qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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|---|---|---|---|---|---|
130,528 | [
"https://security.stackexchange.com/questions/130528",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/44183/"
] | I have a domain name with dynamic DNS (DDNS) for my home server on which I expose multiple services (web server, wikis, issue trackers, etc.) online. Some services are hosted by the same software (e.g. web server for website and wiki run on different ports served by the same <code>apache2</code> instance, others by sep... | <em>"Complexity is the enemy of security"</em>
I would <em>always</em> look to use the least amount of certs possible for a number of reasons, mostly due to the ease of administration. It's my understanding that letsencrypt is not currently allowing wild card certificates (these certificates essentially allow you to s... | It depends on a multiple factors, certificate management strategy, policies and so on.
For general purpose web applications I would go with a single certificate per machine if they use different names. You can run separate certificates on per-service basis, but this will increase administrative efforts in certificate ... | https://security.stackexchange.com |
275,151 | [
"https://math.stackexchange.com/questions/275151",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/56809/"
] | Assuming $$\cos(36^\circ)=\frac{1}{4}+\frac{1}{4}\sqrt{5}$$ How to prove that $$\tan^2(18^\circ)\tan^2(54^\circ)$$ is a <strong>rational</strong> number? Thanks!
| Use the fact that
$$ \tan^2{18^{\circ}} = \frac{1-\cos{36^{\circ}}}{1+\cos{36^{\circ}}} = 1-\frac{2}{5} \sqrt{5} $$
Then use the fact that
$$ \tan^2{54^{\circ}} = \frac{1}{\tan^2{36^{\circ}}} $$
so that
$$ \tan^2{18^{\circ}} \tan^2{54^{\circ}} = \frac{\tan^2{18^{\circ}}}{\tan^2{36^{\circ}}} = \frac{1}{4} (1 -\ta... | $$\tan18^\circ\tan54^\circ=\frac{2\sin18^\circ\sin54^\circ}{2\cos18^\circ\cos54^\circ}$$
$$=\frac{\cos36^\circ-\cos72^\circ}{\cos36^\circ+\cos72^\circ}$$ (applying $\cos(A\pm B)$ formulae)
$$=\frac{\frac{\sqrt5+1}4-\frac{\sqrt5+1}4}{\frac{\sqrt5+1}4+\frac{\sqrt5+1}4}$$ as $$\cos 72^\circ=2\cos^236^\circ-1=\frac{\sqrt5... | https://math.stackexchange.com |
306,574 | [
"https://softwareengineering.stackexchange.com/questions/306574",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/128542/"
] | One part of my program fetches data from many tables and columns in my database for processing. Some of the columns might be <code>null</code>, but in the current processing context that is an error.
This should "theoretically" not happen, so if it does it points to bad data or a bug in the code. The errors have diffe... | I would put the null checks in your mapping code, where you build your object from the result set. That puts the checking in one place, and won't allow your code to get halfway through processing a record before hitting an error. Depending on how your application flow works, you might want to perform the mapping of all... | It sounds like inserting a null is an error but you are afraid to enforce this error on insertion because you don't want to lose data. However, if a field shouldn't be null but is, <em>you are losing data</em>. Therefore the best solution is to ensure that null fields are not erroneously getting saved in the first plac... | https://softwareengineering.stackexchange.com |
21,760 | [
"https://quantumcomputing.stackexchange.com/questions/21760",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/18727/"
] | For educational purposes I would like to make some circuits in the nice IBM quantum experience circuit composer GUI. The only problem is that the set of gates I can use here is quite limited (I would like to use a "delay" instruction which is included in qiskit). The only problem is that the qiskit editor tab... | It's the dimension of the Hilbert spaces. In DV-QKD you have a finite dimensional Hilbert space (like a qubit). Thus your measurement outcomes come from a finite set. On the other hand a CV-QKD protocol uses infinite dimensional systems and therefore you can have a continuum of measurement outcomes.
If there's no speci... | One example to understand it, if someone finds it useful, is the following:
Most QKD is done by sending light through a channel. In DV-QKD we send single photons through the channel, one at a time. We encode the information, for instance, in the polarization of each photon. In CV-QKD we send a continuous beam of light,... | https://quantumcomputing.stackexchange.com |
604,705 | [
"https://physics.stackexchange.com/questions/604705",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/268333/"
] | I have noticed that when I cook porridge in a saucepan, and stir it with a spatula, it only steams a little bit. But the moment I turn off the (gas) hob underneath, and keep stirring it with a spatula, suddenly a noticeably more steam starts coming out of the saucepan.
This seems counter-intuitive, because the heat sou... | What you see of the "steam" is actually condensed water, i.e., more or less fine drops of liquid water.
Turning off the gas means that the temperature of the steam and air column above the pot decreases; therefore, more water condenses.
In reality, what you have is less and slowly rising steam—not more—so it ... | I wonder whether, paradoxically, there is a temporary increase in the rate of heat entry to the bulk of the porridge when you turn off the gas. The reason would be that while you are heating, a relatively poorly conducting stationary layer of solid well-cooked porridge is continually forming on the very hot base of the... | https://physics.stackexchange.com |
337,687 | [
"https://softwareengineering.stackexchange.com/questions/337687",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/168778/"
] | In certain programming languages, the meaning of certain names may be fully determined at compile-time (i.e. without running the program).
Example:
A function in <code>C</code> has global scope; when the name of the function is used somewhere else in the program (and the variable is not shaded by another variable of ... | You're looking for “static”, as in “statically linked”, “statically dispatched”, or “statically resolved”. The term <em>static</em> just means that something can be done at compile time, in contrast to run time (where we'd talk about dynamic linking/dispatching/resolution/binding).
Some languages derive additional mea... | <h3>Static methods</h3>
is what came to mind when reading the title.<br>
Reading the content confirmed it as you yourself noted.
| https://softwareengineering.stackexchange.com |
965,025 | [
"https://math.stackexchange.com/questions/965025",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/151497/"
] | I'm working through some apparently tricky limits (for a basic fellow like me), and I'm not sure how to treat the following situation:
$$\displaystyle\lim_{x\to0} (\cos x)^{\frac{1}{x^2}}$$
How does one deal with powers which include $x$ when evaluating limits? I'm not after an exact evaluation of the limit. I'm just i... | Let $$ L :=\lim_{x\rightarrow 0} (\cos\ x)^\frac{1}{x^2} $$
so that $$ \ln\ L =\lim_{x\rightarrow 0} \frac{\ln\ \cos\ x}{x^2} $$
by L'Hospital, $$ =\lim_{x\rightarrow 0} \frac{-\tan\ x}{2x}
=-\frac{1}{2} $$ Hence $$ L = e^\frac{-1}{2}$$
| just as a first guess note that $\cos x$ is approximated by $1-\frac{x^2}2$ near $x=0$ and
$$
(1-\frac{x^2}2)^{\frac1{x^2}} \to e^{-\frac12}
$$
| https://math.stackexchange.com |
12,404 | [
"https://physics.stackexchange.com/questions/12404",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/540/"
] | Theoretically, what is the difference between a black hole and a point particle of certain nonzero mass? Of course, the former exists while it's not clear whether the latter exists or not, but both have infinite density.
| We should probably distinguish between a particle being "point-like" and a particle being "structure-less". In classical mechanics we talk of "point-like" particles, objects with no extension. It is the case that in general relativity any "point-like" mass would be inside of its event horizon and so would be a black h... | One big difference is that all electrons, for example, are identical, but all black holes are not. In particular, a black hole can have any mass at all, whereas a particle like an electron has a fixed value for its mass. This property of fundamental particles like electrons is ultimately what allows us to define fixed ... | https://physics.stackexchange.com |
286,876 | [
"https://dba.stackexchange.com/questions/286876",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/90813/"
] | This is on MSSQL/Azure SQL.
I have the following Sales Table:
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th>Line_Item_ID</th>
<th>Sales_Order_ID</th>
<th>SKU</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>1</td>
<td>4</td>
</tr>
<tr>
<td>2</td>
<td>1</td>
<td>1</td>
</tr>
<tr>
<td>3</td>
<td... | Room should have PK of (hotel_id,room_number).
Weak entities have compound keys with the strong entity key/foreign key as the leading column(s).
There are people who disagree with this approach, but they are wrong.
<blockquote>
How can i find the room belonging to specific hotel which has the different number of beds l... | The real question is <em>why is there no <strong>primary key</strong> for the <code>Rooms</code> table?</em> In most cases (except a few edge cases like <strong>staging tables</strong>) you should have a <strong>primary key</strong> on your tables.
Despite this, even without a <strong>primary key</strong> on the <code>... | https://dba.stackexchange.com |
202,488 | [
"https://security.stackexchange.com/questions/202488",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/198173/"
] | Does any software or any other way to detect if a website contains any WordPress installation?
For example lets say we have the website example.com which is not a WordPress site, but we have a WordPress site in the path example.com/blog and example.com/blog2.
So far I have use burp suit to crawl the website and then ... | <pre><code>import requests
#Loop through the whole list of domains
with open('ListOfDomainsFile') as f:
for line in f:
domain = line.rstrip()
source = requests.get(domain).text
counter = counter+1
if "wp-include" in source:
results = 'Yes, is powered by WordPress'
else:
... | By the directory structue, like: <code>/wp-admin</code>, <code>/wp-json</code>...
You can also see through the url of images: <code>wp-content/themes/<theme>/</code>.
See:
<pre><code>
[dir] wp-admin
[dir] wp-includes
index.php
license.txt
readme.html
wp-activate.php
wp-blog-header.ph... | https://security.stackexchange.com |
212,904 | [
"https://softwareengineering.stackexchange.com/questions/212904",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/103557/"
] | When compiling C code with <code>gcc</code>, there are compiler optimizations, some that limit code size and others create fast code.
From the <code>-S</code> flag, I see that the <code>-O2/03</code> generates more assembly than the <code>-Os</code> code. How is more assembly still faster than less assembly?
| On a modern processor, there are usually several ways to achieve the result specified in a higher level language (such as C). These solutions can have different trade-offs between code size and speed due to several factors.
<ul>
<li>Not all assembly instructions take the same amount of time to execute. For example, it... | Well, most of the time the complier generates more instructions so that <em>fewer</em> of them are executed in a given run. Usually by generating specific code for different cases:
<ul>
<li>Loop unrolling. The jump is only done in every n (usually 8) iterations.</li>
<li>Function inlining. It saves the call, return, c... | https://softwareengineering.stackexchange.com |
203,180 | [
"https://dba.stackexchange.com/questions/203180",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/148054/"
] | I can get a list of each day of last 30 days row by row with this query and it works..
But I don't think that it is the best one since the "WHERE" part is messed up. I draw a graph and I just want to get daily_total_invoice_amount for sum of each day of last 30 days.
<pre><code>SELECT
sum(b.invoice_amount) daily_tot... | Why include <em>tomorrow</em> (<code>CURRENT_DATE + INTERVAL '1 DAY'</code>)? A future date in <code>order_creation_date</code> would normally indicate a data error. I would not even include <em>today</em> in the statistic, since that is typically incomplete and misleading until the day is over. Consequently I use the ... | Here is my workaround, base on Vérace Apr 5 at 20:18 first referenced article, the performance is not optimal, but it works.
<pre><code>select date(d) ds
, count(distinct case when c.ds = date(d) then c.user_id else null end) d0_user_count
, count(distinct case when c.ds <= date(d) and c.ds >= date(d) - 3 then c... | https://dba.stackexchange.com |
30,050 | [
"https://datascience.stackexchange.com/questions/30050",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/49861/"
] | I have an atypical time format that I need to convert into a datetime index for time series analysis. I'm working in Python / Pandas.
The column is 'BC_DT', and the format is "27-MAR-18". Example is below.
<pre><code>BC_DT
27-MAR-18
28-MAR-18
29-MAR-18
</code></pre>
I tried this method, but I'm getting an error: V... | Let pandas determine what datetime format you are using automatically.
<pre><code>import pandas as pd
raw_data = pd.DataFrame(data={'BC_DT':['27-MAR-18','28-MAR-18','29-MAR-18']})
raw_data['BC_DT'] = pd.to_datetime(raw_data['BC_DT'])
print(raw_data)
</code></pre>
<blockquote>
BC_DT <br/>0: 2018-03-27 <br/>1: 2... | <pre><code>df['Converted_Date'] = df['BC_DT'].apply(lambda x: dt.datetime.strptime(x, '%d-%b-%y'))
</code></pre>
you should use %y instead of %Y. As it is for YYYY format not YY year foramt
| https://datascience.stackexchange.com |
606,432 | [
"https://stats.stackexchange.com/questions/606432",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/380706/"
] | Let <span class="math-container">$X_{1}, ..., X_{n}$</span> be random variables independent of <span class="math-container">$Y_{1}, ..., Y_{n}$</span>, where both groups are iid with associated population means <span class="math-container">$\mu_{1}$</span> and <span class="math-container">$\mu_{2}$</span> and populatio... | The sample average <span class="math-container">$\bar X$</span> has expected value <span class="math-container">$\mu_1$</span> and variance <span class="math-container">$\sigma^2_1/n$</span>. By the same token, <span class="math-container">$\bar Y$</span> has expected value <span class="math-container">$\mu_2$</span> a... | As you note, <span class="math-container">$Var(X + Y) = Var(X) + Var(Y) + 2 Cov(X, Y)$</span>. The variance of the difference of two means just involves a negative covariance term, namely <span class="math-container">$Var(X - Y) = Var(X) + Var(Y) - 2 Cov(X, Y)$</span>.
| https://stats.stackexchange.com |
76,604 | [
"https://electronics.stackexchange.com/questions/76604",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10456/"
] | A mech engineer said that copying puts more load on the microprocessor than "other" operations (e.g. moving data or creating the same amount of new data). Is this true? Can you elaborate? I understand that the assembly instructions are different but not how copying is "more intensive" ?
With copying what is meant is p... | A basic microprocessor works at a fixed speed at assembly level. For the most part it can execute "instructions" in a certain number of clock cycles and that is that. The clock is usually fixed in speed (i.e. 8MHz for example) and an instruction might take 4 clocks cycles for example. This mean it executes an instructi... | No.
A CPU is a complex system, build from sub-systems, and there is probably no load which will stress all the sub-systems heavily and thus no load which merit the name "most CPU intensive operation", whatever you come up, you can probably find a sub-system which can be used more with another load.
Doing memory copy ... | https://electronics.stackexchange.com |
182,113 | [
"https://softwareengineering.stackexchange.com/questions/182113",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/53251/"
] | I always have trouble figuring out if I should name a certain method starting with <code>getSomething</code> versus <code>findSomething</code>.
The problem resides in creating <em>helpers</em> for poorly designed APIs. This usually occurs when getting data from an object, which requires the object as a parameter. Here... | I use <code>Get</code> when I know the retrieval time will be very short (as in a lookup from a hash table or btree).
<code>Find</code> implies a search process or computational algorithm that <em>requires a "longer" period of time to execute</em> (for some arbitrary value of longer).
| I would say that <code>find</code> may fail but <code>get</code> shouldn't.
| https://softwareengineering.stackexchange.com |
392,906 | [
"https://stats.stackexchange.com/questions/392906",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/237966/"
] | I'm thinking about applying Fisher Exact Test for the following contingency table:
<pre><code> Answer Category-1 Category-2
A-1 2 15
A-2 0 17
A-3 0 27
A-4 2 15
</code></pre>
However, I'm not sure if this would b... | <ol>
<li>Having observed zeros is not an issue for a Fisher Exact test -- nor indeed is it a problem for a chi-squared test (it's not clear why you think this would be a difficulty with an exact test; if you can clarify the source of your concern, additional explanation/clarification may be possible). An entire row or ... | In principle, Fisher's exact test can be used on tables of any size, with any entries. The only issue is whether it is computationally feasible, which is an issue when you are using large tables with large values. In this case the <code>fisher.test</code> function in <code>R</code> can comfortably handle the matrix y... | https://stats.stackexchange.com |
45,882 | [
"https://security.stackexchange.com/questions/45882",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/10714/"
] | For example it seems like anti-virus, anti-spam and firewalls have sort of merged into one product. Is there a downside to this? I don't know of any software firewalls that can be purchased without an AV, is there a reason this has happened?
| Here are some to think about, mainly from the "home user" perspective. The enterprise environment is unlikely to use a single vendor for all security needs. If they do, the setup and support package usually eliminates all common mistakes.
<strong>Good:</strong>
<ul>
<li>More integration/less administrative work to do... | For me, a big downside is bloat. For a while I used Comodo firewall on my windows home machines, but gradually updates started including some stuff that really should have been optional, like live chatting and such.
Also, over time, I'd accumulated a large amount of images to make up the gui that weren't really neces... | https://security.stackexchange.com |
66,906 | [
"https://stats.stackexchange.com/questions/66906",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/28940/"
] | I am constructing a model for the prediction of a binary (Yes/No) outcome. I have a learning sample that gives the machine 1500 examples of the "Yes" group and 500 example of the "No" group. Should I be using all the data I have for input to learn the machine? Would this be biased towards the "Yes"?
I had the thought... | Most learning algorithms have a way to deal with skewed data sets. In general, use as much as you can for learning to increase generalization performance.
| Questions you should ask yourself are <strong>"Why is my training set biased?"</strong> and "What will the data look like at application time?" If the bias is a natural property of the data, that bias should probably be represented in the training set as well. If the bias is a selection bias due to the way the data was... | https://stats.stackexchange.com |
4,474,003 | [
"https://math.stackexchange.com/questions/4474003",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1066107/"
] | So I have this limit ...
<span class="math-container">$$\lim_{x\to {0}}\frac{1}{x\arcsin x} - \frac{1}{x^2}$$</span>
Using l'hôpital rule, I know the answer is <span class="math-container">$-\frac{1}{6}$</span>, but it seems like my professor want me to find another way and I can't think of any.
Can you help me?
| <strong>Hint 1:</strong>
Convert the given limit expression as a single fraction.
<hr />
<strong>Hint 2:</strong>
Use the series expansion for <span class="math-container">$\sin^{-1}(x)$</span>. i.e.,
<span class="math-container">$$\boxed{\sin^{-1}(x) = x + \frac{x^3}{6} + \frac{3x^5}{40} + \frac{5x^7}{112} + \frac{35... | Make a substitution <span class="math-container">$y=\arcsin x \implies x=\sin y$</span>. Thus, the limit becomes (assuming the limit exists):
<span class="math-container">$$\lim_{y\to0}\frac{\sin y-y}{y\sin^2y}=\lim_{y\to0}\frac{\sin y-y}{y^3} \cdot \lim_{y\to0}\frac{y^2}{\sin^2y}$$</span>
Now let <span class="math-con... | https://math.stackexchange.com |
21,882 | [
"https://engineering.stackexchange.com/questions/21882",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/16190/"
] | Please bear with me - I'm a lapsed mathematician and I'm self-studying these concepts.
A question asks the following:
<blockquote>
Water flows in a pipe of diameter 5 m at a velocity of 10 m/s. It then
flows down into a smaller pipe of diameter 2 m. The height between the
centre of pipe sections is 5 m. The den... | I think this question is ill posed.
If both pipes are flowing full, the correct answer is 62.5 m/s from continuity.
If there is an abrupt transition from the large to the small pipe, there will be a total pressure loss and Bernoulli's equation will not apply without a loss factor.
| I think @sam is correct. To provide some intuition here, imagine that we have a pipe that does what is described in the problem but that had constant diameter throughout. In this case, the pressure at point 2 is 169 kPa gauge. If we increase the diameter of the pipe at point 2, the pressure increases. You can think of ... | https://engineering.stackexchange.com |
35,686 | [
"https://quant.stackexchange.com/questions/35686",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/26314/"
] | I am trying to calibrate the 1 factor Hull White model to ATM swaptions. The strategy which I use is to minimise the sum of squared difference between model and market prices for the swaptions on the diagonal of the swaption matrix. I am using only swaption maturities till 10 years. So the swaptions which I am using fo... | It depends what kind of people inhabit your world (or your model).
If people are risk neutral, then indeed they will look only at expected return. They will rush into stocks and raise their price until the return is equal to the risk free rate. The risk premium on stocks will drop to zero.
But there is a lot of evide... | Yes, the existence of non-zero market price of risk implies the existence of strategies with a positive expected return. The expected return is the compensation demanded for bearing market risk.
The demand for positive expected return strategies doesn't decrease the market price of risk to zero (equivalently, it does... | https://quant.stackexchange.com |
4,143,884 | [
"https://math.stackexchange.com/questions/4143884",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/881599/"
] | <ul>
<li>We have the set <span class="math-container">$X$</span>. <span class="math-container">$X=\{1,2,3,4\}$</span>.
</li>
<li><span class="math-container">$\tau$</span>- topology in <span class="math-container">$X$</span>, <span class="math-container">$\tau =\{\emptyset, \{1,2,3,4\},\{1,2\},\{2,3\},\{1,2,3\}, \{2\}\... | I think this equivalence is false because the reverse implication(Part 2) is false.
The basic idea is this:
<span class="math-container">$(\forall x)(\exists y)(P(x,y))$</span> basically means, that given any <span class="math-container">$x$</span> you can find a <span class="math-container">$y$</span> such that <span ... | Consider the set of the real numbers, and <span class="math-container">$P(x, y) : x+y=0$</span>. Note that for all <span class="math-container">$x\in\mathbb{R} $</span> you can consider <span class="math-container">$y = - x$</span> and then <span class="math-container">$x+y=x-x=0$</span>. However, for all <span class="... | https://math.stackexchange.com |
263,318 | [
"https://mathoverflow.net/questions/263318",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | If ${\cal C}$ is a collection of subsets of a set $X$, we associate to ${\cal C}$ a graph $G_{\cal C} = (V,E)$ where $V = {\cal C}$ and $$E = \big\{\{A,B\}: A\neq B\in {\cal C} \land A\cap B \neq \emptyset\big\}.$$
If $\kappa$ is a cardinal and ${\cal C}$ is a collection of subsets of $\kappa$, it is easy to see that ... | The following Matlab code (unless I coded something wrong, which is well possible) finds a few random counterexamples each time I run it, even when restricted to off-diagonal entries:
<pre><code>n = 3;
for trie = 1:100
A = rand(n);
B1 = log(expm(A));
B2 = log(expm(2*A));
B3 = log(expm(3*A));
C = B2 - (... | For $2\times2$ matrices, the log-concavity is true. One has $e^{tA}=f(t)I_2+g(t)A$ by Cayley-Hamilton. Writing that the eigenvalues of $e^{tA}$ are the exponentials of those of $tA$, we find
$$g(t)=\frac{e^{t\mu}-e^{t\lambda}}{\mu-\lambda}\,,$$
where $\mu,\lambda$ are the eigenvalues of $A$. Thus we only have to prove ... | https://mathoverflow.net |
1,231,297 | [
"https://math.stackexchange.com/questions/1231297",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/167874/"
] | solve
$$ \sqrt{5x+19} = \sqrt{x+7} + 2\sqrt{x-5} $$
$$ \sqrt{5x+19} = \sqrt{x+7} + 2\sqrt{x-5} \Rightarrow $$
$$ 5x+19 = (x+7) + 4\sqrt{x-5}\sqrt{x+7} + (x+5) \Rightarrow $$
$$ 3x + 17 = 4\sqrt{x-5}\sqrt{x+7} \Rightarrow $$
$$ 9x^2 + 102x + 289 = 16(x+7)(x-5) \Rightarrow $$
$$ 9x^2 + 102x + 289 = 16(x^2+ 2x - 35) \R... | You forgot a factor $4$ and wrote $x+5$ instead of $x-5$ in the third line, which should be
$$
5x+19=x+7+4\sqrt{x+7}\,\sqrt{x-5}+4(x-5)
$$
giving
$$
4\sqrt{x+7}\,\sqrt{x-5}=32
$$
or
$$
\sqrt{x+7}\,\sqrt{x-5}=8
$$
that becomes, after squaring,
$$
x^2+2x-99=0
$$
The roots of this are $-11$ and $9$, but only the latter is... | \begin{align}
\sqrt{5x+19}&=\sqrt{x+7}+2\sqrt{x-5}\\
5x+19&=x+7+4(x-5)+4\sqrt{(x+7)(x-5)}\\
32&=4\sqrt{(x+7)(x-5)}\\
8&=\sqrt{(x+7)(x-5)}\\
64&=x^2+2x-35\\
0&=x^2+2x-99
\end{align}
which gives $x=9$ and $x=-11$ are the solutions.
But both are giving something like this..
$x=9\implies \sqrt {... | https://math.stackexchange.com |
376,429 | [
"https://softwareengineering.stackexchange.com/questions/376429",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/312192/"
] | I am currently working on an implementation that based on a set of user configurations should output a final decision. The multiple configurations are evaluated several times at different stages of the execution.
Example: Let's say I'm building a system that plans the perfect vacation for a user. The User object is th... | Neither is an anti-pattern, the first is the better choice though. It is the parser class as a whole (potentially all of its methods) that depends on the context. The example shows a class with only one method but you could have several and it would be noisy and unnecessary to pass the context to each.
| A recursive descent parser is characterized by recursive functions. There's no need to involve any classes (except of course in languages like Java where everything has to be placed into a class).
However, you will often pass some context through all these functions. This is usually an explicit function argument (your... | https://softwareengineering.stackexchange.com |
280,529 | [
"https://physics.stackexchange.com/questions/280529",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45613/"
] | Provided you know the capacity of a fan (flow rate) at constant speed and at sea level, is there an analytical way to predict what the flow rate would be at altitude? Or is this specific to the fan's design?
| The structure of standard model $SU(3)\times SU(2)\times U(1)$ is chiral which basically tells you the necessity of chiral fermions. If left-handed fermions transform under a representation $R$ of the symmetry group then due to charge-conjugation relating left-handed and right-handed fermions as $$\psi_{Right}=C(\bar{\... | Well the answer of your question is not so trivial, I guess. Here is my try. I want to give a glimpse why a symplectic group is not a good choice for model building from a phenomenological point of view.
Now look at the symplectic group closely.
<ul>
<li>$Sp(1)$ is isomorphic to $SU(2)$ </li>
<li>$Sp(4)$ is isomorph... | https://physics.stackexchange.com |
39,259 | [
"https://dba.stackexchange.com/questions/39259",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/22221/"
] | Imagine you have inherited some project with extensive usage of SQL queries.
Let us assume that Hibernate is used as ORM and PostgreSQL as database, but thats not the point.
A question is: could you suggest a plan to sequentially scan the system and optimize the SQL queries performance?
I suggest the following step... | It appears there is no way to fix this issue. Excel looks at the first few rows of data in the column and will always FORCE the datatype to FLOAT no matter what. I was given a solution of creating a template with a few varchar characters in the first few rows (8+) so EXCEL will pick that up as the data type and then im... | Is it possible to get the file as a .csv file which can be imported like a text file and will not have this problem? I generally kick back all Excel files and ask for another format because SSIS and Excel do not play well together on many levels.
| https://dba.stackexchange.com |
31,125 | [
"https://chemistry.stackexchange.com/questions/31125",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/16096/"
] | I have a base $\ce{M(OH)_{3}}$ having 3 $\mathrm{p}K_{\mathrm{b}}$ values as,
$$
\mathrm{p}K_{\mathrm{b}_{1}} = 0.5\\
\mathrm{p}K_{\mathrm{b}_{2}} = 3.7\\
\mathrm{p}K_{\mathrm{b}_{3}} = 7.7\\
$$
If a strong acid is given as the titrant and phenolphthalein and methyl orange are given as possible indicators, how can I c... | Since:
\begin{align}
K_\mathrm{w} &=K_\mathrm{a} \cdot K_\mathrm{b}\\
K_\mathrm{a} &=\frac{K_\mathrm{w}}{K_\mathrm{b}}\\
\log{K_\mathrm{a}} &=\log K_\mathrm{w}-\log K_\mathrm{b}\\
K_\mathrm{w} &=1 \times 10^{-14}\\
\log{K_\mathrm{a}} &= -14-\log K_\mathrm{b}\\
-\log{K_\mathrm{a}} &=14+\log K_\m... | The first step is to determine the $\mathrm{p}K_{\mathrm{a}}$ values for the indicators and convert them to $\mathrm{p}K_{\mathrm{b}}$ values. Then determine how you would titrate the solution using the indicator(s).
| https://chemistry.stackexchange.com |
43,711 | [
"https://physics.stackexchange.com/questions/43711",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/15764/"
] | I have been given this formula from optics here, with no background:
$$\vec\nabla{n} = \frac{d(n\hat{u})}{ds}$$
Where $n$ is the refractive index and $\hat{u}$ is a unit vector tangent to the path $s$ that light takes inside a medium.
Does anyone know if this formula has a name? I am looking specifically for a deriv... | This equation is called the <strong>ray equation</strong> and it can indeed be derived from Fermat's principle. I guess you can find more about its derivation in, e.g., Born and Wolf's Principles of optics or in Fundamentals of Photonics by Saleh and Teich.
| The optical path length
$$
S = \int\! n \, ds\,
$$
for a ray travelling along some curve is extremized by the path that the ray actually takes (from a wave point of view, the phase is stationary, and so we get constructive interference). We can parameterize the path by some parameter $\lambda$, i.e., $\vec{x}(\lambda)$... | https://physics.stackexchange.com |
69,015 | [
"https://mathoverflow.net/questions/69015",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15311/"
] | This might not be very difficult, but I think I may have gotten a little confused.
Suppose we are given a matrix A, and would like to find the vector x of modulus 1 which maximises the product xt A x (xtranspose times A times x)
Consider the following iteration: We start with some vector y of modulus 1, find the vecto... | Girsanov's theorem tells you that on any <em>finite</em> interval $[0,T]$ you can find an equivalent probability that makes $t+B_t$ a Brownian motion. You just gave the proof that it cannot be done on the whole real line.
| I am afraid that (1) is not correct, since the law of the iterated logarithm states that
$$|B_t|\approx \sqrt{2t\log\log(1/t)}$$
as $t\to0$. This yields
$$\frac{|B_t|}{t}\to\infty$$
as $t\to0$
| https://mathoverflow.net |
50,038 | [
"https://cs.stackexchange.com/questions/50038",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/30481/"
] | I am studying the algorithm of Sollin and we recently studied a lemma:
Let be G a graph which values are diffferent on the edges.
<ul>
<li>We sort the edges <span class="math-container">$e_1,e_2,...e_m$</span> such as <span class="math-container">$v(e_i)<v(e_j)$</span></li>
<li>Every tree of minimal value has at le... | The proof outcomes from the definition of a <em>tree</em> - they are non-oriented, <strong>connected</strong> graphs with no cycles.
Lets assume that there's no cycle after adding $e1$. Let $e1$ = $(v1, v2)$. This means that before adding $e1$ there wasn't any path that connects $v1$ and $v2$, which contradicts to the... | In a tree, there is exactly one path between any pair of vertices. When you add edge <code>e1</code> you close that unique path to form a unique cycle.
| https://cs.stackexchange.com |
79,054 | [
"https://stats.stackexchange.com/questions/79054",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/22478/"
] | When I was a Ph.D. student I was trained in no uncertain terms that
When we had large numbers of data results, that the number of significant results HAD to be, in and of themselves SIGNIFICANT!
I am referring to the use and abuse of statistical significance in a large data set using different methodologies of predi... | It is certainly possible to have a very large sample and a non-significant result. Perhaps this is simplest to demonstrate with categorical data. Suppose you have data on one condition on two groups of data, e.g. Men and women and whether last name ends in a vowel or consonant. Suppose you find, among 1,000,000 people,... | I would suggest to not use the word "significant" alone. Speak of "statistical significance" because this is how the term was historically settled, and speak of substantive "importance", like for example "economic importance", (this will depend on context) to talk about whether an effect or an association that appears ... | https://stats.stackexchange.com |
9,005 | [
"https://physics.stackexchange.com/questions/9005",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2094/"
] | Why does $E=mc^2$ give results in Joules ? Why didn't Einstein need to create a separate unit and how come using two standard units (speed of light in km.s and mass in grams) give another result in Joules ?
| It's an energy. The SI unit for energy is a Joule. If the theory is going to predict an energy-mass correspondance, then it better give the energy in units of energy. If the units of $mc^{2}$ didn't work out, for the equation to make any sense, you'd have to include some constant $\alpha$ so that $E=\alpha mc^{2}$ w... | Because of the definition of Joules in terms of the base kg/m/s units.
If you used lbs feet/second and calories you would need a conversion factor, because calories are defined in terms of heating water rather than mechanics, but the equation still works.
| https://physics.stackexchange.com |
305,417 | [
"https://softwareengineering.stackexchange.com/questions/305417",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/136188/"
] | We're figuring out whether we should write acceptance tests that revolves around preloaded data on a database file, or programmatically added needed data per test, or filling database while testing other application features.
This is a more detailed, easy use case: you want to acceptance test (or UI-test) adding a <co... | <blockquote>
Pass a mutable object to the back-end, and have the back-end make
changes to it on progress. The object notifies the front-end when a
change occurs.
</blockquote>
It's difficult to balance efficiency if the backend notifies in this respect. Without care you might find that incrementing your progress... | This is the difference between a <em>push</em> and <em>pull</em> notification mechanism.
The mutable object (the <em>pull</em>) will need to be repeatably polled by the UI and synchronized if you expect the back-end task to be executed in a background/worker thread.
The callback (the <em>push</em>) will only create ... | https://softwareengineering.stackexchange.com |
31,065 | [
"https://electronics.stackexchange.com/questions/31065",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3975/"
] | I have a TFT display which accepts 24 Bits Per Pixel (BPP) display data, but my connector mechanism supports only 5:6:5 mode.
What is the prefered way of getting the display to drop the extra pixel data and use the 5:6:5 data?
Should I just pull-down the unused data lines?
| There are two common approaches. One approach is to wire all the unused bits to a fixed value (typically zero). This will cause a slight loss of brightness, but 3% really isn't worth worrying about. The other is to wire them to the upper bits, in sequence, so a 5-bit color value would be wired as [D4 D3 D2 D1 D0 D4 ... | For maximum brightness range, connect the unused lsbits to the lowest bit of your source. Just connecting to 0 will limit maximum brightness slightly.
| https://electronics.stackexchange.com |
110,791 | [
"https://chemistry.stackexchange.com/questions/110791",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/73006/"
] | <strong>In the descriptions below, I always assume external pressure to be constant at 1 atm</strong>, the condition where daily observations are made.
1) When I exhale on a mirror, liquid water forms on the mirror. That's condensation. Obviously, the temperature of mirror must be < 100 °C, so water vapor condensin... | <blockquote>
Why do we have water vapors when our body temperature is also <100°C in the first place?
</blockquote>
At normal pressure, water boils at 100°C, meaning that bubbles of pure steam form under water. At lower temperatures, water molecules reversibly move from the liquid to the gas phase and back. The h... | The major difference is that in vapor phase, the water can leave the container (so you can tell it's in a different form), and which prevents it from immediately rejoining the liquid.
In both solid/liquid phases, the water remains in the rest of the bulk. A few molecules of liquid in a solid or a few molecules of a s... | https://chemistry.stackexchange.com |
32,957 | [
"https://mathoverflow.net/questions/32957",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $X$ be a circle that with one corner (i.e. think of a triangle where we smooth out two of the vertices). Now let us consider the topological torus $M \cong \mathbb{T}^n$ which is the product of $n$ copies of $X$. Note that $M$ contains $n$ distinct circles along which it is not smooth.
Finally, suppose we are ... | Answer to your question is negative if $n\ge 1$ ($n$ is a number of smooth circles and I suppose that there is non-smooth circles). Indeed, in that case your manifold is homeomorphic to torus $T^k$ and the homeomorphism $\varphi\colon M\to T^k$ could be taken smooth on the smooth part of $M$. The image of non-smooth pa... | Let $n=2.$ The height function $h$ for the standard embedding of the torus (as in the first pages of Milnor's <em>Morse Theory</em>) has four critical points $A_i, i=1,2,3,4.$ Now draw two simple circles $S_1$ and $S_2$ transversally intersecting in a single point of the torus and containing the points $A_i$ and change... | https://mathoverflow.net |
462,831 | [
"https://physics.stackexchange.com/questions/462831",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/122667/"
] | Consider a system where a block is to be raised from the ground to a height of 1 meter above the ground. It is given that when the force acting on the block and its displacement act in the same sense, the block gains energy. On the other hand, when both quantities act in opposite senses, the block loses energy.
Back ... | You seem to have a misconception. Work done is not the change in total energy. Work done is the change in <strong>kinetic energy</strong> only.
<span class="math-container">$$W=\Delta E_k$$</span>
So, as you point out, since they're equal and opposite forces, no kinetic energy is gained. In fact, the block was at res... | In order to start the block moving from rest it is necessary to exert, at minimum, an upward force greater than the downward force of gravity. Once you get the block moving the upward force can be reduced to equal the downward force of gravity. Although the net force is now zero, the block continues upward at constant ... | https://physics.stackexchange.com |
67,779 | [
"https://electronics.stackexchange.com/questions/67779",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18033/"
] | Can someone please clarify how a PLL works and how it can the result is used to deduce phase?
<img src="https://i.stack.imgur.com/ZfE0l.png" alt="enter image description here">
My understanding is that a PLL is used to demodulate in situations when the demodulator knows the carrier frequency but does not know the pha... | The key here is this statement "My understanding is that a PLL is used to demodulate in situations when the demodulator knows the carrier frequency but does not know the phase."
There is only one small insight that you are lacking:
Lets say we have an input waveform \$ \sin ( \omega t - \phi_1) \$ and the output from... | In general, a PLL tries to keep its VCO phase-aligned (and therefore frequency-locked) to the input signal.
If you'd like to demodulate a frequency-modulated signal, then you make sure the loop bandwidth (set by the LPF) is wider than the modulating signal, allowing the the VCO to track the incoming frequency, and the... | https://electronics.stackexchange.com |
538,581 | [
"https://physics.stackexchange.com/questions/538581",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75085/"
] | The standard (the only way I know) to derive the density of electromagnetic mode (per volume and per unit frequency) for a black body consists in modelling it by a cavity with perfectly reflecting walls.
It implies stationnary electromagnetic waves inside. Then, we say that this electromagnetic field is at equilibrium... | <blockquote>
We modelled the black body by saying it is a cavity with perfectly reflecting walls. We computed some properties of this electromagnetic field at equilibrium.
</blockquote>
This is an extremely common misconception. The model of the black body isn't the cavity, it's the <em>hole</em>.
If you have a ca... | Reflecting radiation is not the same as absorbing and then emitting. Because in the second case, two processes are independent. The intensity of emitted light doesn't depend on the intensity of absorbed, only on internal properties of the body.
In other words, if you switch off the incident light, the radiation from t... | https://physics.stackexchange.com |
14,622 | [
"https://security.stackexchange.com/questions/14622",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/8923/"
] | Imagine having a web application. You then decide that you want to create your own logging system, for whatever reason. What data should be logged to put a very good logging system in place?
I was thinking about the following:
<ul>
<li>Date and time of access for every user</li>
<li>User IP</li>
<li>Number of consequ... | To expand upon Rory's recommendations, you really need to ask yourself what is the driver behind your logging, and what information you need to accomplish those goals.
For example, if you need user attribution then you probably need
<ul>
<li>Username</li>
<li>Timestamp</li>
<li>Source IP</li>
<li>GET string and possibl... | There is certainly value in logging the HTTP headers. Exactly which ones to log vary highly depending on the specific web application.
| https://security.stackexchange.com |
71,616 | [
"https://security.stackexchange.com/questions/71616",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/59502/"
] | What would be a more secure way to encrypt files using TrueCrypt 7.1a. The is an airgapped computer (wifi, bluetooth, speakers and mic removed too). The encrypted files will be on an external drive in either setup and not on the system's HDD.
<ol>
<li>An FDE TrueCrypt notebook running Windows.</li>
<li>A MacBook runni... | <ul>
<li>Make sure you're using WPA2 with a strong password.</li>
<li>Change the password.</li>
<li>Use a Wifi Analyzer to make sure you're on the least crowded channel you can be.</li>
<li>Disable WPS (Wi-Fi Protected Setup), pin can be brute forced.</li>
<li>Change default router configuration login</li>
</ul>
That'... | In you router configuration page (lots of time at 192.68.0.1 or 192.68.1.1), you probably should be able to see the MAC addresses that are currently connect to your router. things you could do on MAC address:
(1) Identify MAC address(es) that are not from your own devices. it will take some time to check all your devic... | https://security.stackexchange.com |
9,350 | [
"https://cstheory.stackexchange.com/questions/9350",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/495/"
] | The PCP theorem states that there is no polynomial time algorithm for MAX 3SAT to find an assignment satisfying $7/8+ \epsilon$ clauses of a satisfiable 3SAT formula unless $P = NP$.
There is a trivial polynomial time algorithm that satisfies $7/8$ of the clauses. So, Can we do better than $7/8+ \epsilon $ if we allow... | One can get a $7/8+\varepsilon/8$ approximation for MAX3SAT that runs in $2^{O(\varepsilon n)}$ time without too much trouble. Here is the idea. Divide the set of variables into $O(1/\varepsilon)$ groups of $\varepsilon n$ variables each. For each group, try all $2^{\varepsilon n}$ ways to assign the variables in the g... | To somewhat restate what Ryan Williams wrote in his last paragraph:
The Moshkovitz-Raz theorem shows that there is a function $T(n) = 2^{n^{1-o(1)}}$ such that if Max-3Sat can be $(7/8 + 1/(\log \log n)^{.000001})$-approximated in time $T(n)$ then the decision version of 3Sat is in time $2^{o(n)}$. It is commonly be... | https://cstheory.stackexchange.com |
120,461 | [
"https://stats.stackexchange.com/questions/120461",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/58792/"
] | I think I understand completely the concept of cross validation, but there is one aspect I've never seen detailed. Let's assume I have a logistic regression model with four parameters I want to train. I perform k-fold cross validation with k, let's say, 5, over my training data, and it yields 5 different sets of four v... | Actually, I've already understood how to do so. Just in case someone stumbles upon this question: cross validation <strong>can</strong> serve as a parameter tuning tool.To tune a model's parameters using K-fold cross validation you train and test each model K times against the K possible data combinations and average t... | Cross-validation just gives you an estimate of your out-of-sample risk. It doesn't produce a better model. To get the most precise estimate of your coefficients, you should use all of your data.
| https://stats.stackexchange.com |
403,372 | [
"https://electronics.stackexchange.com/questions/403372",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/202474/"
] | According to the excellent site of AB4OJ, the Icom 7300 in summary has a 14bit analogue to digital converter with a 1.5 volt peak to peak input (LTC2208-14). I make this to be 91.5uV per quantisation level. There is a 20db gain amplifier (LTC6401-20) ahead of the ADC so best case this would give 9.1uV per quantisation... | You are missing that a correctly dithered quantiser is LINEAR, and that there is more then enough uncorrelated noise in the ADC input bandwidth to correctly dither the quantiser.
You are not digitising just the signal you care about, you are digitising a whole bands worth of mostly uncorrelated stuff, and then reduci... | Thermal Floor (Boltzmann noise, et al) for 1,000 Hertz bandwith is
-174dBm + 30 dB = -144dBm
What the voltage level, across 50 ohms from a standard RF interface, for -144 dBm?
Given 0dBm across 50 ohms is 0.632 volts peakpeak, and -120 dBm is down by 1,000,000 to 0.632 microVolts PP, and -140 dBm is down to 0.0632 ... | https://electronics.stackexchange.com |
55,333 | [
"https://mathoverflow.net/questions/55333",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10408/"
] | Take scheme morphism $f: X\to Y$ and suppose $f$ surjective. If $y \in Y$ can one find affine open $V \subset Y$ containing $y$ and affine open $U \subset X$ such $f(U) = V$ ?
Thank you.
Later: Very good answer of Kevin shows it is not true. Is there hypothese which make it true ?
For example $X$ irreducible and/o... | If $f$ is open (e.g. $f$ finite type and flat over noetherian $Y$), then your condition is trivially satisfied: let $V'$ be any affine open neighborhood of $y$ and let $U'$ be an affine open subset of $X$ such that $y\in f(U')\subseteq V'$. Take a principal open subset $V'_h$ such that $y\in V'_h\subseteq f(U')$, then ... | Consider the disjoint union Spec$(\mathbb{Q})\coprod_{p}$Spec$(\mathbb{F}_p)$ with its canonical map to Spec$(\mathbb{Z})$. This is bijective on points, but the preimage of any open in Spec$(\mathbb{Z})$ won't even be compact, much less affine.
| https://mathoverflow.net |
137,475 | [
"https://softwareengineering.stackexchange.com/questions/137475",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44190/"
] | So I'm very close to releasing an app I've been working on, and the server I integrate with allows me to register users. So I was wondering if I should require users to register with the app before they use it. The app wouldn't "need" the registration for any of the features (although I have some ideas about future u... | well for myself i would prefer an app where i don't have to register , simply cause just like you I am lazy to fill in the registration form for a new app that i am not sure if i will really use or not
well i can give you better options
<ul>
<li>did you concider making registration optional until you really require... | Imagine you live in a small town and you have two supermarkets.
<ul>
<li>The first one is across the street. You go there, you buy what you need, you pay for it, and you can leave with the products you've bought.</li>
<li>The second one is outside the city. You have to use your car to go to it, then you have to find a... | https://softwareengineering.stackexchange.com |
1,567,327 | [
"https://math.stackexchange.com/questions/1567327",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/15381/"
] | Let $N$ be a positive integer with $d\geq 4$ digits, none of which is
zero. Suppose that erasing some digit of $N$ yields another number
$M$ which happens to be a divisor of $N$.
Examples : 1375 divides 12375. 1875 divides 61875.
Question : is it true that $M$ must always end with 25 or 75, and that the two final dig... | Let $n$ be the original number and $m$ the number after a digit is deleted. Suppose that the deleted digit is $d$, that $r$ is the number represented by the $k$ digits to the right of $d$, and that $\ell$ is the number represented by the digits to the left of $d$, so that $m=10^k\ell+r$, and $n=10^{k+1}\ell+10^kd+r$.
... | First, convince yourself that the deleted digit can't be the unit or tens digit.
Then let the last 2 digits form the number $a$, and let $N/M=b$. Then we have $$ab\equiv a\pmod{100}$$ which is to say, $a(b-1)$ is a multiple of 100. Here's what we know about $a$ and $b$: neither digit of $a$ is zero, $11\le a<100$,... | https://math.stackexchange.com |
160,749 | [
"https://stats.stackexchange.com/questions/160749",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/26564/"
] | i am trying to refresh my knowledge of the multivariate normal distribution. the standard formula as per below<img src="https://i.stack.imgur.com/EdxlR.png" alt="enter image description here">
i would normally think of <strong>x</strong> as a tall and slim matrix of the covariate values (rows representing different ob... | $x$ is a column vector, so $(x-\mu)^{T}$ is a $1$ by $n$ row matrix. $\Sigma^{-1}$ is of size $n$ by $n$. Here $n$ is the length of the random vector $X$. There isn't any "data" in this probability density function.
| No, in this case <strong>x</strong> is a vector representing the result of sampling from the distribution and <strong>$\mu$</strong> is a vector of the same size. Each element within the <strong>$\mu$</strong> vector represents the mean of the distribution along that dimension; thus, $(x-\mu)^T$ if also a vector, but i... | https://stats.stackexchange.com |
697,160 | [
"https://physics.stackexchange.com/questions/697160",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/296727/"
] | I am working on planning out nuclear fusion for a fictional world, and I am wondering if two ideas are able to work together, or if they contradict each other.
So Dueterium-Tritium fusion releases energy (approximately 17.6 MeV) alongside helium and a free neutron. But also, if a neutron hits Lithium, it would react an... | In condensed matter physics, or any field theory where particle numbers are not <em>conserved</em> (like particle physics), the Schrodinger equation does not work. The Schrodinger equation needs the condition that particle numbers are constant.
In standard quantum mechanics, where we do use the Schrodinger equation, in... | I'm arguing here in a different way than the answer by @josephh. In my opinion, you can definitely apply the Schrödinger equation -- resp. a probably differently named version of it -- to phonons as well, but you have to extend the framework.
In the standard setting you're basing the whole formalism on a Hilbert space ... | https://physics.stackexchange.com |
80,696 | [
"https://math.stackexchange.com/questions/80696",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/19207/"
] | I am given the following function:
$$f(z)=1+z^2+z^4+z^8+z^{16}+ \cdots$$
and shall show that it is holomorphic in the unit disc, that $f\to\infty$ as $z\to e^{2i\pi/2^n}$, and that every point on the circle $|z|=1$ is singular. I struggle with the last part. It seems intuitive, since we are summing up different point... | Firstly, $f(z)\rightarrow\infty$ as $z\rightarrow 1^-$. So $z=1$ is a singularity.
Since $f(z)=z^2+f(z^2)$ we have that if $z^2\rightarrow 1^-$ then $f(z)\rightarrow\infty$. So $z$ such that $z^2=1$ are singularities.
We may write $f(z)=z^2+z^4+f(z^4)$ so if $z^4\rightarrow 1^-$ then $f(z)\rightarrow\infty$.
Continu... | The second part helps answer the last part. It implies (with a little tweaking) that every point on the circle is a limit point of points where $f$ blows up.
| https://math.stackexchange.com |
158,981 | [
"https://softwareengineering.stackexchange.com/questions/158981",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19900/"
] | We are building a business application (a laboratory management system to be more precise) mostly for internal company use only. To make it easier for users to find items which they work on we are implementing a list of most used items.
We had a little debate on which method would be better to implement: display the m... | This might be down voted for not answering your question directly, but the debate you had with your colleague was a waste of time.
You should have spoken to 3 (mid level, hands on) lab technicians - given them the two options and asked them what they would do.
| Do both. Instead of a simple list, have an "Open Recent" command that opens a page or dialog or window or whatever fits in your design. On that page you can then have two sections, one for most recent and another for most used. Or, a radiobutton that toggles between the two. This gives each user the power to choose.
... | https://softwareengineering.stackexchange.com |
1,252,432 | [
"https://math.stackexchange.com/questions/1252432",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/95162/"
] | What is the limit of the sequence of functions$\frac{\epsilon}{\epsilon^2+x^2}$ as $\epsilon\to 0$?
I think this just doesn't exist, since it goes to $\infty$ in $x=0$ and goes to $0$ everywhere else.
Thanks
| You hit the nail on the head there with your thoughts, except that the interpretation should be that the limit <em>does</em> exist, whenever $x\neq 0$, but does not exist, when $x=0$.
The limit will depend on which value of $x$ you are given.
| For each $f$
$$
\int f(x)\times \frac {\epsilon }{x^2 + \epsilon ^ 2} dx
= \int f(\epsilon y) \times \frac { 1}{y^2 + 1} dy
\to \int f(0) \times \frac { dy}{y^2 + 1}
= \pi f(0)
$$
so $$
\frac {\epsilon }{x^2 + \epsilon ^ 2} \to \pi\delta
$$
| https://math.stackexchange.com |
351,095 | [
"https://physics.stackexchange.com/questions/351095",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/111703/"
] | My question is about the shape of the observable universe or Cosmic Horizon.
In literature it is described as having a radius, constant.
But in an accelerating expanding universe this seems impossible to me. I will explain my doubt.
The universe started at a certain location with the Big Bang, lets call that locati... | While you know the statement of Newton's first law, Newton's second law can be used to answer your question. Newton's second law is stated mathematically as <span class="math-container">$$\vec{F} = m\vec{a}$$</span>
This statement tells us that, for a given object of mass <span class="math-container">$m$</span>, the a... | The Physics term is Inertia, but I will try to explain in non-rigorous terms that I think may help you, and in the future may help you with concepts like relativity.
To take an object at rest and put it into motion, that requires a force which accelerates that object and now it has velocity. Inertia says that velocit... | https://physics.stackexchange.com |
299,930 | [
"https://stats.stackexchange.com/questions/299930",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/107364/"
] | Suppose I fit a quantile regression model with BMI as a response and gender as a predictor. Now, How can I interpret the estimated coefficient for gender.
Note that :gender 1=male , 0=female.
| First, let's streamline the complexity. Quantilte regression is no different from linear regression, except that it centers it on the Median instead of the Mean. In other words, quantile regression is a nifty type of regression that reduces the impact of outliers on the regression coefficients.
So, how would you in... | The coefficient is the amount by which men are expected to outweigh women for the quantile you have selected in the quantile regression.
| https://stats.stackexchange.com |
10,383 | [
"https://engineering.stackexchange.com/questions/10383",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/6914/"
] | I have a heating system with which I heat up 10 liters of water by 24.2°C in 610 seconds.
My system consumed 0.5 KW of electric energy in this time.
Now I used this formula:
Specific heat of water * volume * temperature difference / time
and I get 1,66 KW (created)
efficiency 332%
Is this correct? Or mus... | You are confusing units, which is making your question difficult to understand.
Electrical energy is measured in kW-<em>hours</em> (or Joules), not kW. If your heater consumed 500 W of <em>power</em> for 610 s, then you used 305 kJ of <em>energy</em> to heat your water.
Similarly, if 10 l (10 kg) of water was raised ... | The formula's you use seem correct. The value for efficiency however is impossible as you can never reach an efficiency of 100% let alone over 100%.
Efficiency = ( Usefull energy / Total energy ) * 100% or ( Usefull power / total power) * 100%
Energy = Cp (assume constant) * M * (Tf - Ti) in which M is equal to V * r... | https://engineering.stackexchange.com |
1,807,881 | [
"https://math.stackexchange.com/questions/1807881",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/343252/"
] | When we change the lower limit of a power series by any finite quantity, would it increase or decrease radius of convergence or no change?
<em>Clarification of terminology:</em> There might be confusion about "lower limit" and "upper limit" term.
Let a summation be $$\sum\limits_{i=a}^b a_iz^i$$
Lower limit of summati... | It does not change the radius of convergence. If a series $\sum_{n=N}^\infty a_n$ converges then it still converges if the value of $N$ is changed but all else remains the same, and the fact that $a_n$ is of the form $b_n z^n$ doesn't change that. If $N<M$ then
$$
\sum_{n=N}^L a_n = \sum_{n=N}^M a_n + \sum_{n=M+1}... | No. Let $p(z)=\sum_{k=0}^\infty p_k z^k$ be your power series and $p_n(z):=\sum_{k=0}^n p_k z^k$ some finite partial sum. Then, the function $p_n$ is defined everywhere as it is a polynomial. If $(p-p_n)$ is defined at a point $z$, then $p(z) = (p-p_n)(z)+p_n(z)$.
| https://math.stackexchange.com |
3,746,099 | [
"https://math.stackexchange.com/questions/3746099",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/691776/"
] | Let us say <span class="math-container">$f$</span> is an integrable function on <span class="math-container">$[a,b]$</span> and we want to evaluate <span class="math-container">$\int_a^b f(x)dx$</span> but often the calculation is not easy.So,we have a method of substitution.We substitute <span class="math-container">$... | Strong sufficient conditions are that <span class="math-container">$f$</span> is continuous and <span class="math-container">$\phi'$</span> is integrable. A straightforward proof uses the FTC, and monotonicity of <span class="math-container">$\phi$</span> is not needed.
Defining <span class="math-container">$F(t) = \in... | Think of this as the fundamental theorem applied to a composition.
By the chain rule it holds that <span class="math-container">$(f \circ \phi)'=f'(\phi) \circ \phi'$</span> so, roughly, <span class="math-container">$f \circ \phi=\int (f'(\phi) \circ \phi')$</span>. The remainder conditions over the limits of integrati... | https://math.stackexchange.com |
4,260 | [
"https://mathoverflow.net/questions/4260",
"https://mathoverflow.net",
"https://mathoverflow.net/users/699/"
] | I've heard from multiple sources now that one's CV should include grants you've applied for, even if you didn't receive them or won't find out if you've received them until after your CV goes out. I haven't had much luck finding this in other people's CVs, though. I'd like to have confirmation of this from someone wh... | You have a certain amount of leeway as to what kind of material you wish to include in your CV. I have seen things on CVs that were of little or no interest [edit: here I actually meant "of interest to me as a potential hirer", not personal interest]: high school honors, nonmathematical awards, etc. It doesn't make m... | I've served on tenure-track hiring committees. Notification that you've applied for a grant wouldn't work for or against you at our place, as far as I can tell.
I wouldn't in general include where you've submitted your papers. Maybe there's an exception if the paper is joint with senior person X -- in that case ther... | https://mathoverflow.net |
187,276 | [
"https://stats.stackexchange.com/questions/187276",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/39531/"
] | If subjects are recruited using a convenience sample to take part in a study, and each participant is then randomly assigned to either treatment condition, A and B.
(i) Will my result be generalizable to the broader population? Yes or No
(ii) We need to be realistic that random sampling is not always possible, but ra... | The null hypothesis is that neither group has a biased coin (and so p=0.5 for both); the alternative is that one of them has a biased coin (so p differs from 0.5 for one of the groups).
Let the unknown number of tosses be $t$. Let the number of people in group 1 be $n_1$, the number in group 2 be $n_2$.
Under the nu... | I'm still not sure I would approach this with a chi-square test. Glen_b uses an interesting approach that recognizes that a binomial experiment is nothing more than a series of Bernoulli experiments. Due to the independence assumption, you can string out all of those Bernoulli experiments into one giant experiment an... | https://stats.stackexchange.com |
214,017 | [
"https://softwareengineering.stackexchange.com/questions/214017",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/104543/"
] | I have an ASP.NET MVC 4 solution that I'm putting together, leveraging IoC and the repository pattern using Entity Framework 5. I have a new requirement to be able to pull data from a second database (from another internal application) which I don't have control over.
There is no API available unfortunately for the se... | When talking to an external system you are building an integration. When you integrate with someone, this someone does not become part of your domain model.
As you mentioned, you have no control of that other database. If one day they change something in their tables, your whole application will become unusable and th... | I think at some point you are going to have to write two adapters. Interfaces are a great way to tie things together, but each model needs to access its own data.
I think you are on the rigjt path by seperating out the data access. If you have both models interact through an interface, adding more models in the f... | https://softwareengineering.stackexchange.com |
15,975 | [
"https://electronics.stackexchange.com/questions/15975",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4159/"
] | something has been bothering me for awhile. When I look at a circuit involving anything more complicated than RLC components (and perhaps op-amps) I struggle to figure out what it's doing unless its a configuration I've seen before.
In contrast, I feel pretty confident that no matter how complex an RLC circuit I'm giv... | Transistors are not hard to understand at the first approximation, and that is good enough to at least understand what's going on in many circuits.
Think of a NPN transistor this way: You put a little current thru B-E, and that allows a lot of current thru C-E. The ratio of a lot to a little is the transistor gain, ... | What makes transistors difficult to work with is that you have to be aware of lots of different parameters which influence each other, and none of which are linear. Therefore it's not easy to exactly model their behavior, and that's why we use simulation tools like SPICE. You still have to know what you're doing to des... | https://electronics.stackexchange.com |
28,123 | [
"https://chemistry.stackexchange.com/questions/28123",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/15312/"
] | What is palindromic DNA and why isn't every complementary strand palindromic?
I know AGCT is palindromic, but what is an example of a strand that isn't?
| A palindromic stretch of DNA is a strand whose reverse complement is itself. So <code>5'-AAAT-3'</code> is not palindromic. It's reverse complement is <code>5'-ATTT-3'</code>. Those two pieces of DNA are not identical. However, <code>5'-GGATCC-3'</code> is palindromic, because the reverse complement is identical.
| It has nothing to do with the complementarity (of the other strand).
Try this to figure out whether some sequences are palindromic:
<pre><code>#!/usr/bin/env python3
def is_palindromic(seq):
translation_table = str.maketrans('ACGT', 'TGCA')
translation = seq.translate(translation_table)
#print(seq, tran... | https://chemistry.stackexchange.com |
36,768 | [
"https://electronics.stackexchange.com/questions/36768",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8769/"
] | What is the best way to know the proper direction of current? Lets say we have this circuit below:
<img src="https://i.stack.imgur.com/GQK6h.png" alt="unknown directions">
The correct directions are given below:
<img src="https://i.stack.imgur.com/HrZQy.png" alt="enter image description here">
What are your techni... | No, the result won't be wrong. If you would have chosen the wrong direction the result will be negative, that's all.
It's not always easy to know in advance what direction the current will flow. Don't worry about it, just choose an arbitrary direction. Just make sure that you document your choice by drawing an arrow... | To illustrate just how <em>arbitrary</em> the reference direction of a current variable is, draw another arrow next to and in the opposite direction of \$ i_1\$ and label it \$ i'_1\$.
Now, note that it doesn't matter <em>which</em> current variable, \$ i_1\$ or \$ i'_1\$, you solve for since we have \$i_1 = - i'_1\$.... | https://electronics.stackexchange.com |
13,224 | [
"https://mechanics.stackexchange.com/questions/13224",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4192/"
] | The term Engine life factor going by the name suggests that higher the value more is the life of the engine. If so why doesn't companies specify this as a part of their standard specifications?
| ELF or Engine Life Factor is a calculated number:
<ul>
<li>ELF = 100,000/Max RPM x CR </li>
<li>where: RPM = Revs per minute and CR = Compression ratio</li>
</ul>
It is supposed to indicate the longevity of an engine by reducing the "number" by how fast the engine is able to run and what its numerical compression rat... | I wouldn't personally, I mean for example they try to make EFI a big deal. Here in NZ they were promoting Holdens/Potanics that they had EFI and that's how old now? So just guy with cars you know that have a good reliability behind them like Toyota or Nissan. If your looking at a performance car then read up on reviews... | https://mechanics.stackexchange.com |
242,413 | [
"https://electronics.stackexchange.com/questions/242413",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/114772/"
] | I have (4) 12V 190 Ah AGM batteries connected in series. I want to run a portable A/C unit through a 2000 watt inverter connected to those batteries and charge the batteries simultaniously with a battery charger powered by a generator. The A/C unit requires 7.5 amps continous and 15 amps surge. I would like to do this ... | There is no problem with having a load drawing power while a charger is charging the batteries. The charger is pushing power into the system and the A/C is taking it out again. Most of the power will be going straight from the charger to the A/C, but that just means that your battery array will take longer to charge as... | While this is possible, I also wanted to point out that you are converting AC to DC and then back to AC in this setup. That's a whole lot of lost power. The little "rev" you get when the compressor kicks on is a small price to pay for the extra fuel consumption! Best of luck.
| https://electronics.stackexchange.com |
1,329,840 | [
"https://math.stackexchange.com/questions/1329840",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/117084/"
] | <img src="https://i.stack.imgur.com/dsv0v.jpg" alt="enter image description here" />
<blockquote>
<strong>Text only:</strong>
A <span class="math-container">$2.2 \text{ m}$</span> wide rectangular steel plate is corrugated as shown in the diagram. Each corrugation is a semi-circle in cross section having a diameter of ... | <strong>Hint:</strong> One corrugation that takes the form of a semi-circle which has a diameter of $7 \text{ cm}$ as given by the problem. This means the arc length of one corrugation is half of the circumference, which is $\frac 12(2\pi (\frac{7 \text{ cm}}2))\approx 11.0 \text{ cm}=0.11\text{ m}$.
So $1$ corrugatio... | When corrugated,the length gets reduced by a factor $\dfrac{2 r}{\pi r}=\dfrac{2}{\pi} $.
Reduced length is 2.2 times above factor , calculating to 1.4 m approximately.
| https://math.stackexchange.com |
39,368 | [
"https://softwareengineering.stackexchange.com/questions/39368",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3666/"
] | TDD and unit testing seems to be the big rave at the moment. But it is really that useful compared to other forms of automated testing?
Intuitively I would guess that automated integration testing is way more useful than unit testing. In my experience the most bugs seems to be in the interaction between modules, and n... | One important factor which makes unit tests extremely useful is <em>fast feedback</em>.
Consider what happens when you have your app fully covered with integration/System/functional tests (which is already an ideal situation, far from reality in most development shops). These are often run by a dedicated testing team.... | All types of testing are very important, and ensure different aspects of the system are in spec. So to work backwards, "If I had to choose one type of testing..." I wouldn't. Unit testing provides me different feedback than integration testing or interactive testing by a person.
Here's the type/benefit of testing we... | https://softwareengineering.stackexchange.com |
110,660 | [
"https://physics.stackexchange.com/questions/110660",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21659/"
] | <ol>
<li>In an electroscope, you take metallic balls, and rub them with either a comb or a glass. Touching the balls with your finger is said to undo the effect of rubbing them with the comb or glass, since your finger is connected to ground, and ground is so enormous that it absorbs or releases the electrons to neutra... | It's not necessary to go into lot's of details here e.g. whether it's electrons that move or ions, or if it's some energy barrier that prevents a current from flowing or the mobility of ions or whatever. All those details are completely irrelevant to the question.
All you need to look at is resistance, capacitance, ch... | To understand this, you need to know a few things about electrons. It may help you in understanding situations like this.
<strong>Electrons Like Electrons of Opposite Spin</strong>
Yes, you read that right; electrons which have an opposite spin are attracted to each other. This is better explained using quantum mecha... | https://physics.stackexchange.com |
4,003,102 | [
"https://math.stackexchange.com/questions/4003102",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/791905/"
] | <blockquote>
Find the surface area above the xy plane which is defined by: <span class="math-container">$x^2+y^2+z^2=1, x^2+y^2 \leq x$</span>
</blockquote>
I am first trying to find a parameterization which should be simple enough to work with.
I though about using spherical coordinates:
<span class="math-container">$... | My teacher assigned us this problem in my multivariable calculus class and a classmate and I came to the conclusion that there must be a typo in the problem, because the two lines are skew. <br/> Using the two lines
<span class="math-container">$$
_1:=(−1,1,2)+(1,−3,−2)
$$</span>
<span class="math-container">$$
_2:=(1... | The vector joining points A(-1,1,2) and B(1,1,1) is <span class="math-container">$\vec L=-2i+k$</span> which lies on the plane. Another vector lying in the plane is given as <span class="math-container">$\vec U=i-3j-2k$</span> so the normal to the plane is given by <span class="math-container">$\vec N=\vec L \times \ve... | https://math.stackexchange.com |
642,791 | [
"https://electronics.stackexchange.com/questions/642791",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/318512/"
] | I assembled a homopolar motor based on YouTube videos. I got it to work like you see in the videos, but also slightly burned my fingers in the process. After "turning off" the motor (i.e. removing the copper wire) it took about 10 minutes before the battery and magnets cooled down enough to touch. What is gen... | 18 AWG wire has a resistance of ~6.4 ohms/1000 ft. Assuming you used 100 ft (very high estimate), the combination of the internal resistance of the battery and the wire is ~0.75 ohms, so you have about 2 A current draw, which is a lot to pull out of a AA that's designed for a current draw one or two orders of magnitud... | A hompolar motor is extremely inefficient. That is, the vast majority of the electrical power that goes into it is converted into heat. Very little of it goes into doing work (power out of the shaft). That's why your homopolar motor gets very hot, yet does not provide much torque or speed.
That is why the industry does... | https://electronics.stackexchange.com |
260,395 | [
"https://softwareengineering.stackexchange.com/questions/260395",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/153483/"
] | I'm 15 and have been programming for about 3-4 years. I mostly program in Java as it was my first language.
I would like to be a programmer when I'm older, but I'm not sure about the differences. I've used a website, named hackerrank.com, and struggled immensely on the EASY questions. I can program games, applications... | <blockquote>
If I were to be a programmer, would I have to be able to solve extremely difficult algorithms, or not?
</blockquote>
Maybe, maybe not. There are many professional programmers who do nothing noteworthy, yet are still employed (and horrible).
<blockquote>
I understand Computer Scientists would have to,... | Yes, many developers, especially in challenging fields such as video games or avionics, have to solve challenging logical and computing problems all day long. If this does not suit your taste or if you tend to have lesser logical capacities <em>than people of your age with equivalent experience</em>, then programming m... | https://softwareengineering.stackexchange.com |
174,606 | [
"https://physics.stackexchange.com/questions/174606",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | In undergrad I lost (a lot) of marks in my optics class for writing:
$$A(t) = \exp(i(\omega t + \phi))$$
Instead of:
$$A(t) = \exp(i(-\omega t + \phi))$$
In a derivation where I must have needed a plane wave. At the time I thought the TA was being pedantic. Both forms represent a plane wave and are mathematically ... | I don't think it's very likely, but one other thing I can think of: when the sign before the $\omega$ is a minus then the wave represents a wave travelling to the "right" - positive x direction - and maybe your TA wants only waves travelling to the right. ^^
In case you don't know why the minus sign represents a wave... | You may have lost marks for leaving out the imaginary unit $i$. If not, then understand that <em>either</em> $e^{\pm i\,\omega\,t}$ can be used to represent the real signal with positive frequency $\omega$ - it's wholly a question of convention. But once you have made the choice you must stick with it and the choice ha... | https://physics.stackexchange.com |
202,530 | [
"https://softwareengineering.stackexchange.com/questions/202530",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/94740/"
] | I am creating a flowchart for a program with multiple sequential steps.
Every step should be performed if the previous step is succesful. I use a c-based programming language so the lay-out would be something like this:
<strong>METHOD 1:</strong>
<pre><code>if(step_one_succeeded())
{
if(step_two_succeeded())
... | Sacrificing code readability to save a few clock cycles is a clear sign of premature optimisation.
Your first aim should always be to write the best readable/maintainable code that gives a reasonable performance. Only after measurements have indicated that your N condition tests actually form a bottleneck for the over... | <blockquote>
And let's assume that checking a condition is 1 clock long and performing a step doesn't take up time.
</blockquote>
<em>No.</em>
Let's not make assumptions that completely skew the discussion. In reality, the steps take up time, most likely much, much more time than all the condition checking.
Whic... | https://softwareengineering.stackexchange.com |
636,232 | [
"https://electronics.stackexchange.com/questions/636232",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/184379/"
] | For an experiment I need to check a current sensor but I need to parallel too many resistors to achieve that without damaging the resistors. I don't want to do that. The PSU is 12 VDC, 10 A and I want to sink at least 5 A.
Is there a quick common way engineers use, or is an expensive, bulky resistor needed?
| Does the PSU have an (adjustable) current limit function? If so, then just short the output and adjust the current limit to the value you desire.
| Use a 55W car headlight bulb. That will take about 5A @12V
| https://electronics.stackexchange.com |
370 | [
"https://earthscience.stackexchange.com/questions/370",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/51/"
] | The Coriolis force predicts that winds in the northern hemisphere should be deflected in a clockwise pattern and winds in the southern hemisphere should be deflected in an anti-clockwise pattern. Why is it that in the case of cyclones however, the cyclones spin anti-clockwise in the northern hemisphere and clockwise i... | Don't think of the Coriolis force as deflecting motion clockwise/counter clockwise, but to the right (NH) or left (SH), when looking in the direction of the motion.
So this is sort of 'by definition'. A cyclone is a <em>low</em> pressure system, and air will move from a location with high pressure towards a location w... | To correct your phrasing slightly: The Coriolis force acts to turn flows in the northern hemisphere to the right. This is not <em>quite</em> the same as "in a clockwise pattern", as will become evident in a moment.
Cyclones have a low pressure core and higher pressure outside. Therefore, the wind is flowing from the o... | https://earthscience.stackexchange.com |
47,176 | [
"https://softwareengineering.stackexchange.com/questions/47176",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17066/"
] | In my experience interviewing developers I feel like candidates who've achieved a Masters in Comp Sci tend to be <strong>worse</strong> programmers on average that those who don't have a Masters.
Is that just me, or have others noticed this phenomenon? If so, why would that be the case?
<strong>UPDATE</strong>
I app... | First of all, people with a Master's come in different varieties:
<ol>
<li>A fresh graduate from a Master's
program</li>
<li>A Ph.D. student, who quit the program and left with the Master's</li>
<li>Someone who got a Master's years ago, and who has had lots of experience since then</li>
<li>Someone who has worked for ... | I feel like nobody is going to mention it so let me do it.
In some countries a Bachelor degree is not de-facto accepted in the society. Universities though came through to follow the recommendations of the Bologna process and implement the two-stage education system (Bachelor + Master), the companies and older folks d... | https://softwareengineering.stackexchange.com |
253,663 | [
"https://mathoverflow.net/questions/253663",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23758/"
] | Let $L/K$ be a Galois extension (I am interested in $\overline{\mathbb{Q}}/\mathbb{Q}$ so I do not assume it to be finite).
Let $V\subset L^n$ be a $L$-subvector space, of dimension $d$, such that $g(V)=V$ for each $g\in \mathrm{Gal}(L/K)$. Do you have a reference for the fact that the dimension of the $K$-vector spac... | What you need is the corollary on the bottom of page 60 of Bourbaki, <em>Algèbre</em>, chapitre V : Corps commutatifs ; section 10 (Extensions galoisiennes), subsection 4 (Descente galoisienne).
The statement given there is more precise: given an <span class="math-container">$L$</span>-subspace <span class="math-conta... | Just to elaborate on Adel BETINA's comment, $V
\cap K^n$ is exactly $V^G$, so the part "$f$ is one-to-one" of the proof of Theorem 2.14 in Conrad's text does the job, because from $L\otimes_K V^G\cong V$ follows $\dim_LV=\dim_KV^G$.
| https://mathoverflow.net |
1,953,086 | [
"https://math.stackexchange.com/questions/1953086",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/27385/"
] | Do there exist differentiable almost-everywhere functions on $\mathbb{R}^n \rightarrow \mathbb{R}^n$ such that $\frac{|\langle x, y \rangle|}{|x||y|} \geq \frac{|\langle f(x), f(y) \rangle|}{|f(x)||f(y)|}$? How does one go about constructing one?
| I claim that those maps are precisely those that preserves lines through the origin, followed by an orthogonal movement.
For $n=1$, the condition is void (except that we demand $0\mapsto 0$ perhaps?) and hence the claim holds.
Your inequality demands that image vectors are "at least as orthogonal" as the input vector... | The map on the plane in polar co-ordinates $ (r,\theta)\mapsto (r^2,2\theta)$ is an angle-magnifier.
| https://math.stackexchange.com |
5,209 | [
"https://mathoverflow.net/questions/5209",
"https://mathoverflow.net",
"https://mathoverflow.net/users/498/"
] | There are a few standard notions of matrix derivatives, e.g.
<ul>
<li>If <em>f</em> is a function defined on the entries of a matrix <em>A</em>, then one can talk about the matrix of partial derivatives of <em>f</em>.</li>
<li>If the entries of a matrix are all functions of a scalar <em>x</em>, then it makes sense to ... | There is another interpretation of Elisha's question that I think has not yet been addressed: How, and to what extent, can you do differential calculus with functional expressions of square matrices? For instance, how do you differentiate $\exp(A)$, which is defined for all square matrices $A$?
There is a good answe... | In the first case, there is no difficulty in working with higher derivatives. All you have is a function $f$ of $n^2$ variables $a_{ij}$, and you can form and work with derivatives like $\partial^3f/\partial a_{12}\partial a_{23}\partial a_{34}$ with reckless abandon. Don't let the double indices worry you.
A more abs... | https://mathoverflow.net |
580,868 | [
"https://physics.stackexchange.com/questions/580868",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/237222/"
] | It is my understanding that
<ol>
<li>Hawking radiation is observed by external observers, and
</li>
<li>A necessary condition for having Hawking radiation is the formation of an event horizon during a gravitational collapse.
</li>
</ol>
Since the emergence of an event horizon takes infinite time for an observer far awa... | <h2> External observers and black hole formation </h2>
The event horizon is simply the delineation between the part of spacetime from which light can escape and the part of spacetime from which it cannot. In that sense, it is not directly observable, neither by external observers nor by infalling observers. Still, an e... | Hawking radiation comes from <em>the space outside of the event horizon</em>.
And the event horizon forms as the actual black hole forms. So what is necessary first, is the formation of the black hole, which also forms an event horizon, then phenomena such as Hawking radiation can be considered. And for a distant obser... | https://physics.stackexchange.com |
216,732 | [
"https://physics.stackexchange.com/questions/216732",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/97649/"
] | I am trying to prove some properties of the product of the (unitary) translation operator $\hat{T}(a)\psi(x) = \psi(x-a)$ and the (Hermitian) reflection operator $\hat{R} \psi(x) = \psi(-x)$. In particular, I want to show that $\left(\hat{R}\hat{T}(a)\right)^\dagger$ is both Hermitian and unitary.
Is it correct just ... | <blockquote>
As far my limited knowledge go, things in space aren't slow down
unless something interferes with them, so what prevents me to build a
spaceship powered by nuclear power that will keep accelerating until
we get to the limits of physics?
Like the voyager ship that is now outside our solar syste... | <blockquote>
Wouldn't that greatly reduces the time you need to get to a distant star, since you can increase your speed exponentially?
</blockquote>
In addition to <em>hft's answer</em>, due to relativistic kinetic energy $KE$ , assuming you use high constant thrust your actual <em>acceleration</em> would start tai... | https://physics.stackexchange.com |
445,158 | [
"https://electronics.stackexchange.com/questions/445158",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/138543/"
] | I am working with a large ring launcher and a capacitor bank that has the potential to charge up to 3000 volts in a bank of capacitors totaling 12,000 μF. I need to provide a sort of tap to measure the current capacitor bank voltage outside the circuit with a meter. First thought was a 10:1 voltage divider but I'm w... | Sounds like you need a 1000:1 potential divider with a very high impedance.
A simple resistive divider chain using resistors of a very large value plus an opamp with a high impedance input will work. e.g. Use 1G ohm resistor made of 5 x 200 Meg 1206 resistors, and a single 1 Meg 1206 resistor at the bottom of the cha... | A 1000:1 voltage divider night be better. Make sure your series resistor has an adequate voltage specification. If you don't want to buy high voltage resistors, then often what folks do is put several ordinary ones in series. You are unlikely to run your cap bank down too quickly with (say) 10 off 10Meg resistors in se... | https://electronics.stackexchange.com |
614,801 | [
"https://physics.stackexchange.com/questions/614801",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/207730/"
] | A rifle is fired, and the bullet moves much faster than the rifle, and momentum is conserved.
My question is whether the kinetic energy of the bullet is greater than the kinetic energy of the rifle because the mass of it is smaller, therefore the force acting on it (for the same time it acts on the rifle) results in gr... | Conservation of momentum implies
<span class="math-container">$$mv+MV=0$$</span>
where <span class="math-container">$m$</span> and <span class="math-container">$v$</span> are the mass and speed of the bullet, <span class="math-container">$M$</span> and <span class="math-container">$V$</span> of the rifle. Of course, it... | In effect you are asking what the nature of kinetic energy is.
After the rifle has been fired the bullet and the rifle have the same momentum - in opposite direction. In that sense we can say that momentum is equally shared.
To get a closer look at what kinetic energy is I propose the following demonstration: you set u... | https://physics.stackexchange.com |
33,378 | [
"https://softwareengineering.stackexchange.com/questions/33378",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12155/"
] | <em>disclaimer: for simplicity sake, brackets will refer to brackets, braces, quotes, and parentheses in the couse of this question. Carry on.</em>
When writing code, I usually type the beginning and end element first, and then go back and type the inner stuff. This gets to be a lot of backspacing, especially when doi... | I start out like this <code>{}</code>, then usually fill them with something. Whenever you type <code>{</code>, type a corresponding <code>}</code> and stick it on a new line. The worst thing you have to do in that case is fix indentation prior to committing.
<em>Good</em> syntax highlighters will often alert you to a... | <strong>Indentation</strong>
One-liners like that do introduce a bit of a hazard in terms of keeping the brackets correctly matched. Most decent editors will match the brackets visually to help, but it is easier to expand it.
<pre><code>(function($) {
$('#element[input="file"]').hover(function() {
$(this... | https://softwareengineering.stackexchange.com |
431,083 | [
"https://mathoverflow.net/questions/431083",
"https://mathoverflow.net",
"https://mathoverflow.net/users/130484/"
] | Given <span class="math-container">$\ell\ge 1$</span>, we say a graph <span class="math-container">$G$</span> is <span class="math-container">$\ell$</span>-good if for each <span class="math-container">$u,v\in G$</span> (not necessarily distinct), the number of walks of length <span class="math-container">$\ell$</span>... | A graph without loops cannot be good.
Assume the contrary, let <span class="math-container">$G$</span> have <span class="math-container">$n$</span> vertices and be good.
Let <span class="math-container">$A$</span> be the adjacency matrix of <span class="math-container">$G$</span>, let <span class="math-container">$\lam... | Here is a combinatorial argument; surely, it can also be rewritten in an algebraic way using the adjacency matrices.
As usual, <span class="math-container">$N(v)$</span> denotes the set of vertices adjacent with <span class="math-container">$v$</span>. We also denote by <span class="math-container">$f_n(u,v)$</span> t... | https://mathoverflow.net |
200,329 | [
"https://softwareengineering.stackexchange.com/questions/200329",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/5578/"
] | We are doing agile software development, basically following Scrum. We are trying to do sprint reviews but finding it difficult. Our software is doing a lot of data processing and the stories often are about changing various rules around this.
What are some options for demoing the changes that occurred in the sprin... | During the sprint you create value. There is always some difference between what you had at start and end of sprint. Normally even in a way noticeable by the client. So just show the difference.
in some cases the sprint deals with discovery or internal rearrangements that may sound subtle, still you must be able to ... | My own personal preference for things that do back-end work is to find the end-user change. If the data you are processing eventually winds up in a report, show the before/after differences in the report.
I'm assuming the desire for the change came from a need. What was the problem that triggered the need to do the ... | https://softwareengineering.stackexchange.com |
49,170 | [
"https://mathoverflow.net/questions/49170",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5756/"
] | It's known that all abelian groups are regularly realizable over $\mathbb{Q}(x)$, but it occurred to me that I don't even have an example of a cyclic regular extension of $\mathbb{Q}(x)$ handy.
So: what is an example of a regular realization of $C_5$ over $\mathbb{Q}(x)$?
| Emma Lehmer's quintic
\begin{align*}
y^5 +& x^2y^4 - (2x^3 + 6x^2 + 10x + 10)y^3 +\\
&(x^4 + 5x^3 + 11x^2 + 15x + 5)y^2 + (x^3 + 4x^2 +10x + 10)y + 1
\end{align*}
has Galois group $C_5$ over ${\mathbf Q}(x)$ and the splitting field over ${\mathbf Q}(x)$ is a regular extension. Her paper is "Connection between ... | I wanted to make a certain comment, but it got too long, so here it is as an "answer" that is constructive in principle (and applicable over any field of characteristic 0, suitable to make cyclic regular covers ramified in a controlled locus).
Let $k$ be a field of characteristic 0 and let $X$ be the projective line o... | https://mathoverflow.net |
100,785 | [
"https://chemistry.stackexchange.com/questions/100785",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/67106/"
] | I know that Hess's law is an indirect way to find the heat of reaction using the known heat of reaction of 2+ thermochemical equations, thus the formula is delta heat of reaction = enthalpy of formation (product)- enthalpy of formation(reactant). But then, bond enthalpy also finds the change in heat of reaction with th... | You are confused as to why we take "reactants minus products" when calculating the enthalpy of reaction based on bond enthalpies.
Consider as reference state all your reactants and products in their <em>atomic states</em>, that is, with all bonds broken. Forming a bond releases energy, so the reactants and products al... | ΔH of a reaction in terms of bond enthalpies = Σ bond enthalpies (products) - Σ bond enthalpies (reactants).
Therefore if the products are at a lower energy than the reactants, the reaction would be exothermic therefore ΔH would be negative.
| https://chemistry.stackexchange.com |
59,266 | [
"https://physics.stackexchange.com/questions/59266",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/16191/"
] | The following question is from an physics exercise and I know the answer and the way to solve the problem but just curious why my own way doesn't work. The question is asking "A 2500kg space vehicle, initially at rest, falls vertically from a height of 3500km above the Earth's surface. Determine how much work is done b... | You can't derive the existence or magnitude of diamagnetic properties just from unpaired electrons. On the contrary, diamagnetism mostly comes from the complete shells. They behave as electric current loops that orient themselves in a certain way in the external magnetic field.
Copper has lots of these complete shells... | What is missing here ist the relation to physical/chemical
status of that "copper".
What are You talking about? Copper metal? Copper
atoms as vapour? Copper ions I or II in aqueous
solution?
As a matter of fact, copper atoms are paramagnetic
(one unpaired electron is enough despite the number of
the paired ones!... | https://physics.stackexchange.com |
430,046 | [
"https://electronics.stackexchange.com/questions/430046",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/215725/"
] | I cannot understand the reason for cutting off radio waves with metal mesh.
I do not understand the theory that holes are small enough for wavelengths .
I think the wavelength is vertical to the hole, but is it related to the size of the hole in the horizontal direction?
The amplitude of the wave of the radio wave... | I can provide an easier answer, though I suppose it will just make you ask more of them.
In a metal, you can imagine that there is a veritable ocean of freely mobile (so-called conduction band) electrons available in the metal. (It's why it conducts so well.) Simplified, you can almost imagine these as a gas, in fact.... | A summary answer:
For the signal to get past the mesh, each hole in the mesh must act like a very short waveguide. But if the signal wavelength is too long, then these tiny waveguides will be "cut-off" and not able to pass the signal through to the other side. Mathematically this can be explained in terms of the bound... | https://electronics.stackexchange.com |
4,516,901 | [
"https://math.stackexchange.com/questions/4516901",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1085309/"
] | I'm studying the peoperties of the SVD decomposition <span class="math-container">$A = U\Sigma V^T$</span> and have run into the following statement:
<span class="math-container">$\Delta A := -\sigma_n u_n {v^T}_n $</span> is the smallest possible perturbation such that <span class="math-container">$A + \Delta A$</span... | Assume A is <span class="math-container">$n×n$</span> of full rank. The problem you want to solve is
<span class="math-container">$$ \min_{∆A} ‖{∆A}‖_F \qquad\text{such that}\qquad \operatorname{rank}(A+{∆A})=n-1$$</span>
Substituting <span class="math-container">$B≔A+{∆A}$</span>, this is equivalent to
<span class="ma... | For any <span class="math-container">$\Delta A$</span> that makes <span class="math-container">$A+\Delta A$</span> singular, pick a unit vector <span class="math-container">$x$</span> in the null space of <span class="math-container">$A+\Delta A$</span>. Then <span class="math-container">$Ax=-\Delta Ax$</span> and we m... | https://math.stackexchange.com |
126,652 | [
"https://softwareengineering.stackexchange.com/questions/126652",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/33490/"
] | Should the expected results of a unit test be hardcoded, or can they be dependant on initialised variables? Do hardcoded or calculated results increase the risk of introducing errors in the unit test? Are there other factors I haven't considered?
For instance, which of these two is a more reliable format?
<pre><cod... | I think calculated expected value results in more robust and flexible test cases. Also by using good variable names in the expression that calculate expected result, it is much more clear where the expected result came from in the first place.
Having said that, in your specific example I would NOT trust "Softcoded" me... | What if the code was as follows:
<pre><code>MyTarget() // constructor
{
Field1 = Field2 = Field3 = Field4 = "";
}
</code></pre>
Your second example wouldn't catch the bug, but the first example would.
In general, I'd recommend against soft-coding because it may hide bugs. For example:
<pre><code>string expected... | https://softwareengineering.stackexchange.com |
995,312 | [
"https://math.stackexchange.com/questions/995312",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/122012/"
] | For an $n$-dimensional ellipsoid in $\mathbb{R}^n$ centered at $\mathbf{0}_n$, defined by a set of vectors $\mathbf{v}_i$ giving the directions of the principle axes and $\lambda_i$ representing the corresponding magnitudes of each axis (for $i=1,\ldots, n$), is there a straightforward way to work out the maximal $x$-c... | First, rewrite the equation of your ellipsoid using matrices:
$$\sum_{i=1}^n \frac{(\vec{x} \cdot \vec{v}_i )^2}{\lambda_i^2} = 1
\quad\iff\quad
\vec{x}^T \Lambda\,\vec{x} = 1
\quad\text{ where }\quad \Lambda = \sum_{i=1}^n\frac{\vec{v}_i \otimes \vec{v}_i}{\lambda_i^2}
$$
where $\otimes$ stands for outer product betw... | The problem is to maximize $\langle x,e_1\rangle$ subject to $\sum_i \lambda_i^2\langle x,v_i\rangle^2 = 1$. (Well, $\le 1$, but by convexity the extreme value is attained on the boundary.) Since the $v_i$ are an orthonormal basis,
$$ \langle x,e_1\rangle = \sum_i \langle x,v_i\rangle \langle e_1,v_i\rangle
= \sum_i ... | https://math.stackexchange.com |
112,280 | [
"https://security.stackexchange.com/questions/112280",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/39952/"
] | When setting the bad chars for shell code, is there any downside to just assuming that you should mark \x00 and \x0a as bad?
| For shellcode the only potential issue is size constraints. But assuming null bytes are bad is a bad habit. You might mistakenly think a crash is not exploitable because the only viable pop pop ret/ROP addresses start with a null byte.
Determining exact bad bytes isn't too time consuming and I always recommend doing i... | Not generally, since NULL and Line Feed are always bad chars. But size of your code will increase. I would not automatize this tho.
For example in IA32 Assembler you can replace the instruction
<pre><code>B8 01000000 MOV EAX,1 // Set the register EAX to 0x000000001
</code></pre>
With
<pre><code>33C0 ... | https://security.stackexchange.com |
4,570,497 | [
"https://math.stackexchange.com/questions/4570497",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/539780/"
] | <span class="math-container">$$A = \left(
\begin{array}{cccc}
1 & 3 & 1 & 0 \\
1 & -1 & 2 & 1 \\
1 & 0 & 1 & 1 \\
0 & 1 & 0 & 2 \\
\end{array}
\right)$$</span>
Its determinant is <span class="math-container">$7$</span> for I used Laplace method. I checked and it's <sp... | Assuming your sampling is with replacement it is easier to note that the chance of each digit is <span class="math-container">$\frac 1{10}$</span>. You draw the first number and note the units digit. The chance you get that units digit on the second draw is <span class="math-container">$\frac 1{10}$</span>, so that i... | Yes, your solution is correct, although your countings need just a bit more formal justification. Here is how you can formally write the solution.
There are <span class="math-container">$9\times 10$</span> ways to choose a 2-digit number (<span class="math-container">$9$</span> for the tens digit, <span class="math-con... | https://math.stackexchange.com |
17,717 | [
"https://bioinformatics.stackexchange.com/questions/17717",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/10296/"
] | I have written a rule for CombineGVCFs in gatk4. The rule is as follow
<pre><code>all_gvcf = get_all_gvcf_list()
rule cohort:
input:
all_gvcf_list = all_gvcf,
ref="/data/refgenome/hg38.fa",
interval_list = prefix+"/bedfiles/hg38.interval_list",
params:
extra = "--variant&qu... | Found out the problem. Turns out I can write a lambda function as follows
<pre><code>params:
extra=lambda wildcards, input: ' -V '.join(input.all_gvcf_list)
</code></pre>
and add '-V' before {params.extra} in the "shell" sction. That solves the problem
| well I came up with the solution. I think it is a little unconventional.
<pre><code> rule gatk_CombineGVCFs:
input:
vcf_dummy = expand("gvcf/{sample}.g.vcf.gz", sample = SAMPLES), # a dummy vcf to connect this rule to gatk_HaplotypeC... | https://bioinformatics.stackexchange.com |
481,039 | [
"https://electronics.stackexchange.com/questions/481039",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/242554/"
] | I have seen in certain problems, they say that <span class="math-container">$$I_E = I_C$$</span> by saying that β is very large. I don't understand what can be considered as large β. So, I want to know the range of the values for β for which I can say <span class="math-container">$$ I_E = I_C $$</span>
| You probably already know that the emitter current <span class="math-container">\$I_E\$</span> is actually the sum of the collector current <span class="math-container">\$I_C\$</span> and base current <span class="math-container">\$I_B\$</span>
<span class="math-container">\$I_E = I_C + I_B\$</span>
Now if we know th... | It's a fuzzy line when something becomes small enough to be insignificant (in this case it is actually Ib relative to Ic, via large beta). It is up to your judgement, not a well-defined threshold. Sometimes it is 1:10 (should probably never be less than this), sometimes you can get away with 1:20 or 1:50, sometimes you... | https://electronics.stackexchange.com |
400,292 | [
"https://softwareengineering.stackexchange.com/questions/400292",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/349803/"
] | I'm having a architecture challenge. Simplified scenario:
We have a CRM-system (for now called This-Is-Our-CRM) that contains person data. We created a rest API so our data could be accessed outside of our own system.
Now our clients wants to be able to use the data available in This-Is-Our-CRM in multiple other appl... | Option 1 provides better security, as all requests must be routed through a gateway that you control.
Option 1 provides better maintainability; it is a single point of modification, and a simpler design. If you're worried about flexibility, use a plugin architecture to add new applications to it.
Option 2 provides l... | Both approaches are equally valid, for the reasons you already expanded on.
Additional thoughts:
Option 1 gives the organization the ability to address a problem once. Not every one who needs Salesforce or MailChimp data needs to know how the API and data structures work which could overall reduce development time an... | https://softwareengineering.stackexchange.com |
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