Can you leave objects behind in the ethereal plane?

After entering the ethereal plane through some means, is it possible to leave objects you brought with you behind, or do they always come back with you?

Does the answer depend on the means you used to enter the ethereal plane, or on the specific object you’re trying to leave behind?

Note: You only need to consider content published in official material when answering this question, but if the official material is completely silent on this matter interpretations are also fine.

Can spells with movable areas of effect be moved out of sight or behind obstacles?

With spells like Moonbeam or Flaming Sphere, how should we treat the movement of their areas-of-effect when it comes to passing them behind a thick pillar or around a blind corner?

Should we treat any movement of them as if they are being ‘re-cast’ (and so requiring a clear unobstructed view)? Or could a mage presumably will them somewhere out-of-sight?

What is the logical reasoning behind Arden’s Theorem proof of unique solution?

Here is the proof for Arden’s Theorem assertion that R=QP* is the unique (only solution) to R=Q+RP. My question is: what is the logical reasoning to prove that any equation is the unique (only solution)? Particularly in this case, how can the procedure

(1) recursively substitute R with R=Q+RP in R=Q+RP, then (2) establish the recursive definition of R, and finally (3) generalize the definition to R=QP*

logically lead to the proof that R=QP* must be the unique (only solution)?

Here is an example of the proof: Arden's Theorem Unique Solution Proof

Intuition behind cellular automaton mixed bulking function?

I’m reading the paper of Nicolas Ollinger on intrisically universal 1d cellular automata: https://arxiv.org/abs/0906.3213.

On page 3 (201), he gave the definition for mixed bulking quasi order. I’m unable to grasp the intuition behind such a defintion, injective universality seems to already capture what I can imagine universality to be. Another issue is that the mixed bulking map $ \phi$ has domain $ 2^{S_B}$ , how is $ \phi$ composed with the global function $ G_B$ when $ G_B$ has domain $ S_B^{Z^d}$ ?

Should Anti Virus and Anti Malware layer be the first layer in web application stack or can it seat behind services?

Can you have Anti Virus and Anti Malware layer sitting deep with the microservice layer and have the malicious file flow through all the services ? Argument being the file is in memory and not getting processed until the service we will put the Anti Virus and Anti Malware layer on.

Shouldn’t this be stopped at the routing layer of the application?

Heap down – What is math logic and intuition behind $\sum_{i=1}^{log(n)}(logn – i).2^i $

In heap (bubble down) we have the formula : $ \sum_{i=1}^{log(n)}(logn – i).2^i = logn\sum_{i=1}^{log(n)}2^i -logn\sum_{i=1}^{log(n)}i.2^i = log𝑛.2^{log𝑛+1}-(log𝑛.2^{log𝑛+1}-(2^{log𝑛+1}−2))=2𝑛−2∈Θ(𝑛) $

  1. Why we have $ \sum_{i=1}^{log(n)}(logn – i).2^i$ ?
  2. How we get to $ 2𝑛−2∈Θ(𝑛)$ ?

Please explain details!

What is it called when someone glides through a building’s external door behind you?

One form of social engineering is the practice of running up to a building’s external door just as an employee is entering. The employee often holds the door open for the intruder, bypassing security systems (RFID systems, for example).

Is there a name for this specific practice?

Mathematics behind Motion Blur

Recently I understood how the Gaussian Filter works and I was awed by the beauty of the mathematics behind it. Now while doing some coding stuffs in Octave I came across another type of blur, which is mentioned as $ image$ $ blur$ , and it gave me an output like this, enter image description here

It is beautiful, but i cannot find on the internet any explanation on the mathematics behind it?

Everywhere I searched $ Gaussian$ $ Filter$ is popping up, but i believe that this 2 are different to some extent as $ Gaussian$ $ Filter$ gave me this output–>

enter image description here

Which u can clearly see is $ different$ in appearance than the $ motion$ $ blur$ .

So, my question is, how is motion blur implemented?

Fundamental motivation behind the use of bits and binary representation

This is a naive question, but what makes binary representation special from a theoretical standpoint and from the standpoint of information theory?

If for technical reasons building ternary computers where the information is encoded as trits was easier than building traditional binary computers, I get the feeling that most theoretical computer science and information theory would still use bits and base-2 representation by default.

Even if I have an intuitive feeling of why, I would have liked to know a formal explanation of that: from a purely theoretical standpoint what makes bits and binary representation special compared to any other base?

If the answer is more complex than one may first think, links to books and scientific papers are welcome.