qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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20,484 | [
"https://dsp.stackexchange.com/questions/20484",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/13701/"
] | This is a conceptual question I am having difficulty to understand due to my limited knowledge of computer vision: If a pinhole calibration or any calibration is a mapping from world coordinates to image coordinate, is it possible to invert this mapping? I understand most of the times camera matrix is 3x4 so non invert... | If you have a single calibrated camera, and you have its 3x4 camera matrix, then you can map image points to the world points on the z=0 plane. This assumes that you know that your image point does indeed correspond to a world point on that plane.
So, you cannot map any image point to its corresponding world point usi... | It is possible to invert the mapping, but projecting a 2D image point into 3D world won't give you a single point but a ray, which is the locus of all 3D world points that map to the same point in the image plane.
This is why the info of depth is being lost during the process of image formation. As Dima said you can ... | https://dsp.stackexchange.com |
96,125 | [
"https://electronics.stackexchange.com/questions/96125",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29336/"
] | I am studying how i2c devices works...and I have downloaded a power point presentation from Google,
I have understood almost every basic concept, like, how the start and end of the transfer occur, what is SDA and SCL and what is master/slave.
but in this timing diagram,
SDA supposed to show the transmission of data b... | Not sure if I understand your question but... The dashed lines in your diagram means, more of the same for some time.. like the gap in SCL between 2 and 7 is dashed to mean there are bits 3, 4, 5, and 6 which repeat the same pattern as 1, and 2.
The reason for double lines.. the upper line is for a 1 and the lower is ... | Where the SDA line is shown with a line at the high and low level at the same time, it means the data could be either high or low (but must remain at that level) during that time period. Whether it's high or low depends on what data you are transferring, and will change from message to message.
Where the lines are sh... | https://electronics.stackexchange.com |
48,857 | [
"https://softwareengineering.stackexchange.com/questions/48857",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/10199/"
] | I've seen that there are several different paradigms in C++ concerning what goes into the header file and what to the cpp file. AFAIK, most people, especially those from a C background, do:
<h3>foo.h</h3>
<pre><code> class foo {
private:
int mem;
int bar();
public:
foo();
foo(const foo&);
... | While the second version is easier to write, it is mixing interface with implementation.
Source files which include header files need to be recompiled everytime the header files are changed. In the first version you'd change the header file only if you need to change the interface. In the second version you'd change t... | I did it the second way back in '93-95. Took a few minutes to recompile a small app with 5-10 functions/files (on that same 486 PC .. and no, I didn't know about classes either, I was just 14-15 years old and <strong>there was no internet</strong>).
So, what you teach beginners and what you use professionally is vast... | https://softwareengineering.stackexchange.com |
147,893 | [
"https://dba.stackexchange.com/questions/147893",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/104354/"
] | I'm trying to query a MySQL database with hourly timeseries data but I'm stuck with (daily) aggregation.
My raw data:
<pre><code>mysql> SELECT * FROM emoncms.custom_registers
-> WHERE timestamp >= '2016-08-24' AND timestamp < '2016-08-25';
+-----+------+---------------------+----------------+
| id ... | <pre><code>INSERT INTO [dbo].Test
select firstname + ISNULL(' ' + lastname,'')
,field1
,field2
,fieldn
FROM RAW.Test
</code></pre>
Try this. It will concatenate empty string to firstname in case of NULL in lastname
In case we are talking about Firstname that can be null your query should be:
<pre><code>... | Liya has a nice solution. This is another that handles both the null case and the empty string last name case as well.
<pre><code>INSERT INTO [dbo].Test
select LTRIM(RTRIM (COALESCE(firstname,'') + ' ' + COALESCE(lastname,'')))
,field1
,field2
,fieldn
FROM RAW.Test ;
</code></pre>
EDIT: Modified to allow... | https://dba.stackexchange.com |
16,608 | [
"https://cs.stackexchange.com/questions/16608",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/11110/"
] | The question is to design a CFG for the language of words that have as many c's as the difference of numbers of a's and b's, that is
$\qquad\displaystyle L = \{(a^l)(b^m)(c^n) \mid l, m \in \mathbb{N}; n = |l-m|\}$.
I have so far go to create the cfg for $(a^l)(b^m)$ but don't know how to do the one for $(c^n)$. It l... | Yuval's answer is headed in the right direction: consider $L_1 = \{a^lb^mc^n \mid n = l - m\}$ and $L_2 = \{a^lb^mc^n \mid n = m - l\}$. Also, as he points out, it's helpful to think of these conditions as $l = n+m$ and $m = n + l$, respectively.
I propose the following grammar for $L_1$:
$$S' \rightarrow aS'c \mid B'... | Hint: Break $L$ into two languages, $L_1 = \{ a^l b^m c^n : n = l-m \}$ and $L_2 = \{ a^l b^m c^n : n = m-l \}$. The conditions are probably better written as $l = m+n$ and $m = l+n$, respectively.
| https://cs.stackexchange.com |
100,894 | [
"https://physics.stackexchange.com/questions/100894",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2440/"
] | <strong>Scenario # 1</strong>
I put gunpowder and then a ball bearing in an old musket and fire the bullet.
<strong>Scenario # 2</strong>
Lets imagine I had a motor with a disk on it and there was the same ball bearing stuck on the edge of the disk somewhere. If I spin the motor up fast and then release the ball bea... | Newton's third law is really a special case of the conservation of momentum. Suppose you have two rigid bodies with momenta $\mathbf{p}_1$ and $\mathbf{p}_2$. If they only interact with each other, then $\mathbf{p}_1 + \mathbf{p}_2$ is constant, since total momentum is conserved. Differentiating this gives $\frac{d\mat... | Newton's first law (really Galileo's law of inertia):
This works as well in Special Relativity as it does for Newton. If an object has a constant relative speed near the speed of light and no force acts on it, it keeps moving at a constant relative speed. Check. Can't go faster than light, though.
Newton's second... | https://physics.stackexchange.com |
172,388 | [
"https://dba.stackexchange.com/questions/172388",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/67056/"
] | impdp import is stuck on:
<blockquote>
Processing object type
SCHEMA_EXPORT/TABLE/INDEX/FUNCTIONAL_INDEX/INDEX
</blockquote>
How can you debug this?
| During the impdp process, it doesn't import indexes, in fact it runs number of <code>CREATE INDEX</code> statements.
There could be various reasons of slow index creations such as inefficient PGA memory allocation and IO performance of underlying storage. Parallel(depending on available server resources-CPU,IO) opti... | It's not stuck. It just does not print every rebuilded index.
You can view status of the process using DBA_RESUMABLE.
<blockquote>
select * from dba_resumable;
</blockquote>
| https://dba.stackexchange.com |
253,693 | [
"https://physics.stackexchange.com/questions/253693",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/115292/"
] | Is it possible for a particle of mass $m$ to complete a circular path on a sphere if it starts from the topmost point and no external force acts on it except gravity and frictional force between sphere and the particle?
If yes, what are the conditions for it?
| The clue here is " how far apart". The question is asking for distance which must be in terms of the wave's wavelength. Phase measures fractions of wavelength. And you are given information of the wave's speed and the periodic time in which it propagates (frequency).
The fundamental "distance = rate * time" applies in... | <blockquote>
Phase is the argument of the wave.
</blockquote>
This is the definition written in my book and quite hard for beginners (<em>like me</em>).
So the question "What is phase?"
<blockquote>
Phase is the quantity which tells us the status of the wave.
</blockquote>
In normal x-y grid like x-axis tells ... | https://physics.stackexchange.com |
19,129 | [
"https://mechanics.stackexchange.com/questions/19129",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10824/"
] | Here's a new one:
Three times in the past week, the wipers have randomly turned themselves on. Each time turning the switch on and back off has fixed the issue.
I haven't seen anything else indicative of an electrical problem.
Suggestions? It's a 10 year-old car, but it seems odd that the switch would just give up ... | I'm pretty sure the electronics on your wiper motor has gone bad (or is going bad). The switch in the cockpit is there to instruct the wiper electronics what your intention is. When you turn the wiper on, it commands the motor to do its thing. If the wipers are coming on of their own volition, it's because the electron... | When the wipers turn on do they always turn on at the same rate? try changing the intermittent speed level if so equipped.
| https://mechanics.stackexchange.com |
92,397 | [
"https://electronics.stackexchange.com/questions/92397",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/27489/"
] | On my multimeter I have two current measurement connection. One for the mA and one for the A.
On the ampere one there's a time limitation but not on the mA one. Also they mention in the manual a kind of "cooldown time" after the measurement for the A one. So, basicaly, probing with this input can really slow down my p... | Your multimeter will be fine. It will display that the resistance is infinite if the resistance is greater than the range.
The reason you don't have to worry is because the multimeter is acting a constant current source, a very small one. So even if you short the probes, there will only be a small current flowing thro... | Not at all I would say. I can't think of any circumstances other than you trying to measure the value while hundreds of volts were across it. You should always ensure, when measuring in-circuit resistances that power supplies are either off or non-effective on that part of the circuit. This includes storage elements li... | https://electronics.stackexchange.com |
185,092 | [
"https://physics.stackexchange.com/questions/185092",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/51930/"
] | I'm somewhat unsure about how we go about counting degrees of freedom in classical field theory (CFT), and in QFT.
Often people talk about field theories as having 'infinite degrees of freedom'. My understanding of this is that we start with classical mechanics, which has one degree of freedom per spatial dimension - ... | You really should split your question. I will answer the part where you do not understand how counting of degrees of freedom work.
Basically we count the number of <strong>propagating (physical) degrees of freedom per point of spacetime</strong>. Of course, the total number of degrees of freedom is infinite because sp... | I have very limited knowledge on this, but I can try to offer a partial answer.
The 4-potential $A^\mu$ has four degrees of freedom (d.o.f.) but two of these are unphysical and can be eliminated exploiting electromagnetism's invariance under gauge transformations $A^\mu \rightarrow {A^\prime}^\mu = A^\mu + \partial^{\... | https://physics.stackexchange.com |
450,421 | [
"https://stats.stackexchange.com/questions/450421",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/257939/"
] | Let <span class="math-container">$X_1,\cdots,X_n$</span> be an i.i.d sample from <span class="math-container">$P_\theta(X=x)=\theta^x(1-\theta)^{1-x}, x=0,1; 0 \le \theta \le \frac{1}{2}$</span>. Its the method of moments estimator of the MLE better? Why?
<strong>My work:</strong>
I found the following two estimators... | There can't be a simple rule on this; it depends on circumstances.
At one extreme, suppose one variable is a <span class="math-container">$(0, 1)$</span> indicator (some people say dummy). Then transforming this is either impossible (e.g. the log or logit of such a variable is not defined for either one or two values... | I would say that it depends:
Many transformations are most likely to be useful on a single variable, and will depend on the distribution of such feature. For example, you might want to trim some values for a feature that has a lot of outliers, impute the ones of a feature that has missing values, log transform one th... | https://stats.stackexchange.com |
199,979 | [
"https://electronics.stackexchange.com/questions/199979",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88094/"
] | So im still trying to understand basic computer architecture, and have been writing a little bit of assembly for the MSP430 (basic LED/Switches stuff).
I've been browsing the instruction set, and things are starting to make more sense.
However for example a JNE/JNZ (Jump if Not Equal/Jump is Not Zero). I understand t... | In the assembler source, the JNE instruction (called BNE - branch if not equal in some instruction sets) will include the destination of the Jump, usually as a lable.
If the comparison before the JNE was equal, the instruction immediately following the JNE will be executed. If it was Not Equal, the distance (offet) t... | Jump instructions on the MSP430 are <strong>relative</strong> jumps. That means that the opcode for the jump instruction holds the distance of the target from the <strong>current instruction</strong>. This distance is called the "offset", and it's the number of words to adjust the execution point by. Multiplying by 2 g... | https://electronics.stackexchange.com |
31,478 | [
"https://dba.stackexchange.com/questions/31478",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | We have a SQL Server 2000 that will shortly be migrated to SQL Server 2005. It has years of Windows Authentication accounts created that no longer exist in Active Directory, which prevent the Copy Database Wizard from creating these accounts on the new server.
Is there a script or some automated way of deleting the a... | What I ended doing is listing the accounts with:
<pre><code> exec sp_validatelogins
</code></pre>
And running
<pre><code> exec sp_dropuser loginname
exec sp_droplogin loginname
</code></pre>
on the results.
| Per my original comment, it appears the <code>SUSER_SID</code> function just grabs whatever sid was recorded when the login was created, and doesn't actually query Active Directory (makes sense, as that could be expensive -- I even tried restarting the server service).
Here is a C# console application that accomplishe... | https://dba.stackexchange.com |
1,506,721 | [
"https://math.stackexchange.com/questions/1506721",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/193195/"
] | <strong>My question: How did Kahneman arrive at the 60% number in the last sentence ("60% of the pairs")?</strong>
From Daniel Kahneman, <strong><em>Thinking Fast and Slow</strong> (Chapter 19, Illusion of Understanding):</em>
Update: from your answers, it appears that the number should have actually been 65%, so it ... | If you have two random variables $X,Y$, the correlation coefficient is
$$\rho=\frac{\mu_{XY}-\mu_X \mu_Y}{\sigma_X \sigma_Y}$$
where $\mu$ denotes the mean of the variable and $\sigma$ denotes the standard deviation of the variable. Suppose now you have two Bernoulli random variables $X,Y$ (so they take on only the v... | For (mostly my own) future reference, here's my intuitive explanation of the answer.
If CEO strength made no difference, then for the stronger CEO, for 100 firms, 50 would be 'more successful' and 50 would be 'less successful'.
If a stronger CEO made a difference (.30 correlation), then out of 100 firms, 30 would be 'm... | https://math.stackexchange.com |
170,138 | [
"https://electronics.stackexchange.com/questions/170138",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/69533/"
] | I want change design from Through-hole technology to SMD design. Some components have no SMD version, for example some transistors in TO-92 package, and Power Mosfets, which available in DPAK SMD package, but since it requires a heat-sink, there is no much benefits of using SMD Mosfets with heat-sinks(DPAK heat-sinks h... | Generally your cheapest costs will be if all the parts are SMT and populated on a single side. Even if the parts cost somewhat more, the overall cost and handling may be worth it. If you can eliminate the heat sink by using copper area you may be able to save money and improve quality by eliminating assembly steps (for... | Nothing in terms of reliability. There are issues if you're making a board for production, though, in that you may be using two processes instead of one. You may need to reflow the SMD parts, and you may need to wave solder the TH parts. If you have SMD parts on both sides of the board, this may get fairly complicat... | https://electronics.stackexchange.com |
471,435 | [
"https://physics.stackexchange.com/questions/471435",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222579/"
] | The energy level of electron in an infinite square well in three dimensions is given by <span class="math-container">$E_{n_1 n_2 n_3} =\frac{ \hbar^2 \pi^2}{2mL^2}(n_1^2 + n_2^2 +n_3^2)$</span>. It is understood that <span class="math-container">$E_{111}$</span> represents the ground state. My question is how do we ran... | What has physical meaning is not the sum <span class="math-container">$n_1+n_2+n_3$</span> but the expression appearing in <span class="math-container">$E_{n_1 n_2 n_3}$</span>: <span class="math-container">$n_1^2+n_2^2+n_3^2$</span>. Therefore
<span class="math-container">$1^2+2^2+2^2=9 < 3^2 +1^2+1^2=11$</span>.
... | I believe I figured it out myself. It is because we rank them based on the equation itself. So defining <span class="math-container">$E_0 = \frac{\hbar^2 \pi^2}{2mL^2}$</span> we have <span class="math-container">$E_{111} = E_0(1+1+1)=3E_0$</span>. Similarly, the first excited state <span class="math-container">$E_{211... | https://physics.stackexchange.com |
51,137 | [
"https://electronics.stackexchange.com/questions/51137",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11280/"
] | Background:
Despite having a degree in Computer Engineering, working for 2 years as a vb.net developer, and someone that enjoys messing around with electronics. I've narrowed my buying options down to the PICKIT 3 or the ICD 3. Cost differential aside, I'd like to get something that I can get started with quickly, and ... | I've used both PICkit 3s and ICD 3s. Never had a problem so far with the PICkits, but have fried a couple of ICD 3s.
The ICD 3s of course are more expensive (and much faster). The good thing though is the ICD 3s have a lifetime warranty; if you have a problem with one, they include a little test board to verify wh... | I damaged the power supply section of the first generation PICkit 2 when I was getting started. Then I looked at the schematic and fixed it.
It is important to understand how your tools work. Troubleshooting broken electronics is not something to fear: If you are getting into electronics, this is exactly what you ... | https://electronics.stackexchange.com |
69,929 | [
"https://chemistry.stackexchange.com/questions/69929",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/42133/"
] | Let's say we want to run a CASSCF calculation of a radical, for example the cation of a neutral closed-shell molecule (therefore, we calculate an open-shell radical cation). MOLCAS, as well as probably every other program package out there, needs starting orbitals when performing a CASSCF calculation. For a neutral spe... | The best starting orbitals for a CASSCF calculation are optimised orbitals of another CASSCF (or RASSCF) calculation. That sounds a bit ridiculous, but this is probably the best way to figure out the active space.
At first you are probably choosing something quite small, like CAS(2,2) to CAS(4,4). For these calculatio... | <strong>Hartree-Fock Orbitals are Always the Wrong Choice for CAS Calculations</strong>
In Hartree-Fock (HF) theory, only the occupied orbitals contribute to the electronic energy. Due to the presence of Fock exchange, the Fock operator is different for occupied and virtual orbitals. For occupied orbitals, the Fock exc... | https://chemistry.stackexchange.com |
148,952 | [
"https://dba.stackexchange.com/questions/148952",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/105202/"
] | I have table that suffers from racing condition and I don't know how to fix it. I can't solve it 100% in code, so I need the server to help me.
<strong>The scenario</strong>
Admins of a system may <strong>accept</strong> or <strong>reject</strong> an appointment.
This can be done by email (via token etc) or by loggin... | We had a similar requirement and so added an extra where clause to the query. E.g.
<pre><code>UPDATE AppointmentTable
SET STatus = [Approved/Rejected]
WHERE AppointmentID = @ID AND Status = Pending
</code></pre>
Then afterwards, check how many rows were updated. If there were 1 rows updated then report back to the ... | As @Kin indicated, the solution hinges on what transaction isolation level you're using. Your DBA should be able to answer that question. If you're using plain old out-of-the-box READ_COMMITTED (the default) and no SNAPSHOT isolation, you should be able to:
<ul>
<li>BEGIN TRANSACTION </li>
<li>UPDATE AppointmentTabl... | https://dba.stackexchange.com |
269,404 | [
"https://dba.stackexchange.com/questions/269404",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/210917/"
] | I store hierarchical data in a Node-table, combined with a closure table (NodeClosure). Each node has a column "name" that should be unique among the sibling nodes (link to parent-Node + name should be unique).
This is definition of the tables:
<ul>
<li>Table "Node"
<ul>
<li>Column "nodeID"... | This looks to be a problem with UDF inlining. As @ScottHodgin suggested, the first step is to install the latest CU to see if the problem persists. If that doesn't resolve the problem, your options are:
<ol>
<li>Turn off <code>TSQL_SCALAR_UDF_INLINING</code> for the database:
<pre><code> USE YourDatabase;
ALTER DATABA... | I just called sp_recompile for all functions and it worked ok.
I faced this same problem when i moved from SQL Server 2014 to 2019. After altering the database option "Compatibility Level" to 150 (SQL 2019) the errors started to come up.
| https://dba.stackexchange.com |
250,871 | [
"https://mathoverflow.net/questions/250871",
"https://mathoverflow.net",
"https://mathoverflow.net/users/90940/"
] | I have a cubic function:
\begin{equation*}
h(x)\triangleq \eta+x-\frac{V(\eta-x)^3}{c\eta}
\end{equation*}
we know that $x\in[0,\eta)$ and all letters are positive and $V>c/\eta$. Hence we know that $h(0)<0$ and $h(\eta)>0$ and $h(x)$ is concave increasing for $x\in[0,\eta)$. So we can infer that there will be... | Differentiating $h(x, \eta) = 0$ implicitly, we get
$$ \dfrac{dx}{d\eta} = \dfrac{-c\eta^2 + V(2\eta+x)(\eta-x)^2}{\eta (3 V (\mu - x)^2 + c \eta)}$$
The denominator is always positive.
On any interval where the numerator doesn't change sign,
$x$ is monotone.
For the numerators of $dx/d\eta$ and $h(x,\eta)$ to bot... | In reply to the follow-up questions from FTXX, here is an argument. Using Israel's notations, suppose $h(x,\eta)=0$ and $\frac{dx}{d\eta}=0$. That means
$$V(\eta-x)^3=c\eta(\eta+x) \tag1$$
and
$$-c\eta^2+V(2\eta+x)(\eta-x)^2=0. \tag2$$
Multiply (2) by $\eta-x$ to get
$$-c\eta^2(\eta-x)+V(2\eta+x)(\eta-x)^3=0.$$
Now, ... | https://mathoverflow.net |
20,239 | [
"https://cs.stackexchange.com/questions/20239",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/11616/"
] | I'm having trouble finding the language represented by the following:
(AA|BB)*
Should the expression be read as... ( A (A|B) B ) *
or... ( (AA) | (BB) )*
If that isn't clear, should this produce something like... ABABAB or should it produce AABBAABBBBAA
My guess is that AABBAA is part of the represented language, w... | This Regular expression $(AA|BB)*$ can accept any string having two consecutive A's or B's i.e. even number of consecutive A's and even number of consecutive B's. so <code>AABBAA</code> is in it but <code>AB</code> is not in it.
| This depends entirely on convention; with respect to a (proper) formal definition, the expression is invalid as it not properly parenthesised. I'd say that typically, the order is (from stronger to weaker binding)
<ul>
<li>Kleene Star/Plus (also finite versions),</li>
<li>concatenation,</li>
<li>alternative.</li>
</ul... | https://cs.stackexchange.com |
152,564 | [
"https://electronics.stackexchange.com/questions/152564",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/65990/"
] | I have an old tv with an IR remote control. It has become quite bothering for me to change the remote control's batteries every other week. I thought to myself why not connect a Chinese phone battery (which costs not more than 2 bucks) to the remote and I'd only have to recharge the battery probably every other week bu... | If you bought a rechargable battery that was listed as 3.7v it may have been a single cell lithium battery. The differnt versions of these can be listed as being from 3.3v to 3.8v output. However this output value is only the nominal voltage, (somewhat of an average). The actual fully charged state of these batterie... | Use a regulator to bring down the voltage from 3.7V (4.2V at maximum charge) battery down to ~2.5V. As for your remote, if you have to replace the batteries every 2 weeks, buy better batteries and a new remote... I use my tv remote daily and I only have to switch out the batteries... well, I got the remote 2 years ago ... | https://electronics.stackexchange.com |
387,445 | [
"https://electronics.stackexchange.com/questions/387445",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/127055/"
] | Why can't capacitors be connected in parallel with ideal voltage sources? In various questions involving it we were asked to ignore the capacitors, by our teachers without valid explanations.
| The problem is that you can not connect an ideal voltage source of a given voltage in parallel with an ideal capacitor that has some initial voltage <strong>different</strong> from the source voltage. Once these two are connected, our definitions of "ideal voltage source" and "in parallel" demand that the voltage acros... | In DC power sources, you will see large capacitors in parallel with the output used to filter the DC voltage output.
In an "ideal" DC voltage source (like a fully charged car battery), putting capacitors in parallel with the battery terminals will initially change the total circuit current until the capacitor is fully ... | https://electronics.stackexchange.com |
61,921 | [
"https://quant.stackexchange.com/questions/61921",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/51780/"
] | I have an access to the order book dataset, which was sampled with resolution that is too high for my sandbox experiments with it. Because of that, I was wondering, what would be the correct way to downsample the order book, say for example, from 1s to 1m? For now I'm just taking snapshots that are separated by some co... | Two chief reasons for subsampling or using a different event space are (i) computational or spatial tractability and (ii) denoising/signal extraction.
Sergei's response seems to focus on the first issue, and I'll focus more on the latter. The two objectives can diverge. For example, options and OTC data can exhibit tra... | This depends on the use case, but there are many options including:
<ol>
<li>Convert full order log to top-of-book quotes and trades. This will probably eliminate 90% of ticks in the file.
</li>
<li>Convert full order log to trades. Even more compression.
</li>
<li>Take snapshots when you're present in the market, i.e.... | https://quant.stackexchange.com |
436,972 | [
"https://physics.stackexchange.com/questions/436972",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/77505/"
] | When one first encounters quantum mechanics, he learns about Bohr's model of the hydrogen atom and one of his biggest problems - electrons were accelerating and not emitting EM radiation (which is sometimes referred to as "radiation friction"). Then when you solve Schrödinger's equation with the following Hamiltonian:
... | <blockquote>
why is this Hamiltonian taken to explain the lack of radiation friction in QM, whereas in classical electrodynamics it is an invalid Hamiltonian for that exact same reason?
</blockquote>
That Hamiltonian is not an explanation of "lack of radiation friction in QM". It is an Hamiltonian that does not <em>... | The Schrödinger hydrogenic hamiltonian, which does not contemplate any interaction with the electromagnetic field, is important because its spectrum is bounded from below, which means that the electron cannot decay by emitting energy if it is already at the ground state. That means that, whatever form the quantized EM ... | https://physics.stackexchange.com |
214,630 | [
"https://softwareengineering.stackexchange.com/questions/214630",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17340/"
] | Generally whenever we're programming in any Programming language, say C, we would pass the parameters we need to pass to a function using the parentheses next to the name of the function. Whereas in jQuery, other than the user defined <code>function()</code> we write the action we need the function to perform inside th... | This is because the jQuery method <code>mouseenter</code> is expecting a single parameter, which is a function. It can then call that function later.
We could just as easily write
<pre><code>function blah(){
/* blah blah blah */
}
$("div").mouseenter(blah);
</code></pre>
| This is less about jquery, and more about how javascript works overall. Passing functions as variables is extremely vital to programming in javascript because javascript is asychronous.
Consider this:
<pre><code> var a = getA();
var b = getB(a);
</code></pre>
Now, we need 'a' first, then we use it to get 'b'. But ... | https://softwareengineering.stackexchange.com |
56,881 | [
"https://stats.stackexchange.com/questions/56881",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13561/"
] | I was wondering if there is a relationship between <span class="math-container">$R^2$</span> and a F-Test.
Usually <span class="math-container">$$R^2=\frac {\sum (\hat Y_t - \bar Y)^2 / T-1} {\sum( Y_t - \bar Y)^2 / T-1}$$</span> and it measures the strength of the linear relationship in the regression.
An F-Test jus... | If all the assumptions hold and you have the correct form for $R^2$ then the usual F statistic can be computed as $F = \frac{ R^2 }{ 1- R^2} \times \frac{ \text{df}_2 }{ \text{df}_1 }$. This value can then be compared to the appropriate F distribution to do an F test. This can be derived/confirmed with basic algebra.... | Recall that in a regression setting, the F statistic is expressed in the following way.
$$
F = \frac{(TSS - RSS)/(p-1)}{RSS/(n-p)}
$$
where TSS = total sum of squares and RSS = residual sum of squares, $p$ is the number of predictors (including the constant) and $n$ is the number of observations. This statistic has a... | https://stats.stackexchange.com |
3,802,087 | [
"https://math.stackexchange.com/questions/3802087",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/764058/"
] | My question revolves around the polynomial
<span class="math-container">$$x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1$$</span>
I know that it can be factorised into
<span class="math-container">$$(x^2+x+1)(x^6+x^3+1)$$</span>
but what method can we employ to obtain this result in the first place? Any method that works will be of g... | Method 1: Use what you know about polynomials of the form <span class="math-container">$x^n-1$</span>. For instance, your polynomial is <span class="math-container">$\frac{x^9-1}{x-1}$</span>. So if you can factor the numerator, many of those factors would be inherited to your polynomial. And indeed, we have
<span clas... | The essential key to answering your question is to recognize that your polynomial is <span class="math-container">$(x^9-1)\big/(x-1)$</span>.
Thus, in effect, you’re asking for the complete factorization into <span class="math-container">$\Bbb Z$</span>-irreducible factors, of <span class="math-container">$x^9-1$</span... | https://math.stackexchange.com |
10,242 | [
"https://astronomy.stackexchange.com/questions/10242",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/5343/"
] | Where there is fire, there is always smoke. So why there isn't any smoke near the Sun?
| The sun isn't on fire. Fire is actually very rare in the solar system. It requires chemical potential energy, which happens on earth because of life. Photosynthesis uses solar energy to build things out of carbon, oxygen, nitrogen and hydrogen (and some other elements). It's these carbon chain structures that ar... | The sun is not actually on fire, like a log burning. In the core of the sun, a nuclear reaction takes place that generates heat. Because the sun is so large, it generates a lot of heat and it glows like an incandescent light bulb.
| https://astronomy.stackexchange.com |
469,100 | [
"https://electronics.stackexchange.com/questions/469100",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/232475/"
] | When we measure an electrical quantity on Digital multimeter (DMM) like current, if we dont get readings of small range scale we switch the range utill we get our reading, same goes for voltage. But what is the quantity for which we do not change the scale on DMM and why?
| In most circuits the Ground symbol just indicates the point in the circuit that we will call "Zero Volts". It rarely indicates an actual connection to the earth.
In your circuit, "Ground/Zero Volts" is connected to the negative terminals of the Vcc and Vbb supplies. Voltages eleswhere in the circuit are measured rel... | <blockquote>
Also, what is the use of defining a voltage reference point?
</blockquote>
All voltages are relative, a concept which a lot of people have trouble understanding.
It is rather common to say that "at Point A we have X Volts" but actually it is wrong!
Officially you should say "Between point B and poin... | https://electronics.stackexchange.com |
308,979 | [
"https://physics.stackexchange.com/questions/308979",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/112820/"
] | Suppose we have a circuit with a voltage source, a switch open and an inductor all in series. If we close the switch, the potential difference of the voltage source is instantaneously applied to the inductor. As the current starts to build up, induced voltage from the inductance opposes it. If the induced voltage (back... | Lenz's law states that the induced current is in such a direction as to oppose the change producing it.
Back emf and a complete "conducting" circuit will result in an induced current.
The back emf can never exactly equal the applied voltage as then the current would be zero and not changing which would mean that th... | First of all, the condition that you are talking about, induced emf = voltage, is achieved at $t=0$. This is because at that instant no current is flowing in the wire and hence it follows from initial conditions and Kirchoff's law. (No current is flowing at $t=0$ since in $dt$ time from $t=0$ if $di$ has a finite value... | https://physics.stackexchange.com |
34,016 | [
"https://dsp.stackexchange.com/questions/34016",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/17157/"
] | Usually in radio systems in order to move the frequency response of the message signal to a new frequency band centered at f, the message signal is mixed with $\cos(2\pi ft)$.
What would change in frequency if we multiply the message signal to $\sin(2\pi ft)$ instead of $\cos(2\pi ft)$?
| It does the same thing (i.e. shift the frequency to another band), though mathematically it differs a bit. Fourier transforms of the two choices are as shown below:
$$
\begin{array}{|c|c|}\hline
f(x)\cos(ax) & \displaystyle\frac{\hat{f}\left(\xi-\frac{a}{2\pi}\right)+\hat{f}\left(\xi+\frac{a}{2\pi}\right)}{2}\\
\h... | Short answer: a phase shift of 90°, since $\cos(t) = \sin(t+\frac\pi2)$.
| https://dsp.stackexchange.com |
414,054 | [
"https://mathoverflow.net/questions/414054",
"https://mathoverflow.net",
"https://mathoverflow.net/users/130868/"
] | Sheafification is needed in limits and colimits of condensed abelian groups? If I have a functor <span class="math-container">$T: i \mapsto T_i$</span> from an index category to condensed abelian groups the limit and colimit of this functor are just <span class="math-container">$S \mapsto \lim_i T_i (S)$</span> and <sp... | I'll ignore the set-theoretic issues since I don't understand them well enough to say anything about them.
As with any site, the limits (and in particular, the kernel) of sheaves may be computed pointwise. On the other hand, the colomits are usually not computed pointwise (cokernels included). For example, an exact seq... | Let me complement Thiago's answer with what we said in the comments below. This is just a very long comment.
Note that if we restrict our attention to extremally disconnected sets, the situation is much nicer. Indeed, <span class="math-container">$Cond(Ab) \simeq Fun^\times(ExDisc^{op}, Ab)$</span>, where <span class="... | https://mathoverflow.net |
107,899 | [
"https://softwareengineering.stackexchange.com/questions/107899",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6987/"
] | After a year programming a web based business management system, I got my idea divided into two differents ways to do what I'm doing... I will try to explain in follow lines:
<strong>First I will describe my enviroment:</strong>
<ul>
<li>Webserver: <em>apache, ngynx</em> </li>
<li>Programming Language: <em>PHP, Shell... | Use SaaS:
<ul>
<li>You will update your product ASAP, users will always have last version</li>
<li>You will decide, which version of PHP and MySQL (etc) you will use</li>
<li>It's much more easy to users to pay per month / per day, than for whole product</li>
<li>"Cloud technologies" it's a future of IT world :)</li>
... | Considered simply shipping a virtual machine image with your favorite Linux and your application to the customer?
Then you can have it exactly as you want, and then let the Linux update mechanism handle your application too.
| https://softwareengineering.stackexchange.com |
1,678,257 | [
"https://math.stackexchange.com/questions/1678257",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Let $m,n$ be positive integers and $0\leq k\leq \min\{m,n\}$ an integer.
Prove or disprove that the subspace of $M_{m\times n}(\mathbb{C})$ consisting of all matrices of rank equal to $k$ is connected.
Frankly, I have no idea how to even start this...
I guess this is not path connected atleast...
<strong>Please giv... | A matrix $A$ has rank $k$ if and only if it is equivalent to the rank $k$ canonical matrix, ie
$$A=Q^{-1}BP$$
with
$$B=\begin{pmatrix}
I_k & 0\\
0 & 0
\end{pmatrix}$$
From this, try to prove that the space of rank $k$ matrices is path-connected.
| Here are the step i would follow :
<ol>
<li>Show that you can restrict yourself to $M_n(\mathbb{C})$ if $n \leq m$</li>
<li>Show that $GL_n(\mathbb{C})$ is connected. (or use it if you already know that)</li>
<li>Show that the space of matrices having rank $k$ in $M_n(\mathbb{C})$ is the image of $GL_n(\mathbb{C}) \t... | https://math.stackexchange.com |
145,424 | [
"https://electronics.stackexchange.com/questions/145424",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/38220/"
] | Here are the schematics <img src="https://i.stack.imgur.com/nHpkL.png" alt="Miniature Solid State Tesla Coil">
What is the use of>
-Transformer (I assume it is providing higher voltage? and what does it do) <BR>
-Transistor (Is it common emitter? and what does it do) <BR>
-LED (What does it do?)
I do not need this f... | As you said, the LED is build in reversed and so would act like a Zener diode with some volts. But the B-E junction of the transistor forms a diode in forward direction, hence it limits the voltage to about (below) 1V.
When you switch on the circuit, there will be a current into the base, and the transistor is ON (=co... | Your primary circuit serves as a high frequency oscillator to provide the excitation of the coil.
But to get optimal response from your Tesla coil, or perhaps any response at all you need to match the resonance of the secondary circuit with the driving frequency of the oscillator.
Number of turns (inductance) is on... | https://electronics.stackexchange.com |
180,108 | [
"https://softwareengineering.stackexchange.com/questions/180108",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/75552/"
] | I am new to web crawling and I am testing my crawlers. I have been doings tests on various sites for testing. I forgot about robots.txt file during my tests.
I just want to know what will happen if I don't follow the robots.txt file and what is the safe way of doing the crawling?
| The Robot Exclusion Standard is purely advisory, it's completely up to you if you follow it or not, and if you aren't doing something nasty chances are that nothing will happen if you choose to ignore it.
That said, when I catch crawlers <em>not</em> respecting robot.txt in the various websites I support, I go out of ... | There are no legal repercussions that I'm aware of. If a web master notices you crawling pages that they told you not to crawl, they <em>might</em> contact you and tell you to stop, or even block your IP address from visiting, but that's a rare occurrence. It's possible that one day new laws will be created that add le... | https://softwareengineering.stackexchange.com |
265,696 | [
"https://mathoverflow.net/questions/265696",
"https://mathoverflow.net",
"https://mathoverflow.net/users/106571/"
] | Suppose $M$ is a 2-dimensional smooth Riemannian manifold and $P\subset M$ is an open and connected subset with compact closure and a piecewise geodesic boundary.
My question is: What further conditions must $P$ (and $M$) satisfy such that the Gauss-Bonnet theorem is fulfilled for $P$?
I have found a lot of differen... | There are no other conditions, and in fact a more general statement is true.
The standard reference is the survey of Reshetnyak, Two-dimensional surfaces of bounded curvature,
in the book:
MR1263963
Geometry. IV.
Nonregular Riemannian geometry. A translation of Geometry, 4. Translation by E. Primrose. Encyclopaedia ... | See Pressley's Elementary Differential Geometry book, Chapter 13, to be specific, for an exhaustive discussion.
| https://mathoverflow.net |
26,690 | [
"https://electronics.stackexchange.com/questions/26690",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3552/"
] | Google search reveals a lot of pictures of three-phase transformers. Looks like a common setup is to have three pairs of winding and a shared core. The core typically consists of three "bars" in parallel and each pair of windings is wrapped onto its own "bar" and the "bars" are connected on both ends so the core is clo... | You are correct that in each winding, the magnetic field varies in phase with the current in the windings. What you're having a problem with is the concept of flux being 'annihilated' at where the cores are joined.
It's helpful here to think about 'magnetic circuits'. Think about a single phase transformer for a mome... | The key here is that each individual core has the primary and secondary pairs for that phase on it. While you are correct that for the transformer as a whole the fluxes should sum to zero, in each individual core you effectively only see the flux for that particular phase - the entire flux does not pass through each of... | https://electronics.stackexchange.com |
303,134 | [
"https://physics.stackexchange.com/questions/303134",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/105043/"
] | <blockquote>
<em>Problem from BdPHO 2016:</em>
A resistance of 4 Ohm is connected across a cell. Then it is replaced by another resistance of 1 Ohm. It is found that power dissipated in the resistance in both cases is same. What is the internal resistance of the cell?
</blockquote>
This doesn’t make sense to me... | The power dissipated in the external resistor is the product of current and voltage. The equation you need to solve is going to be a quadratic. If we assume the voltage of the unloaded cell is $V_0$, we can write
$$I_1 = \frac{V_0}{R_1+R_i}\\
P_1 = I_2^2R_1$$
And the same for $I_2$, with appropriate changes. If $P_1=... | To calculate the internal resistance use
$$ R_{int}=\bigg(\frac{V_o}{V_L}-1\bigg)R_L$$
you have enough info to get rid of unknowns $V_o$ and $V_L$, having two instances of this equation.
| https://physics.stackexchange.com |
1,135,252 | [
"https://math.stackexchange.com/questions/1135252",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/213296/"
] | Show that:
$$f'(x) = \frac{f(x + h) - f(x - h)}{2h} \tag 1$$
<em>Proof:</em>
If $(1)$ is true then $f'(x) = \displaystyle \frac{f(x + h) - f(x) + f(x) - f(x - h)}{2h} = \frac{f(x + h) - f(x)}{2h} - \frac{f(x - h) - f(x)}{2h}$
But here is the confusion, how do I modify the $f(x- h)$ on the RHS? <strong>PLEASE ONLY S... | $$\lim_{h \to 0}\frac{f(x + h) - f(x) + f(x) - f(x - h)}{2h} = \lim_{h \to 0}\frac{f(x + h) - f(x)}{2h} - \lim_{h \to 0}\frac{f(x - h) - f(x)}{2h}$$
In the second limit make a change of variables $u=-h$ to obtain:
$$= \lim_{h \to 0}\frac{f(x + h) - f(x)}{2h} - \lim_{u \to 0}\frac{f(x + u) - f(x)}{-2u}$$
$$=\frac{1}{2... | HINT:
$$2f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{x+h-x}+\lim_{h\to0}\frac{f(x)-f(x-h)}{x-(x-h)}$$
| https://math.stackexchange.com |
32,586 | [
"https://engineering.stackexchange.com/questions/32586",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/24083/"
] | I have tried to compare two courses, and there seems to be some overlap, but not as much. Which method is better when controlling a nonlinear system? Also, what is the main difference between the two?
| In nonlinear control theory, you will recognize most concepts such as controllability and observability where the linear case is often a special case of the nonlinear case. I would highly recommend digging into linear control theory first if you have not done so. Depending on the course you take, concepts such as Lyapu... | In control systems, the main focus is the design of a controller for machines or robots, here we mainly deal with linear systems application of linear control theory.
While non-linear systems is an advanced topic, where we deal with advance and mathematically more complex systems.
If its ur first course in control sys... | https://engineering.stackexchange.com |
24,516 | [
"https://mechanics.stackexchange.com/questions/24516",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/14180/"
] | So I have begun doing some research on the effects of idling. So my question is, does idling with the AC or heater on affect how much gas is given off? If possible, please give the percent of extra gas given off (e.g. AC causes 10% of extra gas to be given off). Thanks for your help!
| In most cars (except for some of those sold in very cold countries, I believe) the heating works by using waste heat from the engine, so the only additional energy used for heating is that to run the fans. Conversely, air conditioning requires energy to operate. Therefore, using AC will usually use more energy than usi... | Heat is basically free: your car's heating system works by diverting some of the engine coolant through the heater block rather than the radiator, with the result that waste heat gets dumped into the cabin rather than the outside world.
In contrast, air-conditioning works by connecting the AC's compressor to the engin... | https://mechanics.stackexchange.com |
197,145 | [
"https://physics.stackexchange.com/questions/197145",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/87238/"
] | When I am seated in a car that is accelerating in a particular direction I could, for example, throw a ball and it would appear to be flying the opposite way. With the windows covered etc. An observer on the earth's surface would tell me it's not the ball accelerating backwards, but the car speeding up forward.
As f... | I was confused by this too -- pop descriptions of the equivalence principle don't mention the problem where the gravitational field points in different directions in different places.
It <em>is</em> true that gravity is equivalent to acceleration, and that as a result, if you are freely falling, you feel like you're i... | The Earth's gravitational field extends inward from all of space to the Earth's surface, with it's origin at the center of the Earth. The Earth's gravitational field is characteristic of space-time that has been "curved" by a massive object.
If you stand on the ground and let go of a ball, it falls away from you at t... | https://physics.stackexchange.com |
358,305 | [
"https://math.stackexchange.com/questions/358305",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/72081/"
] | Find the number of three element subsets $A$ of $\{1,2,...,10\}$ such that $A$ contains at least one even and one odd integer.
I think in this way:
First we distribute one even and one odd number to 3 sets.Then there are 4 digits left of which 2 are even and 2 are odd.But how to distribute this 4 digits into 3 sets?
| I think you might be able to get what you want by determining how many subsets of three elements you can get (with no constraints), and remove all subsets which only have even or odd integers in it.
Which would be: $$\binom{10}{3}-2\binom{5}{3}=100$$
| This seems to be where you're heading:
<ul>
<li>Step 0: We start with an empty set.</li>
<li>Step 1: We add in an odd number; which can be done in $5$ ways.</li>
<li>Step 2: We add in an even number; which can be done in $5$ ways regardless of the choice in Step 1.</li>
<li>Step 3: We add in any other number; which ca... | https://math.stackexchange.com |
3,988,845 | [
"https://math.stackexchange.com/questions/3988845",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/866587/"
] | I need to prove that <span class="math-container">$9^{n+1}+2^{6n+1} $</span> is divisible by <span class="math-container">$11$</span> <span class="math-container">$\forall n\in N$</span> <br />
Steps I did:
<ol>
<li>basis step
<span class="math-container">$$\\ P(0)\ 11\mid(9+2 ) \ (True)$$</span></li>
<li>inductive ste... | Hypothesis gives that if <span class="math-container">$9^{n+1} \equiv r \pmod{11}$</span> then <span class="math-container">$2^{6n+1} \equiv -r \pmod {11}$</span>
The induction step follows:
<span class="math-container">$$\begin{align}P(n+1) &=9^{n+2}+2^{6n+7} \\
&= 9\cdot 9^{n+1}+2^6\cdot2^{6n+1} \\
&\equi... | <strong>Hint:</strong>
<span class="math-container">$$9^{n+2}+2^{6n+7}=9\times9^{n+1}+2^6\times2^{6n+1}=9\times(9^{n+1}+2^{6n+1})+55\times2^{6n+1}$$</span>
| https://math.stackexchange.com |
329,609 | [
"https://stats.stackexchange.com/questions/329609",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/196043/"
] | if I have a data-set of places where accidents happened in certain city , is identifing danger zones in that city considered as clustering problem ?
if for example I use KMeans , I would have to pass the n_clusters which I don't really know. I can't find the way to approach this.
| Comparison between
$$\hat{I}^1_N=\frac{1}{N}\sum_i I(x_i,y_i)\quad\text{and}\quad\hat{I}^2_N=\frac{1}{N}\sum_i \sum_j I(x_i,y_j)$$is possible since
$$\text{var} \hat{I}^1_N=\frac{1}{N}\,\text{var}\{I(X,Y)\}$$while
\begin{align*}\text{var} \hat{I}^2_N
&=\frac{1}{N^2}\,\text{var}\left\{\sum_{i,j}I(X_i,Y_j)\right\}\\... | Note that @Xi'an answer above also provide us with the optimal choice of $n,m$ when using the second estimator. Denoting:
$$a=Var^Y [E^X [I(x,y)]]$$
$$b=Var^X [E^Y [I(x,y)]]$$
by multiplying the expression with $N=mn$ we seek to minimize
$$\min_{nm=N} na+mb$$
which is solved using Lagrange multipliers and yields:
... | https://stats.stackexchange.com |
302,984 | [
"https://electronics.stackexchange.com/questions/302984",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/124196/"
] | Let's say I wanted to power two circuits: a 12V circuit and a 3V circuit. Could I use a 15V power supply and a 12V voltage regulator with three pins: Input, Output, and Ground. Input to Ground would be 15V, Output to Ground would be 12V, and presumably Input to Output would be 3V. Can I use the Input to Output volta... | Most positive regulators can only source current, not sink it, so what you suggest would only work if the current being drawn from the 12V to ground was more than the 3.3V circuit. If it was not then the 12V output would rise towards the 15V rail and your 12V circuit would experience overvoltage, and the 3V circuit wou... | This will not work. A voltage regulator will use some manner of letting energy from the input go to the output. It will measure the output constantly to verify that the output at the right level - if it is too low, it will increase the amount of energy let through, if it is too high, it will decrease it (this process i... | https://electronics.stackexchange.com |
270,014 | [
"https://electronics.stackexchange.com/questions/270014",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/130275/"
] | I am interested in replacing my doorbell chime with a new one. The existing button and transformer work, but I want to make sure that the chime I get is compatible with the output of the transformer. I'm not sure where the transformer is actually located in the house. I've taken a voltmeter, set it to 20v AC maximum... | All of those voltages (specified and measured) are NOMINAL. You can expect an open-circuit (no-load) voltage of 20~24VAC, and 10~16VAC under load. These things are rather sloppy by electronics standards and your design should be able to tolerate and operate on probably anything between 10VAC and 30VAC.
| Doorbell transformers are <em>weak</em> to make them safe against shorting. So their voltage changes a lot with load. Plus, the bell installation cables are usually very thin and have much and unpredictable voltage drop.
So there's not much sense in trying to "match" the voltages of transformer and chime. Instead, sta... | https://electronics.stackexchange.com |
158,201 | [
"https://electronics.stackexchange.com/questions/158201",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/54580/"
] | The first time I heard the term "shield" in connection with arduino [some years back], I had to google it. So, I'm curious if this term—which seem to me to translate roughly as "daughterboard" in pre-arduino terminology—was in use [roughly with this or a similar meaning] in some other EE context before ardu... | No.
The whole "shield" thing came about at about the exact time as the arduino became popular.
"Shield"s were, are, and will still be daughterboards or modules in pretty much any serious context for the foreseeable future.
<hr>
<< snark>><br>
Speaking loosely, "shield" means "extension module I don't really u... | <h2>Shield</h2>
A <i>shield</i> has always meant some sort of barrier for protection. Think 2000 years ago of something large and flat you hold so that the other guy can't clobber you with his sword.
In electronics, the term <i>shield</i> means a conductive layer that prevents capacitive coupling to whatever you are... | https://electronics.stackexchange.com |
315,871 | [
"https://mathoverflow.net/questions/315871",
"https://mathoverflow.net",
"https://mathoverflow.net/users/83700/"
] | It is a well-known result in functional analysis that the sum <span class="math-container">$M+N$</span> of two subspaces of a Banach space with <span class="math-container">$M\cap N=0$</span> is closed if and only if the inclination
<span class="math-container">$$\widehat{(M,N)} := \inf_{x\in M, \|x\|=1} d(x,N)$$</span... | You can find this result in the book of T. Kato. Perturbation theory for linear operators. Springer 1980, 1995. In Theorem IV.4.2, page 219.
| References are boring if the proof is simple:
The open mapping theorem tells you that <span class="math-container">$L+M$</span> is closed if and only the canonical map <span class="math-container">$S:L\times M \to L+M$</span> <span class="math-container">$(x,y)\mapsto x-y$</span> is an isomorphism (where the product ... | https://mathoverflow.net |
45,978 | [
"https://dsp.stackexchange.com/questions/45978",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/32840/"
] | I wrote a very basic C program to play a sine of a user-specified frequency. In the interest of portability, I have it spit values directly to stdout, so hopefully you can reproduce my problem on your own machine. This is the code I wrote:
<pre><code>#include <math.h>
#include <stdio.h>
#include <stdlib... | You are using 32-bit floats, and not resetting the phase by subtracting 2 pi. That means the phase will eventually climb up to where the sin() function's phase unwrapping algorithm doesn't have enough bits of quantization, or valid mantissa, left over afterward unwrapping.
Add this:
<pre><code>if (phase > M_PI)... | the following proposed code:
<ol>
<li>incorporates the comments to the question.</li>
<li>cleanly compiles</li>
</ol>
and now, the proposed code:
<pre><code>#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#define RATE 48000.0
#define TWOPI (3.14159 * 2.0)
int ma... | https://dsp.stackexchange.com |
94,125 | [
"https://electronics.stackexchange.com/questions/94125",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9332/"
] | I have a Kill-A-Watt Power meter on my computer that has a GPU mining bitcoins. It draws 500W from the wall outlet.
My question is, is my computer outputting any less heat than an equivalent 500W heater? Or is 100% of the power drawn from the wall converted into heat?
I'm not sure where the energy would go, so my gut... | Pretty much all those 500 watts are turned to heat - the motors stop spinning eventually and no energy has been siphoned off for re-use so heat is the 99%+ by-product. Your screen produces light but this is a small fraction of the energy usage. Your internet connection needs a few volts to drive signals down the wire b... | All the energy will be converted to heat, the less noble form of energy, thus increasing the entropy of the universe.
In your case, all the 500W will turn in heat. This is located for 99,9% in your home, as the other answer says.
| https://electronics.stackexchange.com |
1,680,707 | [
"https://math.stackexchange.com/questions/1680707",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/118224/"
] | I've been asked to determined whether the following are fields, PIDs, UFDs, integral domains:
$$\mathbf{Z}[X],\quad \mathbf{Z}[X]/(X^2+1),\quad \mathbf{Z}[X]/(2,X^2+1)\quad \mathbf{Z}[X]/(2,X^2+X+1)$$
<ol>
<li>The first is a UFD since $\mathbf{Z}$ is, but not a PID since $\mathbf{Z}[X]/(X)\simeq \mathbf{Z}$ is not a f... | <ol>
<li>$\mathbb{Z}[X]$ is not a PID because the ideal $(2,X)$ is not principal.</li>
<li>$\mathbb{Z}[X]/(X^2+1)$ is the ring of Gaussian integers, which is a PID. It is not a field, because $2$ is not invertible (for instance).</li>
<li>$\mathbb{Z}[X]/(2,X^2+1)$ is not even a domain, because as you noticed $X^2+1=(X+... | Hint: $(X+1)^2 = X^2+2X+1= X^2+1+2X$, so the class of $(X+1)^2$ in $Z[X]/(2,X^2+1)$ is zero and thus the class of $X+1$ is a divisor of zero.
| https://math.stackexchange.com |
154,380 | [
"https://chemistry.stackexchange.com/questions/154380",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/100905/"
] | <blockquote>
An ion with mass number 37 possesses one unit of negative charge. The ion contains 11.1% more neutrons than the electrons in its nucleus. An ion with a mass of 37 has % negative charge compared to % positive charge.
</blockquote>
With the aid of Periodic table, I doubt if the given ion is Chloride <span cl... | Let the number of electrons in the ion carrying a negative charge bex
Then Number of neutrons present
<span class="math-container">$$
\begin{array}{l}
=\mathrm{x}+11.1 \% \mathrm{of} \mathrm{x} \\
=\mathrm{x}+0.111 \mathrm{x} \\
=1.111 \mathrm{x}
\end{array}
$$</span>
Number of electrons in the neutral atom <span class... | You are overly complicating the solution with even or odd atomic numbers.
It is by definition that <span class="math-container">$Z+N=A$</span> where <span class="math-container">$A=$</span> atomic mass number, <span class="math-container">$Z=$</span> atomic number, and <span class="math-container">$N=$</span> number of... | https://chemistry.stackexchange.com |
4,508,309 | [
"https://math.stackexchange.com/questions/4508309",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/982108/"
] | On the problem below, I am unsure why my answer was wrong.
Arithmetic sequences <span class="math-container">$\left(a_n\right)$</span> and <span class="math-container">$\left(b_n\right)$</span> have integer terms with <span class="math-container">$a_1=b_1=1<a_2 \le b_2$</span> and <span class="math-container">$a_n b... | The assumption is that the increments are <strong>positive</strong> integers. So we have
<span class="math-container">$$[a_1+(n-1)k][b_1+(n-1)\ell] = 2010, $$</span>
where <span class="math-container">$k,\ell$</span> are the increments of <span class="math-container">$(a_n)$</span> and <span class="math-container">$(b_... | Let <span class="math-container">$c=a_2-a_1>0$</span>, <span class="math-container">$d=b_2-b_1>0$</span>, then <span class="math-container">$a_n=a_1+(n-1)c=1+(n-1)c$</span>, <span class="math-container">$b_n=1+(n-1)d$</span>. Let <span class="math-container">$n-1=k$</span>, then <span class="math-container">$a_nb... | https://math.stackexchange.com |
26,797 | [
"https://datascience.stackexchange.com/questions/26797",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/44456/"
] | I think the question is self-explanatory. But let's say you have a data with a few features with categorical data, and when building a model for example XGBoost you one-hot encode categorical features. Now you want to do prediction based on test data using the saved model. Obviously the test data needs to be one-hot en... | Since its pretty old post, possibly this response is helpful for others.
Its true that some of the algo's accept data in Categorical format and internally converts into OneHotEncoding. In such cases, model accept the data in raw format and doesnt require any explicit conversion handling.
In case if it's not supported... | A model is built on a specific set of features, which may include categorical features encoded using one-hot encoding. If you have new data with additional categories, your model has no idea how to interpret the significance of those categories. You should either map the new value to <em>none</em> of the 1-hot values... | https://datascience.stackexchange.com |
806,357 | [
"https://math.stackexchange.com/questions/806357",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/152865/"
] | I got this question on a test and I am really curious hoe you would approach it. I tried to prove stuff using the congruence laws but I didn't manage to prove anything.
| We have $$N=6^{2n}-25=(6^n-5)(6^n+5)$$
none of these factors equal $1$(unless for $n=1$), Therefore $N$ is always composite.
| Hint: You are looking at a difference of squares.
| https://math.stackexchange.com |
173,020 | [
"https://security.stackexchange.com/questions/173020",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/42265/"
] | I have two network segments (call them <code>A @ 192.168.1.x</code> and <code>B @ 192.168.2.x</code>) plugged into two separate NICs (<code>NIC-A</code> and <code>NIC-B</code>).
The OS on the physical machine is standard stock Ubuntu, with nothing configured to do any bridging on routing. So it can "see" both network... | Email addresses do not send spam. Email servers do.
Anybody can forge your email address as the From address without hacking you at all. That's how you get spam all the time that says it comes from you. You can however tell from the email headers what servers it was sent through.
Best thing to do would be to conta... | Most likely they were the victim of phishing (likely the exact same phishing template as the spam being sent) and their accounts were compromised. However, it's also possible that they have gained domain admin access and is using that to send spam. Also, depending on your mail security, authentication could be IP based... | https://security.stackexchange.com |
16,120 | [
"https://ai.stackexchange.com/questions/16120",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/8385/"
] | I am trying to predict crime. I have data with factors: location, keyword description of the crime, time crime occurred and so on. This is for crimes that occurred in the past.
I would like to treat the prediction of crimes as a binary classification problem. In this model, the data I have collected would form the "p... | It might be more informative to:
<ol>
<li>Label each combination of location, type, and time of crime with a crime <em>rate</em>. For example, theft, in Crystal City, at 11pm at night, occurs 20 times per year, or 0.4 times per resident per year.</li>
<li>Predict the crime <em>rate</em>, rather than individual events.... | I would go so far as to say that unless the training examples include predicate data- that is, data about conditions leading up to a crime or non-crime-, then you cannot have enough information to predict the occurence of a crime from conditions or events that happen in advance of a potential crime not yet committed.
| https://ai.stackexchange.com |
63,684 | [
"https://stats.stackexchange.com/questions/63684",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/27772/"
] | Two players are throwing each one die. The one that has higher value, receives a number of points equal to the difference of the values on both dice.
How do you estimate probability for a winner to collect more than 100 points in 100 throws?
| Begin with an array of the possible (equiprobable) outcomes of the two dice, with <em>my</em> die indexing the rows and <em>your</em> die indexing the columns. In this table, the entries are the payoffs to each of us: the first is my payoff $X$ and the second is your payoff $Y$.
$$\begin{array}{c|cccccc}
& 1 &a... | If you want to check the solutions given above using a simulation study, here is some useful code for it:
<pre><code>B = 100000
counter = 0
for(i in 1:B){
player1 = sample(1:6,100,replace=TRUE)
player2 = sample(1:6,100,replace=TRUE)
dice.diff = abs(player1 - player2)
player1.wins = ifelse(player1&g... | https://stats.stackexchange.com |
564,037 | [
"https://electronics.stackexchange.com/questions/564037",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/266589/"
] | I've learn today that when you applie a potencial V in a transmission line, we get a V in positive way, but we have to a V in negativa way, being reflected. What does it means? Like, I can understand it if we talk about electromagnetics waves, it colides with a superficie and be reflected, but what happens in a electri... | When you say,
<blockquote>
I can understand it if we talk about electromagnetics waves, it colides with a superficie and be reflected, but what happens in a electrical circuit?
</blockquote>
You must understand that a signal propagating in a transmission line <em>is</em> propagating as an electromagnetic wave. Consider... | <blockquote>
It is a potential being applied at a extremity and not a real/physical wave, right?
</blockquote>
Whether it is real or not is a matter for philosophers.
It <em>acts</em> exactly as if it were real. So whether you want to think of it as being <em>actually</em> real, or a figment of someone's mathematical ... | https://electronics.stackexchange.com |
674,250 | [
"https://physics.stackexchange.com/questions/674250",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/264332/"
] | As far as I know, the electromagnetic field strength tensor is defined to be the simplest object involving the electric and magnetic fields that transforms properly under Lorentz transformations. However, I don't get why such an object should be an antisymmetric rank <span class="math-container">$(2, 0)$</span> tensor,... | I think a very nice observation here is that if the force between field and current is
<span class="math-container">$$
f^a = F^{a\mu} j_\mu
$$</span>
then in order for the force to be <em>pure</em>, i.e. rest-mass-preserving, it is sufficient that <span class="math-container">$F^{ab}$</span> be antisymmetric.
Proof. L... | Forget everything you know about electromagnetism for a moment. Newton's second law (for constant mass) <span class="math-container">$m\ddot{x}=F$</span> tells us in Galilean-invariant terms how a scalar is linearly driven by a force, meaning its second time derivative appears on the LHS. Let's try the same thing for a... | https://physics.stackexchange.com |
576,884 | [
"https://math.stackexchange.com/questions/576884",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I can prove that
$$\int\sin(x)dx=-\cos(x)+C$$
by using $\cos'(x)=-\sin(x)$ and $\sin'(x)=\cos(x)$. Are there other proofs not involving this (at least, not explicitly) ?
| Let $x=\sec^{-1}u$ then we have
$$\sin(\sec^{-1}u)=\frac{\sqrt{u^2-1}}{|u|},dx=\frac{du}{|u|\sqrt{u^2-1}}$$
therefore
$$\int\sin x\,dx=\int\frac{du}{u^2}=\frac{-1}{u}=-\cos x.$$
Note that
$$\sec'x=\lim_{h\to0}\frac{\sec(x+h)-\sec x}{h}=\lim_{h\to0}\frac{\sin\frac{h}{2}\sin\frac{2x+h}{2}}{\frac{h}{2}\cos x\cos(x+h)}=\ta... | Just use the taylor series and integrate term by term, you recognise the new Taylor series as $-\cos x$
| https://math.stackexchange.com |
46,864 | [
"https://dba.stackexchange.com/questions/46864",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/9617/"
] | Suppose I am running multiple column update on one row. Does the database engine physically write new data to the database if some of the columns contain the same values as existed previously in the database? If so, how can it be avoided?
I'm about to implement a job which will run an update on a large table and most ... | You should assume the UPDATE is always writing the new value, even when identical. Write the query to eliminate no-ops with an appropriate WHERE clause. Approach it as a large table update, ie. do it in batches and make it idempotent. Is the only safe approach that is not victimized by assumptions and implementation sp... | I can't speak for all database engines, but most will perform an update if told to even if the result is no real change. MSSQL operates this way in some circumstances, though as pointed out in comments below it has since SQL2005 had some optimisations in the area, and I would be surprised if that isn't the case for mos... | https://dba.stackexchange.com |
285,701 | [
"https://mathoverflow.net/questions/285701",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7519/"
] | While studying cohomology theories on the stable homotopy setting, I have come up with the following basic question:
Consider the additive formal group law, $F_a$, and the multiplicative formal group law, $F_m$, both defined over a ring $R$.
If $R$ is a $\mathbb{Q}$-algebra, the exponential series defines a morphism... | Let $D$ be the divided power ring
$$ D = \mathbb{Z}[a_0,a_1,a_2,\dotsc]/(a_0-1,a_na_m-(n,m)a_{n+m}) $$
(where $(n,m)$ denotes the binomial coefficient $(n+m)!/(n!\,m!)$). Then ring maps from $D$ to $R$ biject with power series $f(t)=\sum_ka_kx^k\in R[[x]]$ satisfying $f(s+t)=f(s)f(t)$ and $f(0)=1$, and thus with homo... | To complement Neil Strickland's answer, one can lift the description of $\mathbb{F}_{(p)} \otimes D$ to a description of $\mathbb{Z}_{(p)} \otimes D$ where $\mathbb{Z}_{(p)}$ is the localisation of $\mathbb{Z}$ at $p$. One has
$$
\mathbb{Z}_{(p)} \otimes D = \mathbb{Z}_{(p)}[b_0,b_1,b_2,\dots]/(b_i^p - p b_{i+1}).
$$
I... | https://mathoverflow.net |
92,755 | [
"https://mathoverflow.net/questions/92755",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7392/"
] | It is well known that most topological spaces can be studied via their algebra of continuous real-valued (or complex-valued) functions. For instance, in the setting of compact Hausdorff spaces, there is a complete dictionary between topological properties of the space $X$ and corresponding algebraic properties of the a... | A very complete reference is the book "Lipschitz Algebras" by Nik Weaver. In there you will find various types of spaces of Lipschitz functions that can be associated to a metric space, and several results of the kind you are asking about.
From the book's introduction:
<blockquote>
Thus, there is a robust duality
... | I guess I'm late to the party, but here are a couple of points:
<ol>
<li>Yes, an arbitrary complete pointed metric space <span class="math-container">$X$</span> with finite diameter is characterized up to isometry in terms of <span class="math-container">$Lip_0(X)$</span>. <span class="math-container">$X$</span> is na... | https://mathoverflow.net |
457,270 | [
"https://physics.stackexchange.com/questions/457270",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/137908/"
] | Consider the Schwarzschild metric
<span class="math-container">$$ \left(1-\frac{2M}{r}\right)dt^2-\left(1-\frac{2M}{r}\right)^{-1}dr^2-r^2\left(d\theta^2+\sin^2\theta\, d\phi^2\right)$$</span>
Final goal: calculate the observed velocity of a photon on a radial geodesic according to an observer that's stationary at so... | If we want to be precise, your calculations seem correct but it is just the coordinates you are using that are not locally inertial and that is why you are not getting what you would like. Just a comment, do not set <span class="math-container">$\theta = 0$</span> that is a coordinate singularity of spherical coordinat... | What you've calculated is called a coordinate velocity. Coordinates don't mean much in general relativity, because GR allows you to use any coordinates you like. For example, I could change to a new coordinate <span class="math-container">$u=7r$</span> rather than <span class="math-container">$r$</span>, and then the c... | https://physics.stackexchange.com |
21,366 | [
"https://quant.stackexchange.com/questions/21366",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/6661/"
] | Why is the US 30 day t bill traditionally used as a risk free rate instead of Euro bonds for example? They are both not going to default surely?
| For many purposes we need a short term risk free rate. T-bill rates are ideal for this. Most Euro bonds have maturities measured in years, they cannot be considered "short term" or "money market" rates.
Also, Eurobonds are issued by a variety of issuers. Although generally highly rated, they may differ somewhat as to ... | Is a proxy.
Depending on what you are calculating and your considerations.
If you are calculating something in EUR and in Europe you might want to use the German bond. It just depends on your own criteria.
| https://quant.stackexchange.com |
446,964 | [
"https://stats.stackexchange.com/questions/446964",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/272213/"
] | I computed an odds ratio from a contingency table (exposure/disease). My odds ratio ended up being 3329.044 which is ridiculously large. The reason it is large is because the prevalence of the disease in the unexposed group is very small and the number of individuals in the unexposed group is very large. My question is... | Norm Breslow argued that we should prefer the odds ratio as an association measure <em>precisely because</em> it's possible to have an odds ratio of exactly <span class="math-container">$\infty$</span>. Some exposures in reality have deterministic relationship with the outcomes, but relative risks have theoretical uppe... | It looks like those who were exposed have a WAY higher risk of disease. The disease risk little under 50% in the exposed group and is .02% in the unexposed group. That is consistent with a massive odds ratio. What's the problem?
I guess you could use the absolute risk difference, or the risk ratio, as alternative mea... | https://stats.stackexchange.com |
415,478 | [
"https://softwareengineering.stackexchange.com/questions/415478",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102664/"
] | Okay, I was being interviewed at a company and the interviewer asked me a recursion problem. It was an online interview, so, he had set up the problem statement and a function signature on CodeSandbox (an online code editor/collaboration tool). I was supposed to fill-up the function body. He had only one parameter in t... | Well I like the index solution simply because it doesn't require creating multiple sub strings on the heap.
The problem with interview questions is they're mostly "guess what I'm thinking" games. So while you and I might be fully objectively right about which is the better solution the point is to show that y... | It is often necessary to introduce additional parameters when turning an iterative solution into a recursive, especially into a tail-recursive one.
The reason is that the implicit state that the iterative version has must go <em>somewhere</em> and the only place it can go is on the call stack … either in the return val... | https://softwareengineering.stackexchange.com |
280,678 | [
"https://softwareengineering.stackexchange.com/questions/280678",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8598/"
] | I have a program that is used by customers to do some computational work. And how long it takes always depends on how much data customer wants to compute. Some customers have a little data, some have a lot (bigger amount of customers have smaller data, but once with bigger data are richer).
It's possible to make a scal... | Create just one application which has on/off switches for various features. Developing and maintaining one application is much easier than doing the same with two apps. You can think that it won't be a big problem since two applications will be very similar, so there will be a lot of code reuse and as a benefit you'll ... | Two versions of the same thing is to be avoided at all costs. Build one thing that can be configured to hide some windows/menus/features instead. The alternative is very very expensive.
Let's say you build two versions. Both versions needs to be written, written tests for, tested manually. Bug fixes in both versions. ... | https://softwareengineering.stackexchange.com |
597,581 | [
"https://physics.stackexchange.com/questions/597581",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/260157/"
] | I have read many answers on stack exchange about what is the physical meaning of enthalpy, and there are some wonderful explanations.
one analogy i find very satisfying is it is the energy we need to create space for our system in our environment
but heating a gas a constant volume increases its internal energy ,but wh... | Not all increases in enthalpy are associated with <span class="math-container">$pv$</span> work. A simple example is the increase in enthalpy of a substance undergoing a phase change from a solid to a liquid at constant pressure and temperature. In this case there is heat transfer and no <span class="math-container">$p... | Enthalpy is defined as <span class="math-container">$H=U+PV$</span>, so <span class="math-container">$$\Delta H=\Delta U+\Delta (PV)$$</span>At constant volume, this reduces to <span class="math-container">$$\Delta H=\Delta U+V\Delta P$$</span>
| https://physics.stackexchange.com |
69,698 | [
"https://electronics.stackexchange.com/questions/69698",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/6423/"
] | I'm a beginner in electronics, and I'm ignorant of many basic things.
Check out these black things on the board:
<img src="https://i.stack.imgur.com/MPwRy.png" alt="enter image description here">
These are from a keyboard.
I'm disassembling it and I want to connect my own switches to it. All the connections seem to... | Those black sections are either a carbon-glue paste, or a conductive, carbon-doped elastomer. The carbon makes them (somewhat) conductive, and the rest holds it together. They then make contact by simply pressing against the silver-laden ink traces of the keyboard (in the background of your picture, I would guess).
If... | Easier than scraping away the black stuff may be to follow a copper trace from the black pad to a nearby via, and solder to the via. Or take it further and follow the via through the board, where another trace may take you to a larger copper pad that's easier to solder onto.
To solder onto a via, you'll need pretty t... | https://electronics.stackexchange.com |
60,876 | [
"https://dsp.stackexchange.com/questions/60876",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/45289/"
] | I read somewhere that the signal of speech has a bandwidth from 300 - 3400 Hz(Why), and audio files have a bandwidth from 50 Hz to 50000 HZ(Why).
Could someone help me , why are those constant sampling frequencies ?
| It's the human hearing which defines associated bandwidths. Then the sampling frequency will be chosen to be larger than twice the bandwidth for satisfying the sampling theory and still as small as possible to reduce processing costs.
Human hearing for the general sound signals is accepted to be between 20 Hz and 20 k... | There is a difference between a speech signal where what is said can be reasonably comprehended, a speech signal that sounds good, and speech signal that sounds so realistic that the speaker might be there. 300 to 3400 Hz is for a tolerable level of communication quality (people get used to it), 20 Hz to 20 or 40 kHz ... | https://dsp.stackexchange.com |
69,105 | [
"https://physics.stackexchange.com/questions/69105",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26250/"
] | Consider a particle confined in an infinite square well potential of width L,
$$V(x)=\left\{ \begin{array}{ll}\infty, &{\rm for}\ (x \le 0)\vee (x \ge L) \\0, &{\rm for} \ 0 < x < L \end{array}\right. $$
The ground state solution of the time independent Schrödinger equation is given by $\psi$(x)=Asi... | The explict notation is the folowing.
you have i,j particle indexes, and you have the following definitions:
$\vec r_{ij} = \vec r_j - \vec r_i $ , where $\vec r_i$ is the position of the $i$-th particle.
$W(\vec r_{ij},h_i)$ is the smoothing-kernel evaluated between the 2 SPH particles, using the smoothing paramete... | Suppose you have a quantity depending on multiple coordinate sets. $ f(x_i,y_i,z_i,x_j,y_j,z_j)$ the gradient $\nabla_i$ indicates that you must take the gradient with respect to $x_i,y_i,z_i$.
A 1 dimensional example to make it explicit. Suppose we have the following
$$
f(x_1,x_2,x_3) = \exp(-x_1)*x_2 - x_3
$$
(wher... | https://physics.stackexchange.com |
699,425 | [
"https://physics.stackexchange.com/questions/699425",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/330662/"
] | Say a spaceship is traveling though space in a uniform circular motion.
It's not orbiting any planet, it just flies in circles in an empty space.
The only force working on the spaceship would be the centripetal force caused by the ship's engine.
Thus, the work would be <span class="math-container">$0$</span>, as the fo... | You are right in saying that the centripetal force doesn't do any work, in fact the kinetic energy of the system doesn't increase as the absolute value of the velocity <span class="math-container">$|\vec{v}|$</span> stays constant.
I guess what you find counter intuitive is that the spaceship has to burn some fuel to k... | Without a force the spaceship would be floating in straight line at constant velocity. The reason why work is zero and the object is accelerated comes from its very definition.
From the second Newton's law:
<span class="math-container">$$\mathbf F = m\frac{d\mathbf v}{dt}$$</span>
Making a dot product with an infinites... | https://physics.stackexchange.com |
379,222 | [
"https://softwareengineering.stackexchange.com/questions/379222",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/246166/"
] | Coming from Desktop development, I'm in the middle of my very first web project (as a small side/learning-project). I'm using ASP.NET Core 2. I'm already thinking about going mobile too.
What are my best options here?
First thing that comes to my mind is separating logic and data interactions into web API, which will... | My experience with xamarin is that its a bit of a jack of all trades.
If you are keen to keep with a single tech stack then yes, .net core/framework apis + xamarin + azure is great. You can quickly get an app out on iPhone, Android and Windows
But, if you want a very polished app, which uses the UI specific to each p... | I would add to the previous answer above to avoid Xamarin Forms if you really want good UI. And use instead Xamarin Native which means you would need to create 2 separate UI, one for Android and one for IOS. The only disadvantage is that you need Mac for the IOS
| https://softwareengineering.stackexchange.com |
363,239 | [
"https://softwareengineering.stackexchange.com/questions/363239",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/292160/"
] | I am building a web/mobile application with Django Rest Framework (DRF) that enables authenticated users to post snippets and/or vote for other user's snippets. All users (authenticated or not) can also get the list of recent snippets (paginated, ex: 5 per page). Snippets, users and votes are stored backend in database... | As opposed to serverless, you might be thinking of a microserver architecture.
In either case, you break up the API into smaller pieces. For example have a micro server handle all authentication and authorization requests. So if you have another microserver that returns a list of items specific to a user, you need... | 'Serverless' is supposed to save you money by running your app via AWS Lambda or similar PASS hosting arrangements.
You pay per api call rather than having a server running 24/7
If your app is called only occasionally then you will save money. But if you app is in constant use you are probably better off with a norma... | https://softwareengineering.stackexchange.com |
31,694 | [
"https://physics.stackexchange.com/questions/31694",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10427/"
] | A friend of mine told me that because water heat capacity is higher. He also mentioned that it was similar to alcohol on skin effect.
Assume that there are 3 situations.
1. I did not get wet
2. I got wet by water
3. I got wet by pure alcohol
I believe the cold order is 3>2>1
Base on the heat capacity order is water>... | I think "quasi-circular" is a misleading name for this problem. Perhaps "quasi-elliptical" would be better? I say this because this problem does, in fact, contain a closed circular orbit (the radius of which you have called $r_c$). For that orbit you can find the period using Kepler's second law, which gives the result... | Your problem is one of a potential that depends only on radius. Newton proved that with these sorts of problems, angular momentum is conserved. Your instructor used this well known fact.
| https://physics.stackexchange.com |
290,738 | [
"https://softwareengineering.stackexchange.com/questions/290738",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/99719/"
] | I finished building a Python script containing eight functions which download files, extracts them, manipulate and analyze their data and then produce graphs and export them into PNG files.
The input files are located in a remote FTP site, but some intermediate files and the output PNG files as well are saved locally... | Have the 8 function calls wrapped in
<pre><code>if __name__ == '__main__':
</code></pre>
Then you can call the script by running
<pre><code>python NAME_OF_YOUR_SCRIPT.py
</code></pre>
If you need to pass any variables in when running it, use the argparse module
| I would suggest implementing command line parameters and command line help using argparse. The different functions could then be selected by command line options. If others without python installed need to use your program, then I would package it as an executable using pyinstaller.
Pyinstaller can be used to build ... | https://softwareengineering.stackexchange.com |
2,985,437 | [
"https://math.stackexchange.com/questions/2985437",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/460856/"
] | I used mathematica to check the values of <span class="math-container">$\ln{(\frac{x+1}{x})}- \frac{1}{x+1}$</span> are positive for any <span class="math-container">$x\geq 0$</span>.
How do I analytically show the statement is true for all <span class="math-container">$x\geq 0$</span>?
Any idea?
| Let <span class="math-container">$f(t)=\ln (1+t)-\frac t {1+t}$</span>. Then <span class="math-container">$f(0)=0$</span> and <span class="math-container">$f'(t)=\frac 1 {1+t}-\frac 1 {(1+t)^{2}}>0$</span> for all <span class="math-container">$t>0$</span>. Hence <span class="math-container">$f(t) >0$</span> fo... | It should be <span class="math-container">$x>0.$</span>
We need to show that
<span class="math-container">$$\ln\frac{x}{x+1}\leq-\frac{1}{x+1}$$</span> or
<span class="math-container">$$\ln\left(1-\frac{1}{1+x}\right)\leq-\frac{1}{1+x}.$$</span>
It's enough to prove that <span class="math-container">$$\ln(1+x)\leq ... | https://math.stackexchange.com |
25,777 | [
"https://scicomp.stackexchange.com/questions/25777",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/22351/"
] | Once again, I am not entirely sure how to describe what I am looking for, hence I have a hard time finding answers using Google or any other literal search method.
Let's say I have a time series:
$$(x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4),\ldots, (x_n, y_n)$$
Let's say I also have 2 key values: $V_1$ and $V_2$... | Nick Alger gives a nice explanation. Here is another one, possibly slightly simpler because it avoids the "should stay roughly the same" part.
Let's say you want to compute the derivative of any matrix function $X=X(C)$ with regard to entry $C_{ij}$:
$$
\frac{\partial X}{\partial C_{ij}}.
$$
In other words, you ask ... | We know that
$$C C^{-1} = I$$
If we perturb C a little bit, by a matrix $X$, and recompute the inverse, the result should stay roughly the same. In symbols:
$$(C + X) \left(C^{-1} + \underbrace{\frac{\partial C^{-1}}{\partial C}\cdot X}_{\text{matrix}}\right) \approx I,$$
where "$\frac{\partial C^{-1}}{\partial C}\cdot... | https://scicomp.stackexchange.com |
426,313 | [
"https://electronics.stackexchange.com/questions/426313",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/212389/"
] | MCU: STM32f030f4p6
There is garbage in reception buffer, when I use SPI and 2 DMAs (for reception and transmission).
<pre><code>void sendMsg2(uint32_t size, uint8_t* rx, uint8_t* tx){
DMA1_Channel2->CMAR=rx;
DMA1_Channel2->CNDTR=size;
DMA1_Channel2->CCR=DMA_CCR_MINC
|DMA_CCR_TCIE
|DMA_CCR_EN;... | <blockquote>
how the above calculations can be translated to bits per second, because everyone filters the optocouplers according to their Data rate (bps).
</blockquote>
A 10 us pulse would be equivalent to a 100 kbps digital data rate.
<blockquote>
Another question is about the input current of the optocoupler. ... | Your input current should be designed considering:
1- A comfortable value that your source (in this case, the Beaglebone) can sustain. In this case, I would choose 1mA.
2- Looking the graphics of how your optocopler works.
3- Look for the current transfer ratio of your part.
In your case, you probably want to work ... | https://electronics.stackexchange.com |
32,199 | [
"https://mechanics.stackexchange.com/questions/32199",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10905/"
] | I suspect that my 1999 <em>Volvo V40 T4</em> has a leaky exhaust manifold gasket. In winter there used to be some odd faint whistling while the engine was cold and now I'm trying to find the reason of a ticking sound that is audible when revving the car (frequency follows revs).
It can be heard anywhere outside the c... | Seeing as how your car has a turbo, the only place it would be leaking and you'd hear a ticking noise is pre-turbo, so the exhaust manifold at the head (header) and the down pipe on the hot side to the turbo. The turbo, due to it's nature of homogenizing the exhaust flow, will pretty much eliminate <em>any</em> ticking... | I'd say hyd lifter failure is pretty unlikely unless you ran your engine to extremely high RPM's right before this started. A leaking exhaust manifold can produce a sharp and short puff of exhaust that sounds like a tick. (Happened on my '92 Mustang often) If you can reach your manifold bolts, trying tightening them a ... | https://mechanics.stackexchange.com |
401,715 | [
"https://physics.stackexchange.com/questions/401715",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101916/"
] | So I'm working on a nuclear physics problem and am looking at radioactive decay. The common unit used for very long decays is years within the literature. Is this the sidereal or tropical year? I want to use units of seconds but seeing as how these 20 minutes 24.5 seconds that differential will add up over time...
I w... | A "year" without qualification may refer to a Julian year (of exactly $31\,557\,600~\rm s$), a mean Gregorian year (of exactly $31\,556\,952~\rm s$), an "ordinary" year (of exactly $31\,536\,000~\rm s$), or any number of other things (not all of which are quite so precisely defined).
Radioactive decay tables tend to ... | Years are merely an approximation, as you pointed out, they really aren't precisely defined. In physics seconds are used as they can be calculated exactly using atomic clocks.
For instance, no application requires an exact decimal representation of years, you can round to approximate numbers and then use a remainder o... | https://physics.stackexchange.com |
11,925 | [
"https://math.stackexchange.com/questions/11925",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/2587/"
] | Let $f:A \rightarrow B$.
The complements indicated below are taken within $A$ or $B$.
I need to prove that
$f(S)^c \subseteq f(S^c)$, $\forall S \subseteq A$, if and only if $f$ is surjective.
So I need to prove $f(A) = B$ right?
How can I prove this?
| You want to prove <em>two</em> things:
<ol>
<li><em>If</em> the complement of the image is always contained in the image of the complement, <em>then</em> $f(A)=B$; and</li>
<li><em>If</em> $f(A)=B$, then for every subset $S$ of $A$ you have that the complement of the image is contained in the image of the complement.<... | <strong>HINT</strong> $\rm\ (\Rightarrow)\ $ Put $\rm S\ =\ \ldots\ \ (\Leftarrow)\ $ Consider $\rm\ {\overline {f(S)}} \cap (f(S) \cup f(\overline S))$
| https://math.stackexchange.com |
357,416 | [
"https://softwareengineering.stackexchange.com/questions/357416",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/105068/"
] | I got asked a question today that was so basic I was unsure how to answer it.
I had added some logging statements to our integration testing package, to find out what part of it was taking so long (many hours) to finish. These tests are huge, so I've been going through them adding logging to different parts as time p... | <blockquote>
I had added some logging statements to our integration testing package, to find out what part of it was taking so long (many hours) to finish.
Our QA manager looked at these statements and said "Why do we need these? We never had logging before, why should we have it now?"
</blockquote>
They're n... | You don't say what you're logging. In my experience logging is a suboptimal solution for most things because what ends up happening is that logging is added and never removed. Then more is added and never removed, and soon you have so many logs that if you want to log something you can't find it in the logging output. ... | https://softwareengineering.stackexchange.com |
1,326,026 | [
"https://math.stackexchange.com/questions/1326026",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/205000/"
] | Det$
\begin{bmatrix}
1 & 2 & 3 &\ldots &n\\
1& 2^3& 3^3& \ldots & n^3\\
1 &2^5& 3^5& \ldots & n^5\\
\vdots & \vdots& & \vdots \\
1&2^{2n-1}& 3^{2n-1}& \ldots &n^{2n-1}
\end{bmatrix}
$
If the powers were consecutively increasing down the... | If you multiply the second column by $2$, the third by $3$ and so on, you get
$$
\det
\begin{bmatrix}
1 & 2 & 3 &\ldots &n\\
1& 2^3& 3^3& \ldots & n^3\\
1 &2^5& 3^5& \ldots & n^5\\
\vdots & \vdots& & \vdots \\
1&2^{2n-1}& 3^{2n-1}& \ldots &... | Call $\Delta$ your determinant. It seems to me that $$\Delta = n! \det \left( \begin{array}{ccccc}
1 & 1 & 1 & \dots & 1 \\
1 & 4 & 9 & \cdots & n^2 \\
1 & 4^2 & 9^2 & \cdots & (n^2)^2 \\
\vdots & \vdots & \vdots & \cdots & \vdots \\
1 & 4^{n-1} &... | https://math.stackexchange.com |
742,521 | [
"https://physics.stackexchange.com/questions/742521",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228556/"
] | I'm not a physicist, asking for knowledge. Is there any moon orbiting a planet, but bigger than that planet? If not, is it mathematically possible for a bigger object to orbit around a smaller object in space?
| As pointed out in earlier answers: in celestial mechanics the <em>shape</em> of the (orbital) motion is determined by one factor only: the <strong>mass</strong> of the respective objects.
In our solar system the motion of the celestial bodies is dominated by the Sun, because the Sun has so much more mass than the secon... | A moon does not orbit a planet. They both orbit around their centre of mass. This is true regardless of the masses of the bodies. It's even true for the sun and the earth: the earth really does make the sun move.
For a small moon, the centre of mass is inside the planet. If moon and planet were of equal mass, they woul... | https://physics.stackexchange.com |
124,011 | [
"https://security.stackexchange.com/questions/124011",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/111418/"
] | I'm fairly new to HTTPS and therefore risk this being a dumb question. I have a server hosted on my Raspberry Pi that allows me to configure it remotely, over a network and I'd like to convert to HTTPS to make it more secure. But since the IP address of the device changes from time to time due to DHCP, I'm not sure how... | Why not register the certificate for a fully-qualified domain name, instead of for the IP address? Assuming you're running it as a server, and leave it running for good stretches of time, you'd visit the DNS provider, and change the mapping between IP address and domain name, only when you received a new IP address.
A... | The most logical solution is to place the name in the subject of the certificate, and use dynamic DNS to make the name point to the same raspberry PI. Of course, one would need a DNS server.
If you can use IPv6 and having a DNS server is too much work, with it the Rasbperry would have a fixed address automatically wit... | https://security.stackexchange.com |
368,957 | [
"https://mathoverflow.net/questions/368957",
"https://mathoverflow.net",
"https://mathoverflow.net/users/163643/"
] | My guess is that there exists a constant <span class="math-container">$C$</span> such that <span class="math-container">$A(X) \sim C (\log X)^2$</span>.
| <span class="math-container">$$ \sum_{1 \leq i,j \leq X} \frac{1}{\mathrm{lcm}(i,j)} = \sum_{1 \leq i,j \leq X} \frac{\mathrm{gcd}(i,j)}{ij} $$</span>
<span class="math-container">$$ = \sum_{1 \leq i,j \leq X} \frac{\sum_{d|i,j} \phi(d)}{ij}$$</span>
<span class="math-container">$$ = \sum_{d \leq X} \phi(d) \sum_{1 \le... | If we are talking about "elementary", then just multiply the original sum by the sum of inverse squares and note that if we have three numbers <span class="math-container">$a=a'd, b=b'd, n^2$</span> where <span class="math-container">$(a',b')=1$</span>, <span class="math-container">$d,n$</span> are arbitrary,... | https://mathoverflow.net |
105,086 | [
"https://electronics.stackexchange.com/questions/105086",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/38315/"
] | When trying to drive a high capacitive load why do we gradually increase size of inverters in buffer design. Why not give the output of a circuit to one large inverter?
| Let us assume that we have given the output to one large inverter. Now the signal that has to drive the o/p cap will now see a larger gate capacitance of the large inverter. This results in slow rise or fall times. A unit inverter can drive approximately an inverter that 4 times bigger in size. So we need to drive a c... | Driving a very large inverter from the output of a normal (tiny) logic gate means that a large capacitance will be charged and discharged with tiny transistors. This takes a very long time, causes slow rise/fall transitions on the output pin, and causes considerable power waste in the large inverter.
Depending on the ... | https://electronics.stackexchange.com |
24,728 | [
"https://quant.stackexchange.com/questions/24728",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/19698/"
] | An investor deposits USD 300 in a bank account at time 0, reinvests all interest payments and continuously invests USD 300 per annum, until the total value of the deposits reaches USD 3312. At that point the investor stops making additional deposits, but still lets the interest payments accumulate in the account.
The ... | Let be $V_0=300$ the deposit at $t=0$, $V(T)=3312$ the value at $t=T$, and $r(t)=\frac{1}{20+t/2}=\frac{b}{a+t}$ the interest rate with $a=40$ and $b=2$. Denote $$I(t)=\rho\left(1-H(t-T)\right)$$ the rate of payment at any time in the range $[0,T]$ where $\rho=300$ and $H(t)$ is the Heaviside function or step function ... | Let's suppose $P$ is total annual deposits made continuously, then the change in value of total deposits $dV_t$ is (<strong>assuming no condition</strong> on additional deposits)
$$dV_t= V_t r dt + P dt $$
where we assumed $r$ is constant. Solving above differential equation, we have:
$$V_T = V_0 e^{rT} + \frac{P}{r}... | https://quant.stackexchange.com |
1,738,432 | [
"https://math.stackexchange.com/questions/1738432",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/239763/"
] | In real analysis there was an easy property that converted limits to infinity in limits at zero. More precisely, $1/z_n$ converges to 0 if and only if $z_n$ diverges (this is converges to infinity).
I want to apply this property to complex numbers as follows:
<blockquote>
Let $z_n$ a complex sequence. $1/z_n$ conv... | This is the way I look at it now:
If $1/z_n$ converges to 0, that implies $1/|z_n|$ converges to zero (note that the implication $|z_n|$ converges to |z| does not imply that $z_n$ converges to z). Now, using the real case |zn| converges to infinity $\iff$ zn converges to infinity.
For the other side, we just need to ... | The proposed proposition is false. The sequence $z_n = (-1)^n$ diverges, but $1/z_n$ does not approach $0$.
Here is a somewhat modified proposition that is true:
<blockquote>
$1/z_n$ converges to $0$ if and only if $z_n$ diverges to $\infty$.
</blockquote>
To prove this, you can use the following facts:
<ul>
<li... | https://math.stackexchange.com |
10,521 | [
"https://bioinformatics.stackexchange.com/questions/10521",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/6271/"
] | Is it possible to merge two files together using awk? I have two files with matched Chrom and pos column
file1 has the columns
<pre><code>CHROM POS ID REF ALT QUAL FILTER INFO
</code></pre>
file2 has the columns
<pre><code>CHROM POS ID REF ALT FATHER MOTHER DAUGHTER1 DAUGHTER2 DAUGHTER3 SON1 SON2
</code><... | If you just need to merge column together, you can use <code>paste</code> command:
<pre><code>paste file1 <(cut -d\ -f6- file2)
</code></pre>
In this case the whole <code>file1</code> is taken and only part of <code>file2</code> starting from column 6.
Assuming your data are sorted, another alternative is to use... | I'd recommend using R and either <code>merge</code> or one of the <code>join</code>s. Assuming your data is not too large, <code>data.frame</code> + <code>read.delim</code> should suffice to hold the two datasets. If not, try <code>data.table</code> + <code>fread</code>..
| https://bioinformatics.stackexchange.com |
1,866,705 | [
"https://math.stackexchange.com/questions/1866705",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/293123/"
] | <blockquote>
Given $$A =\begin{pmatrix} 0 & 3 & 0 \\ 3 & 0 & 4 \\ 0 & 4 & 0\end{pmatrix}$$ find a matrix $P$ such that $P^T A P$ orthogonally diagonalizes $A$. Verify that $P^TAP$ is diagonal.
</blockquote>
I'm not sure how to approach this problem. Any help is appreciated. Thanks!
| You want to find the eigenvalues and eigenvectors of $A$. Since $A$ is a real symmetric matrix, the eigenvectors should be orthogonal if the eigenvalues are distinct (which it is in this case): if they were not distinct you might have to use the Gram-Schmidt procedure to make the eigenvectors orthogonal.
Divide each b... | This should be easy even without calculating any eigenvalues or eigenvectors explicitly. Note that $A=5(uv^T+vu^T)$, where $u=(0,1,0)^T$ and $v=\frac15(3,0,4)^T$ are already two orthonormal vectors. So, if you take $w=\frac15(4,0,-3)^T$, then $Q=(u,v,w)$ is real orthogonal and
$$
A=5Q\pmatrix{0&1\\ 1&0\\ &&... | https://math.stackexchange.com |
89,687 | [
"https://mathoverflow.net/questions/89687",
"https://mathoverflow.net",
"https://mathoverflow.net/users/49/"
] | If $G$ is a finitely generated free group, then its classifying space $B G$ can be presented as a finite CW complex (a finite bouquet of circles), and therefore is Spanier-Whitehead dualizable. Are there any other discrete groups $G$ with the property that $B G$ is Spanier-Whitehead dualizable?
| Any finitely presented group of type FL admits a finite classifying space. (A group $G$ is of type FL if $\mathbb{Z}$ admits a finite length resolution by finitely generated, free $\mathbb{Z}G$-modules.) This is Theorem VIII.7.1 in Brown's book "Cohomology of groups".
More examples are given in section VIII.9 of Brown... | I'll answer a related question: in the $K(n)$-local stable category, $BG$ is dualizable for all finite groups $G$, moreover, each is self-dual. You can find this in Hovey and Strickland's 'Morava $K$-theories and localisation' Corollary 8.7.
More precisely, the result states that if $G$ is finite, then the $K(n)$ loca... | https://mathoverflow.net |
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