How do I get all cryptocurrencies in real time without limit and for free?

How can we retrieve almost all real-time cryptocurrency information (prices, transactions, live prices, block information, wallets, etc.) to develop new cryptocurrency statistics and reference data (such as Binance)?

We can use the API of blockchain.com for BTC and LTC and some other references like chain.so, block.io etc., but what do we need to get all statistics for all crypto currencies?

I mean, how does Binance get that information? and where can we get it?

I know that there is a website selling this information and their own APIs, but how did they come up with that? and indeed, how can we get that information free?

real analysis – I seem to have a simple problem with job statistics …

I've been struggling with this problem for a while. I'll get right to it. Suppose that $ X $ will be delivered $ N (0,1) $. $ Y $ is distributed normally with positive mean and given variance, and $ Z $ is normally distributed with a positive mean and given variance. All three are independent. I am interested in the following calculation:

$ P (X> min (Y, Z)) $,

What I want to show is that if I increase the variance of either $ Y $ or the $ Z $ variable, this probability increases.

Graphically it seems to work: Imagine your three normal distributions on the same axis. We are interested in when the values ​​of the variables with the fixed distribution are furthest to the right $ N (0,1) $ is bigger than one of the two on the right. By increasing the variances from either of the two to the right, this distribution becomes flatter and "smoother," and hence the likelihood that $ X $ is larger than this variable seems to be increasing.

The following reference (https://www.untruth.org/~josh/math/normal-min.pdf) is a good way to get an overview of these probabilities. However, it is difficult to prove that their variance increases.

Any help would be appreciated.

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Real Analysis – Dominated Convergence Theorem

I have trouble understanding the proof in the paper Learning about the temporal evolution of spatial dependence
Generalized spatiotemporal Gaussian process models
,

Theorem 2.1 on page 33 uses the dominated convergence theorem (DCT) to show that the following series converges $ L ^ 1 ( mathcal {Z} times mathcal {Z}) $ feel where $ mathcal {Z} = mathbf {X} times mathcal {T} $
$$ sum_ {l = 1} ^ infty lambda_l (t) mathcal {C} _ { mathcal {T}} (t, t & # 39;) lambda_l (t & # 39;) phi_l ( mathbf {x}) phi_l ( mathbf {x} & # 39;) $$
by showing that
$$ sum_ {l = 1} ^ infty Bigg vert int _ { mathcal {Z}} int _ { mathcal {Z}} lambda_l (t) mathcal {C} _ { mathcal {T}} (t, t)) lambda_l (t)) phi_l ( mathbf {x}) phi_l ( mathbf {x}) d mathbf {z} d mathbf {z} & # 39; Bigg vert < infty $$
Where $ mathbf {z} = ( mathbf {x}, t) $ and $ mathbf {z} = ( mathbf {x} & # 39 ;, t & # 39;) $,

For me, however, the direct application of DCT would be the limits of
$$ sum_ {l = 1} ^ infty int _ { mathcal {Z}} int _ { mathcal {Z}} Big vert lambda_l (t) mathcal {C} _ { mathcal {T}} (t, t #) lambda_l (t #) phi_l ( mathbf {x}) phi_l ( mathbf {x} & # 39;
Big vert d mathbf {z} d mathbf {z} & # 39; < infty $$

with a monotonous sequence of dominating functions
$$ sum_ {l = 1} ^ L Big vert lambda_l (t) mathcal {C} _ { mathcal {T}} (t, t & # 39;) lambda_l (t & # 39;) phi_l ( mathbf {x}) phi_l ( mathbf {x} & # 39;
Big vert ge Bigg vert sum_ {l = 1} ^ L lambda_l (t) mathcal {C} _ { mathcal {T}} (t, t & # 39;) lambda_l (t & # 39;) phi_l ( mathbf {x}) phi_l ( mathbf {x} & # 39;
Bigg vert quad forall L in mathbf {N} $$

have the following condition
$$ int _ { mathcal {Z}} int _ { mathcal {Z}} sum_ {l = 1} ^ L Big vert lambda_l (t) mathcal {C} _ { mathcal { T}} (t, t)) lambda_l (t)) phi_l ( mathbf {x}) phi_l ( mathbf {x} & # 39;
Big vert d mathbf {z} d mathbf {z} & # 39; $$

$$ xrightarrow () {L rightarrow infty} sum_ {l = 1} ^ infty int _ { mathcal {Z}} int _ { mathcal {Z}} large vert lambda_l ( t) mathcal {C} _ { mathcal {T}} (t, t & # 39;) lambda_l (t & # 39;) phi_l ( mathbf {x}) phi_l ( mathbf {x} & # 39)
Big vert d mathbf {z} d mathbf {z} & # 39; < infty $$

Do I miss something?

Thank you in advance.

Calculus and Analysis – Real and imaginary part of the complex logarithm

I have to use Mathematica to get the real and imaginary parts of the following expression:

$ (- i a – m ^ 2) ln ( frac {i m ^ 2} {2 a}) $.

Where $ a $ and $ m $ are real.

So we have:

Refine(Re((-I a - m^2) Log((I m^2)/(2 a))), {Element(a, Reals), Element(m, Reals)})

However, Mathematica returns the command again. How can I proceed?

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swift – Why does not Starscream work on a real Apple Watch (WatchOS 6)?

Recently I upgraded my Apple Watch to WatchOS 6, my iPhone to iOS 13.1, Xcode to 11.1. MacOS still 10.14.6.

I've created an independent Apple Watch project in which I test the communication between Watch and a WebSocket server using Starscream: https://github.com/daltoniam/Starscream

It Works fine on the simulator but continue real Apple Watch When I try to connect to server I have these errors:

2019-10-08 18:57:53.064887+0200 BackgroundWebSocketOnlyWatch WatchKit Extension(251:31011) () nw_connection_get_connected_socket (C1) Client called nw_connection_get_connected_socket on unconnected nw_connection

2019-10-08 18:57:53.068928+0200 BackgroundWebSocketOnlyWatch WatchKit Extension(251:31011) TCP Conn 0x16d8d5f0 Failed : error 0:50 (50)

websocket is disconnected: Optional("The operation couldn’t be completed. Network is down")

I show you the code of my app:

InterfaceController.swift

import WatchKit
import Foundation
import Starscream

class InterfaceController: WKInterfaceController, WebSocketDelegate {

let socket = WebSocket(url: URL(string: "ws://echo.websocket.org/")!)

@IBOutlet var label: WKInterfaceLabel!

/**************************************************************************************************/

override func awake(withContext context: Any?) {
    super.awake(withContext: context)

    socket.delegate = self
}

override func willActivate() {
    // This method is called when watch view controller is about to be visible to user
    super.willActivate()
}

override func didDeactivate() {
    // This method is called when watch view controller is no longer visible
    super.didDeactivate()
}

/************************************************************************************************/

@IBAction func connectButtonPressed() {

    socket.connect()
}

@IBAction func sendButtonPressed() {

    socket.write(string: "Hi!")
}

@IBAction func disconnectButtonPressed() {

    socket.disconnect()
}

/******************************************************************************************/

func websocketDidConnect(socket: WebSocketClient) {
    print("websocket is connected")
    label.setText("Connected")
}
func websocketDidDisconnect(socket: WebSocketClient, error: Error?) {
    print("websocket is disconnected: (error?.localizedDescription)")
    label.setText("Disconnected")
}
func websocketDidReceiveMessage(socket: WebSocketClient, text: String) {
    print("got some text: (text)")
    label.setText("Received: (text)")
    createVibration()

}
func websocketDidReceiveData(socket: WebSocketClient, data: Data) {
    print("got some data: (data.count)")
}
/******************************************************************************************/

// Creates vibration
func createVibration() {

    WKInterfaceDevice.current().play(.notification)
    print("Vibration created")
}

}

I tried with star scream With iOS 13.1 and it Works perfectly on simulator and real iPhone,

Is that a error from WatchOS 6 or does Starscream need an upgrade?

Thank you in advance! 🙂

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cv.complex variables – Investigation to generate new inequalities for real or complex numbers: two special cases

I was wondering about the question in the title, as I knew some examples in the literature for proposed problems in journals or articles, about inequalities concerning the complex module or the inequalities for real numbers.

My motivation is my desire to know simple techniques to generate inequalities in two special cases. These inequalities apply to certain values ​​of our (real or complex) variables.

The first example I invoke is (1) (in Spanish), for which I have tried to get a variant with the following identity as a starting point $$ log (1-z) sum_ {k = 0} ^ nz ^ k = log (1-z) cdot frac {z ^ {n + 1} -1} {z-1}. $$

The second nice example comes from (2), and I tried to create inequalities for real numbers by combining the authors' examples and Wikipedia, which is known as Fischer's inequality.

Question.

A) What simple techniques can be proposed to create examples of inequalities with the complex module? Feel free to illustrate it with an example of an original inequality.

B) What simple techniques can be proposed to produce examples of inequalities for real numbers, using a determinative inequality as a starting point? Feel free to illustrate it with an example of an original inequality.

Many thanks.

Therefore, I know the techniques of the following references and ask for other different techniques that give us similar inequalities. My experiments were artificial and I ask if I speak colloquially: about a professor's recipe for an amateur to create difficult inequalities with the complex module (question A) or to create difficult inequalities for real numbers (question B). Starting from an inequality of determinants.

references:

(1) Oscar Ciaurri, PROBLEM 24, Section Problemas y Soluciones of La Gaceta de La RSME, Vol. 8.3 (2005), page 756.

(2) Daniel Sitaru and Leonard Giugiuc, Application of Hadamard's Theorems
inequalities
, Section of Crux Mathematicorum, Vol. 44 (1), January 2018, Canadian Mathematical Society.