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210,272 | [
"https://softwareengineering.stackexchange.com/questions/210272",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/101245/"
] | I really don't know where else to ask. So here it goes.<br/>
I'm working at a very tiny company that makes ERP software and websites.<br/>
1 developer with + 10 years experience.<br/>
2 developers with + 3years experience.<br/>
3 developers with + 1 year experience.<br/>
<br/>
That's it.<br/>
No team, no DBA, no sys... | In my experience, yes, it is perfectly normal for developers in small companies to be expected to cover a broad range of roles. It is certainly normal for a company so small that it only has three developers to not have a specialized DBA or sysadmin.
However, I would find it unusual for such a small company to use suc... | From experience I can tell that live as a software developer varies widely based on the size of the company you're working in.
Smaller shops tend to require more multi-tasking and taking on multiple roles, while large companies usually have very strictly described role for each person.
One extreme being a one-man-sho... | https://softwareengineering.stackexchange.com |
273,805 | [
"https://stats.stackexchange.com/questions/273805",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/139330/"
] | If i were To perform a likelihood ratio test where I compare two models A and B I would basically try to find out which of these models are the better one of these models fits the data best. But if i were to perform a LR test on only one of these models, what am i actually trying to find out? and by that i mean, what i... | SmallChess is right when they say you can't do an LRT with a single model.
However, you can compare your model to an intercept only model, which would be equivalent to testing if all the coefficients except the intercept are 0.
(As an aside, you could specify that all coefficients, including the intercept, are 0, but... | The LR test can't be done on a single likelihood. We can't form a ratio without two likelihoods.
However, you may test a model with the null model to test for goodness of fit. Your null hypothesis would be that the two models are statistically equivalent. Your alternative hypothesis would be that they are statistical... | https://stats.stackexchange.com |
368,404 | [
"https://mathoverflow.net/questions/368404",
"https://mathoverflow.net",
"https://mathoverflow.net/users/117299/"
] | During my studies I faced a function <span class="math-container">$f:\mathbb{R} \to \mathbb{R}^+ $</span> with the property: for all <span class="math-container">$x \in \mathbb{R} $</span> and all <span class="math-container">$y$</span> in open interval <span class="math-container">$(x-\frac{1}{f(x)} ,x+\frac{1}{f(x)})... | My answer is: Such a function must be constant. Suppose (for puoposes of contradiction) <span class="math-container">$f$</span> is a nonconstant function <span class="math-container">$f : \mathbb R \to (0,+\infty)$</span> such that
<span class="math-container">$$
\forall x\in\left(a-\frac{1}{f(a)},a+\frac{1}{f(a)}\rig... | This is <strong>not an answer</strong> but it greatly narrows down the class of functions <span class="math-container">$f$</span> with the described property.
<ol>
<li>If <span class="math-container">$c>0$</span>, then the sets <span class="math-container">$f^{-1}([c,+\infty))$</span> and <span class="math-container... | https://mathoverflow.net |
151,574 | [
"https://cs.stackexchange.com/questions/151574",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/150698/"
] | If we have a BST but want to keep it balanced, how much more expensive does adding an element to it become? Clearly adding an element (without maintaining balance) is of time complexity O(log(n)), as we traverse the tree down to the point where we should add the element, but if we want to maintain a balanced tree such ... | The split in a product is between the two outermost pairs of parantheses. For example, in <span class="math-container">$((a*b)*(c*d))*(e*f)$</span>, the split is between the <span class="math-container">$d$</span> and <span class="math-container">$e$</span> because the last multiplication that is performed is between t... | Suppose you have <span class="math-container">$n$</span> matrices <span class="math-container">$M_1, M_2, …, M_n$</span>.
The product of all matrices is <span class="math-container">$M_1\times M_2\times…\times M_n$</span> and since the matrix product is associative, there is no need for parentheses from a mathematical ... | https://cs.stackexchange.com |
2,479,274 | [
"https://math.stackexchange.com/questions/2479274",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/466932/"
] | The following proof is wrong, and I'm not 100% sure why.
<hr>
$a_n$ is a sequence s.t. $|a_{n+1} - a_{n}| < \frac{1}{n}$. Determine whether $a_n$ converges.
We want to show that $\forall \epsilon > 0, \exists N: n, m > N \implies |a_m - a_n| < \epsilon$.
WLOG, let $m \geq n$.
Let $k = m - n$, so that $... | Your error is the equals-sign at the beginning of line (2). You're presumably thinking of the principle "the limit of a sum equals the sum of the limits (provided the latter exists)." But this principle is correct only when the number of summands is fixed. In your situation, the number $k$ of summands is not fixed, an... | First, note that $$\log(n+1)-\log(n) = \log(1+\frac{1}{n}) < \frac{1}{n},$$ so it isn't just that the proof is wrong: the statement isn't true.
The problem with the proof is with your order of limits. To show it's Cauchy, you need to show for all $\epsilon>0$ there is an $N$ such that for <em>any</em> $m,n >N... | https://math.stackexchange.com |
79,221 | [
"https://security.stackexchange.com/questions/79221",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/61316/"
] | This was a question on an exam:
Two persons are using a one way communication channel and the HMAC functionality (concretely HMAC-SHA1). Choose the correct statement below:
1) We can prove who the sender is, because HMAC-SHA1 uses a shared secret, which is known to both of them. Even more, the communication channel o... | Answer 2 is nonsensical; it literally says "we can prove who the sender is because <em>two</em> people have the ability to create the MAC." With a MAC, <em>either</em> party could have created the MACed message; <em>each party</em> knows who created it (you know if you wrote something or not, and if you didn't the othe... | I would say 2.
The reason:
Theres 2 types of non-repudiation: One that you can prove to others, and one that you cannot.
There is schemes out there that are specifically made to prevent the possibility to prove to someone else that X sent it.
Its called non-transferable PGP signatures, and goes on this way:
You hash... | https://security.stackexchange.com |
60,427 | [
"https://mathoverflow.net/questions/60427",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13244/"
] | As we know, for $1<p<\infty$, the Fourier series of $f\in L^{p}(T)$ converges to $f$ in $L^{p}$-norm.
But is there any results concerning the convergence of Fourier series in $L^{\infty}$-norm?
Since $L^{\infty}(T)$ is not separable, the trigonometric system fails to form a Schauder basis of $L^{\infty}(T)$, this... | If Fourier series of continuous functions would converge in $L^\infty$, then, by the Uniform Boundedness Principle, the operator norms in $C(\mathbb{T})$ of the partial Fourier series operators $S_Nf(t):=\sum_{n=-N}^N\hat{f}(n)e^{int}$ would be uniformly bounded. You can find, for example in Katznelson book, a proof of... | I think you can find the answer in P191 "Classical Fourier Analysis",second edition, Loukas Grafakos
| https://mathoverflow.net |
5,540 | [
"https://softwareengineering.stackexchange.com/questions/5540",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1564/"
] | How should code in version control be stored?
<strong>Developer friendly</strong>? so that programmer can quickly take the latest and able to run from his editor without doing many changes? (like config files pointing to dev DB..etc)
or
Should it be <strong>production friendly</strong>? source should be in a manne... | Why choose ? It should be both.
Your development environment should be configured so it's as easy as doing a checkout, open, build, run, debug (eg: no absolute path!). You can do that easily with compilation directives, configuration class + dependancy injection, or even tricks like the perso.config in ASP.NET
Your a... | When it's an open source project where people are expected to contribute, I'd certainly opt for developer friendly.
My biggest dislike about open source projects is that very rarely does the repository contain all the dependencies needed to build the code (sometimes for practical or legal reasons), but when they don't... | https://softwareengineering.stackexchange.com |
205,314 | [
"https://electronics.stackexchange.com/questions/205314",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/94058/"
] | I want to set a clearance rule between different layers in a multi-layer board. In particular, I have a signal class on one internal layer that a polygon pour in another layer needs to avoid. I would also want to make sure that traces of certain net classes don't pass too close to each other on adjacent planes. I tr... | Without a resistor in series with each LED is is likely that the corresponding Q output is being dragged down to a voltage that is not high enough to be recognized as a legitimate high level by the following J input.
| On CMOS parts, all unused inputs must be connected, directly or through a resistor, to either Vcc or ground, whichever is required to make the part work as required. For the Preset pin where you have a switch to pull it to ground, you must also have a resistor (5K - 10K) to Vcc to ensure the preset pin is high when the... | https://electronics.stackexchange.com |
32,412 | [
"https://electronics.stackexchange.com/questions/32412",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9902/"
] | Most of the BPSK waveform examples in text books/online are for carrier frequencies that are integer multiples of the bit rate. This means that when the symbol polarity changes there is a discontinuity in the waveform - but it doesn't jump signal level, it just heads the other way. When the carrier frequency is not an ... | The examples in the textbook are chosen for clarity. They will have like what, a 2:1 ratio between carrier and data frequency? In practice this may be 10 000:1 or more. And even with the carrier being an exact multiple you can't be sure of the phase; chances that zero crossings of carrier and data coincide are slim. ... | Any jump in the time domain has a very wide bandwidth in the frequency domain (theoretically infinite). So an encoding that has jumps usually needs to be lowpass or bandpass filtered (or will be by the channel). Thus the received signal won't have the discontinuity, but some smoothed (filtered) interpolation for some... | https://electronics.stackexchange.com |
74,947 | [
"https://chemistry.stackexchange.com/questions/74947",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/45550/"
] | For my alkaline diet, I need to maintain a pH that's above 7, I need to achieve the objective like this:
I have eaten 300 g of grapefruit (pH = 13), and eaten 70 g of chocolate (pH = 5,5). What pH level have got my body from both these products?
| Additionally, the body has several of mechanisms to maintain homeostasis in the blood and extracellular fluid. So what you consume does not have the final effect on pH of your body as this is tightly regulated around the 7.35-7.45 pH range.
The most important way that the pH of the blood is kept relatively constant is... | This question has no answer, from two main reasons.
<h3>Chemistry does not work that way</h3>
It's impossible to calculate resulting pH of solution obtained by mixing known volume or mass or amount of substance of solution A with pH<sub>A</sub> and known amount of solution B with pH<sub>B</sub> without knowing compos... | https://chemistry.stackexchange.com |
3,310,498 | [
"https://math.stackexchange.com/questions/3310498",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/687479/"
] | Suppose <span class="math-container">$f:[a,b]\to\mathbb{R}$</span> is continuous and differentiable in <span class="math-container">$(a,b)$</span>. Suppose that also
<span class="math-container">$$\frac{f(a)}{f(b)}=\frac{b}{a}$$</span>
then there exists <span class="math-container">$c\in(a,b)$</span> such that <span ... | Hint:
use the mean value theorem for the function <span class="math-container">$g(x)=xf(x)$</span>, note that <span class="math-container">$g'(x) = xf'(x)+f(x)$</span>.
| You have <span class="math-container">$$af(a)=bf(b)$$</span> thus if you define <span class="math-container">$$g(x)=xf(x)$$</span>then <span class="math-container">$g(a)=g(b)$</span>
Also we have <span class="math-container">$$g'(x)=f(x)+xf'(x)$$</span>
The conditions of Roll's theorem applied to <span class="math-c... | https://math.stackexchange.com |
145,787 | [
"https://physics.stackexchange.com/questions/145787",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/930/"
] | It is often quoted, that it's emission is 10.6um. But we also know that CO2 lasers have huge number of possible emission lines in 2 main bands: 10.6um and 9.6/9.4um.
But what is emission spectra of generic sealed tube CO2 laser (let's say ~1m long, ~40W CW) without any line selection devices?
Should I expect single l... | The effect of gravity is only to shift the equilibrium point, so at equilibrium (at rest), a vertical spring will be extended as compared with the same spring in a horizontal position. But this does not affect the period.
The equation for the dynamics of the spring is <span class="math-container">$m\frac{d^2x}{dt^2}=... | Just look at the equation of motion.
Suppose you hang a spring from the ceiling, and that it hangs a distance $y_0$ from the ceiling in equilibrium (we orient our axis so that positive $y$ points downward). Then, the equation of motion is
$$
m\ddot{y}=-k(y-y_0)+mg,
$$
and so
$$
\tfrac{\mathrm{d}^2}{\mathrm{d}t^2}(y-y... | https://physics.stackexchange.com |
213,739 | [
"https://softwareengineering.stackexchange.com/questions/213739",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/65669/"
] | I have written an Android application. The application requires a Bluetooth connection to a very specific piece of hardware, currently a prototype. The only way I can test the app at present is to drive hundreds of miles to see if it works. If I end up with an ANR it can be very embarrassing in front of my client. The ... | As @MrSmith42 suggested, you should do the best you can to mock the interface. You don't need an actual bluetooth connection in order to mock it. Call an interface. That interface, in debug, sends what you'd expect for a given input. When not in debug, it performs the actual work of sending and receiving the data. ... | I think this is a project management issue, not so much a software development issue.
You should have a week or two with access to the device (on your client's premises or at your office) to evaluate the basic behavior of the device and to see how it interacts with your software.
Afterwards you can mock the interface ... | https://softwareengineering.stackexchange.com |
92,700 | [
"https://mathoverflow.net/questions/92700",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22530/"
] | I'm trying to follow Hopkins' construction of the Serre Spectral Sequence, but some "obvious" things are not that obvious to me.
He starts with considering a double complex $C_{\bullet,\bullet}$ with $C_{p,q}$ to be a free $\mathbb{Z}$-module generated by the maps $\Delta[p]\times\Delta[q]\rightarrow E$ ($E$ is a tota... | The double complex has a horizontal differential $\partial'$ and a vertical differential $\partial''$ such that $\partial'\partial''=\partial''\partial'$. This gives rise to a total complex $TC_n=\bigoplus_{p+q=n}C_{pq}$ with differential $\partial|C_{pq}=\partial'+(-1)^p\partial''$. This can be filtered by $F_p=\bigop... | I wanted to post the following as a comment, but it's too long.
It might help to realize where the differential comes from. Let $p: E \to B$ be a Hurewicz fibration. Assume $B$ is a connected CW complex.
Then $B$ has a cellular filtration $B_k \subset B_{k+1} \dots$. If we pull back $p$ along this filtration we obta... | https://mathoverflow.net |
181,349 | [
"https://electronics.stackexchange.com/questions/181349",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/81660/"
] | I'm trying to build a device that alerts me when I leave home without locking the door. I have a little space inside the door (width 8mm x height 130mm x depth 8mm) where I plan to install the microcontroller, a small button that gets pressed when the piece of metal of the door slides in (door locked), a battery and a ... | There are two kinds of push buttons. There are some with a lock mechanic (which will remain on the last state until it's pressed again) and there are some without this lock (which will remain open/closed while the button is pressed).
The problem I can see with the push buttons as sensors in this case is because they h... | Instead of using a button you could make it so that when the lock is in the locked position it completes the circut (i.e touches a conductive material) which would change the state of the input pin on the ardunio.
Good luck!
| https://electronics.stackexchange.com |
1,398,253 | [
"https://math.stackexchange.com/questions/1398253",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/25384/"
] | I am computing some stuff, and I came accross such problem:
Find such $g(x)$ for which $$(b-a)\sqrt{f(a)f(b)}=g(b)f(b)-g(a)f(a)$$ holds, where:
$g(x)$ and $f(x)$ are any real-valued functions of a real variable, and $a$ and $b$ are any reals such that $a<b$.
If such function were found it would simplyfy greatly th... | Take $a = 0, b = 1$ for simplicity, and assume that there is a function $g$ (actually just two numbers $g(0), g(1)$ for which this works for the functions $f(x) = 1, f(x) = x, f(x) = 1-x$. Then taking $f(x) = x$ we see that
$$0 = g(1)f(1) - g(0) f(0) = g(1).
$$
Similarly taking $f(x) = 1-x$ we get $g(0) = 0$. But taki... | It only holds for certain $f(x)$ and certain $g(x)$.
We need $$[g(b)f(b)-g(a)f(a)]+[g(c)f(c)-g(b)f(b)]=[g(c)f(c)-g(a)f(a)]\\
(b-a)\sqrt{f(a)f(b)}+(c-b)\sqrt{f(b)f(c)}=(c-a)\sqrt{f(a)f(c)}$$
It follows that $$\frac{b-a}{\sqrt{f(c)}}+\frac{c-b}{\sqrt{f(a)}}=\frac{c-a}{\sqrt{f(b)}}$$
Let $h(x)=1/\sqrt{f(x)}$, and we n... | https://math.stackexchange.com |
454,581 | [
"https://physics.stackexchange.com/questions/454581",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/84158/"
] | The 4 dimension distance from the origin of a point is <span class="math-container">$\sqrt{x^2+y^2+z^2-t^2}$</span>. Which means the 4 dimensional distance on the light-cone is zero.
Take a point A and a point B in the future at roughly the same position. Now move away from point A at the speed of light (and so going ... | Geodesics are not necessarily the shortest path between two points. In fact timelike geodesics are always the longest timelike curve connecting two points (or more specifically a local maximum of the proper time). Spacelike geodesics on the other hand are (only) saddle points of the path length.
| Your "paradox" is not specifically related to 4D Minkowski space. (Also, your confusion seems to be related to the Minkowski metric, not the dimensionality of spacetime, as the "paradox" already works in 1+1 dimensions.)
Basically, you show that two spacetime points at, say, <span class="math-container">$x_A=(t_A,0,0,... | https://physics.stackexchange.com |
18,517 | [
"https://engineering.stackexchange.com/questions/18517",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/13810/"
] | At my workplace I have been assigned to create an accurate 3D model of our Dell PowerEdge R820 servers so we can insert our custom cards and run a CFD and thermal analysis on them. The end goal is to have an exact understanding off all the airflow and heat transfer within the servers and server racks to help in designi... | Your options are a bit limited. Either you get the model from Dell, or you model it yourself.
Getting the model is a long shot, but if you are a really big customer that might happen. However this is not necceserily a godsend, since:
<ul>
<li>The model may not be accurate enough for your need. They may have ripped s... | For your IR camera, you need an image of a known object at a known temperature in the same environment as a temperature reference , then when you have the IR image you can cross-reference the colours to approximate the temperatures. Check out some building thermal images for the idea.
| https://engineering.stackexchange.com |
27,636 | [
"https://mathoverflow.net/questions/27636",
"https://mathoverflow.net",
"https://mathoverflow.net/users/6714/"
] | I tried this question over in the algorithms section of stackoverflow and never really got a handle on the problem. I know it concerns non-linear mixed integer programming.
[In the following, 1...n and k are subscripts. n will be relatively small - like say 5-20, or something like that. No more than a second or two ... | If $R$ is a commutative ring with $K_{0}(R)=\mathbb{Z}$, then $\mathop{\rm Spec} R$ is connected, because otherwise $R$ would split as a product, and $K_{0}(R)$ would contain a copy of $\mathbb{Z} \oplus \mathbb{Z}$. Hence there is a well defined surjective rank homomorphism $K_{0}(R) \to \mathbb{Z}$, which must then b... | No. Since $K_0(R)=\mathbb{Z},$ the ring $R$ is not a direct product, i.e. $\operatorname{Spec} R$ is connected. Therefore, every projective module has constant rank.
The rank function is an isomomorphism between $K_0(R)$ and $\mathbb{Z}$ which maps the free module of rank 1 $R$ into the generator 1 of $\mathbb{Z}$. The... | https://mathoverflow.net |
32,655 | [
"https://electronics.stackexchange.com/questions/32655",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9971/"
] | I have made an amplifier using TDA2002 but it's not working properly.
Pot. R1 is not included in mine as it doesn't make a lot of difference and produces noise when I try to adjust the volume.<br>
How can this be solved?
Above a certain volume set in the music player, the 8 ohm, 3 inch diameter speaker gives out di... | <strong>Distortion</strong>
Distortion can be caused (in this amp, assuming everyting is connected like it should be) by one of four causes:
<ol>
<li>Speakers gets overloaded - small speakers cannot handle a lot of power so it produces distortion if you try to play the music too loud, it probably would distort the lo... | You say you're using a 5V supply. The datasheet doesn't say in so many words, but the graphs don't show any values for supply voltages below 8V. Most probably it's your voltage which is too low.
<img src="https://i.stack.imgur.com/mHb1c.png" alt="enter image description here">
| https://electronics.stackexchange.com |
69,328 | [
"https://mathoverflow.net/questions/69328",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2837/"
] | Given a morphism $f:X\rightarrow Y$ between smooth complex varieties, one can define functors from the bounded derived category with holonomic cohomology on $Y$ to the same category on $X$. The easiest one is $Lf^{*}$ which can be obtained by putting a $D$-module structure on the inverse image of $\mathcal O$-modules a... | Just to clear up some notational confusion (there doesn't seem to be any completely standard notation):
<strong>In Bernstein's notes</strong>:
The "easy" pullback (i.e. the one that coincides with the pullback of the underlying $\mathcal O$-module) is denoted $Lf^\Delta$.
$f^! = Lf^\Delta [dim X - dim Y]$ (right adj... | The two standard D-module pullbacks agree (up to a shift) for smooth morphisms. Bernstein, Borel or Kashiwara are standard references for this.
A couple of comments: First you should restrict to coherent D-modules to get the duality functor (on the derived level). Next I think the notation is a little off from the sta... | https://mathoverflow.net |
306,305 | [
"https://dba.stackexchange.com/questions/306305",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/179908/"
] | I am working on setting up LDAP authentication for a PostgreSQL database and have added the following in my <code>pg_hba.conf</code> file:
<pre class="lang-bash prettyprint-override"><code># TYPE DATABASE USER ADDRESS METHOD
host all all all ldap ldapurl="ldap://example.local/dc=e... | Since my final goal is to keep passwords out of version control and the database is running in a docker container, I made the image process the <code>pg_hba.conf</code> file on initialization.
<ol>
<li>Create a <code>.env</code> file for the service with the contents:</li>
</ol>
<pre><code>LDAPCONFIG=ldapurl="ldap... | You cannot specify these settings via environment variables in PostgreSQL. Remember that <code>ldapbindpasswd</code> is specific to a certain <code>pg_hba.conf</code> line, and different lines could have different settings.
| https://dba.stackexchange.com |
137,079 | [
"https://stats.stackexchange.com/questions/137079",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/68628/"
] | I have a data set with some categorical variables and factor scores extracted by using factor analysis. Can I use both categorical variables and factor scores in logistic regression?
| Factor scores are often used in regression (including logistic regression), primarily for two reasons:
<strong>Data reduction:</strong> You have a lot of collinear variables and you want to be able to model them together. This is tricky because even if you have two variables $X_1$ and $X_2$ that are correlated (say <e... | It is common. You may want to consider that your factor scores are uncertain as they are estimates and not observations. I have seen this issue often enough ignored though.
| https://stats.stackexchange.com |
66,718 | [
"https://physics.stackexchange.com/questions/66718",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10531/"
] | I'm starting from this expression
$$ \alpha dt = \gamma^3 dv $$
where $\alpha$ is proper acceleration of a point particle, $dv$ and $dt$ are coordinate differentials of velocity and time, and $\gamma$ is the relativistic factor of the particle being subject to the acceleration
If $\alpha$ is constant, one arrives a... | Let's start with
$$\frac{\text{d}v}{\left(1-v^2/c^2\right)^{3/2}} = \alpha\text{d}t = \frac{\alpha(x)}{v}\text{d}x.$$
As Clem suggested, multiply both sides by $v$, so that
$$
\int_{v_0}^{v}\frac{v'\text{d}v'}{\left(1-v'^2/c^2\right)^{3/2}} = \int_{x_0}^x\alpha(x')\text{d}x' = A(x),
$$
which yields
$$
\frac{1}{\sqrt{1-... | In your equation $\alpha dt = \alpha(x) \frac{dt}{dx} {dx}$, just multiply each side by v before you integrate.
| https://physics.stackexchange.com |
24,317 | [
"https://engineering.stackexchange.com/questions/24317",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/16582/"
] | I'm trying to wrap my head around the question: "what is the optimal slip ratio and how do I go about controlling it?". I'm working on a control strategy for an electrical vehicle. The issue I'm facing is that of maximizing traction. The way I can measure slip ratio is by measuring difference between wheel velocity and... | Ultimately it is empirical.
For absolution maximum traction rubber tyres tend to deliver maximum grip in a fairly narrow window in the transition between purely static friction and full sliding friction.
This is very contextual and will depend on tyre construction and chemistry as well as tyre temperature and the n... | If you want to design a performance tire just for best traction, just before slippage and are not at the moment concerned with endurance, heat control, and many other factors, first you need to select quality material rubber which is soft and will leave a sacrificial black track under high acceleration when it heats up... | https://engineering.stackexchange.com |
667,752 | [
"https://physics.stackexchange.com/questions/667752",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/252181/"
] | At each level of physics, between rotating galaxies, orbiting planets, wind and motion of matter, to motion of molecules, atoms, particles, and maybe strings, there's always some degree of uncertainty in predicting the physics from theory. Relativity and quantum mechanics are the usual culprits in this uncertainty, but... | From a purely practical standpoint, there are a number of fields of study which by now contain very few unanswered questions and can be considered (again, for practical purposes) "solved". These include AC and DC circuit analysis (both lumped and distributed), continuum mechanics (elastic behavior of beams, c... | How can you guarantee that there will be no physics discovered in the future that will resolve to our theoretical physics of today, while at the same time providing a greater depth of knowledge?
You can't, no one can. Only mathematical proofs can be considered to be solved, or closed.
| https://physics.stackexchange.com |
391,228 | [
"https://softwareengineering.stackexchange.com/questions/391228",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/150257/"
] | Everyone knows that new developers write long functions. As you progress, you get better at breaking your code into smaller pieces and experience teaches you the value of doing so.
Enter SQL. Yes, the SQL way of thinking about code is different from the procedural way of thinking about code, but this principle seems... | I think the main problem is that not all databases support Common Table Expressions.
My employer uses DB/2 for a great many things. The latest versions of it support CTEs, such that I'm able to do things like:
<pre><code>with custs as (
select acct# as accountNumber, cfname as firstName, clname as lastName,
... | Locking down the creation of database views is often done by organizations paranoid of performance problems in the database. This is an organizational culture issue, rather than a technical issue with SQL.
Beyond that, large monolithic SQL queries are written many times, because the use case is so specific that very l... | https://softwareengineering.stackexchange.com |
622,010 | [
"https://physics.stackexchange.com/questions/622010",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I am trying to determine the equation of state and see if <span class="math-container">$PV = nRT$</span> is satisfied. For an ultra-relativistic gas of identical particles in a volume <span class="math-container">$V$</span> the energy (I am assume there is no potential) is <span class="math-container">$E = c\sum_{i = 1... | Hint: You have to use
<span class="math-container">$$dE=TdS-PdV+\mu dN$$</span>
<span class="math-container">$$\frac{P}{T}= \left. \frac{\partial S}{\partial V}\right|_{N,E}$$</span>
Where <span class="math-container">$$S=k_B\ln\Omega$$</span>
<hr />
| The calculation is easier in the canonical ensemble. Use
<span class="math-container">$$P=-{\partial F\over\partial V}$$</span>
where the free energy is given by
<span class="math-container">$$F=-k_BT\ln{\cal Z}$$</span>
Note that for free particles, the partition function factorizes
<span class="math-container">$${\ca... | https://physics.stackexchange.com |
60,432 | [
"https://physics.stackexchange.com/questions/60432",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7270/"
] | Suppose we have Hamiltonian on $\mathbb{C}^2$
$$H=\hbar(W+\sqrt2(A^{\dagger}+A))$$
We also know $AA^{\dagger}=A^{\dagger}A-1$ and $A^2=0$, letting $W=A^{\dagger}A$
How can we express $H$ as $H=\hbar \Big(\begin{matrix}
0 & \sqrt2 \\
\sqrt2 & 1
\end{matrix} \Big)$
So far I've shown that if we consider the... | As @MichaelBrown has pointed out in the answer, to get the matrix element you just have to sandwich the operator between two states. So in the case of your Hamiltonian $H$, the matrix elements are given as
$$H_{ij} = \langle i|H|j \rangle $$
I should point out that the $i$'s that you use should be the basis set that ... | The matrix element $O_{ij}$ of an operator are defined by
$$O_{ij} = \langle i | \hat{O} | j \rangle,$$
and it is traditional that the $i$ index labels the row and $j$ labels the column. This way matrix multiplication works as you would expect:
$$ (O P)_{ij} = \sum_k O_{ik} P_{kj}, $$
which you can show by inserting a ... | https://physics.stackexchange.com |
306,261 | [
"https://electronics.stackexchange.com/questions/306261",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/134429/"
] | Imagine you have an input signal s(t).
And the signal of course has some noise n(t).
So lets say the SNR value is x.
Now if we attenuate this signal by a voltage divider by 100 lets say, will the SNR of the attenuated signal remain same or?
Consider the following two scenarios:
1-) I log voltage data of a signal var... | Here is the thing, noise is actually a misnomer, signal distortion is what it should really be called.
Every time you pass a signal through any component or even a trace of wire, the signal that comes out the other end WILL have some distortion compared to the original signal. Some of that is "filtering" and "reflect... | With a signal that is ten times larger, the quantisation noise from the ADC will be about ten times lower. On the other hand, if the x10 amplifier has an error of 2% then you will have to factor this into the bigger picture because it may represent a more significant error than just ADC quantisation noise. Amplifiers m... | https://electronics.stackexchange.com |
508,413 | [
"https://electronics.stackexchange.com/questions/508413",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/108363/"
] | I think I understand fairly well by now why one wouldn't want tap water to get in contact with an electric circuit as it is conductive.
However, assuming the circuit will dry out completely before it is turned on, are there any risks for the circuit associated with having some tap water splash on it while it is powered... | First of all: "turned off" != unpowered. There's batteries and large caps on many boards, and only luck determines whether these discharge in a non-damaging way when the board comes into contact with water.
Many PCBs are washed in distilled water after assembly, to get rid of flux and glue residue. Most compo... | When a completely powered off circuit is exposed to tap water and dried, there is no obvious hazard as there is no electricity flowing. Though I don’t recommend applying water to electronics and then drying it. However, when electronics circuits are exposed to tap water and then dried eventually, the metals in circuit ... | https://electronics.stackexchange.com |
618,542 | [
"https://physics.stackexchange.com/questions/618542",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/156987/"
] | In introductory quantum physics, particles are described by the Schrodinger equation wave-function, which describes only an abstract probability wave.
But in quantum field theory, particles are vibrations in the fabric of their field. This would make them a literal wave in space (like sound in air)
Are particles both o... | It's tempting to try to interpret the mathematics of QM or QFT too literally, however this can be a dangerous game to play. Quite often you will cause more problems for yourself than you will solve by asking what exactly particles are (are they points, are they waves, are they fields, are they strings etc.), not least ... | Here is another way to look at this which might be helpful.
For objects small enough that quantum mechanical effects cannot be ignored, material particles begin exhibiting wavelike properties. Whether we detect their material aspect or their wavelike aspect then starts to depend on the physical details of the detection... | https://physics.stackexchange.com |
108,710 | [
"https://physics.stackexchange.com/questions/108710",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/36582/"
] | <em>I haven't studied much about this, so if I am mistaken about something please correct me.</em>
From what I have seen around the Internet, a force applied to a object takes time to propagate through the object because it has to interact with the molecules around the ones that the force was applied to. That means th... | The deformation wave will travel in both directions - there's no way for it to "know" the shortest path. And the resulting set of vibrations will interfere with each other in interesting ways, causing complicated resonances.
So, let's look at a simpler example: just a thin, large torus. We'll look at two points $90°$ ... | It is true that the deformation wave travels at the speed of sound, but you have to get away from thinking of objects as rigid if you ask about deformation waves. One good image is striking a foam ball with your fist. The overall shape of the ball will change as the ball wraps around your fist. Some of the deformati... | https://physics.stackexchange.com |
43,002 | [
"https://dba.stackexchange.com/questions/43002",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/24163/"
] | I am currently updating a table with millions of records, its been 4 days and query is still executing.
I checked the activity monitor its shows that query is running.
In event log there is no errors at all.
Performance wise:
<ul>
<li>Tempdb in disk A (850 gb free space) </li>
<li>database file in disk B (750 gb... | There is an interesting detail to this query that I did not spot at first. Thanks to Fabricio Araujo's answer I now see it: you are accessing two tables. I have never seen this kind of usage of the update statement before and I do not advise using it. I recommend you use the more intuitive join syntax per Fabricio's an... | This query requires you to scan every row in the table because
<ul>
<li>I guess procodet or ProviderCode are not indexed</li>
<li>Even if they were indexed, you have a LEFT which is a function on a WHERE predicate</li>
<li>And you have COLLATE too which is effectively a function on a WHERE predicate</li>
</ul>
"a fun... | https://dba.stackexchange.com |
68,772 | [
"https://quant.stackexchange.com/questions/68772",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/47092/"
] | Say I want to write call options on a stock, with no options written already on it. I know some asset which is highly correlated to it.
How can I proceed to make use of the correlation between this asset and the first one, to recreate some implied volatility surface on this unknown option ?
| This is a problem commonly faced by investment banks and buy-side firms (such as hedge funds) that deal in lots of derivatives.
There isn't much more one can do than employ a few rules of thumb, and those rules have not changed much over the decades. In this case, those tricks look something like the following:
First,... | EDIT:
Apologies, one more edit, but an important one:
Note, as kindly pointed out to me by an interested reader a short time ago: there is a potential issue with the simple model I proposed. Namely, as it stands the model implies that the illiquid asset<span class="math-container">$Y_t$</span> is not a martingale. But ... | https://quant.stackexchange.com |
103,720 | [
"https://softwareengineering.stackexchange.com/questions/103720",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7369/"
] | It is always difficult for me to choose between singular and plural forms for classes names:
<blockquote>
<pre><code>CustomerRepository vs. CustomersRepository
CustomerService vs. CustomersService
CustomerController vs. CustomersController
</code></pre>
</blockquote>
And for composite names it is even more difficult:... | The only thing I pluralize is collections.
<pre><code>foreach (var customer in customers)
{
// do something with customer
}
</code></pre>
All of your examples are individual objects, so they are not pluralized. Yes, the names refer to objects that might have multiple instances, but all you need to know in the ... | Use singular. The tool to turn screws with is called "screw driver" not "screws driver".
However, pluralize your method and property names accordingly, to indicate whether one value or a collection of them will be returned.
| https://softwareengineering.stackexchange.com |
800,401 | [
"https://math.stackexchange.com/questions/800401",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/9223/"
] | I am trying to generate such odd numbers $p$ that satisfy
$$\sum_{i=0}^n{2^{ik}p} = 2^m-1$$
for some $m, n, k, p \in \mathbb N$.
In other words, numbers that can be left-shifted (multiplied by $2^k$) so that in base 2, the 1s do not "overlap".
<h3>Example 1:</h3>
$$
\begin{array}{@{}cr}
& 10101 \\
+ &... | Suppose you want to find $p$ for which the sum of some copies of $p$, appropriately shifted, is $2^n-1$. The shifted copies of $p$ each have the form $2^ap$ for some $a\ge 0$, and their sum is therefore $$2^{a_1}p + 2^{a_2}p + \ldots + 2^{a_k}p$$ for some set of distinct non-negative integers $a_i$. Factoring out the ... | The general form of your examples falls in the cases of strings formatted with alternating, constant length strings of 1's and 0's where the length of the 0 strings are some multiple of the length of the 1 strings. In Python, the generating statement would look something like this:
<pre><code>binaryString = "{0}{1}" *... | https://math.stackexchange.com |
233,353 | [
"https://security.stackexchange.com/questions/233353",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/111829/"
] | I understand there are techniques to prevent someone from spoofing your domain in emails.
Is there any guarantee or check that the receiver can do to ensure the sender is authentic?
Gmail shows TLS and signature information, is that sufficient to guarantee the authenticity of the sender when present?
| Message authentication methods such as SPF, DKIM, and DMARC can be used by a message recipient to determine whether the domain of the apparent sender may have been spoofed. These standards are based on information published in the DNS for the sender’s domain.
In the case of SPF, an SPF record is published in the DNS f... | <blockquote>
Gmail shows TLS and signature information, is that sufficient to guarantee the authenticity of the sender when present?
</blockquote>
No. TLS does not provide any protection against sender spoofing at all.
The "signed-by" in the interface you refer to is about DKIM signatures. If the domain shown... | https://security.stackexchange.com |
532,674 | [
"https://stats.stackexchange.com/questions/532674",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/41374/"
] | I have a problem in which I'm trying to maintain a binomial distribution likelihood function. The wrinkle is that I have uncertainty about the results of an individual trial.
For example, each trial's success may come as a probability value (say, 0.78) rather than as a binary value (1 or 0).
Is there a standard or reco... | <strong>There's no supporting theory, because this doesn't work except by chance alone.</strong>
Your choice of null and alternative hypotheses depend only on what you're trying to prove and not the sample value. Suppose you have some new drug that's supposed to lower cholesterol, and you want to test if it works. The ... | You decide on your null and alternative hypothesis before you analyze the data (preferably before you even collect the data), so you have made a mistake in peeking.
By flipping the inequality to point away from the observed value, you assure yourself of not being able to reject (perhaps with some exotic exceptions, but... | https://stats.stackexchange.com |
116,042 | [
"https://mathoverflow.net/questions/116042",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3106/"
] | Suppose I have an $n\times n$ real (or complex) matrix of rank $k$, and I want to pick $k$ linearly independent rows from it. I want to do this in a continuous fashion as the matrix varies continuously. I'm being a bit vague here, but I think it doesn't matter, because a colleague tells me that it's a standard fact t... | Picking $k$ linearly independent rows is harder than picking a basis for the row space. The row space forms a vector bundle on the manifold of rank $k$ matrices. Picking a basis continuously would be equivalent to picking a trivialization of the vector bundle.
So your colleague's claim is weaker than the fact that th... | As Angelo points out, this statement is trivial if by "rows" you mean rows with respect to a fixed basis. A generalization would be to allow the "rows" to come from any basis. Up to some duality, this is equivalent to asking to be able to continuously choose a set of $k$ linearly independent vectors whose span is dis... | https://mathoverflow.net |
10,226 | [
"https://dba.stackexchange.com/questions/10226",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5551/"
] | <img src="https://i.stack.imgur.com/ko4vx.png" alt="installation screen">
I need to add fulltext capabilities to an existing SQL Server 2008R2 instance but the one I need to upgrade is not actually available. The combobox shows only the one selected, as in the picture. It looks like it could be related to different ve... | I finally solved my problem by uninstalling SP2. Then, the instance version got back to the one matching the DVD and I was able to add FullText feature to the default existing one.
| I agree with Mark's comment. Perhaps the default instance was installed with SQL 2012 (code name denali) beta or release candidate? If that's the case then you should be able to use that installer to try to add features but older versions of the binaries (like SQL 2008 R2) would not be able to.
| https://dba.stackexchange.com |
25,323 | [
"https://mathoverflow.net/questions/25323",
"https://mathoverflow.net",
"https://mathoverflow.net/users/622/"
] | First, yes, I've seen Mumford's paper of this title. I'm actually interested in specific ones, and looking for really the most elementary/elegant proof possible.
I'm told that for $g\geq 2$ it is known that the Picard groups of $\mathcal{M}_g$ and $\mathcal{A}_g$ (the moduli spaces of curves of genus $g$ and abelian ... | I'll just talk about the calculation of $\text{Pic}(\mathcal{M}_g)$ as a group (showing that it is generated by the Hodge bundle is then a calculation).
I think the most elementary way to view this problem is to think in terms of orbifolds rather than stacks. Recall that $\mathcal{M}_g$ is the quotient of Tecichmulle... | The fact that the Picard group of the moduli variety (not stack) A(g) is of rank 1, is sketched in a footnote of Mumford's paper on the Kodaira dimension of A(g), in LNM 997. This footnote is elaborated (over Z) in a paper of Smith-Varley: in LNM 1124. Another reference is Freitag's paper in Arch. Math. 40 (1983), pp... | https://mathoverflow.net |
288,226 | [
"https://softwareengineering.stackexchange.com/questions/288226",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/148842/"
] | Macros are considered a good thing by one and evil by another.
Is there a rule of thumb when to and when not to use macros in C++?
When are macros idiomatic and when should they be avoided?
| <blockquote>
When are macros idiomatic and when should they be avoided?
</blockquote>
Macros are idiomatic only when there is no alternative to their use. Examples are include guards (they are the only portable form), embedded domain-specific languages, special compiler support not available through other language f... | As a rule, you should only use macros, when a better alternative does not exist.
They <strong>should not</strong> be used to generate code; you should simply write the code instead (if the code is type-agnostic, write a template instead).
They <strong>should not</strong> be used to define constants; constants should ... | https://softwareengineering.stackexchange.com |
270,368 | [
"https://stats.stackexchange.com/questions/270368",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/130141/"
] | From <em>The Elements of Statistical Learning</em> I know that logistic regression parameters can be fit using the Newton Raphson (NR) method on the likelihood function. So then why would you ever want to use MCMC?
| If you're doing a fully Bayesian treatment of logistic regression you could use MCMC, but if you're just doing a frequentist maximum likelihood (possibly penalized) it would be very unnecessary to use MCMC. One big difference is with the Bayesian regression you need to sample from the posterior of your parameters, whil... | MCMC is usually used to fit complicated models. For example, if the response has some missing values in a logistic regression model.
| https://stats.stackexchange.com |
105,256 | [
"https://physics.stackexchange.com/questions/105256",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/43321/"
] | I read that the soda's temperature allows it to contain its $\text{CO}_2$: colder means it can retain its bubbles better.
So, why does soda fizz when it meets ice?
If anything, because the soda is made colder, it should retain its gas better, as per above. The ice is taking away energy from the soda, thus freezing. W... | This isn't the definitive answer that DumpsterDoofus was hoping for since I can't point to any scientific publications - they must exist but a quick Google failed to find anything from a reputable journal though there are loads of blog articles.
Anyhow, although in soda the carbon dioxide solution is supersaturated the... | John Rennie's answer is pretty good. I will only add the reason for the energy curve is the different forces between adjacent molecules. And this mean different potential energies.
H2O - H2O and CO2 - CO2 are more energetically favorable than H2O - CO2
CO2 - CO2 is found in the interior of a bubble. The energy drop i... | https://physics.stackexchange.com |
89,158 | [
"https://physics.stackexchange.com/questions/89158",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/32284/"
] | I am trying to understand net force intuitively and this is what I think.
<blockquote>
If a net force is towards the positive $x$ direction, which of the following is true ?
<strong>a)</strong> It can be moving in the negative $x$ direction
<strong>b)</strong> It can be speeding up
<strong>c)</strong>... | <blockquote>
If a net force is towards the positive x direction,
</blockquote>
then <em>the $x$ component of velocity of the object is increasing</em>; period.
Now, knowing this, are any of the statements (a) through (d) true?
<blockquote>
a) It can be moving in the negative x direction
</blockquote>
Sure, <em>... | The <strong>only</strong> thing that a net force in the positive $x$ direction means is that the net acceleration is in that direction. It tells you nothing about its position or velocity.
a) Imagine placing the $x$-axis vertically and letting the positive $x$ direction be downward. Now imagine that the constant force... | https://physics.stackexchange.com |
122,299 | [
"https://dba.stackexchange.com/questions/122299",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/25590/"
] | <pre><code>Summary: Materialized View across DB link eating up too many system resources
Question: Is there a way to throttle a materialized view refresh?
</code></pre>
We have some fairly large tables that we copy from one oracle DB to several others as a cached backup if the network to the central database is down (... | Materialized views over a DB link most certainly can be set up as fast refreshes (i.e. only changes since the last refresh) as we use this approach ourselves. However, what cannot be done are refresh on commit mviews over a DB link, so the mview will have to be on a refresh schedule (unless you simply want to refresh ... | We also have a lot of MVs that are refreshed with data coming over a database link. Do you do an atomic refresh? If you do then switch it off. An atomic refresh does a <code>delete from table</code> while the other option does a <code>truncate table</code>. The last option is faster but (nothing for free :-)) when the ... | https://dba.stackexchange.com |
9,066 | [
"https://security.stackexchange.com/questions/9066",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/5953/"
] | Does it make any sense at all to salt a hash which might be available publicly?
It doesn't really make sense to me, but does anyone actually do that?
<strong>UPDATE - Some more info:</strong>
An acquaintance of mine has a common salted-hash function which he uses throughout his code. So I was wondering if it made an... | Yes. It's normally taken for granted that the salt will be available to an attacker. The salt does <em>not</em> need to be kept secret to be useful.
Salting a hash is done primarily to protect against a dictionary attack. A dictionary attack works by hashing common words (e.g., everything in a dictionary, thus the nam... | The idea of a salt for a hash is that the same message does not result in the same hash for every hash, but that it depends on the salt, too.
(The same idea applies to an initialization vector for encryption functions.)
If I understand the question right, you are hashing the contents of a user-contributed page to cre... | https://security.stackexchange.com |
21,586 | [
"https://quantumcomputing.stackexchange.com/questions/21586",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/12265/"
] | The toric code and other popular codes can be decoded using minimum weight perfect matching.
Is this an optimal decoder? Here by optimal, I mean it gives the best logical error rate
vs physical error rate performance in depolarizing channel. "Threshold" is often used to characterize toric codes, does that ass... | <blockquote>
Is [minimum weight perfect matching] an optimal decoder?
</blockquote>
No, it's not optimal. For example, it uses the weight of the shortest path between two detection events as an approximation for the contributions of all topologically equivalent paths. An optimal decoder would exactly compute the contri... | In light of the comments above, I'm going to try to answer this question, with the caveat that I am taking my first steps in this field so I might have errors here.
<strong>TLDR</strong> - it seems to me that in an independent errors model, the MWPM decoder is an optimal decoder for the <em>Pauli frame</em>, rather tha... | https://quantumcomputing.stackexchange.com |
321,932 | [
"https://electronics.stackexchange.com/questions/321932",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/39266/"
] | When I'm handling an IC that is sensitive to ESD that comes packaged in an antistatic bag, do I nullify my ESD protection procedures if I peel back the cut-tape and dump out the IC into a plastic cup instead of dumping it directly onto the surface of my ESD mat? Do I need to dump the IC out directly onto the surface o... | Trust me, it is totally fine to dump it on to the ESD mat. Think about what the antistatic bag does: it keeps any stray charge from going through the contents, but still can have a slight charge on its exterior.
So, if you are touching your mat with one hand and holding the open antistatic bag in the other hand, then... | Is this an antistatic bag or a static shielding bag? Sensitive components should never be shipped in a poly bag. If that's the case you should be contacting whoever packaged it because it could already be compromised. Antistatic or even dissipative bags don't prevent charges from penetrating to the interior, static shi... | https://electronics.stackexchange.com |
369,026 | [
"https://physics.stackexchange.com/questions/369026",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75085/"
] | I am trying to prove that the covariant derivative is a tensor (ie it transforms well under a change of coordinates) but I can't succeed to it.
Here is the definition of the covariant derivative :
$$ \nabla_XV= X^{\mu}(\partial_{\mu} V^{\rho}+V^{\nu}\Gamma_{\mu \nu}^{\rho})\partial_{\rho}$$
I write then the $\rho$ c... | Since $\frac{\partial x^\rho}{\partial y^\lambda}\frac{\partial y^\lambda}{\partial x^\nu} = \delta^\rho_\nu$, we obtain
\begin{align*}
0 &= \partial_\mu \left(\frac{\partial x^\rho}{\partial y^\lambda}\frac{\partial y^\lambda}{\partial x^\nu} \right)\\
&= \frac{\partial^2 y^\lambda}{\partial x^\mu \partial x^\... | We start from the identity:
<span class="math-container">$$\frac{\partial \mathbf{V}}{\partial Z^S} = \nabla_S V^i \mathbf{Z}_i$$</span>
where <span class="math-container">$\nabla_S V^i$</span> is the covariant derivative whose components are: <span class="math-container">$\nabla_S V^i = \frac{\partial V^i}{\partial Z^... | https://physics.stackexchange.com |
4,486,531 | [
"https://math.stackexchange.com/questions/4486531",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1050393/"
] | I saw the following problem in Linear Algebra Done Right and thought if the general version of it would hold.
Problem: Suppose that <span class="math-container">$v_1,. . .,v_4$</span>. spans <span class="math-container">$V$</span>. Prove that <span class="math-container">$v_1 - v_2,v_2-v_3,v_3-v_4,v_4$</span> also sp... | Assuming <span class="math-container">$x, y$</span> are non zero column vectors in <span class="math-container">$K^n$</span> where <span class="math-container">$x=\begin{pmatrix}x_1\\x_2\\\vdots \\x_n\end{pmatrix}$</span> and <span class="math-container">$y=\begin{pmatrix}y_1\\y_2\\\vdots \\y_n\end{pmatrix}$</span>
The... | Hint:
<span class="math-container">$xy^T$</span> is a matrix where the columns are <span class="math-container">$x$</span> multiplied by the elements in <span class="math-container">$y$</span>
| https://math.stackexchange.com |
103,922 | [
"https://stats.stackexchange.com/questions/103922",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/48618/"
] | In section 7.10.2 of Elements of Statistical Learning, it says that the true (test) error rate of any classifier is 50%. I'm having trouble understanding the intuition behind this. If you have a binary class (1 or 0) and your classifier is a die where if you roll a 1-5, the classification is 1 and if you roll a 6, the ... | That's not a general statement about classifiers. In this particular case where the class frequencies are half & half, & none of the predictors are any use, the true error rate, of any classifier, is 50%. Imagine trying to predict the result of coin tosses from denomination, year of issue, metal content, &... | To expand on the answer above, the key point is that the predictors are <em>independent</em> of the class labels (of no use) i.e. any forecast using these predictors is equivalent to a random draw from the class labels.
| https://stats.stackexchange.com |
30,456 | [
"https://stats.stackexchange.com/questions/30456",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11090/"
] | I know that linear regression can be thought as <em>"the line that is vertically closest to all the points"</em>:
<img src="https://i.stack.imgur.com/IXibx.png" alt="enter image description here">
But there is another way to see it, by visualizing the column space, as <em>"the projection onto the space spanned by the... | Sorry for my painting skills, I will try to give you the following intuition.
Let $f(\beta)$ be the objective function (for example, MSE in case of regression). Let's imagine the contour plot of this function in red (of course we paint it in the space of $\beta$, here for simplicity $\beta_1$ and $\beta_2$).
There is... | The intuition I have is the following:
In the least-squares case, the hat matrix is an orthogonal projection thus idempotent. In the penalized case, the hat matrix is no longer idempotent. Actually, applying it infinitely many times, will shrink the coefficients to the origin. On the other hand, the coefficients still ... | https://stats.stackexchange.com |
9,269 | [
"https://cs.stackexchange.com/questions/9269",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/5291/"
] | For a language $L$ with pumping length $p$, and a string $s\in L$, the pumping lemmas are as follows:
<strong>Regular version</strong>:
If $|s| \geq p$, then $s$ can be written as $xyz$, satisfying the following conditions:
<ol>
<li>$|y|\geq 1$</li>
<li>$|xy|\leq p$</li>
<li>$ \forall i\geq 0: xy^iz\in L$</li>
</ol>
... | When proving that a language isn't regular/context free it is quite useful to be able to limit the area containing the pumped string. The classical example is proving $\{a^n b^n \colon a \ge 0\}$ non-regular: If you take $\sigma = a^p b^p$, where $p$ is the lemma's constant, then without condition (2) you have to consi... | Consider the language of words over $\{a,b\}$ consisting of words with an equal number of $a$s and $b$s. This language is context-free but not regular. To show that it is not regular using the pumping lemma, you start with the word $a^pb^p$ and pump $y$, which must consist solely of $a$s. Without condition (2), this wo... | https://cs.stackexchange.com |
616,620 | [
"https://physics.stackexchange.com/questions/616620",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/289991/"
] | I am trying to wrap my head around index notation and I have found a question in a textbook I am unsure of the answer of. It gives the expression:
<span class="math-container">$$
t_{jk} = Γ^{i}_{jk} u_{i}
$$</span>
and asks for an explanation as to whether this has sensible index placement?
I have only seen the Christ... | A sensible index placement has a contraction between an upper and a lower index. In this case, an upper <span class="math-container">$i$</span> is contracted with a lower <span class="math-container">$i$</span>, so the expression makes sense.
| If by a vector you mean contravariant vector <span class="math-container">$u^i$</span> then this wouldn't be correct since you can not contract it with the Christoffel symbol <span class="math-container">$\Gamma^{i}_{jk}$</span> and obtain <span class="math-container">$t_{jk}$</span>. You can perform the contraction be... | https://physics.stackexchange.com |
176,308 | [
"https://dba.stackexchange.com/questions/176308",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/126785/"
] | I have a simple LAMP server on Amazon EC2. (find the specs towards the end of this message.) I used the following command in the terminal to see status of each query
<strong>watch --interval=2 "mysqladmin -u{username} -p{password} processlist"</strong>
I see roughly 4-5 queries running every now and then that result ... | First of all, I would rewrite this condition. As it is, it can't use any index effectively.:
<pre><code>datefromparts(cast(year as char(4)),cast(month as char(2)),'01') < getdate()
</code></pre>
Rewrite it so there is no functions or calculations applied to the columns:
<pre><code> ( year < year(getdate())
or... | I will remove cgcode from Group By since I know what is cgcode and it is not range.So removing cgcode (varchar(60)) will give tremendous push.
So if I am correct my index will change too.
Use Variable in place of getdate()
<pre><code>declare @CurDate date=getdate()
declare @yr int=year(@CurDate )
declare @month tin... | https://dba.stackexchange.com |
2,837,404 | [
"https://math.stackexchange.com/questions/2837404",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/114720/"
] | My class notes say that because $U=\mathbb{R}\backslash\{x_1,x_2,..,x_n\}$ has the same cardinality than $\mathbb{R}$, there exists a homeomorphism between:
$(U,T_{cof})$ and $(\mathbb{R},T_{cof})$, where $T_{cof}$ is the finite complement topology.
I initially thought that having the same cardinality is a necessary ... | You are right that in general having the same cardinality is not enough (e.g. $[0,1]$ vs $(0,1)$ with Euclidean topology). However in the case of finite complement topology it is enough.
For that consider any bijection $f:X\to Y$ with finite complement topology on both sides. It is continuous because the preimage of a... | Enumerate a countably infinite subset $\{a_k\}_{k \in \mathbb{N}}$ of $\mathbb{R}$ for which the first $n$ terms are $x_1$ through $x_n$. Here is an explicit homeomorphism from $\mathbb{R} \rightarrow U$ where the latter is endowed with the finite complement topology:
If $x = x_k$, then map $x \mapsto a_{k+n}$; otherw... | https://math.stackexchange.com |
159,528 | [
"https://softwareengineering.stackexchange.com/questions/159528",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/56691/"
] | Some time ago I was to learn iOS development at my work. I didn't manage to learn it because I was moved to more important task with another technology already familiar to me. But the short time I spent on iOS, I felt that I could do better if I spent a few hours at the workplace during which I could discuss some matt... | Why do you feel that you could do better at home rather than at the office?
I'm guessing that it's due to interruptions and distractions. Since you mention being moved between tasks, I assume your work involves multiple simultaneous projects with developers moving between them. In this line of work, interruptions and ... | We adopted so called FedEx days. Any team member is allowed to spend all working day for learning. Once per several weeks. Then he has to make some little project/presentation and share his knowledge with colleagues.
Learning at home is natural I believe to most of the professionals. But I feel lerning under some prea... | https://softwareengineering.stackexchange.com |
3,785,113 | [
"https://math.stackexchange.com/questions/3785113",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/756147/"
] | Let <span class="math-container">$a \in \mathbb{R}$</span> such that <span class="math-container">$a>0$</span>. Consider the set <span class="math-container">$S=\{a, a, a, \dots\}$</span>. Would it be valid to conclude that <span class="math-container">$\inf S >0$</span>? Or can we just say that <span class="math... | The key to this problem is in factoring the denominator. We note the following identity:
<span class="math-container">$$b^4-2a^2b^2+a^4 = (b^2-a^2)^2 = (b-a)^2(b+a)^2 = (b^2+2ab+a^2)(b^2-2ab+a^2)$$</span>
We see that the denominator splits into the goal denominator and another term. We divide the numerator by <span cla... | <strong>Hint:</strong> Notice that substituting <span class="math-container">$a=b$</span> gives us numerator as zero for both the expressions. Hence, <span class="math-container">$(a-b)$</span> is one of the factors.
<blockquote class="spoiler">
<span class="math-container">$$1.\ -\frac{(a-b)^3(a^2+3ab+b^2)}{(a^2-b^2)... | https://math.stackexchange.com |
16,654 | [
"https://electronics.stackexchange.com/questions/16654",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | What would happen if I short the terminals of a DC motor together while power is disconnected but it is still freewheeling?
According to several sources, it would brake the motor. This makes sense. But they also mention using an array of power resistors and not just shorting the terminals. What would happen if I just ... | What they said ... plus / but:
When a short circuit is applies to a DC motor's terminals the rotor and any attached load will be braked rapidly. "Rapidly" is system dependant but as braking power may be somewhat above peak motor design power the braking will usually be significant.
In most cases this is a bearable t... | Your motor will be working as a generator - so-called "electrical braking". The circuit will be formed of the motor coil and whatever you connect to it. The current will depend on that circuit resistance.
Since the coil and the other components are connected sequentially the current will be equal in all parts of the c... | https://electronics.stackexchange.com |
618,984 | [
"https://math.stackexchange.com/questions/618984",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/117774/"
] | Given $2$ prime numbers,$ p$ and $q$, that are both not even, and $3$ doesn't divide $p-1$ or $q-1$, and
$n=pq$, how many elements in $Z^*_n$ exists that has $b$ such that $b^3\equiv a\pmod n$ .
I know that the answer is $\phi(n)$ - that is, $(p-1)*(q-1)$, but I can't find out how to prove it :(
| Let $a \in \Bbb (Z/n \Bbb Z)^\times$. We show that there is $k$ such that we can choose $b=a^k$, so $a^{3k}\equiv a \mod n$.
By Fermat's Little Theorem, we have $a^{\varphi(n)}\equiv 1 \mod n$.
As $3 \nmid (p-1)(q-1) = \varphi(n)$, we know $\gcd(3,\varphi(n)) = 1$. So by the Euclidean Algorithm you can choose $k \in... | $\rm x\mapsto x^3$ is onto, being $1$-$1\!:$ $\, \begin{eqnarray}\rm a^3 &=&\rm b^3\\\Rightarrow\rm (a/b)^3 &=& 1\end{eqnarray}\!$ so $\rm\,a/b\,$ has order $\,n\mid 3,\phi,\,$ so $\,n\mid (3,\phi) = 1\ \ $ <strong>QED</strong>
| https://math.stackexchange.com |
78,624 | [
"https://softwareengineering.stackexchange.com/questions/78624",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25939/"
] | Most engineering manager positions require X years of managerial experience in the job description. That means as an individual contributor I can never qualify. But this experience has to come from somewhere. How can I bootstrap the managerial experience? Is internal promotion to some lead position the only possible wa... | You can get X years of "management experience" without ever being a manager. If you look at management as a series of disciplines (building a team, coaching people, building a schedule, etc.) then you are building a management pedigree. Some recommendations:
<ul>
<li>Find a mentor (someone in a management position)... | Mostly it does come as you guess from internal promotion. You have coded a lot and after years of practice you were asked to take the ownership of the code, mentor juniors perhaps on occasion even be a contact for the customers of the company. Then you discover the years you are doing now count more towards managerial ... | https://softwareengineering.stackexchange.com |
334,036 | [
"https://electronics.stackexchange.com/questions/334036",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/161495/"
] | I have to test prototype PCBs that convert household AC into several DC voltage levels.
I concern about my safety when working with AC and would like to know how to properly setup a testbench that, for example, will trip a circuit breaker or break a fuse if something goes wrong.
I plan to build a testbox that is loca... | An isolation transformer will make it safe to touch live, but definitely not live and neutral simultaneously.
Another option is a RCD (residual current device). I purchased a sensitive one which trips at 10mA leakage current to ground, which is safer than the 30mA one which protects the whole house. You will still get... | You are missing the very first thing I'd use, which is a isolation transformer. The next most useful device is the variac. Your redundant fuse and circuit breaker are just silly.
When using both a variac and a isolation transformer, put the variac in front of the isolation transformer. This is because many common i... | https://electronics.stackexchange.com |
560,580 | [
"https://physics.stackexchange.com/questions/560580",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99211/"
] | In Chapter 6 of <em>Spacetime and Geometry</em> by S. Carroll, he says
<blockquote>
‘‘Because the event horizon is a global concept, it might be difficult to actually locate one when you are handed a metric in an arbitrary set of coordinates.’’.
</blockquote>
I understand what local and global variables are, and I have... | Formally defined, an event horizon bounds a region which is causally disconnected from future null infinity. To truly know if a boundary meets this definition, requires knowing a good amount of the complete future history of the spacetime: local knowledge of the event horizon and its surroundings for part of the histor... | I will essentially say the same thing as in John's answer, but in a different way, and maybe this will be easier to understand (judge for yourself).
"Global," here, does not mean global variables, it means that you need to know more than just the geometry local to the event horizon to know that you are at an ... | https://physics.stackexchange.com |
94,939 | [
"https://dba.stackexchange.com/questions/94939",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/61104/"
] | I'm new in databases so I need help. I have two tables:
First table:
<pre><code>| Date .........| Diagnostics ................| ID ...............|
| 2015-03-08 ...| Diag1 ......................| 2932 .............|
| 2015-03-09 ...| Diag2 ......................| 2932 .............|
</code></pre>
Second table:
<p... | <pre><code>;WITH First_table
AS (SELECT '2015-03-08' AS [Date],'Diag1' AS Diagnostics, 2932 AS ID
UNION ALL SELECT '2015-03-09','Diag2', 2932
)
,Second_table
AS (SELECT '2015-03-09' AS [Date], 'Eval1' AS Evaluation ,2932 AS ID
UNION ALL SELECT '2015-03-09','Eval2',2932
UNION ALL SELECT '2015-03-10' ,'E... | A script to create the temporary tables:
<pre><code> CREATE TABLE #Diagnostics (
DATE DATE
,Diagnostics NVARCHAR(40)
,Id INT
)
CREATE TABLE #Evaluation (
DATE DATE
,Evaluation NVARCHAR(40)
,Id INT
)
INSERT INTO #Diagnostics
VALUES (
'20150308'
,'Diag1'
,2932
)
,(
... | https://dba.stackexchange.com |
74,925 | [
"https://softwareengineering.stackexchange.com/questions/74925",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3792/"
] | I'm sure everyone has experienced something like this. You go into a meeting with a client who has a project. They have no/few requirements in mind and the vaguest understanding of what they want/need. At this point, there seem to be two options:
1) Tell the users, "Ok, so I can't build something for you if you cannot... | I have to admit that sometimes I choose option 3)
<blockquote>
3) Listen to the clients vague ideas,
blanch at the idea of spending weeks
helping them figure out exactly what
they want... so figure out what it is
they need, build that, and refactor as
required.
</blockquote>
This works, particularly for s... | if you want to be just a programmer, then you wait until someone else has figured out what the client needs and then code that
if you want to be a <strong>developer</strong>, and this is <em>your</em> client, then you take your client's hand and gently walk them through the dense scary forest of possibilities until to... | https://softwareengineering.stackexchange.com |
30,297 | [
"https://softwareengineering.stackexchange.com/questions/30297",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6415/"
] | In legacy code I occasionally see classes that are nothing but wrappers for data. something like:
<pre><code>class Bottle {
int height;
int diameter;
Cap capType;
getters/setters, maybe a constructor
}
</code></pre>
My understanding of OO is that classes are structures for data <em>and the methods of ope... | Definitely not evil and not a code smell in my mind. Data containers are a valid OO citizen. Sometimes you want to encapsulate related information together. It's a lot better to have a method like
<pre><code>public void DoStuffWithBottle(Bottle b)
{
// do something that doesn't modify Bottle, so the method doesn'... | Data classes are valid in some cases. DTO's are one good example mentioned by Anna Lear. In general though, you should regard them as the seed of a class whose methods haven't yet sprouted. And if you are running into a lot of them in old code, treat them as a strong code smell. They are often used by old C/C++ pro... | https://softwareengineering.stackexchange.com |
751,432 | [
"https://physics.stackexchange.com/questions/751432",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/359072/"
] | <blockquote>
An object mass <span class="math-container">$1 \, \rm kg$</span> hangs on a rope length <span class="math-container">$1 \, \rm m$</span>. The object gets pushed with minimal horizontal velocity required to swing a full vertical circle, i.e.: keeping the rope stretched.
What time <span class="math-container... | <blockquote>
But, if there's no resistance when a current flows through a superconductor, doesn't that mean there's no energy lost as heat? That would seem to imply we're adding energy to a system (by getting a curent going) without increasing the entropy, which should be impossible
</blockquote>
Second principle only ... | You correctly wrote:
<blockquote>
there will always be some energy lost as heat to any system that converts energy to a useful form. Or in other words, it's fundamentally impossible to convert energy to work with 100% efficiency.
</blockquote>
Now, a steady current in a superconductor does not do any work. No work, no ... | https://physics.stackexchange.com |
2,401,303 | [
"https://math.stackexchange.com/questions/2401303",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/473670/"
] | Let $a_0, a_1, a_2,$ ... be the sequence of natural numbers defined by the recurrence relation
$a_0 = 1; a_1 = 3; a_n = 2 a_{n-1} + a_{n-2}$ for all $n > 2$
Show that $a_n$ is odd for all n > 0.
So far, I've computed the recurrence relation for the first few terms but I'm unable to determine the n-th term of rela... | The base of the induction is obvious (it's just given).
Let $a_n$, $a_{n-1}$ be odds.
Thus, $a_{n+1}=2a_{n}+a_{n-1}$ is odd and we are done!
| $a_0$ and $a_1$ are obviously odd.
Suppose $a_n$ is odd for some $n\geq 2$:
Then
$a_{n+1}=2a_n+a_{n-1}$ is odd, since $2a_n$ is even and $a_{n-1}$ is odd.
| https://math.stackexchange.com |
18,282 | [
"https://mathoverflow.net/questions/18282",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4250/"
] | Suppose you start at position 0. You then roll 2 6-sided dice. You move to the integer, call it z, that is the sum of the two dice. You then roll again. If the result of the roll is z', you move to z+z'. You then continue in this fashion. I am looking for formulas (recursive or non-recursive) for the probability ... | The probabilities do converge to 1/7. One way to see this is to start from Tony Huynh's comment: the probability that $n$ is hit is the coefficient of $t^n$ in $$f(t) = {1 \over (1-(t+t^2+t^3+t^4+t^5+t^6)^2/36)}$$. The denominator is a polynomial of degree 12; its roots are $t = 1$ and eleven points $r_1, \ldots, r_{... | Let p(n) be the required probability. Then p(n) satisfies the following recursion
p(n)=1/36 p(n-12) + 2/26 p(n-11) + 3/36 p(n-10) + 4/36 p(n-9) + 5/36 p(n-8) + 6/36 p(n-7) + 5/36 p(n-6) + 4/36 p(n-5) + 3/36 p(n-4) + 2/36 p(n-3) + 1/36 p(n-2),
with the obvious initial conditions.
| https://mathoverflow.net |
619,599 | [
"https://electronics.stackexchange.com/questions/619599",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/313451/"
] | Let's assume I have a 12V 90Ah battery and 12V(15v max) 20A SMPS. I want to use this SMPS to charge the battery. I heard that 1/10 of the battery current is good to charge the battery. So that means 9A is the best current to charge the battery.
The matter is if I use the above SMPS will that SMPS reduce the current acc... | Without looking at the other side of the code, it is more important to transfer the third byte than what the value of third byte is.
The value is 0xAA which is an alternating pattern of ones and zeroes, and it might be chosen just because it is quite easy to recognize on oscilloscope and it might be used to check the t... | It helps provide a visual indication of success or failure. Note the line that says "This can be visually verified on STK600 with the help of onboard LEDs".
If the LEDs represent the register (i.e. PORTD) success is alternating lights, while failure is one half lit, the other half dark.
If it is blinking out... | https://electronics.stackexchange.com |
21,351 | [
"https://electronics.stackexchange.com/questions/21351",
"https://electronics.stackexchange.com",
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] | I've run into an unusual problem. I'll start off by describing my goal: I'm designing a circuit that can test for short circuits and open circuits in a wiring harness. The wiring harness does not have a CAN bus or anything complicated like that - just simple wires.
Here's how it works
I have two CPLDs, one as a desig... | I would personally use tri-state outputs in this situation.
Instead of driving a 0 or a 1, you could have pull-down (or pull up depending on your preference) resistors on the outputs, and drive the pin you're interested in high or low - the opposite of your chosen pull-up/-down resistor. The other outputs should be s... | Some ideas:
<ul>
<li>If it's for a short-term prototype, don't worry too much. Damage of that sort takes quite a long time to kick in! Likely a '0' will "win" over a '1', so you may find you get no '1's at all if there's a short.</li>
<li>Add series resistors to the drive pins to limit the current to a safe value.</... | https://electronics.stackexchange.com |
424,930 | [
"https://physics.stackexchange.com/questions/424930",
"https://physics.stackexchange.com",
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] | When we are calculating speed from the graph for a uniform motion the speed which get as an answer is actually the average speed and since in uniform motion the average speed is same as that of instantaneous speed so its correct,right? Now if this is right if we calculate the variable speed with the help of a tangent i... | Uniform motion is a special case. The instantaneous speed is the same at all times. If you draw a graph, it is a figure where the slope is the same at all points. That is a line.
For a line, the average slope between two points is the same as slope of the tangent at any point. So yes, the average speed and the instan... | Average velocity between two points in time is given by the slope of the secant line between the two corresponding points on the position vs. time graph.
Instantaneous velocity is found at a point in time. It is given by the slope of the tangent line at that point on the position vs. time graph.
In the case on consta... | https://physics.stackexchange.com |
5,988 | [
"https://engineering.stackexchange.com/questions/5988",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/3581/"
] | <strong>Regarding micro inverters for solar power systems:</strong>
Is there technically a difference between an inverter classified as a "micro inverter" and and inverter classified as a "pure sine wave" inverter? Or is it simply a matter of using extra jargon to describe the size of the inverter?
<strong>Problem I... | "Micro" and "pure sine wave" are orthagonal, even if "micro" had a real definition. "Micro" is just a relatively content-free marketing term. It says that the inverter is intended for a small array or single panel, but of course without a spec it doesn't mean anything.
Anything connected back to the power line shoul... | Stop.
You can't just attach <em>any</em> inverter on a PV panel or array, even if it does have the right power rating.
Your inverter needs to be a PV inverter specificaly. It has to be designed to do max-power-point tracking. That's because the panel doesn't have any specific potential difference: that has to be impo... | https://engineering.stackexchange.com |
127,296 | [
"https://security.stackexchange.com/questions/127296",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/107891/"
] | Short Question:
Is it important for a sniffing device to be in the broadcasting range of a client (NOT THE ROUTER) to sniff its packets?
Complete Scenario:
I assume that a wireless sniffing tool, like airodump-ng, is able to capture the packets from a client because the client sends its packets in all the directions... | Let's check out what PGP and SSH actually offer for this purpose:
<ul>
<li>PGP:<br>
Client must install PGP software which is not installed by default in the majority of the systems. Client must create a PGP key pair. Then he must send the public key to the server so that the server can use it later for validation. Wh... | <strong>Lack of portability</strong>
SSH and PGP are widely used, but they are not web technologies. There has been an equivalent web technology for many years - SSL client certificates. However, this is not much used.
The reason is the lack of portability. If you have an SSL client certificate on your home desktop, ... | https://security.stackexchange.com |
395,233 | [
"https://mathoverflow.net/questions/395233",
"https://mathoverflow.net",
"https://mathoverflow.net/users/176218/"
] | Let <span class="math-container">$A$</span> be an infinite-dimensional noncommutative algebra over a field, let <span class="math-container">$B$</span> be an infinite-dimensional subalgebra of <span class="math-container">$A$</span>, and let <span class="math-container">$A$</span> be a direct sum of projective simple <... | @BugsBunny answered the original version of the question. I'll answer the new version. The algebra <span class="math-container">$B$</span> must be finite dimensional and semisimple under these hypothesis, and even stronger, it must be separable meaning that it remains semisimple even under base extension.
Let <span c... | No. Take any <span class="math-container">$A$</span> and take the ground field <span class="math-container">$k=k1_A$</span> as <span class="math-container">$B$</span>.
| https://mathoverflow.net |
653,547 | [
"https://physics.stackexchange.com/questions/653547",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/284697/"
] | I am attempting to find the energy stored in assembling an spherical shell (denoted by <span class="math-container">$S$</span>) uniformed distributed of total charge <span class="math-container">$q$</span>, and radius <span class="math-container">$R$</span>.
To do so, I want to use the formula: <span class="math-contai... | The integral does not diverge. Although |r −r′|→0, <span class="math-container">$da'=\sin(\theta)d\theta d\phi$</span> approaches <span class="math-container">$0$</span> as well. Using spherical coordinates with the point at which the potential is being evaluated placed at the north pole we get:
<span class="math-conta... | We know that the electric field inside a uniformly charged spherical shell is zero, because all the charges lies on the outside surface. i.e.,
<span class="math-container">$$\vec E_{in}=0$$</span> and <span class="math-container">$$ \vec E_{out}=\frac{Q}{4\pi \epsilon_o r^2} \hat{r}$$</span>
<span class="math-container... | https://physics.stackexchange.com |
607,634 | [
"https://physics.stackexchange.com/questions/607634",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/281589/"
] | In Lab experiment, to verity the inverse square radiation law, we observe the solar cell current changes with the distance from the light source. How would we relate the solar cell current and the light intensity impinging upon it?
| Assuming all speeds are relative to the ground, air friction is negligible, and the gun is fired forwards, then you would add the gun's speed to the bullet's speed. Since the thief is moving away from the bullet you would subtract their speed from the bullet's speed to have the relative speed of the bullet to the thief... | Assuming that the muzzle velocity is measured relative to the gun, then the speed of the bullet relative to the ground is 192.5 m/s. If the thief is being chased, then he is in front (and separated). You are given no information about distance or time.
| https://physics.stackexchange.com |
162,937 | [
"https://softwareengineering.stackexchange.com/questions/162937",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/46290/"
] | My company is currently at a rebranding process and the brand names have been used in the sources' package names but these names are only visible to developers who maintain this code so nobody from project management is really interested in changing them considering also that it would imply the recompiling of several o... | This is usually a political/marketing question as much as technical. I have been involved in mergers where changing all references to the old name was mandated
Assuming it is just a technical question, are you missing buildable source for any of the components or are there similar significant technical risks? Will mak... | While there's no immediate need, eventually as new code gets the new name it's going to become a pain remembering whether something uses the old or the new name. It's a simple fix, so you may as well get it over with. The main reason not to would be if your code was widely shared outside your company. If you control... | https://softwareengineering.stackexchange.com |
3,874,988 | [
"https://math.stackexchange.com/questions/3874988",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/839748/"
] | Let <span class="math-container">$f(x)= a x^2 + x +1 , x \in \mathbb{R} $</span>. Find all values of parameter <span class="math-container">$a \in \mathbb{R} $</span> such that <span class="math-container">$f(f(x)) \geq 0 $</span> holds for all real <span class="math-container">$x$</span>.
<span class="math-container"... | As you mention, <span class="math-container">$a \geqslant \frac14$</span> works. The only case that remains is when <span class="math-container">$0<a<\frac14$</span>, i.e. when <span class="math-container">$f(x)$</span> has two distinct real roots. In this case, it is enough to ensure that the midpoint of the r... | Firstly, <span class="math-container">$1-4a\leq0$</span> is valid and since <span class="math-container">$a=0$</span> is not valid, it's enough to check <span class="math-container">$0<a<\frac{1}{4}$</span>, which gives
<span class="math-container">$$ax^2+x+1=\frac{-1+\sqrt{1-4a}}{2a}$$</span> and
<span class="m... | https://math.stackexchange.com |
171,929 | [
"https://math.stackexchange.com/questions/171929",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/35177/"
] | I have been working with a system which involves computing the roots of functions that look like
\begin{equation}
e^t (g\cos(\omega t) + b) = c
\end{equation}
where $t$ is the independent variable and the parameters $g$, $\omega$ and $b$ are real and positive and $c$ is real.
This, apparently has no analytical solu... | <strong>(New answer)</strong>
Some of this overlaps with the answer by Jayesh Badwaik, but it does not hurt to see two people's perspective.
Concerning the sequence $t_k$, let's begin with a simple observation based on Rolle's theorem: there exists $t$ strictly between $t_k$ and $t_{k+1}$ where the derivative of $e^... | Let
\begin{equation}
y \left( x \right) = \exp( t )\left( g \cos \left ( \omega t \right) + b \right)
\end{equation}
For $\omega \ll 1$, I don't know if next solution will exist or not. The next solution will only exist if the slope of the function is negative at that point.
<em><strong>CASE 1 : $b < g\sqrt{\o... | https://math.stackexchange.com |
227,736 | [
"https://dba.stackexchange.com/questions/227736",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/166988/"
] | I want to select every first and last event of every user id, if no first event exists,then just the last event instead . tried using partition over , but i am getting first 2 events instead.
Input:
<pre><code>id timestamp event
10096 1545136190 songs
10096 1545136202 tv
10096 1545136239 book
10096 1545... | Here's one way:
<pre><code>SELECT id, timestamp, event
FROM (
SELECT id, timestamp, event
, ROW_NUMBER() OVER(PARTITION BY id ORDER BY timestamp asc) as r1
, ROW_NUMBER() OVER(PARTITION BY id ORDER BY timestamp desc) as r2
FROM table
) MyData
WHERE 1 IN (r1,r2)
</code></pre>
The idea is t... | <pre><code>SELECT id,
MIN(`timestamp`) first_timestamp,
FIRST_VALUE(event) OVER (PARTITION BY id ORDER BY timestamp ASC) first_event,
MAX(`timestamp`) last_timestamp,
LAST_VALUE(event) OVER (PARTITION BY id ORDER BY timestamp ASC) last_event
-- or FIRST_VALUE(event) OVER (PARTITION BY id... | https://dba.stackexchange.com |
193,276 | [
"https://math.stackexchange.com/questions/193276",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/21335/"
] | This is an exercise for the book Abstract Algebra by Dummit and Foote
(pg. 530):
<blockquote>
Let $F$ be a field of characteristic $\neq2$ . Let $a,b\in F$ with $b$
not a square in $F$. Prove $\sqrt{a+\sqrt{b}}=\sqrt{m}+\sqrt{n}$ for
some $m,n\in F$ iff $a^{2}-b$ is a square in $F$.
</blockquote>
I am having pr... | $$\sqrt{a+\sqrt b}=\sqrt m + \sqrt n \Rightarrow a+\sqrt b = m+n+2\sqrt{mn}$$
Since $\phi(\alpha+\beta\sqrt b)=\alpha-\beta\sqrt b$ for $\alpha,\beta\in F$ defines an automorphism $\phi\colon F[\sqrt b]\to F[\sqrt b]$ that leaves $F$ fixed, we have that $\phi(\sqrt{mn})= \pm\sqrt{mn}$ because $\phi$ maps the polynomial... | $$\sqrt{a+\sqrt{b}} = \sqrt{m} + \sqrt{n}$$
$$a+\sqrt{b} = m+n+2\sqrt{mn}$$
Thus $a = m+n$ and $b = 4mn$ as $b$ is not a square . Finally, $$a^2 -b = m^2 + 2mn + n^2 -4mn = (m-n)^2$$.
| https://math.stackexchange.com |
142,144 | [
"https://softwareengineering.stackexchange.com/questions/142144",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19295/"
] | Consider the following code:
<pre class="lang-java prettyprint-override"><code>public void doSomething(int input)
{
while(true)
{
TransformInSomeWay(input);
if(ProcessingComplete(input))
break;
DoSomethingElseTo(input);
}
}
</code></pre>
Assume that this process involves a fini... | Stick with your first solution. Loops can become very involved and one or more clean breaks can be a lot easier on you, anyone else looking at your code, the optimizer, and the program's performance than elaborate if-statements and added variables. My usual approach is to set up a loop with something like the "while ... | It's only a meaningful problem if the loop body is non-trivial. If the body is so small, then analyzing it like this is trivial, and not a problem at all.
| https://softwareengineering.stackexchange.com |
105,675 | [
"https://electronics.stackexchange.com/questions/105675",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/39620/"
] | I need to make a mechanism with a RaspberryPi like in CD-ROMs, so I can easily move a plate from the minimum position (CD-Rom closed) to maximum (CD-ROM open). I have a DC motor (from CD-ROM) and I can only tell it to turn around a given angle. I've also tried using the CD-ROM itself, but it is far to big.
How can I d... | The easiest method is limit switches. Have a reversible drive mechanism and put limit switches at each end. These can be wired in series with the driving power in a normally closed configuration to physically remove power at the stops. Or the switches can be used as logic inputs to tell the micro to stop. With a do... | Well an ad-hoc solution would be to look for current spikes. When you want to move someting in a direction but it can't it will take more current. If you measure that you can say when you reached the endpoint. It is not elegant or precise, but depending on the application it can do the work.
You would just have to set... | https://electronics.stackexchange.com |
313,140 | [
"https://mathoverflow.net/questions/313140",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9652/"
] | Here is question I tried to answer for some time - it seems to be straightforward, but I have trouble figuring it out.
Let <span class="math-container">$\Omega$</span> be a compact domain in <span class="math-container">$\mathbb{R}^n$</span>. For any signed Borel measure <span class="math-container">$\mu$</span> on <s... | If <span class="math-container">$\mu =f\cdot \lambda$</span> for a positive measure <span class="math-container">$\lambda$</span> (i.e., <span class="math-container">$\mu(A)=\int_A fd\lambda$</span>), isn't then <span class="math-container">$\mu_+= f_+ \cdot\lambda$</span> (where <span class="math-container">$f_+$</spa... | The Borel measures on <span class="math-container">$\Omega$</span> can be identified with continuous linear functionals <span class="math-container">$\newcommand{\bR}{\mathbb{R}}$</span> <span class="math-container">$\mu:C(\Omega)\to\bR$</span>. Assume that <span class="math-container">$\Omega$</span> is compact so <... | https://mathoverflow.net |
16,972 | [
"https://electronics.stackexchange.com/questions/16972",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1633/"
] | After a lot of research and experimentation I have come to learn that the sentence "This is a 1.5V, 2800mAh battery" is entirely a lie.
(i.e., the potential difference between the terminals of a battery changes over time and the shape of the graph is dependent on battery chemistry, ambient temperature and current draw... | Good question. Big question. Partial answer ...
Reputable manufacturers provide specification sheets (yes, even for batteries) and these will provide recommended maximum continuous currents and may provide peak allowable discharge currents.
The maximum value is NOT a hard and fast limit which may not be exceeded, and... | If a battery is specified to deliver 9 amps, and you limit current to nine amps, the battery will likely achieve lifetime performance reasonably similar to what is specified in the datahseet. Going beyond the rated current may not cause immediate failure, but is likely to adversely affect device lifetime. Trying to d... | https://electronics.stackexchange.com |
82,987 | [
"https://stats.stackexchange.com/questions/82987",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/34623/"
] | I have a simple contingency table with two nominal variables. Let's say Age and Gender. The software that I'm using reports the relationship between the two variables using Pearson's Chi-Square Test of Independence, to which I understand.
But when I select only two cells in the table and try to do a test for that, the ... | In the case of 2x2 contingency tables, the $z$-test of whether two proportions are equal is equivalent to the Pearson $\chi^2$ test of independence: the quantity $z^2$ <strong>is</strong> the Pearson $\chi^2$ statistic (Agresti, <em>Introduction to Categorical Data Analysis</em>, p. 26).
Keep in mind that the $t$-tes... | You seem to reduce age to a binary information (18-24 = young vs. old) and to test the null hypothesis "Proportion of young is equal between genders". This is equivalent to claim "Independence between age and gender". Since both "age" and "gender" are categorical, a chisquared-test of independence is suitable (among ot... | https://stats.stackexchange.com |
115,748 | [
"https://stats.stackexchange.com/questions/115748",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/24423/"
] | What is the best way to simulate ANOVA data for a 2 x 2 design with interaction using a regression approach? I want to generate the data so that I know the true regression coefficients of the model when running lm() in R.
<pre><code>lm(A * B, data=df)
</code></pre>
Thanks in advance
| You can simulate this by running your regression equation backwards into R.
You equation is
$$y = \alpha + \beta_1 A + \beta_2 B + \beta_3 A B + \epsilon$$
where $y$ is the dependant variable, $\alpha$ the intercept, $\beta_n$ your coefficients for your $n$ predictors, in this case, $A$, $B$, and $A*B$ (the interact... | In addition to the answers already given, note that one can easily take a fitted model and simulate from that by using the <code>simulate</code> command.
It takes a fitted model object and returns one or more simulated sets of data (specified by <code>nsim</code>). See <code>?simulate</code>.
<pre><code>> df
... | https://stats.stackexchange.com |
364,934 | [
"https://physics.stackexchange.com/questions/364934",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/173308/"
] | For the field to be a conservative field, does the field have to satisfy the both conditions?
<ol>
<li>Work done is independent of path followed by the body.</li>
<li>Work done in a closed path is zero. </li>
</ol>
| <em>Normal force</em> is a <em>constraint force</em>. The aim of this normal force in your example is to keep the object in contact with the slide. The normal force is always perpendicular to the displacement of the object and hence does no work.
| <blockquote>
Since there is also a normal force [...] this normal force also contributes to the work done
</blockquote>
To do work, the force must make something move. There mere fact that a force is present does not imply work being done (a table does no work on the apple it is holding up in spite of the constant n... | https://physics.stackexchange.com |
52,251 | [
"https://electronics.stackexchange.com/questions/52251",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10660/"
] | I've recently jumped on the Arduino bandwagon and am attempting to upload my very first sketch to my Arduino Uno installed on COM port 3. However, I get errors that another device is using COM port 3 and I need to disable that device.
Specs:
Win XP, all current SPs.
Arduino drivers 1.0.3, dated 12/10/2012, downloaded... | There's an easy way to force windows to drop anything on that port and that's to rename/reassign it. I've done it myself when the serial gets abruptly disconnected and windows doesn't handle it. To do this you need to:
1) Go to Control Panel-> Device Manager
2) Look for the COM port and right click, go to properties... | I remember vaguely that something similar happened with me too. If i remember correctly after some abrupt stop of Arduino IDE. The COM port wasn't really used by anything else, but somehow windows (7) didn't close the connection and as much as I hate to do it, had to restart the PC. That fix it for me. YMMV, but try t... | https://electronics.stackexchange.com |
45,103 | [
"https://security.stackexchange.com/questions/45103",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/32948/"
] | One of friends hacked my laptop and now whenever I come online he can tell what tabs are opened in my browser, so I think he is remotely monitoring me. I don't know how he did this, since I didn't take anything from him.
I use Ubuntu, the firewall is enabled, remote connections are switched off, so how can he see what... | You need to run:
<pre><code>gpg --card-status
</code></pre>
and gpg will do it for you:
<pre><code>/tmp$ mkdir gpgtmp
/tmp$ chmod go-rwx gpgtmp
/tmp$ GNUPGHOME=/tmp/gpgtmp gpg --keyserver pgp.mit.edu --recv F8713BDF
gpg: sleutelring ‘/tmp/gpgtmp/secring.gpg’ is aangemaakt
gpg: sleutelring ‘/tmp/gpgtmp/pubring.gpg’... | When you start with a fresh installation, you have two options:
<ol>
<li>Plug the smart card (Yubikey) and run
<pre><code>gpg --card-edit
fetch
quit
</code></pre>
Then, running <code>gpg</code> with the <code>--card-status</code> option to create the stubs for the secret keys:
<pre><code>gpg --card-status
</code></... | https://security.stackexchange.com |
70,040 | [
"https://mathoverflow.net/questions/70040",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16364/"
] | A standard example of an ind-scheme over a field $\mathrm{k}$ which is not a
$\mathrm{k}$-scheme is $\mathrm{k}((\varepsilon))$.
My question is how to prove that rigorously? To put it more precisely,
let $$\mathrm{k}((\varepsilon)) = \{ a \in \prod_{-\infty}^{\infty}\mathrm{k}:
a_i =0, i \ll 0 \}$$
An ind-scheme is ... | I think you can just consider the decreasing sequence of ideals of the increasing sequence of algebraic subsets $\epsilon^i k[[\epsilon ]]$ of $\prod_{-\infty}^{\infty}k$. For each $i$, the ideal is $( a_j | j\leq i-1 )$. The intersection of this sequence of ideals is $\{ 0 \}$. The corresponding algebraic subset o... | Based on the comments, it looks like you have two questions mixed up. There is the question of whether the colimit exists in the category of schemes, and there is the question of whether the ind-scheme described by the colimit in the category of set-valued functors on schemes (or the category of Zariski sheaves of set... | https://mathoverflow.net |
36,386 | [
"https://quant.stackexchange.com/questions/36386",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/11655/"
] | <ul>
<li>Yield graphs seem to be predominant.</li>
<li>This is in contrast to price graphs in equity based products.</li>
<li>I can work out the price if I know the face value, but still -- would imagine for consistency purposes price would be a frequent value measure for both products.</li>
</ul>
| You can't show the term structure easily with prices. Say you have 2 bonds, a 5 year at 2% and a 10 year at 3%. If both have coupons of the same, so no premium or discount, they both will trade at $100. There's then no way to see how interest rates should evolve in that chart. This is why we show spot rates--it helps s... | Investing in equities is different than investing in bonds. With equities, you don't know the outcome. When you invest today and sell in five years, you don't know if the investment will be positive or negative.
Investing in bonds is different, because you know that the outcome is 100 (with the exception that the bon... | https://quant.stackexchange.com |
1,603 | [
"https://cs.stackexchange.com/questions/1603",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/1057/"
] | I have a general question about mapping reductions. I have seen several examples of reducing functions to $A_{TM}$
where $A_{TM} = \{\langle M, w \rangle : \text{ For } M \text{ is a turing machine which accepts string } w\}$
which is great for proving undecidability. But say I want to prove unrecognizability instead... | Let's take $L_{\emptyset}=\{ \langle M \rangle \mid L(M) = \emptyset \}$, that is, all the machines that accept no word (i.e., whose language is empty).
Now we show the reduction $\overline{A_{TM}} \le L_\emptyset$. The reduction is done by taking an input $(\langle M \rangle,w)$ of $\overline{A_{TM}}$ and converting ... | You cannot show, for an arbitrary unrecognizable language $C$, that $\overline{A_{TM}} \leq_m C$. If $\overline{A_{TM}} \leq_m C$ then in particular the Turing degree of $C$ is greater than or equal to the Turing degree of $\overline{A_{TM}}$, because many-one reducibility implies Turing reducibility. The Turing degre... | https://cs.stackexchange.com |
166,778 | [
"https://math.stackexchange.com/questions/166778",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I am trying to find the $x$ values that make this series converge:
$$\sum_{n = 1}^\infty (x+2)^n.$$
To me it seems like $x = -2$ would make the series converge but that is a wrong answer, I am not sure why either.
| Recall the geometric progression $$\sum_{n=1}^{N} a^n = a \left(\dfrac{1-a^{N}}{1-a} \right)$$ and hence the geometric series $\displaystyle \sum_{n=1}^{\infty} a^n$ converges if and only if $\vert a \vert < 1$.
In your problem, $a = x+2$.
| If you're familiar with the infinite geometric series
$$
\sum_{n=0}^\infty r^n = 1 + r + r^2 + r^3 + \cdots = \frac{1}{1-r}
$$
then the series you've got is the same thing with $r=x+2$.
The series above converges if $-1<r<1$ and otherwise diverges.
So you'd need $-1<x+2<1$.
That's the same as $-3<x<... | https://math.stackexchange.com |
126,356 | [
"https://electronics.stackexchange.com/questions/126356",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9983/"
] | I've printed, populated and baked a test PCB with most components that I needed. I left off a GPS chip and associated passives because the GPS chip itself costs more than the rest of the board, and I'm testing unrelated functionality at the moment (and I thought there would be a good chance that I'd have to change some... | If you are only doing a few for your development then I would suggest you manually solder the missing parts on, using an iron or a hot air tool. Put on the flux as you said and then reflow just the added components.
Modules sometimes try to use a slightly higher temperature solder so the standard reflow profile will ... | Check if your components can tolerate double reflow. Certain modules cannot (GPS, RF modules etc), most discrete components can (Think a double sided, double loaded PCBs).
| https://electronics.stackexchange.com |
799,211 | [
"https://math.stackexchange.com/questions/799211",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Let $G$ be a Lie group
Let $m:G\times G\rightarrow G$ denote the multiplication map. Show that the differential $dm_{(e,e)}:T_eG\oplus T_eG\rightarrow T_eG$ is given by
$$dm_{(e,e)}(X,Y)=X+Y$$
This question comes from Lee, introduction to smooth manifolds second edition, problem 7-2.
Here is my attempt:
$$dm_{(e,e)}... | One of the problems here is the Lee uses the projections <span class="math-container">$\pi_1 : G \times G \rightarrow G, (x,y) \mapsto x$</span> and <span class="math-container">$\pi_2$</span> defined analogously to identify <span class="math-container">$T_{(e,e)}(G\times G)$</span> and <span class="math-container">$T_... | <strong>Algebraic Approach</strong>
Consider the sections:
$$s_1:G\to G\times G:p\mapsto (p,e)\quad s_2:G\to G\times G:q\mapsto(e,q)$$
This makes the identification explicit:
$$\Psi:\mathrm{T}_eG\oplus\mathrm{T}_eG\to\mathrm{T}_{(e,e)}(G\times G):(\delta,\varepsilon)\mapsto \mathrm{d}_es_1\delta+\mathrm{d}_es_2\varep... | https://math.stackexchange.com |
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