks in advance.

documentation – Nonexisten function apply_impulse in base Node2D

Why when I run it to my app has been closed and write it – Nonexisten function apply_impulse in base Node2D. I see Godot’s doc and I find it method and your parent is RigidBidy2D, but I do this code by the video and he use KinematicBody2D and it is alright

extends KinematicBody2D

var movespeed = 500 
var bulletspeed = 2000
var bullet = preload("res://Bullet.tscn") 

func _ready():

func _physics_process(delta):
    var motion = Vector2()
    if Input.is_action_pressed('up'):
        motion.y -= 1
    if Input.is_action_pressed('down'):
        motion.y += 1
    if Input.is_action_pressed('right'):
        motion.x += 1
    if Input.is_action_pressed('left'):
        motion.x -= 1
    motion = motion.normalized() 
    motion = move_and_slide(motion * movespeed) 

    if Input.is_action_just_pressed('LMB'):

func fire():
    var bullet_instance = bullet.instance()
    bullet_instance.position = get_global_position()
    bullet_instance.rotation_degrees = rotation_degrees
    bullet_instance.apply_impulse(Vector2(), Vector2(bulletspeed, 0).rotated(rotation))
    get_tree().get_root().call_deferred("add_child", bullet_instance)

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