## ACME protocol without LetsEncrypt, using dedicated CA [closed]

I have a question about the ACME protocol without using LetsEncrypt, and using our dedicated CA instead.

Can anyone enlighten me what should I consider in my client-server application which satisfies the ACME protocol which we can implement in our Network Security standard?

## Homeomorphisms coinciding on closed irreducible subsets

Let $$f_1$$, $$f_2:X\rightarrow Y$$ be two homeomorphisms of sober spaces. Assume that for any closed irreducible subset $$Z\subset X$$, we have $$f_1(Z)=f_2(Z)$$. In particular, $$f_1$$ and $$f_2$$ coincide on closed points. Are $$f_1$$ and $$f_2$$ necessarily equal?

## Closed points on scheme locally of finite Krull dimension

Let $$X$$ be an irreducible scheme that has a possibly infinite cover by open sets of finite Krull dimension. Does $$X$$ have a closed point?

## let $I_{p,q}=\int_{\gamma}p(z)\overline{q(z)}dz$ where $\gamma$ is the closed contour $\gamma(t)=e^{it},0\leq t \leq 2\pi.$ Then

Consider the polynomial $$p(z),q(z)$$ in the complex variable $$z$$ and let $$I_{p,q}=\int_{\gamma}p(z)\overline{q(z)}dz$$ where $$\gamma$$ is the closed contour $$\gamma(t)=e^{it},0\leq t \leq 2\pi.$$ Then

1. $$I_{z^m,z^n}=0,\forall m,n\in \mathbb Z^+,m\neq n$$

2. $$I_{z^n,z^n}=2\pi i,\forall n\in \mathbb Z^+$$

3. $$I_{p(z),1}=0,\forall$$ polynomials $$p$$

4. $$I_{p,q}=p(0)\overline{q(0)},\forall$$ polynomials $$p, q$$

My Attempt

When I flashed through the options, I got (3) as the answer. Since Polynomial function is analytic. By Cauchy’s theorem, $$\int_{\gamma}p(z)dz=0$$. option (1) is wrong. Since, If $$m-n+1=0$$, I got $$I_{z^m,z^n}=2\pi i$$. For option (2), $$I_{z^n,z^n}=\int_{\gamma}z^n\overline{z^n}dz=\int_0^2\pi 1.e^{it}i dt=2\pi i.$$ Using option (2), We can deduce that (4) is a wrong answer. But the answer given in the answer key is only (3). Can you please help me?

## Chitika has closed.

Chitika Is Shutting Down Effective Immediately

## Why does Apple make it hard to run laptops with lid closed?

No, this is not a duplicate to Is there any way to set a MacBook Pro to not sleep when you close the lid? . (The answer to that question is that there are 3rd party applications that may or may not work, or you can make it work if you have an external display/keyboard attached.)

But what I’m asking here is does anyone know WHY there isn’t a simple system setting to control what the machine does with the lid closed. Has Apple ever offered any rationale for (what seems to me) unnecessarily crippling their machines this way?

Some people have commented that it’s dangerous to run with the lid close due to heat buid-up. That seems far-fetched. There are cooling slots on the bottom of my MacBook Pro, and it just seems silly that the hardware would be designed that way. Plus, you can run with the lid closed if you have an external monitor and keyboard connected. So what is it? I mean, it can’t be that Apple engineers couldn’t figure this out, it seems like they’ve gone to extra trouble to prevent it. Are they trying to stop people from running servers on Apple laptops?

## Closed manifold with non-vanishing homotopy groups and vanishing homology groups

Is there a closed connected $$n$$-dimensional topological manifold $$M$$ ($$n\geq 2$$) such that $$\pi_i(M)\neq 0$$ for $$i>0$$ and $$H_i(M, \mathbb{Z})=0$$ for $$i\neq 0$$, $$n$$? The manifold $$S^1\times S^2$$ satisfies the first requirement but not the second (generally, the direct product of two positive-dimensional manifolds does not seem to satisfy the second requirement because of Kunneth).

## How to prove regular languages are closed by some operations?

I don’t how to prove these.

Show that the regular languages are closed under the following operations:

(a) $$\mathbb{DROPOUT}(L) = \{ xz \mid xyz \in L \text{ where }x,z \in \Sigma^*, y \in \Sigma \}.$$ Namely, $$\mathbb{DROPOUT}(L)$$ is the language containing all strings that can be obtained by removing one symbol from a string in $$L$$. For example, if $$L = \{012\}$$, then $$\mathbb{DROPOUT}(L) = \{12, 02, 01\}$$.

(b) $$\mathbb{INIT}(L) = \{ w\in \Sigma^+ \mid \text{ for some } x\in\Sigma^*,\ wx \in L\}.$$ For example, if $$L = \{01, 110\}$$, then $$\mathbb{INIT}(L) = \{0, 01, 1, 11, 110\}$$. (HINT: Start with a DFA $$A$$ for $$L$$ and describe how to construct an FA for $$\mathbb{INIT}(L)$$ using $$A$$. We assume that $$A$$ has no sink states.)

## every compact subset k of a manifold m is closed

Is every compact subset K of a manifold M is closed? If yes, then justify your answer.

I tried to prove this by contradiction. Using the fact that every cover of K admits finite subcover.

## The must-read User Interface Book? [closed]

I’m looking for the Book that explains the essentials of user interface and user experience design.

I read Beautiful Visualization and Designing Interfaces from O’Reilly. I think they are very good but, I’m still looking for the one.

Please provide your recommendation and why it stands as the essential reference.