## formal languages ​​- Show that if A is regular, a subset is also regular

You must use an intersection operation. It is a well-known locking feature when two languages $$A, B$$ are regular, then the intersection $$A cap B$$ will also be regular. In this case, $$A$$ is the default regular language. The other, $$B = textrm {even} ( Sigma ^ *)$$is the language of all strings with an even length. The language you want to prove is the language in which all strings are contained $$A$$ AND with an even length (in $$B$$).

It's easy to show $$B$$ is also regular. His regular expression is `(..)*`, where the period is the metacharacter that matches any character in the alphabet.

Your language is synonymous with it $$B$$ is regular, and then states that $$A cap B$$ is also regular. However, determining the regular expression of the intersection will take twice the exponential time to do this.

## Graphs and networks – discretize a (kinked) line and show how the points were determined

For example, suppose I have a (kinked) line

``````2-x==y && x< 1
3-2x == y && 1.5>=x>= 1
``````

I want to take this kinked line and discretize it (i.e. I want to show points along this line).

For example, I can do this with discretized regions

``````r=ImplicitRegion(2-x==y && x<1 , {x,y});
r2=ImplicitRegion(3-2x == y && 1.5>=x>= 1,{x,y});
DiscretizeRegion(RegionUnion(r,r2))
``````

This gives me a graphic of the line and some discrete points (I would prefer not to include the line here, but that's not too important)

• How can I show how these points are determined?
• How can I control how these points are determined?

I suspect there is a network function or something similar, and if so, I could control how the points are determined by specifying the network, but I couldn't find out.

Alternatively, maybe it is better to use something like MeshRegion?

An explanation of what I want to do:

I want to take on a function (in this case a kinked line, but the function doesn't matter).

Then I want to build a grid Consists of points created by the intersection of vertical and horizontal grid lines at intervals of size $$d$$

Next, I want to find the intersection of these points and the function, and just display those points and the underlying grid that generated them

• (I cannot display the grid if it is in the way of the visualization as long as I can separately generate a graphic that shows the grid used. Basically I want to be able to visualize how the points are selected.)

I realize that I can simply write custom code to do this. If that's the route you'd like to suggest, I'd rather try writing the code yourself to get better at Mathematica unless you have a particularly elegant (or short) solution to suggest.

It is also clear to me that I may be able to perform the above tasks with a network where the network cells are points. If this is possible, I would like to see how that works because I don't understand enough about how mesh works (and mesh cells, etc.).

## topological groups – Show the set \$ {(s-t, s + t): s, t in mathbb {Q}, t> 0 } \$ is a basis for the topology in \$ mathbb {R} \$

So far I have: Let $$O subseteq mathbb {R}$$Be open and let $$x in O$$, Since the set $${(a, b): a, b in mathbb {R} }$$ forms a basis for $$mathbb {R}$$There is an open interval $$(p, q)$$ Which $$p, q in mathbb {R}$$, so that $$x in (p, q) subseteq O$$,

Because of the density of the rational numbers of the real numbers, there is a rational number, $$s$$, so that
$$p , Then I just said there $$s – p> 0$$ There is one at the archemedian property $$n in mathbb {N}$$ so that $$1 / n , Therefore, $$p> s – 1 / n$$,

I am not sure how to reach the upper limit because the goal is to determine the interval $$(s-1 / n, s + 1 / n)$$,

Am I on the right path? Thanks a lot!

## icloud – iMessage's Send and Receive option does not show the option to select my cell phone number [iOS 13.3 iPhone 11]

I recently got a new iPhone 11 and inserted the Sim as part of the setup. When I send a text message to someone, my email ID is displayed instead of my phone number.

I went to `Settings > iMessage > Send & Receive` but i don't see my phone number there and only see my apple id. The same applies to my FaceTime settings. Nobody can display me with my number in FaceTime and only with the email ID.
I have also confirmed my phone number at `Settings > iCloud > Name, Phone Numbers & Email` and I see my phone number added there.

I've checked this similar question, but as the answer suggests I've been waiting for more than 24 hours. Also check out Apple's support article, but still no luck: https://support.apple.com/en-nz/HT201422

I can see that a lot of people are facing this problem and can see posts on the internet, but nothing seems to work for me. I have also confirmed that my wireless service provider allows sending and receiving SMS.

## Show the visitor certain content based on the IP

I have a request for how I want to show the specific content when users use network firewall. I plan to use the IP restriction module for this and save here the list of IPs for which I want to display the content. However, the challenge here is how to get the list of IPS in the IP restriction module. Any other approach is very welcome

## Show child view and subscribe to its event on ReactiveUI

I am very confused as to what is the best approach to view a child's view and subscribe to their event in ReactiveUI WPF. So far I have 2 implementations that somehow work for my case:

Implementation 1:

``````public class ChildWindowView
{
public event EventHandler Error;
public event EventHandler Closed;

internal void ShowSomeChild()
{
var vm = new SomeChildViewModel();
var view = new SomeChildView { DataContext = vm };

ChildWindowManager.Instance.Show(view, "Child Title");

Observable.FromEventPattern
(h => vm.Error += h, h => vm.Error -= h)
.Subscribe(p => Error?.Invoke(p.Sender, p.EventArgs));

Observable.FromEventPattern
(h => vm.Close += h, h => vm.Close -= h)
.Subscribe(p => Close?.Invoke(p.Sender, p.EventArgs));
}
}
``````
``````public class MainViewModel
{
private readonly ChildWindowView child = new ChildWindowView();

public MainViewModel()
{
// this commmand executed several times during runtime
ShowSomeChild = ReactiveCommand.Create(() => child.ShowSomeChild());

// this commmand executed several times during runtime
ShowOtherChild = ReactiveCommand.Create(() => child.ShowOtherChild());

// this commmand executed several times during runtime
ShowAnotherChild = ReactiveCommand.Create(() => child.ShowAnotherChild());

// handle child view error message
Observable.FromEventPattern
(h => child.Error += h, h => child.Error -= h)
.Subscribe(e => /* Error Handling */);

// do something when child closed
Observable.FromEventPattern
(h => child.Close += h, h => child.Close -= h)
.Subscribe(e => /* Do Something */);
}
}
``````

As you can see, the first implementation `ChildWindowView` Subscribe to an event at the `ChildViewModel` before calling his own event, the event is then subscribed to `MainViewModel`,

The advantage with this implementation is `MainViewModel` However, you only have to subscribe to the child event once for a child `ChildWindowView` will subscribe `ChildViewModel` every time `ShowSomeChild()` is called.

Implementation 2:

``````public class ChildWindowView
{
public event EventHandler Error;
public event EventHandler Closed;

internal void ShowSomeChild(SomeChildViewModel vm)
{
var view = new SomeChildView { DataContext = vm };

ChildWindowManager.Instance.Show(view, "Child Title");
}
}
``````
``````public class MainViewModel
{
private readonly ChildWindowView child = new ChildWindowView();

public MainViewModel()
{
// this commmand executed several times during runtime
ShowSomeChild = ReactiveCommand.Create(() =>
{
var vm = new SomeChildViewModel();

// handle child view error message
Observable.FromEventPattern
(h => vm.Error += h, h => vm.Error -= h)
.Subscribe(e => /* Error Handling */);

// do something when child closed
Observable.FromEventPattern
(h => vm.Close += h, h => vm.Close -= h)
.Subscribe(e => /* Do Something */);

child.ShowSomeChild(vm)
});

// this commmand executed several times during runtime
ShowOtherChild = ReactiveCommand.Create(() =>
{
var vm = new OtherChildViewModel();

// handle child view error message
Observable.FromEventPattern
(h => vm.Error += h, h => vm.Error -= h)
.Subscribe(e => /* Error Handling */);

// do something when child closed
Observable.FromEventPattern
(h => vm.Close += h, h => vm.Close -= h)
.Subscribe(e => /* Do Something */);

child.ShowOtherChild(vm)
});

// this commmand executed several times during runtime
ShowAnotherChild = ReactiveCommand.Create(() =>
{
var vm = new AnotherChildViewModel();

// handle child view error message
Observable.FromEventPattern
(h => vm.Error += h, h => vm.Error -= h)
.Subscribe(e => /* Error Handling */);

// do something when child closed
Observable.FromEventPattern
(h => vm.Close += h, h => vm.Close -= h)
.Subscribe(e => /* Do Something */);

child.ShowAnotherChild(vm)
});
}
}
``````

In the second implementation, I postpone child VM creation and event subscription to MainViewModel, but I lose the central subscription, which can handle all close events from any child.

And here it is `ChildWindowManager` that used to display child view on both implementations

``````public class ChildWindowManager : ReactiveObject
{
public static ChildWindowManager Instance { get { return lazy.Value; } }
private static readonly Lazy lazy =
new Lazy(() => new ChildWindowManager());

(Reactive) public string Title { get; set; }
(Reactive) public bool IsOpen { get; set; }
(Reactive) public FrameworkElement XmlContent { get; set; }

public ChildWindowManager ()
{
XmlContent = null;
}

public void Show(FrameworkElement content, string title)
{
XmlContent = content;
Title = title;
IsOpen = true;
}

public async void Close()
{
IsOpen = false;
XmlContent = null;
}
}
$$```$$
``````

## eclipse – Command & # 39; Show Monitors & # 39; in debug view

I'm currently learning how to use threads, etc. in Java with Eclipse, and I've been trying to figure out where the command to display a specific thread's monitor, Show Monitors, is in Eclipse. The help page is very vague (just that it's a view action and I don't find anything there), and I can't find it anywhere in the user interface for my whole life. Does anyone know where I can find it?