Features – Basic examples of mathematica encoding packages

Since the documentation from Google and Mathematica turned out to be completely useless in answering my question …

Does anyone have some basic examples of how to encode a packet? For my coursework, I need to create a critical point package with modules that use the second derivative test and the first derivative test.

And I couldn't even find a SIMPLE example of how to write a package that takes a function as a parameter and contains multiple modules.

I have coding experience in C ++ and Java, but I have zero experience with Mathematica.

Physical-mechanical examples for "M-of-N" locks?

Any "M-out-of-N" secret sharing protocols are a well-researched topic in cryptography and appear to be so useful that Bitcoin Script dedicated an entire opcode to them.

In this blog post I write:

Suppose we run a bank and our bank stores all of its gold in a large vault. Suppose we have three members on our board of directors. We want to make sure that one unscrupulous director cannot open the safe and steal all the gold. So we cut three different keys and make the safe so that it can do it requires two of these three keys to be inserted at the same time, to open the safe.

Sean Connery fans might recognize this as more or less the setup The big train robbery, with the exception of our "two out of three" requirement. I haven't been able to find a real mechanical analogue of the two-out-of-three mechanism.

So I'm asking you!

There is certainly an easy way to construct an "N-out-of-N" locking mechanism so that you can only open the safe when all N keys are inserted. (You simply stack the locks vertically in the door and make sure that every single bolt is strong enough to keep the door closed.) 2-out-of-2 mechanisms are used in bank lockers.

I can imagine that it is not difficult to design a "1-out-of-N" locking mechanism based on the Borromean rings, but I have not found any patented or commercially available mechanisms.

I have found no evidence of "M-out-of-N" lock mechanisms in the real world, nor can I imagine how to construct one (except for the brute force method, which is used to select N-select-M different ones) protected key safes) by an M-out-of-M mechanism). Has an inventor ever designed such a physical mechanism? Is there a real use case for such a mechanism?

soft question – early examples of evidence

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Explicit examples of (probability) measures for $ prod mathbb {R} $

To let $ prod_ {n in mathbb {N}} mathbb {R} $ be equipped with the Tikhonov product of the Euclidean topologies $ mathbb {R} $ and let $ B $ the corresponding Borel $ sigma $-Algebra. What are some concrete examples of:

  • Locally positive Borel probability measures $ ( prod_ {n in mathbb {R}} mathbb {R}, B) $.
  • Locally positive $ sigma $– finally (but not finally) Borel continues to measure$ ( prod_ {n in mathbb {R}} mathbb {R}, B) $?

How does the situation change when the product is indexed? $ mathbb {R} $?

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General topology – examples of topologies of sheaves

The following definition comes from Warner & # 39; s:

Definition: let $ S $ and $ X $ be topological spaces. A continuous card $ phi: S rightarrow X $ is a bunch of $ mathbb {Z} $Modules if the following three conditions are met:

  1. $ phi $ is a local homomorphism
  2. For all points $ x in X $. $ phi ^ {- 1} (x) $ is equipped with an Abelian group structure
  3. The operation $ (s_2, s_1) rightarrow s_2-s_1 $ is continuous $ S circ S rightarrow S $ Where $ S circ S $ is the subspace of $ S times S $ consisting of the pairs $ (s_2, s_1) $ above the same point $ X $ ($ phi (s_1) = phi (s_2) $).

This definition shows that (I hope I made no mistake):

  1. The covering $ mathbb {R} rightarrow mathbb {S} ^ 1 $ (Equipped with a $ mathbb {Z} $ on every fiber) is not a sheaf. One can show that the surgery $ (s_2, s_1) rightarrow s_2-s_1 $ is not continuous.
  2. The skyscraper sheaf $ O_0 ( mathbb {Z}) $ about $ mathbb {R} $ is homemorphic to the line with the beetle eyes.

Are there other examples (counterexamples) of sheaves with topologies that are known elsewhere?

Controls – Examples of good user experience design for virtual joystick in mobile or touchscreen games?

The problem here is that a virtual joystick is just a joystick that doesn't work well. Developers use them because they're used to games that require a joystick and a touchscreen phone doesn't have a joystick, but hey, you can just bring one up on the screen, right? In this way, however, you inherit all of the weaknesses of a touchscreen that you have described.

The solution is to make your game completely different to take advantage of the hardware. After all, joysticks were only invented because there was no way to interact directly with the game world at that time. This problem does not occur with touch screens. Your players can touch game objects and manipulate them directly with their fingers.

Why should an abstract indirect control system be used for a device designed for direct, intuitive interfaces?

To answer your question exactly, just touch where the player wants to go. This works especially well in top-down games, but I'm not sure what your game is.

Edit: Just wanted to clarify some games to do require a virtual joystick, but these are not games that are well suited for a touchscreen.

Change all tax examples to VAT?

I try to use all of the word & # 39; Excl. Taxes & # 39; to & # 39; Excluding VAT & # 39; because I'm building a website in the UK.
I found 3 examples of this, but which is the right way?

  1. Change any use of & # 39; Tax & # 39; in /vendor/magento/module-tax/view/frontend/layout/{checkout_cart_index.xml} & {checkout_index_index.xml} in & # 39; Vat & # 39 ;.
  2. Adding a translation to an en_GB file / I'm not sure how to do it
  3. Install a language pack – Composer requires cubewebsites / magento2-language-en-gb: *

-version 2.3.3

dnd 5e – What are the examples of a successful DC 30 ability check using an ability?

Simply put, are there official examples such as a DC 30 skill review chart that uses skills for each skill?

I would like to see what a character's potential for a skill is, but I have trouble finding clues.

That said, I understand what athletics does, but I'm not sure what the maximum potential for an athletics check (around 30) would do.

I would prefer to avoid the static / scaling examples in the book, such as how a skill (stealth) can be challenged against a hidden wisdom (perception). These can be used at any level and are not unique for a DC 30.

Design Patterns – Best practices for getting a file in both directories. (Ex: Examples of multiple elements.)

Sorry for the title. I could not make it clear.

I am trying to develop a CSS library in which I format each item and give each one a sample HTML page.

However, I came across these two elements (

), whose examples must be shared because they are always used together. Here is the sample code:

It was a bright cold day in April, and the clocks were striking thirteen.

(Code from MDN staff, link above.)

To demonstrate these two elements, I have to put the examples into two directories that look like this:

+-- cite
    +-- index.css
    +-- index.html
+-- blockquote
    +-- index.css
    +-- index.html

So I'm creating duplicate code and I really want to avoid this because I need to update these examples in the future, for example if the MDN document changes. And of course there is more behind it.

I have researched the StackExchange network and am surprised that I have not found any question about it. So I don't have to use the right keywords. Please suggest.

Since this question is not specific to HTML, the tags are not appended.

So please help me how to best view a file in two directories. If this is not possible, it can be helpful to limit it to certain file types.

If that's still impossible, I'd like to know how best to tolerate it. Thank you in advance and sorry again for the title.