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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|---|---|---|---|---|---|
2,679,671 | [
"https://math.stackexchange.com/questions/2679671",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/472288/"
] | Question one:
<blockquote>
The derivative of function $f$ at the point where $x=t$ is defined by the following two equivalent limit expressions:
$$\lim_{x\to t} \frac{f(x)-f(t)}{x-t}$$
$$\lim_{h\to0} \frac{f(t+h)-f(t)}{h}$$
</blockquote>
I understand the first expression - same as basic algebra (change in $y$ o... | $Q1$: Ok, suppose you have points $(t, y1), (x,y2)$, without loss of generality, let $x>t$, since we want distinct points on the function. Then let $h$ denote this horizontal distance, then the two points translate to $(t, f(t)), (t+h,f(t+h))$, the slope of the secant line between the two points is $$ \frac{f(t+h)-f... | Question one:
The idea behind both expressions is, as you pointed out, change in $f(x)$ over change in $x$.
With the first expression, the inner expression is the change between two points, $x$ and $t$. The overall expression, including the limit, represents the value of this change in $f(x)$ over change in $x$ as $... | https://math.stackexchange.com |
150,553 | [
"https://physics.stackexchange.com/questions/150553",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/63691/"
] | Consider a particle in two dimensions with position vector $r(t)=<x(t),y(t)>$ and the shape of the path is described by a function $y(t)=f(x(t))$ (Thus $r(t)$ is a parametrization of $f$ with respect to time). Given some function $f$ and a speed $s$, how do we find the position vector $r(t)$ such that the particl... | It is not amplification! The purpose of the guitar body is to impedance and mode match between the string and the surrounding air.
<h1>Intuition</h1>
When a an object vibrates it pushes on the surrounding air creating pressure waves which we hear as sound.
A string vibrating alone without the body of the instrument doe... | <strong>Simple version:</strong> When something vibrates, it puts pressure on the air molecules around it, making them vibrate. So if just 1 or 2 strings that vibrate, it won't make very many molecules vibrate because it's not touching many of them. So you can imagine that when a large flat piece of wood is vibrating a... | https://physics.stackexchange.com |
548,141 | [
"https://physics.stackexchange.com/questions/548141",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/262229/"
] | What is the difference between angular acceleration and centripetal acceleration? Don't they both apply to circular motion?
| angular acceleration:<span class="math-container">$\frac {d\omega} {dt}$</span> the change of angular velocity with respect to time
centripetal acceleration: <span class="math-container">$\omega^2r$</span> if the orbital is circular. The component of linear acceleration of a object that causes it to have a angular mo... | Angular acceleration <span class="math-container">$\vec{\alpha}$</span> is defined as <span class="math-container">$$\vec{\alpha}=\frac{d\vec{\omega}}{dt}$$</span>
<span class="math-container">$\vec{\omega}$</span> is the angular acceleration of the particle.
Centripetal acceleration in circular motion is given as
<... | https://physics.stackexchange.com |
62,337 | [
"https://dsp.stackexchange.com/questions/62337",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/15911/"
] | I have implemented FIR filter using tapped delay line method. I start getting output as soon as first input sample is passed to it, I am wondering from which sample I will get the proper output(without transient outputs) from filter.
Does it depend on location of highest magnitude tap or it's just dependent on the len... | If it's a <strong>linear phase</strong> FIR filter, then the inputs signals will be shifted (delayed) by an amount of <strong>group delay</strong> at the output.
For a linear phase FIR filter of length <span class="math-container">$L = 2K+1$</span> the group delay will be <span class="math-container">$N = K$</span> sa... | It depends on what you mean by "meaningful". All outputs are meaningful in the sense that they combine the current input value with past input values. Initially, there are of course no past input samples. But if you agree that "no past samples" means "past samples with value zero" then that's exactly what happens if th... | https://dsp.stackexchange.com |
176,517 | [
"https://physics.stackexchange.com/questions/176517",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74253/"
] | [If anything goes against any mathematical or physical rules please let me know. I am a first year undergraduate student perusing a joint major in mathematics and physics so I do not have a complete background in those fields. I am just using my imagination and what I already know]
Consider an isolated electron in spa... | Yes, the force points along the vector of the relative velocity between the object and the air.
Quadratic drag is an interesting phenomenon. You have to calculate the net velocity vector (which includes a horizontal and vertical component) and compute the force along that axis; when you then decompose it into horizont... | "The vertical drag is greater" Could this be "lift"?
The vertical and horizontal velocity components do indeed produce a higher net velocity vector, but the vertical and horizontal kinetic energy components also have a Velocity squared function.
Interestingly, if you dropped an unpowered object from a tower in a 2 ... | https://physics.stackexchange.com |
171,004 | [
"https://security.stackexchange.com/questions/171004",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/160854/"
] | How to hide the Wi-Fi info from the people who are connected to my Wi-Fi?
| Most Wifi routers come with a 'guest' network option to enable. This sets up a type of DMZ that gives people access to your wifi but limits, and with things like VLAN and completely separate sub-netting, changes the information they can see about your network so that it would be completely different than your actual ne... | We assume you are looking the ways to hide your Access Point Name from being listed on users' devices?
You can set Hide Access Point Name (SSID broadcast OFF) on your Access Point so potential users who don't know your access point name will not see it on their devices.
| https://security.stackexchange.com |
218,692 | [
"https://mathoverflow.net/questions/218692",
"https://mathoverflow.net",
"https://mathoverflow.net/users/58096/"
] | Let $n$ be an even positive integer and $K_{2n}$ be the complete graph on $2n$ vertices. There are $\dfrac{1}{2}{{2n}\choose n}={{2n-1}\choose n}$ subgraphs of $K_{2n}$ which is isomorphic to $K_{n,n}$ and we use $E_1,E_2,\dots,E_{{2n-1}\choose n}$ to denote the edge sets of the ${2n-1}\choose n$ subgraphs respectively... | <strong>No,</strong> this is not possible. Towards a contradiction, suppose such a partition $S_1, \dots, S_{2n-1}$ of $E(K_{2n})$ exists. I first claim that each $S_i$ must be a matching. If not, then some vertex $v$ has degree at least 2 in say $S_1$. But now if we sort the $S_i$ according to the degree of $v$ in ... | If $n\geq 3$, then there are three sets (say, $S_1$, $S_2$, $S_3$ --- some may coincide) containing the edges of some triangle $v_1v_2v_3$. Then any collection of $S_i$ containing $S_1$, $S_2$, $S_3$ gives a non-bipartite graph.
On the other hand, for $n=1,2$ this is possible. An example for $n=1$ is trivial; for $n=2... | https://mathoverflow.net |
830,567 | [
"https://math.stackexchange.com/questions/830567",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/156491/"
] | I know that
$$
\ln(1+x)=\sum _{n=1}^{\infty }\:\left(-1\right)^{n-1}\frac{x^{n}}{n}
$$
| <strong>Hint:</strong>
$$\ln(5-x)=\ln\left[5\left(1-\frac{x}{5}\right)\right]=\ln 5+\ln\left(1-\frac{x}{5}\right). $$
| In your case it's more convenient to use
$$
\log \bigg( \frac{1}{1-w} \bigg) = \sum_{k=1}^{n} \frac{w^k}{k}
$$
just multiply by $-1$ and set $w=5x$.
| https://math.stackexchange.com |
449,155 | [
"https://physics.stackexchange.com/questions/449155",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/179934/"
] | By the first law, we know <span class="math-container">$\text{d}U=\delta Q+\delta W$</span> and, on adiabats, we know <span class="math-container">$\text{d} U=\delta W$</span>. But what is <span class="math-container">$\delta W$</span> for irreversible adiabatic processes? Take a thermally isolated container. If I stir... | Basically, it depends on the reference frame. There are two obvious reference frames you can pick to work with here. The first is the "lab" observer who is watching you twirl the string from some inertial viewpoint. The other is of an observer who is riding on mass. This second one is noninertial frame, so things can b... | Only conservative forces contribute potential energy, so there is no potential corresponding to the centrifugal pseudoforce. For the case of a mass on rotating string, the total energy is the sum of the linear kinetic energy and rotational kinetic energy, assuming gravitational and other potential energies are negligib... | https://physics.stackexchange.com |
248,184 | [
"https://physics.stackexchange.com/questions/248184",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101312/"
] | I have a few short questions about an interpretation of what happens with position and momentum wave functions described in literature I am using. Given momentum space wave function and position space wave function:
<span class="math-container">$$\Phi(p,t) = \frac{1}{\sqrt{2 \pi \hbar}}\int^{\infty}_{-\infty}e^{-(ipx... | I think you are getting something wrong in the 2nd and 3rd point, but i am going to try and give you an explanation. If i got something wrong in your questions, please do point it out.
1) If you measure the position, then Ψ(x)=δ(x-z) where z is the position that you measured(not a variable). If you plug this into the ... | The act of measuring cannot be represented by an operation in Linear Algebra, because <strong>postulate</strong> of QM says that upon measurement of observable $A$ with eigenvectors and eigenvalues given by $|a_i>$ and $a_i$ respectively on $|\psi>$ .
$$|\psi>=\sum_i c_i |a_i>$$
Gives $|\psi_{after}>$.... | https://physics.stackexchange.com |
3,143,176 | [
"https://math.stackexchange.com/questions/3143176",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/639323/"
] | Suppose <span class="math-container">$X_1$</span>,<span class="math-container">$X_2$</span>,<span class="math-container">$X_3$</span>,.....,<span class="math-container">$X_n$</span> are i.i.d. random variables with a common density poisson(λ)
(I is an indicator function) (t = a value)
E <span class="math-container">... | There is a very simple way to find this conditional expectation: <span class="math-container">$E(X_j|\sum\limits_{i=1}^{n} X_i=t)$</span> is independent of <span class="math-container">$j$</span> because <span class="math-container">$(X_i)$</span> is i.i.d.. If you call this <span class="math-container">$f(t)$</span> a... | Here is a correct proof, after all.
Express the conditional probability as a ratio of joint and marginal:
<span class="math-container">$P_k = P(X_i = k|\sum_{j=1}^n X_j=t) = P( X_i = k, \sum_{j=1}^n X_j=t ) /
P(\sum_{j=1}^n X_j=t ) = P( X_i = k) P( \sum_{j<>i}^n X_j=t-k ) /
P(\sum_{j=1}^n X_j=t )
$</span>
Give... | https://math.stackexchange.com |
172,383 | [
"https://dba.stackexchange.com/questions/172383",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/123840/"
] | I have 2 tables:
<code>conversation</code>
<pre><code>CREATE TABLE `conversation` (
`conversation_id` int(11) NOT NULL,
`title` varchar(200) COLLATE utf16_czech_ci NOT NULL,
`beginning_date` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,
`user_id` int(11) DEFAULT NULL
)
</code></pre... | For the specific query that gets only one row from the table:
<pre><code>SELECT *
FROM message
WHERE conversation_id = @some_id
ORDER BY add_date ASC
LIMIT 1 ;
</code></pre>
you only need a common (btree) index on <code>(conversation_id, add_date)</code>. The query will need to do only an index seek (which will find ... | It appear that performance here is of utmost importance and message order is also of utmost importance i.e. message order will be frequently use and it will be use for so many purposes.
you can keep one extra column in message table called "MessageOrder" int ,either autoincreament or user define increaament.
In nutsh... | https://dba.stackexchange.com |
30,384 | [
"https://cs.stackexchange.com/questions/30384",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/22152/"
] | If $\Sigma^*$ is the set of ALL strings including the empty string, then what can its complement possibly be? The empty set?
| Yes, the complement of all possible strings<sup>1</sup> is no strings at all. A machine that decides $\Sigma^*$ accepts every input; a machine that decides the complement of $\Sigma^*$ rejects every input.
<sup>1</sup> Strictly speaking, all finite strings over some fixed alphabet $\Sigma$.
| Note that the complement of $A \subseteq \Sigma^*$ is defined as $\Sigma^* \setminus A$; so yes: the complement of $\Sigma^*$ itself is the empty set.
To be completely accurate, you need to state with respect to <em>which universe</em> you want to take the complement. For instance, if you were to take the complement ... | https://cs.stackexchange.com |
102,809 | [
"https://datascience.stackexchange.com/questions/102809",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/113735/"
] | There are two ways to convert object datatype into numeric datatype, first is One-Hot encoding and second is simply map the numerical tags to different values.
For example for column Age containing three distinct values 'child', 'adult' and 'old', for that column One-Hot encoding is:
<div class="s-table-container">
<ta... | Which encoding technique to use depends on your data/features. Ordinal encoding is used when there ia a sense of order in your feature. For example you have a feature <strong>performance</strong> which has values <strong>worst</strong>, <strong>bad</strong> <strong>good</strong>. Here you should use ordinal encoder whi... | You are correct - one hot encoding, by definition, increases your dimensions and (most likely) also the sparsity.
Your numerical mapping can be rather misleading since e.g a random forest would interpret <code>adult>child</code> which, in the case of age, makes sense. But say the mapping was <code>{1:"dog"... | https://datascience.stackexchange.com |
255,010 | [
"https://softwareengineering.stackexchange.com/questions/255010",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/100505/"
] | Given the following interface
<pre><code>interface Modem {
public void Dial(string pno);
public void Hangup();
public void Send(char c);
public char Recv();
}
</code></pre>
Uncle Bob writes
<blockquote>
However, there are two responsibilities being shown here. The first responsibility is
connecti... | Let's say that for some reason we'd like to extend the Dial method to accept a structure
<pre><code>struct Endpoint
{
public string pno;
...
}
class Modem
{
public void Dial(Endpoint ep);
...
}
</code></pre>
This would cause the whole class to be recompiled - depending on the language and compiler -... | I think the worst part of the interface is the fact that there is temporal coupling.
Clients of the interface are expected to call methods in the right order, and this order isn't enforced by the type system, so it can only be infered by trial-and-error or by pre-existing domain knowledge.
My initial thought is to ke... | https://softwareengineering.stackexchange.com |
364,982 | [
"https://mathoverflow.net/questions/364982",
"https://mathoverflow.net",
"https://mathoverflow.net/users/69190/"
] | Let <span class="math-container">$G$</span> and <span class="math-container">$H$</span> be connected Lie groups. A Lie group homomorphism <span class="math-container">$\rho:G\to H$</span> is a smooth map of manifolds which is also a group homomorphism.
<strong>Question</strong>: Can we find a smooth (or real-analytic) ... | If <span class="math-container">$G$</span> is a compact simply-connected simple Lie group, then any nontrivial homomorphism <span class="math-container">$G\to G$</span> is an automorphism (it is injective because <span class="math-container">$G$</span> is simple, and any immersion of closed connected manifolds of the s... | I’m not sure if this is what you’re looking for, but the map <span class="math-container">$\mathbb{Z}/2\mathbb{Z}\to \mathbb{Z}/2\mathbb{Z}$</span> given by sending <span class="math-container">$0\mapsto 1\,, 1\mapsto 0$</span> isn't homotopic to a homomorphism. More generally if the codomain is disconnected the answer... | https://mathoverflow.net |
119,537 | [
"https://dba.stackexchange.com/questions/119537",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/12971/"
] | Our application developers run a lot of <code>SELECT *</code> queries against our database system, unfortunately.
The missing index suggestions of <em>sys.dm_db_missing_index</em> contain a lot of cases that indicate to create a 100% covering non-clustered index for those cases. For example actually there is an index ... | The missing index suggestions are <em>opportunistic</em> entries added whenever the optimizer happens to notice that an exact-match index for the current set of predicates it is considering do not exist on the base object.
The information recorded in the DMVs is intended to be a helpful input to the normal activities ... | Amending Paul's answer: You seem to be confused why an index that essentially copies the whole table can be beneficial. Indexes can be used to accelerate <code>WHERE</code> predicates and <code>ORDER BY</code> directives. The fact that your query plans have key lookups shows that the queries have at least a <code>WHERE... | https://dba.stackexchange.com |
121,253 | [
"https://cs.stackexchange.com/questions/121253",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/116269/"
] | I'm working on an example which says that a string x is obtained from a string w by deleting symbols if it is possible
to remove zero or more symbols from w so that just the string x remains. For example, the
following strings can all be obtained from 0110 by deleting symbols:
λ, 0, 1, 00, 01, 10, 11, 010, 011, 110, a... | Hint 1: As <span class="math-container">$A$</span> is regular, it is recognized by finite automata. Try to modify this automata to make it recognize <span class="math-container">$B$</span>.
Hint 2: Skipping "deleted" symbols might be handled by adding <span class="math-container">$\epsilon$</span> - transitions to the... | Use closure properties of regular languages: Apply substitution <span class="math-container">$\sigma(x) = \{x, \epsilon\}$</span>. This replaces symbols by themselves or nothing.
| https://cs.stackexchange.com |
3,837,296 | [
"https://math.stackexchange.com/questions/3837296",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I was just doing the following question:
If <span class="math-container">$a,b,c>0$</span> such that <span class="math-container">$a+b+c=abc$</span>, prove that:
<span class="math-container">$\frac{1}{\sqrt{1+a^2}}+\frac{1}{\sqrt{1+b^2}}+\frac{1}{\sqrt{1+c^2}}\le \frac{3}{2}$</span>
I think that this question can be ... | The homogenization gives:
<span class="math-container">$$\sum_{cyc}\frac{1}{\sqrt{\frac{abc}{a+b+c}+a^2}}\leq\frac{3}{2}\sqrt{\frac{a+b+c}{abc}}$$</span> or
<span class="math-container">$$\sum_{cyc}\sqrt{\frac{bc}{(a+b)(a+c)}}\leq\frac{3}{2},$$</span> which is true by AM-GM:
<span class="math-container">$$\sum_{cyc}\sq... | A different approach, but the desired result is equivalent to <span class="math-container">$\cos A+\cos B+\cos C\le\tfrac32$</span> in acute-angled triangles, which is true by Jensen's inequality.
| https://math.stackexchange.com |
502,664 | [
"https://physics.stackexchange.com/questions/502664",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/227750/"
] | A stone being thrown from the surface must have a velocity of <span class="math-container">$11.2$</span> km/sec if it wants to escape Earth's gravity. However, a stone that has a constant force being applied on it need not have an escape velocity. A stone with a thruster with infinite fuel can travel as slow as 1 m/s a... | While we can look at Newtonian physics and see that an object with escape velocity greater than <span class="math-container">$c$</span> would give rise to many of the properties of what we now know as blacks holes, the behavior of black holes is more complicated than what is visible from a Newtonian perspective. The f... | As long as it never crosses the event horizon, sure. Once it crosses the event horizon, it's gone forever. Gravity isn't <em>really</em> a force. It's a side effect of the curvature of space. Once you cross the event horizon, space becomes so curved there is simply no path out anymore. All worldlines point towards... | https://physics.stackexchange.com |
331,692 | [
"https://softwareengineering.stackexchange.com/questions/331692",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/236742/"
] | I'm trying to simulate an elevator, as always I started very simple by taking only a single order at a time, then added memory to the elevator in the form of queues so that floors are traveled in the order in which they were pressed, which obviously isn't the best approach.
So at the moment I'm using a very simple and... | "Efficiency" is not the most important feature, the most important is to make sure every order is followed, that there is no starvation. If someone presses 100 and people keep pressing 1 and 2 it may be efficient to keep going between those floors, but it'd be nice for 100 to be visited at some point.
I <em>think</em>... | The other answer correctly gives the standard elevator algorithm, which is basically "keep going in the same direction as long as possible and make every necessary stop along the way".
There are other elevator algorithms. For example, consider an apartment building where apartments get more expensive as you go up. The... | https://softwareengineering.stackexchange.com |
117,253 | [
"https://softwareengineering.stackexchange.com/questions/117253",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27844/"
] | I feel that the often seen C/C++ doesn't really describe my skills in my CV. So I'm planning to separate it into advanced C++ knowledge and mediocre C skills.
Do you think this is confusing for the reader? She could think: "C is a subset of C++, so what is this guy trying to tel me?" Well, what I'm trying to tell is: ... | You have asked so many questions in one; let me try to answer while segregating them. I hire many people which falls in this profile type and quite often i have to take so many interviews and reject people because often they don't quite have clear answer to the questions you asked.
<ol>
<li><strong>Is having good mas... | For the people that really matter, <strong>no, it shouldn't confuse them.</strong>
Anyone who knows anything about real-world C and C++ programming knows that although despite their similarities and history, production programming in either is more often than not a <strong>completely</strong> different animal.
| https://softwareengineering.stackexchange.com |
342,989 | [
"https://physics.stackexchange.com/questions/342989",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/133874/"
] | Do electrons have sea electrons and other stuff like protons have sea quarks? As I understand it a proton is basically 3 quarks interacting via the EM, weak and strong interaction. If you describe the interactions with Feynman diagrams you get an infinite number of diagrams with all sorts of virtual particles. Dependi... | As for your first question, this is roughly the idea but I have to emphasise that gluons play a big role, especially at small fractions of the proton momentum (indeed in proton-proton collisions at high energy, the protons are described by a set of probabilities to find a given constituent particle carrying a given fra... | I am guessing that the answer to your title question is no.
The quark "Sea" results from the fact that the protons is a composite particle, with 3 Valence quarks, and a collection of virtual quarks.
By contrast, because the electron has no known substructure, there is probably no scope for interactions that produce t... | https://physics.stackexchange.com |
251,341 | [
"https://electronics.stackexchange.com/questions/251341",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/120149/"
] | I understand that it is common for a UART scheme to use 8N1, meaning 1 start bit, 8 data bits, and 1 stop bit. Something like this:
<strong>0</strong>xxxxxxxx<strong>1</strong>
Where 0 is the start bit, the x's are the data, and 1 is the stop bit. In the case of multiple frames being sent back to back continuously, y... | This sounds like a question coming from someone trying to emulate a UART receiver in software or an FPGA. For RS-232, they use the term <em>mark</em> and <em>space</em>. But these usually correspond, once digitized, into a '1' and '0', respectively.
UART receiver often divides up each bit time (must be known, a priori... | It is <em>detecting</em> the start bit. That's exactly the purpose of it. The idle line will look like this:
<pre><code>...1111111111111111111111111111111...
</code></pre>
Once the receiver is seeing <code>0</code> after a long time of ones (or after a stop bit, as we will see shortly), it knows the transmission is s... | https://electronics.stackexchange.com |
187,492 | [
"https://softwareengineering.stackexchange.com/questions/187492",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/66745/"
] | I just started playing around with async/await in .Net 4.5. One thing I'm initially curious about, why is the async keyword necessary? The explanation I read was that it is a marker so the compiler knows a method awaits something. But it seems like the compiler should be able to figure this out without a keyword. So wh... | There are several answers here, and all of them talk about what async methods do, but none of them answer the question, which is why <code>async</code> is needed as a keyword that goes in the function declaration.
It's not "to direct the compiler to transform the function in a special way"; <code>await</code> alone co... | it changes the method from a normal method to a object with callback which requires a totally different approach for code generation
and when something drastic like that happens it is customary to signify it clearly (we learned that lesson from C++)
| https://softwareengineering.stackexchange.com |
265,749 | [
"https://physics.stackexchange.com/questions/265749",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/122515/"
] | Let's take plutonium-239 for example. $10\, Kg$ (sphere $9.9\, cm$) need for a nuclear reaction.
Are we talking about these numbers in Earth environment with $\approx 9.8\, m/s^2$ gravitational acceleration value? What if our environment is a high Earth orbit?
UPD:
I think more correct comparison in this question - a... | Actually, the critical mass is not affected by external gravitational fields. Gravity does not effect nuclear reactions. And, for the most part, gravity does not effect even chemical reactions either. Intermolecular forces (electromagnetic in nature) are vastly stronger than gravitational forces.
Rather, the critica... | The mass is the same to a very good approximation: gravity is absurdly weak compared to the factors that influence this.
One way that it <em>might</em> influence things was if the shape of the mass was significantly macroscopically distorted by gravity (ie a sphere might become flattened and you might therefore need s... | https://physics.stackexchange.com |
438,941 | [
"https://physics.stackexchange.com/questions/438941",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/199563/"
] | I'm asked to prove that the fractional change of density of a fluid (<span class="math-container">$\frac{\Delta\rho}{\rho_0}$</span>) is so that <span class="math-container">$$\frac{\Delta\rho}{\rho_0}=-\beta\,\Delta{T},$$</span> where <span class="math-container">$\beta$</span> is the volumetric coefficient of expansi... | Your analysis is not wrong. Note that the general definition of the coefficient of expansion is <span class="math-container">$\beta \equiv \frac{1}{V} \frac{dV}{dT}$</span>; so when you write it as <span class="math-container">$\beta \simeq \frac{1}{V} \frac{\Delta V}{\Delta T}$</span>, you're implicitly assuming that ... | Note that you can also rearrange the definition of <span class="math-container">$\beta$</span> in terms of the density <span class="math-container">$\rho=\frac m V$</span> to get that approximation:
<span class="math-container">$$\beta \equiv \frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_{p} = \frac{1}{m / \rho... | https://physics.stackexchange.com |
311,445 | [
"https://dba.stackexchange.com/questions/311445",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/208118/"
] | I have 2 tables, and the CASE statement below should only evaluate to 1/true if the record with the same lead_id exists in both tables. Here I have 2 ways of achieving this but just want to verify if its in fact the most optimal way of achieving this and which one is the better option here? The lead_id in t1 is the pri... | You can try something like this:
<pre><code>SELECT t2.lead_id IS NOT NULL AS '1'
FROM table1 AS t1
LEFT JOIN table2 AS t2 ON t1.lead_id = t2.lead_id ;
</code></pre>
Tested on my server:
<pre><code>SELECT vs.status IS NOT NULL AS '1'
FROM vicidial_log vl
LEFT JOIN vicidial_statuses vs ON vl.status = vs.status
WHERE ca... | even shorter...
<pre><code>SELECT t2.lead_id IS NOT NULL
FROM table1 AS t1
LEFT JOIN table2 AS t2 ON t1.lead_id = t2.lead_id ;
</code></pre>
A boolean expression evaluates as 0 (false) or 1 (true).
If really want the ids that match instead of 0/1, even simpler:
<pre><code>SELECT t1.lead_id
FROM table1 AS t... | https://dba.stackexchange.com |
599,512 | [
"https://physics.stackexchange.com/questions/599512",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/277789/"
] | <blockquote>
"Gradient of a tensor field of rank <span class="math-container">$n$</span> is a tensor of rank <span class="math-container">$n + 1 $</span>, In cartesian coordinates".
</blockquote>
I came across this statement in the Mathematical physics by Arfken. How does this statement relate to the definiti... | It's common for physicists to think about tensors in terms of the transformation rules for their components when you change the coordinates, such as rotating the coordinate axes.
The two "prototypical" tensors are simple geometric notions: the coordinate differential <span class="math-container">$dx^\mu$</spa... | Very roughly, the idea is simply that the partial derivative transforms as a rank 1 covariant tensor under coordinate transformations. Explicitly, if I change coordinates from <span class="math-container">$x^i$</span> to <span class="math-container">$y^i$</span>, then the derivative transforms as
<span class="math-cont... | https://physics.stackexchange.com |
379,582 | [
"https://stats.stackexchange.com/questions/379582",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/228334/"
] | I would do Wilcoxon rank sum test to compare mean equal. In R <code>>wilcox.test(a, b)</code>
We can assume non-normality of the samples.
| The Wilcoxon's test is a non-parametric alternative to the paired Student's t-test, is that what you want? Or do you want to compare the global mean? In which case you could use the Mann–Whitney U test.
| What are the assumptions of the data? Are you assuming non-normality of the data? If so, non-parametric tests are appropriate. However, t-tests are appropriate if you believe the data has normality. If I recall precisely (hehe) there's a goodness of fit test to test for normality.
| https://stats.stackexchange.com |
178,018 | [
"https://softwareengineering.stackexchange.com/questions/178018",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/16851/"
] | I have a background as UI designer. And I realized that it is a bit hard for me to write a pieces of logic. Sometimes I get it right, but most of the time, I end up with something hacky (and it usually takes a lot of time). And is not that I don't like programming, in fact, I'm starting to like it as much as design. It... | Baby steps.
Break up a big problem into smaller problems. Then solve the smaller problems.
Bonus points if you can back up your solutions to the smaller problems with automated unit tests.
| I usually write things down on paper while I'm thinking things through. That way I can write pseudo-code or do drawings (usually both), and I don't have to worry about the limitations of the drawing software or what can fit in a comment.
I find that if I'm doing something at least mildly complicated, I really need ... | https://softwareengineering.stackexchange.com |
440,430 | [
"https://softwareengineering.stackexchange.com/questions/440430",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/384551/"
] | I was reading a bit about garbage collectors and I am wondering if the garbage collector of a program scans the entire <code>heap</code> memory or what is allocated to it? If it reads the entire system memory, does it mean it is reading memory locations that are used by other applications? I understand that this does n... | <blockquote>
I was reading a bit about garbage collectors and I am wondering if the garbage collector of a program scans the entire <code>heap</code> memory or what is allocated to it?
</blockquote>
That depends on the garbage collector. There are many different kinds of garbage collectors.
For example, Reference Count... | There are a <em>lot</em> of details in garbage collection. Lots lots lots lots lots. Each one of them has different behaviors, so it's hard to cover everything.
Garbage collectors almost universally scan the memory within a single process. This is for two natural reasons. One is that garbage collection is always cl... | https://softwareengineering.stackexchange.com |
3,769,996 | [
"https://math.stackexchange.com/questions/3769996",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/616791/"
] | how to find eigenvalues of <span class="math-container">$T_n:R^n\to R^n$</span> where <span class="math-container">$T_n (x)=(0,x_1,\frac{x_2}{2},\ldots,\frac{x_{n-1}}{n-1})$</span> what happen if <span class="math-container">$n\to\infty$</span>, well by definition i do <span class="math-container">$T_n(x)=\lambda x$</... | It is clear that <span class="math-container">$0$</span> is an eigenvalue because <span class="math-container">$T_n(x) = 0$</span> iff <span class="math-container">$x_1 = \ldots = x_{n-1} = 0$</span>. Thus all <span class="math-container">$(0,\ldots,0,x_n)$</span> with <span class="math-container">$x_n \ne 0$</span> ar... | Notice that <span class="math-container">$T^n = 0$</span> so by the spectral mapping theorem we have
<span class="math-container">$$\sigma(T)^n = \sigma(T^n) = \{0\} \implies \sigma(T) = \{0\}$$</span>
so <span class="math-container">$0$</span> is the only eigenvalue.
For the case <span class="math-container">$n\to \in... | https://math.stackexchange.com |
142,418 | [
"https://chemistry.stackexchange.com/questions/142418",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/100813/"
] | I have heard conflicting reports:
<ol>
<li>Copper leaches to water only when the water is high in acid or the Copper is corroded.</li>
<li>Copper leaches to water any time, especially when it is new copper or the water is hot.</li>
</ol>
Which one would be correct?
| The second answer would be correct in an analytical context as the auto-ionization of water decreases in pH as temperature increases. And new copper does not have the surface of reacted material to shield the metal underneath, as such, scenario 2 always occurs, scenario one occurs faster, however, it's conditional stat... | Don't they sell copper tea kettles? This implies copper does not dissolve appreciably, even in hot water.
But have you seen houses with those copper rain gutters and downspouts that pour out rainwater onto concrete patios? You know, where the concrete turns that nasty-looking green color? Could be due to acid rain. Now... | https://chemistry.stackexchange.com |
32,007 | [
"https://physics.stackexchange.com/questions/32007",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10561/"
] | Say I have a charged molecule running along a linear evacuated tube (so no wind resistance). In the laboratory frame, we can measure that the particle is moving at some speed $v_1$. Provided that kinetic energy scales as the square of the velocity, how much energy do we need to impart on the particle to accelerate it... | <blockquote>
Why should this depend on v1 and not strictly the difference v2−v1?
</blockquote>
If I understand your question correctly, you're not so much asking for a mathematical explanation as you are for a physical one?
Remember that KE is essentially the energy <em>stored</em> from work done by a force on the ... | The kinetic energy depends on $v_1$ because it's not a linear function of velocity. You can show the problem with a bit of algebra - nothing too scary!
Take your example of accelerating from $v_1$ to $v_2$, then the energy required is:
$$ \Delta E = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2 $$
To make the problem cleare... | https://physics.stackexchange.com |
74,259 | [
"https://electronics.stackexchange.com/questions/74259",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25259/"
] | Two settings on a system I've got can be changed using jumpers. This is the connector and the pin description:
<img src="https://i.stack.imgur.com/yzeww.png" alt="enter image description here">
<img src="https://i.stack.imgur.com/v8Rn1.png" alt="enter image description here">
There seems to be three pins needed to ch... | (That looks like an AVR programmer)
The jumper is a tiny plug that connects two pins.
<img src="https://i.stack.imgur.com/UsiJ3.jpg" alt="enter image description here">
You put the jumper either on the left two pins or on the right two pins. The middle pin is a common pin.
<img src="https://i.stack.imgur.com/x3E6a.... | Jumpers are metal clips that short circuit two pins. The pins select which parts of the circuit are connected.
| https://electronics.stackexchange.com |
70,086 | [
"https://softwareengineering.stackexchange.com/questions/70086",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17252/"
] | C++ templates are notorious for generating long, unreadable error messages. I have a general idea of why template error messages in C++ are so bad. Essentially, the problem is that the error isn't triggered until the compiler encounters syntax that is not supported by a certain type in a template. For example:
<pre... | Template error messages may be notorious, but are by no means always long and unreadable. In this case, the entire error message (from gcc) is:
<pre><code>test.cpp: In function ‘void dosomething(T&) [with T = X]’:
test.cpp:11: instantiated from here
test.cpp:6: error: no match for ‘operator+=’ in ‘x += 5’
</code... | A few of the obvious reasons include:
<ol>
<li>History. When gcc, MSVC, etc., were new, they couldn't afford to use lots of extra space to store data to produce better error messages. Memory was scarce enough that they just couldn't.</li>
<li>For years, consumers ignored error message quality, so vendors mostly did to... | https://softwareengineering.stackexchange.com |
71,190 | [
"https://softwareengineering.stackexchange.com/questions/71190",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23813/"
] | Arguing for code generation, I am looking for some examples of ways in which it increases code quality. To clarify what I mean by code generation, I can talk only about a project of mine:
We use XML files to describe entity relationships in our database schema, so they help us generate our ORM framework and HTML forms... | Code generators cannot generate better code than the person who wrote the generator.
My experience with code generators is that they are just fine <em>as long as you never have to edit the generated code</em>. If you can hold to that rule, then you're good to go. This means you can reliably re-generate that part of th... | I think automated code generation and code quality are somewhat orthogonal and do not necessarily correlate.
Code generation is merely a way to solve a specific technical task. Whether it results in increased code quality very much depends on what you're doing.
Your situation is a good example of code generation resu... | https://softwareengineering.stackexchange.com |
336,628 | [
"https://physics.stackexchange.com/questions/336628",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/157785/"
] | I have been using an app called Quantum on the play store.
It says that the uncertainty principle can be explained by wave function, that is when we try to determine position , the wave function should be localised which means momentum is uncertain and vice versa.
My question is that if we measure anything of the par... | The question isn't dumb at all, it's great to think about these things.
Yes, when you measure a wavefunction, you collapse it. But it's what you collapse it into that's interesting. You collapse it into a special wavefunction called an "eigenfunction" of the operator.
In general, we can build any wavefunction by ad... | <blockquote>
My question is that if we measure anything of the particle, the wave
function should collapse and any uncertainty should vanish.
</blockquote>
If an ideal position measurement is made and the particle if found to be at $\mathbf{x}$, and then another ideal position measurement is made immediately after... | https://physics.stackexchange.com |
205,954 | [
"https://mathoverflow.net/questions/205954",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16702/"
] | In sub-Riemannian geometry, one considers manifolds $P$ equipped with a subbundle $\mathcal{H}$ of $TP$, the <em>horizontal distribution</em>. One then has a Riemannian metric only on this distribution $\mathcal{H}$, and is interested in horizontal curves $\gamma$, i.e. those with $\dot{\gamma}(t) \in \mathcal{H}$.
If... | Re question 2. The answer is provided by the Ambrose Singer theorem. You can see how it connects with your question in my book <em>A Tour of sub-Riemannian Geometry</em>. When the connection form is analytic then it is easy to state the Ambrose-Singer theorem.
The curvature of the connection, together with all ... | I like to think of a sub-Riemannian manifold as a space you are trying to move around in, but you have the restriction that from point $x$ you may only move in the directions $\mathcal{H}_x \subset T_x P$. (The sub-Riemannian metric $g$ can be thought of saying that the (marginal) cost to move an infinitesimal distanc... | https://mathoverflow.net |
737,580 | [
"https://physics.stackexchange.com/questions/737580",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Why do particles of a real gas have intrinsic random motion (before to collide with each other when the gas is heated)?
| There's a bunch of great answers already. Let me try another picture. This time focusing on the cosmological scale you seem to be interested in based on some comments.
Let's imagine there are stationary particles of hydrogen that just got created in the middle of perfect vacuum at some random position. This is our star... | It's a model. The random motion is an assumption of the model. If it's not a decent approximation, the model won't reflect the physics.
| https://physics.stackexchange.com |
688,370 | [
"https://physics.stackexchange.com/questions/688370",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/246795/"
] | Consider a point charge <span class="math-container">$q$</span> a distance <span class="math-container">$z$</span> from an infinite grounded conducting surface in the <span class="math-container">$xy$</span>-plane. Using the method of images, we know that the potential <span class="math-container">$V$</span> can be fou... | The resolution is that the image charge doesn't exist, so it doesn't take any "work" to "move" it.
More specifically, the image charge represents the effect of all the surface charges distributed on the grounded plane. "Moving" the image charge actually physically corresponds to moving cha... | The force the charge <span class="math-container">$q$</span> at a position <span class="math-container">$\vec{x}$</span> experiences is, as you correctly note, the negative gradient of its potential energy. Its potential energy is the product of the value of the charge <span class="math-container">$q$</span> and the el... | https://physics.stackexchange.com |
86,723 | [
"https://mathoverflow.net/questions/86723",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16716/"
] | Hi everyone. It is well known that a polynomial of degree $n$ is completely determined by $n+1$ points. Now, is there any similar result for rational functions?
| This answer builds on Joe Silverman's, and uses the same notation. He writes "as your conditions $F(x_i)=c_i$ ... are independent".
Suppose, for $1 \leq e \leq d$, that there do not exist any $2d+1-e$ of the points which can by interpolated by a rational function of degree $d-e$. Than I claim the conditions are indep... | A rational function of degree $d$ (of 1 variable) has the form
$$F(x) = \frac{a_dx^d+a_{d-1}x^{d-1}+\dots+a_0}{b_dx^{d}+b_{d-1}x^{d-1}+\dots+b_0},$$
where one should view the coefficients $[a_d,\ldots,a_0,b_d,\ldots,b_0]$ as homogeneous coordinates in the projective space $\mathbb{P}^{2d+1}$. Fixing a value $F(x_i)=c_i... | https://mathoverflow.net |
115,915 | [
"https://cs.stackexchange.com/questions/115915",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/110808/"
] | I really need some help with this problem. I'm running into the issue that the input is running out of space to append the 11 or 10. I could really use some help conceptualizing this problem and how to think about Turing machines in general.
Change the original input with a 1 into 11 and 0 into 10. You must also appe... | So, basically in heap representation, <span class="math-container">$LEFT(i)$</span> refers to the index of <span class="math-container">$i's$</span> left child. What we want to show is that index <span class="math-container">$⌊/2⌋+1$</span> is a leaf and is not a middleware node which can be proved if we could show the... | It's mathematical ture that
<pre><code>floor(n/2) > n/2 - 1
</code></pre>
Maybe rearrange the equation can help understanding the question.
<pre><code>Left[floor(n/2) + 1]
= 2 * (floor(n/2) + 1)
> 2 * (n/2 - 1 + 1)
= 2 * n/2
= n
</code></pre>
| https://cs.stackexchange.com |
177,208 | [
"https://mathoverflow.net/questions/177208",
"https://mathoverflow.net",
"https://mathoverflow.net/users/40883/"
] | Maybe this question is not suitable for here, but I don't think I would receive a satisfactory answer in Math StackExchange.
I could never understand the intuition behind polarization of abelian varieties and how it arises. I know that there is an analogy roughly with a prequantum line bundle, but I think the concept... | Weil introduced the term "polarization" in connection with his study of abelian varieties with complex multiplication. His definition is slightly different from what one sees today; one might call it a polarization up to isogeny instead of a polarization. One can find a discussion in Weil's article "On the theory of co... | Let me answer your last question "How can I think geometrically (in the lattice) about fixing a polarization?". I will follow the treatment given in [Birkenhake-Lange, <em>Complex Abelian Varieties</em>, Chapter 3].
Let $X = V / \Lambda$ be a complex torus of dimension $g$ and $L$ a line bundle on $X$ with first Chern... | https://mathoverflow.net |
335,966 | [
"https://softwareengineering.stackexchange.com/questions/335966",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/224451/"
] | I'm using MVC 5 Core on my Web API and I wanted to know what is the most optimal way of storing an Array into a database? Should I store Arrays, does it matter, or should I parse the array and input them individually into their own separate rows?
By optimally, I mean being able to have more control over the data and c... | (Assuming you have an RDB) You should create another table and put each array item in it as a row.
Don't try and reinvent the wheel with xml columns or string parsing. The RDB is designed to store and retrieve this kind of data as related tables.
| <code>Portfolio</code> has a one to many relationship with <code>ProjectDescriptions</code>. That's the structured database way to look at this. You can hack around that in a multitude of ways but if you want to be friendly to a structured SQL database that's the deal.
There are other kinds of DB's that don't even... | https://softwareengineering.stackexchange.com |
209,815 | [
"https://electronics.stackexchange.com/questions/209815",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/96291/"
] | My question is if lithium-ion batteries just lose capacity over time or if they also become more wasteful. From a practical perspective, can you easily get around loss of capacity in older batteries/devices by just carrying a powerpack or would an older battery also use up more power in a certain amount of time, thus d... | The primary aging effect in a Lithium-ion battery is increased internal resistance (caused by oxidation of the plates). This doesn't affect the Ah capacity, but it does reduce voltage and waste power at high current. Since voltage also drops as the battery discharges, the increased resistance causes it to reach cutoff ... | Yes, both effects take place. As Bruce mentions, because of the aging effect, the internal resistance of the batteries increases. The internal resistance <strong>is the main cause</strong> of "wasted" power (converts it to heat) and loss of effective capacity, so as it increases, more power is wasted and capacity red... | https://electronics.stackexchange.com |
11,404 | [
"https://mathoverflow.net/questions/11404",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1238/"
] | I tried to read the definition of it on Rubin's book "Euler systems" but it looks highly technical. Can anyone shed some light on it? In particular, is there some starting examples?
The wiki entry is too short and does not contain much useful information.
And what is the motivation of such objects? In particular, why ... | My understanding is that they're named "Euler systems" because that "Frobenius acting on T" in the definition (line 4, p. 22 of Rubin's book) is an "Euler factor" as in Euler's product decomposition of the Riemann zeta function.
The two easiest examples of Euler systems are the so-called cyclotomic units (not the ro... | A small correction to Hunter Brooks's answer: Kato's Euler system is unrelated to Heegner points but comes from Beilinson's elements on modular curves. The fact that Heegner points form an Euler system for the Galois representation attached to an elliptic curve (or more generally to a modular abelian variety) is due to... | https://mathoverflow.net |
334,134 | [
"https://physics.stackexchange.com/questions/334134",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/154632/"
] | Consider
$$
\langle a''|(AB - BA)|a' \rangle = (a'' - a') \langle a''|B|a' \rangle
$$
where $a''$ and $a'$ are eigenvalues of observable, $A$, which is Hermitian (real eigenvalues). $A$ and $B$ are compatible observables. Also, the eigenvalues of $A$ are nondegenerate.
This equation is from <em>Modern Quantum Mecha... | The parentheses are needed.
With parentheses:
$$
\langle a''|(AB - BA)|a' \rangle = \langle a''|AB|a'\rangle- \langle a'' |BA|a' \rangle = \langle a'' | a'' B | a' \rangle- \langle a''|B a' | a'\rangle = (a''-a') \langle a'' | B | a' \rangle
$$
without:
$$
\langle a''|AB - BA|a' \rangle = \langle a''| a'' B- B... | What you have in the parenthesis is not an operator but a number which can be taken out.
| https://physics.stackexchange.com |
102,865 | [
"https://mathoverflow.net/questions/102865",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25268/"
] | Say I have a polynomial <span class="math-container">$F$</span> of degree <span class="math-container">$n$</span> with coefficients in <span class="math-container">$Z_m$</span> and I wish to find <span class="math-container">$x$</span> such that <span class="math-container">$F(x)=0$</span> (mod <span class="math-contai... | The distinction between Morley rank as defined by arbitrary formulas and by definable families of formulas is essential. $\aleph_1$- categoricity in particular implies the rank can defined by
definable families. Since my 1973 [?] article in the transactions AMS or Shelah's book or
say Pillay's geometric model theory ... | Maybe the following remark will help you:
For any strongly minimal forumla $\varphi (x)$ and any formula $\psi(x_1,..,x_n,y)$ which implies $\varphi (x_i)$ for all i, the class $ \lbrace b : MR(\psi(x_1,..,x_n,b))=k \rbrace$ is definable for every k.
This is $26.4$ of Tent and Ziegler's book "A course in model the... | https://mathoverflow.net |
453,669 | [
"https://electronics.stackexchange.com/questions/453669",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/229101/"
] | If a microcontroller has USB functionality, can I program it directly from a USB port? Can I design the PCB without a USB to serial converter? What are the precautions I should take? The example that came to my mind was STM32F070 series.
| <blockquote>
If a microcontroller has USB functionality, can I program it directly from a USB port?
</blockquote>
That depends entirely on the microcontroller.
In the case of the STM32F070, the answer is "no". While this part supports USB, its bootloader only supports programming over the USART. Another option to c... | The bootloader needs to receive the application binary and save it to flash. It is always possible to create a bootloader that receives the binary over USB or any other communication channel.
EDIT: my answer implies that you don't need an USB to TTL Serial adapter on your PCB. But make sure you can connect one externa... | https://electronics.stackexchange.com |
136,680 | [
"https://electronics.stackexchange.com/questions/136680",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29305/"
] | As shown in the photo below, the PCB design was sent for fabrication without the drill data. Is it still possible to drill the via holes so we can save the PCBs?
This is a 2 layer board, most of the traces are on the top, a few are below. Is it practical to send the drill file to a machining shop and have them drill t... | It will be possible to drill these if you have a very rigid drill press and carbide bits. Back the PCB up with a sacrificial piece of laminate, get bright light and safety glasses and get very close to get the holes near the center. Use the highest spindle RPM your drill press is capable of (30,000 RPM is not too much)... | The problem with drilling the holes is that they won't be plated. Normally the top and bottom rings are connected through the board. In addition to electrical routing, this allows strong solder connections.
In your case, these look like connector locations. When you solder the connectors in place, you'll only be ma... | https://electronics.stackexchange.com |
3,565,434 | [
"https://math.stackexchange.com/questions/3565434",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/104576/"
] | Let <span class="math-container">$p:Y \mapsto X$</span> be a <strong>finite</strong> covering map, and let <span class="math-container">$\sim$</span> be the equivalence relation on <span class="math-container">$Y$</span> induced by <span class="math-container">$p$</span>: <span class="math-container">$y_1 \sim y_2$</sp... | Show that <span class="math-container">$id:(\Bbb N,d)\to (\Bbb N,\delta)$</span> is a homeomorphism.
It is clearly a bijection.
Also it is continuous since <span class="math-container">$id^{-1}(\{n\}) = \{n\}$</span> and this is open in <span class="math-container">$(\Bbb N,d)$</span> since <span class="math-contain... | In both metric, all singletons are open, and hence all subsets of <span class="math-container">$\mathbb N$</span> are open.
Hence, every function <span class="math-container">$f: (\mathbb N,d) \to (\mathbb N,\delta)$</span>, which is one-to-one and onto (for example, the identity map), is continuous, as it inverts ope... | https://math.stackexchange.com |
56,227 | [
"https://stats.stackexchange.com/questions/56227",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/24412/"
] | I try to understand and visualize myself covariance matrix. Supposing I have a matrix <code>A = [ 2 3 4; 5 5 6 ]</code>, how do I calculate its covariance matrix, and what is its practical meaning? (All I was able to understand by now is that on the diagonal of the covariance matrix, variances for particular variables ... | The off diagonal entries are typically covariances rather than correlations. The practical meaning depends on the context. In the most simple case it is just a table summarizing the variation within variables and the strength of the bivariate linear association between variables. For some models (e.g. SEM or LISREL mod... | If you have a vector of random variables $X = (X_1,...,X_n)^T$, the co-variance matrix $\Sigma$ can be calculated finding the pairwise co-variance of each of the variables. E.g. $\Sigma_{ij} = Cov(X_i,X_j)$.
So, like you say, along the diagonals you have $\Sigma_{ii} = Cov(X_i, X_i)=Var(X_i)$ and the upper and lower ... | https://stats.stackexchange.com |
533,883 | [
"https://electronics.stackexchange.com/questions/533883",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/175573/"
] | Ok, long story short.
I have a new TV that occasionally switches on all by itself. In case anyone is wondering it's a Sony XH90 and this problem is documented on www. Not trying to go into details about this, makes no sense.
The thing is, someone suggested to me, try reversing the power plug. For the heck of it, I trie... | <h2>Background (with a little speculation)</h2>
Inside the TV's switch mode power supply will be one or several Y capacitors that connect the internally produced DC voltages to either live or neutral. They are there to reduce the common mode noise produced by the high frequency switching transformer from affecting the ... | You talk about reversing the plug, so it seems it is an ungrounded appliance. In that case reversing the plug should not have any influence, as there is no reference for live and neutral.
However, it is a tv, so it has a third connection being the antenna or cable. I'm going to assume a cable connection, as there are t... | https://electronics.stackexchange.com |
2,414,201 | [
"https://math.stackexchange.com/questions/2414201",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/433761/"
] | $$\frac{1}{4\times6}+ \frac{\sqrt3}{6\times8}+\frac{\sqrt5}{8\times10}+\dots$$
The general formula for this that I got is : $$\sum_{n=4}^{\infty}\frac{\sqrt{n-3}}{n(n+2)}$$
the problem I am facing is that I am not able to choose the correct test, any help would be appreciated.
| Maybe you want to check convergence of $\displaystyle \sum_{n=1}^{\infty}\frac{\sqrt{2n-1}}{(2n+2)(2n+4)}$. $p$-series test says
<ul>
<li>If $p<-1$, then $\sum n^p$ converges.</li>
<li>If $p\ge -1$, then $\sum n^p$ diverges.</li>
</ul>
$\sum n^{-3/2}$ converges, and you may compare $\frac{\sqrt{2n-1}}{(2n+2)(2n+4)... | First of all, you have to mention that $n$ above is even, but I claim that does not matter: even if you include odd $n$, the series is convergent, so that it anyway is convergent in the even case.
Note that $\frac{\sqrt{n-3}}{n(n+2)} \leq \frac{\sqrt n}{n^2} = \frac 1{n^{1.5}}$ as the numerator has become bigger, but ... | https://math.stackexchange.com |
7,676 | [
"https://scicomp.stackexchange.com/questions/7676",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/4566/"
] | I'm testing Quicksort based on Niklaus Wirth algorithm. I'm checking how much time I need to sort an array. There is interesting thing that for an array consisting elements in these sequence:
1 3 5 7 9 10 8 6 4 2 (example how an array looks like for bigger instance)
0.14 seconds - array wit... | Quicksort exhibits suboptimal time performance if it consistently selects a pivot that results in a uneven partition.
The usual speed $O(n \log n)$ in time depends of getting a division of the input into two equal (or at least nearly equal) parts at each pass. If you get a highly unbalanced division regularly then you... | I'm guessing you're seeing a large number of non-compulsory cache misses due to address conflicts, but it's hard to verify this without actually measuring the number of cache misses. That said, 50x is a rather large performance difference. This sort of large inconsistency should go away if you adjust your pivoting st... | https://scicomp.stackexchange.com |
4,216,639 | [
"https://math.stackexchange.com/questions/4216639",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/952237/"
] | Now, the question is fairly specific, <span class="math-container">$ABC$</span> is a triangle, and <span class="math-container">$AD$</span> is an altitude. Midpoints of the sides being <span class="math-container">$A'$</span> for <span class="math-container">$BC$</span>,<span class="math-container">$B'$</span> for <spa... | If the warping is due to roundoff, you cannot eliminate it, but you can prevent it from <strong>compounding</strong> between additional rotations, by storing the original shape and the rotations that led to the new shape, and applying them to the floating point points, and only rounding at the <strong>final</strong> st... | You can reduce it by using larger whole numbers. If you multiply all the coordinates by a million, say, the fractional stretching becomes much smaller. You are just measuring distances in mm instead of km.
| https://math.stackexchange.com |
19,061 | [
"https://cs.stackexchange.com/questions/19061",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/1829/"
] | I thinkt this question fits better here than on english.stackexchange.
When describing a figure in a computer science paper, is it safe to use "tick" meaning "tick mark"?
Examples:<br>
<code>... (see the thick line right of tick "17")</code> meaning <code>tick mark "17"</code><br>
or <code>... increase at tick "1e+0... | Yes, if by tick you mean
<img src="https://i.stack.imgur.com/cUrqJ.png" alt="enter image description here">.
No, if you mean
<img src="https://i.stack.imgur.com/cixeq.jpg" alt="enter image description here">.
| I've never heard those marks on the axes referred to as "ticks", though Wikipedia agrees with your usage. Since Dave Clarke also didn't realise that's what you're talking about, I suspect that at least a sizeable minority of people aren't familiar with the term.
Why do you need to talk about the marks on the axes at ... | https://cs.stackexchange.com |
468,141 | [
"https://physics.stackexchange.com/questions/468141",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/204203/"
] | Assume the Earth to be a uniform sphere of mass M and radius R. Also let the Earth be stationary initially. Assume further that there is all other stellar bodies are very far away so as to have no influence in this problem.
A ball of mass <span class="math-container">$m$</span> is to be thrown from the surface of the ... | This problem has one solution. h=0. Throw the ball horizontally at orbital velocity for your altitude.
If you think about it, one of the rules of orbits is that they must eventually come back to where they were. If you throw a ball and it orbits, it must eventually come back around and hit you in the back of the he... | If there is no air resistance, the orbit will always pass through the initial point, so the ball cannot have a circular orbit at a height <span class="math-container">$h\neq 0$</span>.
| https://physics.stackexchange.com |
22,652 | [
"https://dsp.stackexchange.com/questions/22652",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/15340/"
] | A Band-limited signal is defined as a signal whose Fourier Transform is zero above a specified frequency. Shannon Sampling Theorem is also stated for a strictly band-limited functions,i.e,
<blockquote>
"For a band-limited case, 2W numbers per second are sufficient."
</blockquote>
Where, "W" is the max. frequency co... | A discrete-time signal represents a continuous-time signal that is band-limited to at most half the sampling frequency. Sampling a continuous-time signal that contains higher frequencies than half the sampling frequency will result in aliasing: Samples of those high frequencies are identical to and cannot be discerned ... | All the frequency component above W will be aliased, but if they are small, it would be nothing more than noise, everything below will be properly sampled.
| https://dsp.stackexchange.com |
71,101 | [
"https://physics.stackexchange.com/questions/71101",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26982/"
] | I have accumulated a large amount of R/C gear over the years. I have several antennas which are not labelled as to their original use. This antenna is either for 5.8ghz, 2.4ghz, or 910mhz.
<img src="https://i.stack.imgur.com/qVfp6.jpg" alt="enter image description here">
The connector is SMA with a male pin, threaded... | No, you can't really tell by looking at it, at least when all the details are covered with a skin so you have no idea what might be inside. If those markings are in mm (it would be helpful to say), then it's probably 910 MHz, but again, there is no way to know without measuring it.
You don't even know if this is a se... | the two grooves at the base of the antenna just above the elbow identify it as 2.5ghz
a single groove would be 900mhz
| https://physics.stackexchange.com |
150,164 | [
"https://cs.stackexchange.com/questions/150164",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/149323/"
] | So I am doing an exercise in which there are <span class="math-container">$n$</span> people who are either knight or rogue, more than <span class="math-container">$\frac{n}{2}$</span> are knights. You are a princess and would like to marry a knight and do not want to accidentally marry a rogue.
You can select any pair ... | <h4>An efficient algorithm using stack</h4>
<ol>
<li>Initialize an empty stack.</li>
<li>For each person <span class="math-container">$p$</span> in the given people:
<ul>
<li>If the stack is empty, push <span class="math-container">$p$</span> to the stack.</li>
<li>Otherwise, pit <span class="math-container">$p$</span>... | Our princess proceeds as follows:
<ul>
<li>she asks her suitors to form up on a line</li>
<li>starting from the left, she asks each person about the virtue of their neighbour (and vice versa)
<ul>
<li>if there is an accusation of rogueness
<ul>
<li>she sends both of them away</li>
<li>if there are people on either side... | https://cs.stackexchange.com |
257,690 | [
"https://mathoverflow.net/questions/257690",
"https://mathoverflow.net",
"https://mathoverflow.net/users/102697/"
] | The Riemann Hypothesis is known to be equivalent to the statement that $\zeta'$ (the derivative of the Riemann zeta function) has no zeros in the region $0< \Re(s) < 1/2$. By the functional equation, this seems to be equivalent to saying that the zeros of $\zeta'$ are actually on the critical line $\Re(s) = 1/2$.... | 1) No. $W$ consists of elements of determinant 1 and -1. According to your wikpedia, all elements of determinant 1 are "rotations". Elements of determinant -1 are not necessarily reflections because they are not necessarily of order 2. Just think of a 4-cycle $(1,2,3,4)\in S_4$: his order is 4, not 2. It is a proper ro... | Every coxeter group consists of reflections. An even number of reflections around two elements is a rotation, which is what $(s_is_j)^{m_{ij}}$ means. The infinite coxeter groups consists of sets of parallel mirrors, which equate to a translation rather than a reflection.
One might note the root lattice consists o... | https://mathoverflow.net |
2 | [
"https://physics.stackexchange.com/questions/2",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23/"
] | How would you explain string theory to non-physicists such as myself? I'm especially interested in how plausible is it and what is needed to successfully prove it?
| I've noticed that none of these answers actually answer the question.
The simplest explanation of string theory I can think of:
<strong>Particles we currently consider "point particles" (electrons, quarks, photons, etc.) are actually tiny pieces of string with each a characteristic vibration. They interact in a sort... | String theory is the theory of gravity which starts out by postulating that only things at the boundary of space-time make sense. The local space and time have to be reconstructed from the boundary description. This is called the holographic principle. In the 1960s, a primitive vesion of this idea was called the S-matr... | https://physics.stackexchange.com |
22,158 | [
"https://physics.stackexchange.com/questions/22158",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2578/"
] | Wouldn't it be more energy efficient and or safe to use microwaves to heat our home's water boiler instead of using dangerous gas or hot electric coils that could catch other things on fire? I'm kinda asking two questions at once, safety and efficiency.
It seems to me that a microwave heats water very quickly and woul... | A microwave oven is only about 65% efficient i.e. 65% of the electricity consumed is converted to microwaves and the rest is dissipated as heat. I suppose you could use the 35% dissipated as heat to heat the water as well, but then why not just use a heating element that dissipates 100% of the electricity as heat?
As ... | Regarding speed, an immersion heater is a clear winner. Microwave ovens heat small amounts of water quickly, but larger amounts heat slowly. If it takes 2 minutes to boil a cup of water (about 120 ml) in a 1000 watt microwave oven, 2 cups take almost twice that. A gallon of water is almost 4,000 ml - a hot water tank h... | https://physics.stackexchange.com |
31,177 | [
"https://stats.stackexchange.com/questions/31177",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2750/"
] | Is it (always) true that
$$\mathrm{Var}\left(\sum\limits_{i=1}^m{X_i}\right) = \sum\limits_{i=1}^m{\mathrm{Var}(X_i)} \>?$$
| The answer to your question is "Sometimes, but not in general".
To see this let $X_1, ..., X_n$ be random variables (with finite variances). Then,
$$ {\rm var} \left( \sum_{i=1}^{n} X_i \right) = E \left( \left[ \sum_{i=1}^{n} X_i \right]^2 \right) - \left[ E\left( \sum_{i=1}^{n} X_i \right) \right]^2$$
Now note t... | $$\text{Var}\bigg(\sum_{i=1}^m X_i\bigg) = \sum_{i=1}^m \text{Var}(X_i) + 2\sum_{i\lt j} \text{Cov}(X_i,X_j).$$
So, if the covariances average to $0$, which would be a consequence if the variables are pairwise uncorrelated or if they are independent, then the variance of the sum is the sum of the variances.
An examp... | https://stats.stackexchange.com |
57,864 | [
"https://math.stackexchange.com/questions/57864",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/13576/"
] | By the <strong>center</strong> of a group $G$ we mean the set of all elements of $G$ which commute with every element of $G$, that is, $C = \{ a \in G: ax = xa \text{ for every } x \in G \}$.
We want to show that $C$ is a subgroup:
(i). Let $m, n \in C$, then $mx = xm$ and $nx = xn$ for every $x \in G$. Show that $(m... | I think you would find it less confusing if you weren't using $x$ for two different things.
In (i) you know that $(mx)^2 = (xm)^2$ for all $x\in G$ and that $(nx)^2 = (xn)^2$ for all $x\in G$. You want to show that $mn\in C'$. So, let $y\in G$, and we want to show that $\Bigl((mn)y\Bigr)^2 = \Bigl(y(mn)\Bigr)^2$. ... | For (i), write
$$
(mnx)^2 = m(nx)m(nx).
$$
Since for each $y \in G$ we have $mymy = ymym$, what can you do to the right-hand side of this? Do that, then do it again.
| https://math.stackexchange.com |
1,147,154 | [
"https://math.stackexchange.com/questions/1147154",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/211392/"
] | Let $A$ be a reduced ring (i.e. no nilpotents). Take any $f \in A$
and I would like to show that $\operatorname{Supp} f = \overline{D(f)}$, where $D(f)$
denotes the distinguished open set of $\operatorname{Spec}A$ where $f$ does not vanish.
I think that the fact that reducible is crucial here, but somehow my argument
... | 1) Given a scheme and a global section $f\in \Gamma(X,\mathcal O_X)$, the support of $f$ is the set of points $x\in X$ where the germ of $f$ is non-zero: $f_x\neq0$ .<br>
Note carefully that this subset $\operatorname {supp} f\subset X$ is trivially closed (since its complement is open by the very definition of "germ" ... | Yes, reducedness is crucial for this. In general, all you can say is that $\operatorname{Supp} f$ contains $\overline{D(f)}$.
<hr>
You might want to consider the ring $k[x,y]/(xy,y^2)$, taking $f = y$. One
has $D(y) = \emptyset,$ but $\operatorname{Supp} y$ is equal to the closed point $(x,y)$. (Georges's exampl... | https://math.stackexchange.com |
317,264 | [
"https://electronics.stackexchange.com/questions/317264",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/155492/"
] | this is probably a weird question that has never been asked... but I was wondering how/if it is even possible to <strong>decrease the range of a infrared emitter?</strong>
<h3>here is why I need to know:</h3>
I am playing around with making laser tag weapons and I was working on a shotgun. how I have always seen shotgu... | As someone who has played around with laser tag weapons, there are some easy options.
The better, as a permanent approach, is simply to increase the resistance of the current limiting resistor that should already be in series with the emitter (or add a second resistor). LEDs will glow even down to very small currents... | Add a lens or other means to cause the beam to spread over distance.
| https://electronics.stackexchange.com |
28,273 | [
"https://chemistry.stackexchange.com/questions/28273",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/15380/"
] | Which one of hydrogen and helium behaves more like ideal gas <strong>in room temperature</strong>...
I thought hydrogen gas would show more ideal behavior in room temperature because it has lighter mass (less no of electron) although it's diatomic, so there would be less attraction.
However, I saw one question on the ... | For inert gas molecules, intermolecular interactions would be by Van der Waals forces, which are based on the total volume and polarizability of the gas molecule.
The diatomic hydrogen is larger and more polarizable of the two.
| He is more nearer to ideal behaviour than hydrogen because ideal behaviour also depends on the charge spread over area or size of molecule. So the charge density of hydrogen is expanded increases the size of hydrogen due to which interactions between hydrogen molecules increases and hence show less ideal character as c... | https://chemistry.stackexchange.com |
2,097,948 | [
"https://math.stackexchange.com/questions/2097948",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/192092/"
] | In the "Integrating Factors" section of an old introductory differential equations book, this example problem is presented:
$$\frac{x \ dy-y \ dx}{x^2}=xy \ (x \ dy+y \ dx)$$
$$d \left( \frac{y}{x}\right)=xy \ d(xy) \quad (*)$$
The book then simply says, "Integrate," and shows the answer: $\frac{y}{x}=\frac{1}{2} \ x^2... | One of the wonderful things about differentials (as opposed to, say, partial derivatives) is that they don't care about independent/dependent variables, interact extremely well with algebraic manipulations, and so forth.
For example, you know that $\mathrm{d}\left( \frac{1}{2} t^2 \right) = t \, \mathrm{d}t$, and if w... | I guess you could do this:
<ol>
<li>Make the substitution $u = xy$.</li>
<li>Then the integral becomes $\int u\, du$.</li>
</ol>
That should be easy enough to solve, then just "de-substitute" u as xy.
After doing some thinking, I decided to substitute $d(xy)$ as $$(y + xy')dx.
\tag{1}$$
Then, substituting (1) back i... | https://math.stackexchange.com |
78,246 | [
"https://datascience.stackexchange.com/questions/78246",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/91724/"
] | A website says Correlation refers to an increase/decrease in a dependent variable with an increase/decrease in an independent variable. Collinearity refers to two or more independent variables acting in concert to explain the variation in a dependent variable.Could someone clarify the terms ?
| Collinearity usually refers to any linear relationship or association between 2 or more features.
Correlation and correlated are more general, and can refer to any type of relationship between features and responses, including log, exponential and linear associations.
The word "correlation" is a noun. And its... | Pearson correlation is the usual correlation when nothing further is specified and specifically refers to linear association.
<span class="math-container">$$\rho_{XY}=\dfrac{cov(X,Y)}{\sigma_X\sigma_Y}$$</span>
In the world, people use “correlation” to mean any kind of association, but this is wrong from the standpoint... | https://datascience.stackexchange.com |
37,239 | [
"https://mathoverflow.net/questions/37239",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8906/"
] | Does anyone know a continuous group (not necessarily locally compact) with dense cyclic subgroup other than a torus?
| You already have some examples in the other answers. Groups which have a dense cyclic subgroup are called <em>Monothetic</em> groups. In the article "On monothetic groups" by P.R. Halmos and H. Samelson, you can find many of their properties, such as
<blockquote>
Every compact connected separable (abelian) group is ... | First, it is clear the group has to be abelian. Now, if you assume that $G$ is locally compact, then by the classification you can decompose $G$ as $G={\mathbb R}^n \times H$ where
$H$ has a compact open subgroup. Clearly, there can be no ${\mathbb R}^n$ factor, so $G$ has a
compact open subgroup. Now, suppose $G$ is i... | https://mathoverflow.net |
86,521 | [
"https://physics.stackexchange.com/questions/86521",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5805/"
] | Vaporization is an interesting engineering subject, but unfortunately much about it has always been unclear to me.
Recent research of mine has brought my mind to link <i>vapor pressure</i> to <i>boiling</i> and <i>partial pressure</i> to <i>evaporating</i>. So I would just like to confirm the following two understandi... | I think you have a misunderstanding of the technical terms <strong>vapor pressure</strong>, <strong>boiling</strong> and <strong>partial pressure</strong>.
<ul>
<li><strong>Vapor pressure</strong> or better <strong>equilibrium vapor pressure</strong> is the pressure at which an equilibrium is reached between evaporati... | I would like this to be a comment to previous answer but unfortunately I can't comment on answers yet. I just wanted to explain a bit more what is so special about boiling because I feel like most of us feel that vapor pressure=ambiant pressure being the definition of boiling point is just a theoretical technicality an... | https://physics.stackexchange.com |
286,235 | [
"https://softwareengineering.stackexchange.com/questions/286235",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/182954/"
] | I want to POST an array of objects and make an insertion in database concerning each of them.
What is the best practice if one object does not conform and raise an Exception? (cancel all transactions or just one and specify it when I return this list of objects?)
| Your post should be a single, self contained action that succeeds as a whole or fails as a whole. Therefore if one item contains an error you should reject the entire set.
You should also be checking these items if at all possible before even starting your database transaction so you have the chance to error out early... | If it's a batch operation, I'd rather process all the operations one by one, and return the array of objects with their own status.
You can return the HTTP status code 200 OK if all the operations succeeded, or a 207 Multi-Status if you have operations that failed amongst your batch.
| https://softwareengineering.stackexchange.com |
319,059 | [
"https://math.stackexchange.com/questions/319059",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/64732/"
] | I am helping out a friend who can't seem to get these proofs; unfortunately, I can't find them either. Can someone tell me how to solve this or point me in the right direction with resources?
Question 1:
<blockquote>
Prove that for all real numbers x, y, and z, if x + y + z greater than or equal
to 3, th... | Here are three ways you can choose to prove conditionals (if-then statements). There are other ways but these are most common.
<strong>Direct Proof</strong>
If $A$, then $B$.
$(A \implies B)$
Assume $A$ is true, then show that when $A$ is true that $B$ must also be true. This seems like it should be the simplest w... | Proof 1.
By contradiction, x<1 and y<1 and z<1 implies x+y+z <3, so this assumption is false. Thus we have x>=1 or y>=1 or z>=1.
Proof 2 can be done in a similar way.
| https://math.stackexchange.com |
289,440 | [
"https://electronics.stackexchange.com/questions/289440",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/90674/"
] | As much as IP tends to make things easier, I would like to find was to learn more about protocols and interfaces by doing everything myself (I understand the difficulty of the task, and I have resources to aid me as in professors and books). From what I understand though, it is near impossible (without reverse engineer... | There may be a misunderstanding about what 'IP' means.
It's possible to program the fabric of an FPGA, that is the programmable LUTs and things, from the ground up. However, the bits and gates and tables in a Xilinx and an Altera are different, and are different from family to family, so it's like assembly coding a mi... | It is certainly possible to program (using and HDL) and do useful tasks on FPGAs without using any third party IP blocks - if that is what you meant. However you do still have to use the vendors synthesis tools.
Synchronous state machines etc written in appropriately structured VHDL easily synthesize onto the LUTs an... | https://electronics.stackexchange.com |
510,417 | [
"https://physics.stackexchange.com/questions/510417",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/212400/"
] | Does the launching of a satellite need the consideration of the general theory of relativity (GR)?
| Newtonian physics would be sufficient to launch and orbit a satellite. But any equipment, sensors, or experiments on board that required exact timing might need to take into account relativistic time dilations from speed and gravity.
| No. Newtonian gravity is sufficient.
| https://physics.stackexchange.com |
225,737 | [
"https://mathoverflow.net/questions/225737",
"https://mathoverflow.net",
"https://mathoverflow.net/users/40038/"
] | By the Brill-Noether Theorem, a general curve $C$ of genus $g\geq2$ has maximal Clifford index $\lfloor \frac{g-1}{2}\rfloor$. Hence a very naive question is:
(Q1) Is a curve with maximal Clifford index a <em>general</em> curve (in the sense of Brill-Noether theory) ? And if not, what can be said about such a curve (w... | Q2) as stated is obviously true, because if the curve had a pencil of degree less than or equal to c+1, then the Clifford index would be at most c-1 (the clifford index of this pencil). So you probably meant to state the converse statement, which asks if a curve of maximal gonality has maximal Clifford index.
At least... | The answer to (Q1) is definitely no. The first example is in genus 4: a (smooth) complete intersection of a quadric cone and a cubic surface in $\mathbb{P}^3$ has maximal Clifford index (= 1), but is not Brill-Noether general: it has a unique $g^1_3$ whose double is the canonical divisor.
The answer to (Q2) should be ... | https://mathoverflow.net |
1,076,089 | [
"https://math.stackexchange.com/questions/1076089",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/180936/"
] | How would I write the power series $$1+3x^2+8x^4+21x^6+\cdots$$ as a power series representation (something neat similar to $\frac{1}{1-x}$)?
This reminds me of the power series $1+x^2+x^4+x^6+\cdots$ where the power series representation for that is $\frac{1}{1-x^2}$, but how would I add the Fibonacci numbers as co... | Let $f(x) = 1+2x+3x^2+5x^3+8x^4+13x^5+21x^6+\cdots$.
You probably already know a closed form for $f(x)$.
Then, $f(-x) = 1-2x+3x^2-5x^3+8x^4-13x^5+21x^6-\cdots$.
Do you see how to get the series you want from $f(x)$ and $f(-x)$?
<hr>
To get a closed form for $f(x)$ try combining the following equations in a way t... | <strong>Hint:</strong> Show that if $A(x) = a_0 + a_1 x + a_2 x^2 + \cdots $, then:
$$\frac{A(x) + A(-x)}{2} = a_0 + a_2 x^2 + \cdots $$
Can you apply this to your series?
| https://math.stackexchange.com |
14,951 | [
"https://dsp.stackexchange.com/questions/14951",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/595/"
] | Say we have a signal S, and we composite it with a 0.1-volume 30-sample-delayed version of itself, so:
<pre><code>T(k) = S(k) + 0.1*S(k-30)
</code></pre>
How would one rearrange this equation to make S the subject?
i.e given the resultant signal T, and the fact that we know the parameters of the echo (0.1 and 30), h... | The way the signal $T(k)$ is generated is by applying an FIR (finite impulse response) filter to the signal $S(k)$. The transfer function of this FIR filter is
$$H(z)=1+0.1z^{-30}$$
If you want to compensate for such a filter, you need a filter with a transfer function which is the inverse of $H(z)$:
$$G(z)=1/H(z)=\... | To complement Matt L. perfectly correct answer, the easy way to rearrange your equation to solve for $S$ is just like you'd do for any simple arithmetic equation:
$$\begin{aligned}
T_k &= S_k + 0.1 \; S_{k-30} \\
\iff \quad S_k &= T_k - 0.1 \; S_{k-30} \\
\end{aligned}$$
But, I hear you saying, there's still ... | https://dsp.stackexchange.com |
267,852 | [
"https://physics.stackexchange.com/questions/267852",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75387/"
] | <ol>
<li>Is light the thing causing the universal speed limit to be $299\,792\,458\,\mathrm{m/s}$? So the universal speed limit would be different if light travelled faster or slower?</li>
<li>Or, is $299\,792\,458\,\mathrm{m/s}$ the universal speed limit anyway and light just goes that fast? Light is just something we... | It's the second one: the reason the speed $299792458\ \mathrm{m/s} = c$ is special is because it's the universal speed limit. Light always travels at the speed $c$, whatever that limit may be.
The reason there is a "universal speed limit" at all has to do with the structure of spacetime. Even in a universe without lig... | Above all, speed of light is the speed of propagation of fields through space. While light may be slowed down when crossing matter, fields (electromagnetic fields, gravity) are always propagated at c. One of the consequences is the "speed limit for causality" mentioned by DavidZ and the speed limit for transmission of ... | https://physics.stackexchange.com |
331,244 | [
"https://softwareengineering.stackexchange.com/questions/331244",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/232368/"
] | I came across one of the books related to <strong>information security</strong> where i saw these two terms, <strong>fabrication</strong> and <strong>modification</strong> of data.
I can't figure out how they are different?
What is the difference between <strong>fabrication</strong> and <strong>modification</strong> ... | Let's assume you break into a billing system and want to create havoc:
<strong>Fabrication</strong> would, for example mean, you make up a non-existant supplier with made up contracts and regularily payments to your own account.
<strong>Modification</strong> would mean in the same context you pick an existing supplie... | In <strong>fabrication</strong>, you put in a new counterfeit item into the data set. In <strong>modification</strong>, you just take an existing item from the data set and change it.
As you already pointed out, the former compromises the authenticity of your data. Let's use an analogy... Imagine you record your daily... | https://softwareengineering.stackexchange.com |
275,957 | [
"https://softwareengineering.stackexchange.com/questions/275957",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/167735/"
] | When thinking of agile software development and all the principles (SRP, OCP, ...) I ask myself how to treat logging.
<strong>Is logging next to an implementation a SRP violation?</strong>
I would say <code>yes</code> because the implementation should be also able to run without logging. So how can I implement loggin... | I would say you're taking SRP far too seriously. If your code is tidy enough that logging is the only "violation" of SRP then you are doing better than 99% of all other programmers, and you should pat yourself on the back.
The point of SRP is to avoid horrific spaghetti code where code that does different things is al... | <strong>No, it is not a violation of SRP.</strong>
The messages you send to the log should change for the same reasons as the surrounding code.
What IS a violation of SRP is using a specific library for logging directly in the code. If you decide to change the way of logging, SRP states that it should not impact your... | https://softwareengineering.stackexchange.com |
652,772 | [
"https://physics.stackexchange.com/questions/652772",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/300178/"
] | Suppose we have a simple pendulum executing SHM about its mean position. We can easily notice that the bob of the pendulum swings back and forth making an angle, say <span class="math-container">$\theta$</span> about its central perpendicular (mean position). Let <span class="math-container">$\theta_{max}$</span> be th... | Your idea of representing simple harmonic motion as a circle is the right concept. However, you should note that the <span class="math-container">$\alpha$</span> and <span class="math-container">$\beta$</span> in your equation is the <em>phase angle</em> <span class="math-container">$\omega t$</span> and not the actual... | If we remain in the context of SHM (and so avoid the complications of elliptic integrals) then the angle <span class="math-container">$\theta(t)$</span> that the pendulum makes with the vertical at time <span class="math-container">$t$</span> is given by
<span class="math-container">$$\displaystyle \theta(t) = \theta_{... | https://physics.stackexchange.com |
61,280 | [
"https://dba.stackexchange.com/questions/61280",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/35877/"
] | This is the first database I set up so I apologize if my problem is something obvious.
<img src="https://i.stack.imgur.com/ruxKF.png" alt="EER Model">
I'm playing around with my table design and tried to create some link tables with FKs to avoid redundant data. When I try to sync my EER model with the DB I get an err... | While you seem to have fixed the issue, I will quickly explain why it happened in case anyone finding this will want to understand where the problem was.
When setting foreign keys, the Primary Keys Columns must be of exact same type and attributes. E.g. If you have unsigned attribute on one primary key, you must have ... | One of the PKs had an UNSIGNED flag. Removing that resolved the problem.
| https://dba.stackexchange.com |
176,486 | [
"https://physics.stackexchange.com/questions/176486",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10569/"
] | I have been looking at the Schwarzschild metric presented to me as the following within lectures:
<span class="math-container">$$ds^2=-\frac{\textrm{d}r^2}{1+\frac{\gamma}{r}}-r^2\textrm{d}\theta^2-r^2\sin^2\theta\textrm{d}\phi^2+c^2\left(1+\frac{\gamma}{r}\right)\textrm{d}t^2,$$</span>
where <span class="math-contai... | If we get rid of the <span class="math-container">$\dot{r}^2$</span> term in the Lagrangian and apply the Euler-Lagrange equations, we get <span class="math-container">$\dot{\phi}=\text{const.}$</span> and <span class="math-container">$\dot{t}=\text{const.}$</span> This is certainly true for a circular orbit, but as th... | I think it is because circular orbits are unstable (only the innermost is stable), so the radius is not constant. They're not stable because an orbiting object loses energy.
| https://physics.stackexchange.com |
429,517 | [
"https://physics.stackexchange.com/questions/429517",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/203629/"
] | Hamilton's action for classical systems has the units Joule seconds ($\rm J\cdot s$), which in base units is $\rm kg\:m^2/s$.
Does the $\rm m^2$ have anything to do with area?
I'm having a hard time "reading" the units here.
| Not everything has a "nice" explanation in base units. Students often get this idea because a lot of things in introductory mechanics are explained this way ("acceleration has units of $\text{m}/\text{s}^2$, because it's the number of meters per second you speed up per second"). But this works only when you're dealing ... | It's not worth trying to interpret the units that way. To give another "what?" example, light intensity as power per area turns out to be kg/s${}^3$. What does that mean? Arguably, nothing beyond the more insightful W/m${}^2$. You can change the choice of base units in analogy with a change of basis for a vector space.... | https://physics.stackexchange.com |
234,483 | [
"https://security.stackexchange.com/questions/234483",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/238169/"
] | I recently set up a personal website. It contains nothing but a few pieces of information presented in a pretty way; there's no associated database or anything, it wasn't even wordpress - just hardcoded HTML and CSS with some very rudimentary javascript. Because the site was so minimal, I opted not to pay for an SSL ce... | The concept of calculating some form of hash over (url + request payload + ...) is not something uncommon. I wouldn't say it is flat out wrong.
There are a few problems with this specific implementation, though:
<ul>
<li>MD5 is not considered secure. SHA-2 would be a much better choice.</li>
<li>There doesn't seem to b... | Everything about this is unnecessary and redundant. Ignoring the problems with MD5, it adds nothing of value over a simple opaque bearer token and TLS.
<blockquote>
I would like to know what flaws are in this implementation that I am currently not seing?
</blockquote>
Again, use of MD5 not withstanding, the specific fl... | https://security.stackexchange.com |
186,843 | [
"https://softwareengineering.stackexchange.com/questions/186843",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/81149/"
] | I have read in few blogs that as part of agile development , the product owner closely interact with developers to state their requirements and come up with a solution. However in case of a large project (in terms of number of applications involved) involving multiple systems , is this possible? Shouldn't the project h... | "Product Owner" is a term from Scrum, which is only one form of Agile. Scrum is really designed around the notion of small teams of seven plus or minus two, who do all the development and testing of the project solution. The Team would work with a Product Owner, who owns what goes into the project and what does not.
... | <em>Shouldn't the project have a business analyst / solution designer in order to capture the requirements properly and come up with a solution which states how the the requirement could be fulfilled and which systems must do what activity?</em>
At a high level yes but the phrase 'capture the requirements properly' ca... | https://softwareengineering.stackexchange.com |
385,850 | [
"https://electronics.stackexchange.com/questions/385850",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/125197/"
] | Let's say we want to extract 1Hz signal from a noisy signal by using a LPF.
And assume we have sampled it with 100Hz sampling rate.
If we would have sampled it with 1kHz sampling rate and use the same LPF would the SNR be better? Why?
| I see quite a few misstatements and possible misconceptions both in the answers and in the question, so let’s break down what is meant by “noise.”
<ol>
<li>Analog noise within the same bandwidth as the signal. </li>
<li>Analog noise outside of the bandwidth of the signal. </li>
<li>Quantization noise introduced by the... | The SNR would be better, firstly because noise mostly being a higher frequency component would have a lesser chance of being aliased of 1Hz when sampled at 1kHz than at 100Hz
Secondly SNR is directly proportional to bandwidth or just look at Hartley shannon’s law
C = Blog_2 (1+SNR)
Where C is the digital bandwidth a... | https://electronics.stackexchange.com |
372,946 | [
"https://stats.stackexchange.com/questions/372946",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/223551/"
] | In a roll of die, if <span class="math-container">$X$</span> is the number on the first die and <span class="math-container">$Y$</span> is the number on second die, then determine whether the random variable <span class="math-container">$X+Y$</span> and <span class="math-container">$X-Y$</span> are independent.
The c... | <strong>They're not:</strong> If <span class="math-container">$X+Y=12$</span> then both rolls were sixes, so <span class="math-container">$X-Y=0$</span>. So you have:
<span class="math-container">$$1 = \mathbb{P}(X-Y =0|X+Y=12) \neq \mathbb{P}(X-Y =0) = \frac{1}{6}.$$</span>
| When checking if the random variables are independent or not, the first thing needing to check is the range of the random variables. If the range of one random variable varies according to values of other random variables, then they are not independent, and stop. Otherwise, need to check further.
In this problem, when... | https://stats.stackexchange.com |
231,326 | [
"https://physics.stackexchange.com/questions/231326",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/68067/"
] | The Chern-Simons 3-form is given by
$\omega_3={\rm Tr} \left[ A\wedge dA+\frac{2}{3}A\wedge A\wedge A\right]$
where $A$ is a connection one-form in the adjoint representation of a non-Abelian gauge group.
My differential geometry is rather rusty (and this is new to me too) hence my questions;
$A$ is a 1-form. By d... | That's because you are forgetting that $A$ has a Yang-Mills index. You better write this in components, which reads
$\epsilon^{\mu\nu\rho} g_{IJ} \Big( A^I_\mu \partial_\nu A_\rho^J + \frac{1}{3} f^J{}_{KL} A^I_\mu A^K_\nu A^L_\rho \Big) $
This component notation also answers your second question.
| This is an example of lie-algebra valued 1-forms. Actually you may write explicitly, $ A = A_{\mu} ^a T^a dx^{\mu}$. Since the generators also anti-commute so we get the result. And for the same reason sometimes you will find expressions like $[A,A]$ in literature for your term.
| https://physics.stackexchange.com |
35,975 | [
"https://biology.stackexchange.com/questions/35975",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/16657/"
] | Why does a gene have two alleles?
When there is a gene for producing the color pigment for a flower, why are there there two alleles, producing either same color or different color (homozygous and heterozygous)?
| Allele is a variant form of a gene. How many alleles there are depends on number of copies of the gene and number of variants. In theory you can have 5 identical copies or single copy and single allele (Y-linked genes come to mind).
Regulation is very complicated, I'll refer you to reading on recessiveness, dominance.... | A flower (or a person) has two alleles for a gene because it inherits one set of chromosomes from one parent and another, comparable, set of chromosomes from the other parent. Hence there are two copies of each gene, and so there are two alleles for each gene.
| https://biology.stackexchange.com |
182,280 | [
"https://dba.stackexchange.com/questions/182280",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/126261/"
] | I have this portion of code with user's phone extensions:
<pre><code>GROUP BY IFNULL(mxuser.EXTENSION, mxuser_1.EXTENSION)
HAVING Ext IN (207, 213, 235, 214, 226, 218, 224, 227, 216)
</code></pre>
It works fine, and it sorts values in ASC order ( 207, 213, 214..) Is it possible to sort values in different order? Some... | I'm not sure why you're putting the <code>EXT IN</code> a HAVING clause, but this should work.
<pre><code>WHERE IFNULL(mxuser.EXTENSION, mxuser_1.EXTENSION)
IN (207, 213, 235, 214, 226, 218, 224, 227, 216)
GROUP BY IFNULL(mxuser.EXTENSION, mxuser_1.EXTENSION)
ORDER BY ext=235 DESC, ext=207 DESC, ext=218 DESC, ext;
<... | <pre><code>WHERE IFNULL(mxuser.EXTENSION, mxuser_1.EXTENSION)
IN (207, 213, 235, 214, 226, 218, 224, 227, 216)
GROUP BY IFNULL(mxuser.EXTENSION, mxuser_1.EXTENSION)
ORDER BY FIND_IN_SET("207,213,235,214,226,218,224,227,216")
</code></pre>
| https://dba.stackexchange.com |
418,921 | [
"https://stats.stackexchange.com/questions/418921",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20213/"
] | My research question is to check whether the Body fat is associated with Hypertension onset. I am using Body fat as a categorical variable (i.e according to the value of body fat, the person will be categorized lean, overweight or obese).
But the classification of body fat for a healthy individual is different for ma... | OK, I'll post my comment as an answer. So:
Why not categorize each person as lean/overweight/obese according to his/her sex-and-age-specific norms and use this categorization as a predictor?
mkt's answer is also fine, but I'd stick to categorization. It'll give you conclusions like "Being obese increases odds of hype... | I'd recommend just using the continuous <code>body fat</code> values instead of binning them into groups. That allows you to avoid any problems with different classification thresholds, and also uses all the information you have (information is thrown out when you bin continuous data). Then you can do a logistic regres... | https://stats.stackexchange.com |
155,169 | [
"https://security.stackexchange.com/questions/155169",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/143305/"
] | SMB is a well-known network file sharing protocol, and I assume it's supposed to be used internally only. At my company I found someone connecting to a share on a server on the Internet over port 445 using SMB. Is there any risk in allowing such connections? I'm thinking if someone were able to MitM they be able to cap... | I'm not sure what operating system you are using, or if/what firewalls you have implemented, but exposing the SMB service with unfiltered access from the internet is asking to be compromised.
Also, a Man in the Middle attack would be the least of your worries. Someone could easily gain root access to your computer an... | Yes it is risky.
While I don't know about any "exploits" that may be out there in the wild, what I do know is that anybody with the right username and password could get access to the disk drives that are exposed.
Presumably there is an administrator-level account on the computer that would allow full access.
I... | https://security.stackexchange.com |
17,980 | [
"https://dsp.stackexchange.com/questions/17980",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/10934/"
] | Assume signal $x$, sampled at $f_s = 44100\; \mathrm{Hz}$. I tried to filter it using the Butterworth bandpass filter ( $30\; \mathrm{Hz} - 70\; \mathrm{Hz}$) of order $8$. However, as a result I get a vector with most elements being <code>NaN</code> (and some of them extremely small, approx. $-2.5 \cdot 10^{306}$`).
... | Basically you never want to use the Transfer Function representation (with <code>b</code> and <code>a</code>) and rather use the Zeros-Poles-Gain (<code>z</code>,<code>p</code>,<code>k</code>). This will allow you to avoid the numerical errors. In your case you might design your filter in following way:
<pre><code>fs ... | The higher the order, the more poles that need to be fit around a small semi-circular-like ring, and right at the edge of the unit circle. The smaller the ratio of the filter's frequency to the sample rate, the smaller this circular ring becomes in relationship to the unit circle. Try to stuff enough poles into a smal... | https://dsp.stackexchange.com |
1,517,010 | [
"https://math.stackexchange.com/questions/1517010",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/144533/"
] | This question is driving me insane as the solution to part <strong>(b)</strong> makes no sense, I apologize for having to resort to typing out the question and solution - I don't like having to do this, but in this case I make an exception:
<blockquote>
You are measuring gamma rays from the decay of a radioactive so... | The "somewhere" explanation is not correct. For a counterexample, take $n=m=2$. Then the function
$$ f = \{ 1\mapsto 2, 2\mapsto 1 \} $$
is in $F$ but does not satisfy the property in (3).
There are in general $\binom mn$ strictly decreasing functions that are in $F$ but don't satisfythe condition.
| answer of c) is actually C(m,n) because you have to just select any n number from m which can be done in C(m,n) ways, and coming to the arrangement, that chosen n numbers should be in strictly increasing , so you have just 1 way to arrange them. Hence if you do selection followed by arrangement it will be C(m,n) * 1, w... | https://math.stackexchange.com |
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