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Sharp radius for univalent convex functions

Context Koebe 1/4 Theorem states the following: Theorem.- Let $f \in \mathcal{S}$, that is, the set of univalent (analytic and injective) with $f(0)=0$ and $f’(0)=1$ functions from $\mathbb{D}=\lbrace z \in \mathbb{C}: \vert z \vert < 1 \rbrace$ to $\mathbb{C}$, then $D(0,1/4)=\lbrace z \in \mathbb{C}: \vert z \vert < 1/4 \rbrace \subset f(\mathbb{D})$. Furthermore, if there […]

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Ask Mathematics

Sharp radius for univalent convex functions

Context Koebe 1/4 Theorem states the following: Theorem.- Let $f \in \mathcal{S}$, that is, the set of univalent (analytic and injective) with $f(0)=0$ and $f’(0)=1$ functions from $\mathbb{D}=\lbrace z \in \mathbb{C}: \vert z \vert < 1 \rbrace$ to $\mathbb{C}$, then $D(0,1/4)=\lbrace z \in \mathbb{C}: \vert z \vert < 1/4 \rbrace \subset f(\mathbb{D})$. Furthermore, if there […]

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Mastering Development

Python and WebSockets – how to send from server to client without blocking?

Can anybody explain, or better yet provide a working example, of how to write a Python client and server where the server can initiate a send via WebSocket at any arbitrary time based on processing logic, and the client can receive at any time? Both have to be freed up to perform other processing activities […]

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Let $a,b,c$ be integers, then exactly one of the statements $a > b$, $a

Let $a,b,c$ be integers. (a) $a > b$ iff $a – b$ is a positive natural number. (b) If $a > b$, then $a + c > b + c$. (c) If $a > b$ and $c$ is positive, then $ac > bc$. (d) If $a > b$, then $-a < -b$. (e) If $a […]

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Development

Matrix: put only negative value on the diagonal position in a numpy array

i have a question about rearranging a numpy array, I have a numpy array, it looks like this: numpy_array=[[ 1, 2, 3, 4, -10], [ -4, 1, 1, 1, 1], [ 2, -7, 1, 1, 3], [ 1, 6, -12, 2, 3], [ 0, 3, 1, -4, 0]] I would like to rearrange this array: […]

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CMS Development Wordpress

Is it safe to use a global wp nonce per user?

I’m routing all my AJAX requests through a Controller, this is a class that simply localizes an endpoint and calls it further, as such, it’s some sort of a router, it does some checks first: This Controller, on initialization, creates a nonce for the user in question. This nonce is global. Endpoints themselves don’t have […]

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Development

How to reference function more directly?

List directory analyse structure as below: tree analyse analyse ├── __init__.py └── vix.py The __init__.py is blank,vix.py contains a function draw_vix. import analyse analyse.vix.draw_vix() draw_vix is referenced with analyse.vix.,i want to reference it with vix instead of analyse.vix,that is to say ,to add vix in namespace after import analyse. Edit __init__.py: import analyse.vix as vix […]

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Development

SwiftUI – ForEach with Stride

Im trying to create a list of Hstack’d cards, That is to say, I want to create a scroll view of a series of rows. Each row would contain an HStack of two views displayed side by side, and initialized by some list data structure. struct MyHStackView: View { var myArray = [SomeStruct(1), SomeStruct(3), SomeStruct(4), […]

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Development

SwiftUI – ForEach with Stride

Im trying to create a list of Hstack’d cards, That is to say, I want to create a scroll view of a series of rows. Each row would contain an HStack of two views displayed side by side, and initialized by some list data structure. struct MyHStackView: View { var myArray = [SomeStruct(1), SomeStruct(3), SomeStruct(4), […]

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Ask Physics

[ Physics ] Open Question : Does gravity effect the centripetal force acting on an object that spins on a string (vertically)?

That is to say, if I’m spinning something on a string (on a vertical plane), does the centripetal force increase at the bottom of the circle and decrease at the top due to gravity constantly pulling the object downward?