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user expectation – Payment method process on App for e-scooters sharing

Morning folks!
I’ll try to explain the problem as better as I can. Sorry for my English.

I am working on the ux of an app for e-scooters sharing.

The system has two different ways of payment systems.

  1. you scan the QR code, set the payment method and then once you park the scooter you get charged directly on the payment method you selected
  2. you has a wallet, you can recharge 10€-20€-30€, select a payment method and when you finish the money on the wallet the scooter stops.

When the user set a payment method can be tricky for him to understand what is the payment method for.

I am at this stage at the moment: enter image description here

I have two main problems here:

  1. is it clear enough that there are two different ways for paying?
  2. In the second screen, I decided to use the Radio Botton, but I’m not sure of it. If the user select Apple Pay he can pay directly when he click on the CTA. Meanwhile if he’s using a credit card/Paypal, he needs first to fill the apposite form to save it. How can I have this step in the process? If I use a “+” instead of the radio Botton the problem becomes Apple pay D:

Sorry for the long text and thank you for the attention :]

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swift – Data to string in UTF-8 encoding format conversion return nil in PKAddPaymentPassViewControllerDelegate’s generateRequestWithCertificateChain method

I am implementing Apple Wallet, where I need to add the card to the wallet. I am trying to convert the certificates, nonce and nonceSignature that I am receiving in the addPaymentPassViewController(_:generateRequestWithCertificateChain:nonce:nonceSignature:completionHandler:) delegate method of PKAddPaymentPassViewControllerDelegate of PassKit, from ‘Data’ to String encoded in ‘UTF8’ format.

However, the conversion returns nil while converting from Data to String using utf8 encoding format.

Pls find an image attached. I have highlighted where the conversion fails

Could any please help me to identify what is going wrong?

class ViewController: PKAddPaymentPassViewControllerDelegate {
    func addPaymentPassViewController(_ controller: PKAddPaymentPassViewController, generateRequestWithCertificateChain certificates: (Data), nonce: Data, nonceSignature: Data, completionHandler handler: @escaping (PKAddPaymentPassRequest) -> Void) {
        var encodedCertificateString = ""
        for index in 0..<certificates.count {
            if let encodedCertString = String(data: certificates(index), encoding: .utf8) {
                if index != (certificates.count-1) {
                    encodedCertificateString.append(", ")
    func addPaymentPassViewController(_ controller: PKAddPaymentPassViewController, didFinishAdding pass: PKPaymentPass?, error: Error?) {

marketing – What is the best method of incorporating ads/IAPs into your mobile game as an indie dev in 2020?

As the title reads – since the freemium model seems like the only viable for mobile games right now, which route do you tend to go as solo devs/small studios? Do you incorporate all the IAPs and ads you were planning to right away at launch or do you launch the game without them and wait with adding them until it gets some traction, so as not to scare away the initial userbase? Or maybe you incorporate some ads right away (like the less obtrusive ones – static banners at the bottom, for example) while waiting with interstitials/videos for longer?

Also, did you find like some things are a big no-no or that they simply don’t work like you’d like them to? Like, do you still use forced interstitials every X restarts, for example, or did you move away from this? What are your good practices you try to keep in mind?

Which methods proved more viable to make ends meet for you?

Problem with summation by method of difference

Question: What would be the result of: $$sum_{k=1}^{n}frac{1}{n(n+2)}$$

My Approach:

Let $T_n$ denote the $n^{th}$ term of the given series. Then we have

$$T_1=frac12 left(frac11-frac13right)$$
$$T_2=frac12 left(frac12-frac14right)$$
$$T_3=frac12 left(frac13-frac15right)$$

And so on up till
$$T_n=frac12 left(frac1n-frac1{n+2}right)$$

I can see that the series telescopes and the terms start to cut each other after an interval of one. My only problem is, how do I find the terms that remain in the end?

terminology – simple method for expanding binomial with 3 or more expressions?

I’ve seen

Binomial Theorem Question (Expansion of Three Terms)

Binomial Theorem with Three Terms

Expanding Equation with Binomial Theorem

but I’m not such a math expert, I need things explained in simple terms.

Basically I’ve heard that the solve

(x + y)^

it’s essentially

(x + y)(x + y)

and then multiply the first terms, (leftmost), then first term of one with last term of the other (outer) then second term of one with first term of other (inner) then the two last terms of each (right most), and add them up, so

x * x + x * y + y * x + y * y =

x^2 + 2xy + y^2

that is pretty much all I know, now if I want to solve a more complicated binomial, with three or more terms, for example

(x + y + z)(x + y + z)

would I use a similar method? Meaning do I start with the left most terms, then x * y, then, what? then do I do x * z and then move on to the next right term, y, and do y * x + y * y + y * z, and then do the same for z, meaning z * x + z * y + z * z ? Am I missing something here, or is that it?

algorithms – Iterative method for solving certain systems of linear equations

I’ve noticed that a method for calculating the stationary distribution of a finite-state rational-transition-probabilities Markov chain introduced by Arthur Engel many years ago generalizes to give an inefficient but charming method for solving certain systems of linear equations with rational coefficients. E.g., consider the linear system regarding three people sharing money described by Leonardo of Pisa in his Liber Abaci, as recounted by David Mumford in the April 1, 2020 installment of his blog (http://www.dam.brown.edu/people/mumford/blog/2020/Ridiculous.html); we can rewrite it as system of equations $x = frac{5}{6} x + frac{7}{18} y + frac{4}{9} z$, $y = frac{1}{6} x + frac{5}{9} y + frac{5}{18} z$, $z = frac{1}{18} y + frac{5}{18} z$, characterizing $(x,y,z)$ as a fixed point. It’s easy to verify that (33,13,1) is a solution, as is any multiple; the question is how one can find such a solution.

Given a triple $t=(x,y,z)$ of positive integers, define a new triple $t’=(x’,y’,z’)$ where $x’$ is $frac{5}{6} x + frac{7}{18} y + frac{4}{9} z$ rounded up to the next multiple of 18, $y’$ is $frac{1}{6} x + frac{5}{9} y + frac{5}{18} z$ rounded up to the next multiple of 18, and $z’$ is $frac{1}{18} y + frac{5}{18} z$ rounded up to the next multiple of 18. (More generally, you always round each variable up to the next multiple of the common denominator of the fractions associated with the right hand side of the associated equation.)

I claim that for any initial triple of positive integers, the process $x rightarrow x’ rightarrow x” rightarrow cdots$ converges to a positive integer solution to the original underdetermined system.

This method is not efficient; if you start from (18,18,18), you don’t arrive at (594,234,18) until 34 steps later. Still, I find it interesting that this iterative method always terminates. Has anyone characterized the sorts of problems for which this sort of method works?

I’d also be curious to know whether the approach can be modified so that one is guaranteed to find the minimal positive integer solution, or can be modified to converge more quickly.