How can I assign multiple nets to a single plane layer? I've assigned the ground plane to net GND in the layer stack manager. But how can I assign nets 1.5V, 3.3V and 5V to the power plane?
I want to make a plane for my supply on my PCB and a plane for my MCU to isolate the MCU from the power supply noise.  I found this article in Altium designer :  But it isn't clear how the split plane tool work. Can someone explain it in a different manner?  [EDIT]  This is a picture how I see the planes:
Custom Gmail labels sort I want to sort the labels in my own order instead of the default abc order, so that, for example, the label named bills should come up first.  Any way to do that? Restrictive vs Non-restrictive Relative Clause How do I increase the render distance? Does GCM (or GHASH) only provide 64-bit security against forgeries? In a  a doubt was voiced about my answer, which claims GCM to requires $2^{128}$ for a successful forgery. The doubt was that the square root needs to be taken meaning the security would be $2^{64}$.  So of course I immediately checked the relevant security theorem ():  $$\mathbf{Adv}^{\text{auth}}_{\operatorname{GCM}[\operatorname{Perm}(n),\tau]}(\mathcal A)\leq \frac{0.5(\sigma+q+q'+1)^2}{2^n}+\frac{q'(\ell_A+1)}{2^\tau}$$  with $\sigma$ being the total plaintext size in blocks, $q$ being the total number of encryption queries, $q'$ being the total number of decryption queries, $n$ being the size in bits of the underlying permutation, $\ell_A$ being maximum authenticated input length in blocks and $\tau$ being the tag size in bits.  Now clearly from this we can see that performing $2^{n/2}=2^{64}$ queries yields a strong enough advantage for a break.  Now my question is: When talking about "n-bits of security" or "needs $2^n$ operations to break", do we usually talk about "online" security, ie queries to an oracle can be done and cost $1$ or "offline" security where no oracles are available or do we need to make this decision depending on the situation?  TL;DR: Does GCM offer 64 or 128 bit security? How do I count the number of occurrences of a char in a String? I have the string   a.b.c.d   I want to count the occurrences of '.' in an idiomatic way, preferably a one-liner.  (Previously I had expressed this constraint as "without a loop", in case you're wondering why everyone's trying to answer without using a loop). Prerequisites for AIC model comparison What are exactly the prerequisites, that need to be fulfilled for AIC model comparison to work?  I just came around this question when I did comparison like this:  &gt; uu0 = lm(log(usili) ~ rok) &gt; uu1 = lm(usili ~ rok) &gt; AIC(uu0) [1] 3192.14 &gt; AIC(uu1) [1] 14277.29   This way I justified the log transformation of variable usili. But I don't know if I can AIC-compare models when for example the dependent variable is different?  Ideal answer would include the list of prerequisites (mathematical assumptions). Identifying pin numbers from PCB Proving that expression is equivalent to the definition of derivative Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction? How to deal with long pre-bled brake line? Suppose $X$ is infinite and $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous Suppose that $X$ is infinite and that $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous.     My attempt:  Let $|A|=n$. We will prove by induction on n. It's clear that the the theorem is trivially true for $n=0$. Assume the theorem is true for all $n=k$. For $n=k+1$, then $|A \setminus \{a\}|=k$ for some $a \in A$. Thus $X \setminus (A \setminus \{a\}) \sim X$ by inductive hypothesis, or $(X \cap \{a\}) \cup (X \setminus A) \sim X$, or $\{a\} \cup (X \setminus A) \sim X$. We have $\{a\} \cup (X \setminus A) \sim X \setminus A$ since the theorem is true for $n=1$. Hence $X \setminus A \sim \{a\} \cup (X \setminus A) \sim X$. Thus $X \setminus A \sim X$. This completes the proof.       Does this proof look fine or contain gaps? Do you have suggestions? Many thanks for your dedicated help!     Update: Here I prove that the theorem is true for $n=1$.  Assume that $A = \{a\}$ and consequently $X \setminus A= X \setminus\{a\}$. It's clear that $|X \setminus A| \le |X|$. Next we prove that $|X| \le |X \setminus A|$. Since $X$ is infinite, there exists $B \subsetneq X$ such that $B \sim X$ (Here we assume Axiom of Countable Choice). Thus $|X|=|B|$. There are only two possible cases.   $a \in X \setminus B$   Then $B \subseteq X \setminus \{a\}=X \setminus A$ and consequently $|X|=|B| \le |X \setminus A|$. Thus $|X| \le |X \setminus A|$ and $|X \setminus A| \le |X|$. By Schröder–Bernstein theorem, we have $|X \setminus A| = |X|$. It follows that $X \setminus A \sim X$.   $a \in B$.   Let $b \in X \setminus B$. We define a bijection $f:X \setminus \{a\} \to X \setminus \{b\}$ by $f(x)= x$ for all $x \in X \setminus \{a,b\}$ and $f(b)=a$. Thus $X \setminus \{a\} \sim X \setminus \{b\}$. Since $b \in X \setminus B$, it follows from Case 1 that $X \setminus \{b\} \sim X$. Hence $X \setminus \{a\} \sim X \setminus \{b\} \sim X$. Thus $X \setminus \{a\} = X \setminus A \sim X$.  To sum up, $X \setminus A \sim X$ for all $|A|=1$. Howto wildcard SELECT * to query all fields of objects in APEX? I have created sObject and I need all the fields and I have many. Is there a way I can directly get all of them rather then typing each one of them. If $$(1+ \cos A) (1+ \cos B) (1+\cos C)= y = (1- \cos A) (1-\cos B) (1-\cos C)$$ then prove that $$y = \pm \sin A \sin B \sin C$$ I flashed new firmware and before doing so backed up apps and data with Titanium Backup. How do I restore? I have the folder on my PC which contains two .gz files and a properties file. Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate? The standard treatment of the one-dimensional  (SHO) using the raising and lowering operators arrives at the countable basis of eigenstates $\{\vert n \rangle\}_{n = 0}^{\infty}$ each with corresponding eigenvalue $E_n = \omega \left(n + \frac{1}{2}\right)$. Refer to this construction as the abstract solution.  How does the abstract solution also prove uniqueness? Why is there only one unique sequence of countable eigenstates? In particular, can one prove the state $\vert 0\rangle$ is the unique ground state without resorting to coordinate representation? (It would then follow that the set $\{\vert n \rangle\}_{n = 0}^{\infty}$ is also unique.)  The uniqueness condition is obvious if one solves the problem in coordinate representation since then one works in the realm of differential equations where uniqueness theorems abound. Most textbooks ignore this detail (especially since they often solve the problem both in coordinate representation and abstractly), however I have found two exceptions:   Shankar appeals to a theorem which proves one-dimensional systems are non-degenerate, however this is unsatisfactory for two reasons:   Not every one-dimensional system is non-degenerate, however a general result can be proven for a large class of potentials (the SHO potential is in such a class). The proof requires a departure from the abstract solution since it classifies the potentials according to their functional properties.  Griffiths addresses this concern in a footnote stating that the equation $a \vert 0\rangle = 0$ uniquely determines the state $\vert 0\rangle$. Perhaps this follows from the abstract solution, however I do not see how. How to find correct size inner tube Toggle Switch to swap the connections of two buttons $X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$ “How to Ask Questions in Private Beta” is listed in every site’s help centre When I go to /help/asking on any Stack Exchange site (), there is a link to How to Ask Questions in Private Beta (). It starts with:  Welcome to the private beta for [site] The tone and quality of the questions asked during this temporary private beta are critically important. If the private beta doesn't produce enough high quality expert level questions, it won’t proceed onward to the public beta. To help ensure your site makes it out of private beta, here are some tips:  There is no disclaimer or similar that this is outdated. This may lead to unnecessary confusion. I understand that that it is useful to keep this page in public pages for documentary purposes, as it may be linked in early Meta discussions, but it should:  not be listed in the table of contents (/help/asking) have a disclaimer How to shut down the computer safely by pressing the power button? So this is pretty simple: when I press the power button whilst the machine is on, it comes up with a menu (of which one of the options is to shutdown)  However, I just want it to just start shutting down once I press the power button without any further interaction!  How do I accomplish this? $P(x) = 0$ is a polynomial equation having at least one integer root, where $P(x)$ is a polynomial of degree five and having integer coefficients.  If $P(2) = 3$ and $P(10)= 11$, then prove that the equation $P(x) = 0$ has exactly one integer root.  I tried by assuming a fifth degree polynomial but got stuck after that.  The question was asked by my friend.