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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52,767 | [
"https://physics.stackexchange.com/questions/52767",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/20486/"
] | I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding.
The Problem:
A Particle sits in an infinite potential well described by
\begin{align}
V(x) &= 0, & 0 \leq x \leq L \\
V(x) &= \infty, & \text{otherwise}
\end{align}
We ... | The expectation value of the energy stays the same after the doubling of size but it doesn't mean that the spectrum is the same. For a normalized $\psi$, the expectation value of the energy is simply
$$ \int_{-L}^{+L}dx\,\psi^* \left( -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x) \right) \psi $$
because t... | Under sudden perturbation the state does not change, but the basis does. This state gets expanded in the new basis whose coefficients evolve correspondingly. Normally it is covered in chapters with the time-dependent perturbation theory $\hat{V} = \hat{V}(t)$.
If the potential is time-dependent, the energy is not cons... | https://physics.stackexchange.com |
115,791 | [
"https://softwareengineering.stackexchange.com/questions/115791",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/39235/"
] | I'm confused about the PO's responsibility here. I was a developer on a Game Feature Team, but also a PO. The daily work of the developer is almost full time, so I have to work over time to take care my PO duty, and the responsibility of PO seems to be against developer's thoughts.
As a PO, I will chose more features... | It might seem as a bit akward but there really shouldn't be any reason for these roles to be combined. For one, someone has trusted you with this role, therefore your team has to respect that. Secondly you are now in a position where you can prioritze the work that has to be done so you can always explain why things ar... | In my experience, the product owner is either a PM/TPM or a member of the business team. While it isn't impossible for the PO to be a dev, there is some danger of conflict of interest. If your product is highly technical, the PO should have a dev background. If it is less technical and more end-user focused, then a PO ... | https://softwareengineering.stackexchange.com |
319,629 | [
"https://softwareengineering.stackexchange.com/questions/319629",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/186497/"
] | Given
<pre><code><div>
<textarea></textarea>
</div>
</code></pre>
Why is this
<pre><code><div>
<textarea class="width90"></textarea>
</div>
.width90{
width:90%;
}
</code></pre>
any better than this?
<pre><code><div>
<textarea style="width:90%;"&... | Looking at your updated question,
<blockquote>
Why is this
</blockquote>
<pre><code><div>
<textarea class="width90"></textarea>
</div>
.width90{
width:90%;
}
</code></pre>
<blockquote>
any better than this?
</blockquote>
<pre><code><div>
<textarea style="width:90%;"&g... | <strong>In layman's terms:</strong>
<ul>
<li>Because when you have <strong>a lot of pages</strong> with <strong>a lot of inline styling</strong>, and <strong>some user askes for cosmetics change</strong>, the you will have to make a lot of changes in a lot of places, and chances are you will miss something. </li>
<li>... | https://softwareengineering.stackexchange.com |
154,253 | [
"https://mathoverflow.net/questions/154253",
"https://mathoverflow.net",
"https://mathoverflow.net/users/45379/"
] | Let $\Omega$ be a bounded $C^1$ domain with bounded boundary $\partial\Omega$. Can someone point me to a reference where the surface integral of a measurable function $f\colon \partial\Omega \to \mathbb{R}$ is defined:
$$\int_{\partial\Omega} fdS = ?$$
without the use of a transformation of coordinates in the sense tha... | Take any piecewise continuous function $f$ defined on the boundary $\partial \Omega$, and extend $f$ to be constant along all lines perpendicular to the boundary, at least until those lines collide with one another. If $\partial \Omega$ is compact, this extends $f$ to some $\varepsilon$-neighborhood, as long as $\parti... | A general way to define this is to use rectifiable sets. For example, if $\Omega$ is a set of finite perimeter, measurable functions and their integrations are well defined. Moreover, the divergence theorem holds in this setting. You can check the book of Giusti on BV functions or Washek F. Pfeffer's "The Divergence Th... | https://mathoverflow.net |
277,279 | [
"https://softwareengineering.stackexchange.com/questions/277279",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/69409/"
] | I've been writing web applications for a while now , and everyone knows the one golden rule not to assign variables to the window object , don't ever assign a variable without using <code>var</code>.
My question is, why not? In my opinion it is a lot easier especially nice in SPA's to attach objects to the global sc... | For a few reasons:
<ul>
<li>It often forces you to choose longer names, where a shorter one would be more clear and concise within a limited scope. For example, <code>filter</code> versus <code>MyModuleNameFilter</code>.</li>
<li>The process of "taking the responsibility to make sure you have very good names and they... | Because global variables have global scope, they are visible, and mutable, by anything that runs on the page. That introduces implicit coupling between all code running on the page; everything could interact with everything.
That runs contrary to the concept of encapsulation. If your code and variables are local in sc... | https://softwareengineering.stackexchange.com |
96,904 | [
"https://electronics.stackexchange.com/questions/96904",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/22551/"
] | I'm working on a project with lots of op amps and so far had no problem but this one is driving me nuts. I need a 1:2 non-inverting amplifier which I built on breadboard but doesn't work as expected. The circuit is trivial, I tried different op amps (LM741,TL072,LM358), use a rail-splitter or just a voltage divider for... | You have nothing setting the operating point of your positive input to the op-amp. As such the input bias current of the op-amp is causing C1 to charge up to one of the rails, and it's therefore cutting off part of your signal.
This issue will likely be exaggerated in simulations as well, since few simulations properl... | It appears that you are referencing ground for V1 (which implies that V1 goes negative at some point), and you are using a virtual ground for a reference and a rail-splitter to set the reference at 4.5V. I am assuming that this means you are using a single-supply setup (op amp Vcc is connected to 9V and Vee is connecte... | https://electronics.stackexchange.com |
3,235,846 | [
"https://math.stackexchange.com/questions/3235846",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/539257/"
] | I'm currently trying to prove the inequality
<span class="math-container">$$n^2<n(n+2)<(n+1)^2$$</span>
Is it possible to solve this without induction?
| Expanding we get <span class="math-container">$$n^2<n^2+2n<n^2+2n+1$$</span>
Can you proceed?
| <span class="math-container">$n(n+2)-n^2=2n>0$</span>
<span class="math-container">$(n+1)^2-n(n+2)=1>0$</span>
| https://math.stackexchange.com |
147,322 | [
"https://dba.stackexchange.com/questions/147322",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8165/"
] | I need to run a query against a database and group the records by different date ranges. The data type of the date field is <code>varchar</code> and in the format <code>dd-MMM-yyyy</code> e.g. <code>19-Aug-2016</code>.
The date ranges are as follow: <code>13–18</code>, <code>19–35</code>, <code>36–55</code> and <code... | First let me say storing dates in a character column is a horrible horrible idea. Sorts won't work correctly, any form of date calculations are going to require actually casting back to a date anyway, and best of all you probably have bad data in there.
But assuming your table isn't overly large (performance on this ... | Without seeing additional information (and without flat out giving you the answer): I'd suggest to start by adding a CASE statement that will return a "DateGroup" value for each record.
This "DateGroup" value should have all of the DATEDIFF or Date Parsing Functions you're looking to run, and should return your requ... | https://dba.stackexchange.com |
83,993 | [
"https://stats.stackexchange.com/questions/83993",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/38024/"
] | I just wonder what is the difference between <strong>Random Forests</strong> and <strong>MART</strong> (Multiple additive regression trees)?
I have read a few articles, e.g.:
<blockquote>
[1] L. Breiman. Random Forests. Machine Learning 45 (1): 5–32, 2001.<br>
[2] J.H. Friedman. Greedy function approximation: ... | First question
When you consider the prediction error through bias-variance decomposition you face the well-know compromise between how well you fit on average (bias) and how stable is you prediction model (variance).
One can improve the error by decreasing the variance or by increasing the bias. Either way you choos... | We can understand them from the training data.
Random forest is to learn different trees based on partial training data, where the training data sets are drawn from the raw data set and the attribute at each split is on random. It encourages the diversity of samples.
The MART or generally boosting usually train a sing... | https://stats.stackexchange.com |
235,998 | [
"https://stats.stackexchange.com/questions/235998",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/95537/"
] | How many cycles should I have in my time series to model the seasonality component of it so that I can get rid of it and just look at the trend?
| Let's say you have $N$ years of monthly data. Think of FFT (fourier analysis). Your bin resolution is $F/N$, where $F$ - sampling frequency, so we get $12/(12N)=1/N$
So, if your $N=1$, i.e. you have 12 observations, you bin size is 1. This means that your precision is approximately 1. Basically, this is garbage. If yo... | This is a "how long is a piece of string" question, i.e. one that can't be given an objective, quantitative answer without more context. @Aksalal has a nice technical explanation, but your question is effectively the same as "how many data points do I need to characterize the population mean?" - i.e., it depends how no... | https://stats.stackexchange.com |
337,115 | [
"https://softwareengineering.stackexchange.com/questions/337115",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/193831/"
] | <strong>Here is a bit of context:</strong>
I am practicing TDD for a new application that will target .NET 3.5 CF and .NET 4.5.2 FF.
I might have some part of the code that use polymorphisme to decide at run-time a strategy (the design pattern) to use while running on a .NET 3.5 CF machine and an another running on a... | <em>Stop linking the code files.</em>
Instead, start extracting the shared files into actual class libraries that target 3.5. If you're already sharing them between projects, then they must already compile with that version of the compiler. Remember, you can always reference a library built against an older version of... | If there are (expected to be) files that are specific for one of the supported platforms or features that intentionally behave differently on the different platforms, then you should definitely test those parts on both platforms.
Besides that, it is a question of effort versus risk if you want to test the rest on both... | https://softwareengineering.stackexchange.com |
9,231 | [
"https://dba.stackexchange.com/questions/9231",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5127/"
] | I'm running into some unique constraint problems with my database. I can't reproduce them, but see error messages from our production system:
<pre><code>exception 'UniqueViolation' with message
'SQLSTATE[23505]: Unique violation: 7 ERROR:
duplicate key value violates unique constraint...'
</code></pre>
Whe... | I'm not sure how to make those visible in 8.3 except with this:
<pre><code>log_statement = all
</code></pre>
That's going to put a lot of data in to your logs though, so you may not want to keep it turned on for long. Also make sure you have the process ID included in your log_line_prefix if you want to match everyt... | One solution would be to upgrade to PostgreSQL 8.4 or higher. Preferably to the current version 9.1.
If I provoke a unique violation in version 8.4, I get this message in the db log:
<blockquote>
postgres ERROR: duplicate key value violates unique constraint "foo_uni"<br>
postgres STATEMENT: update x.foo set fo... | https://dba.stackexchange.com |
64,268 | [
"https://dba.stackexchange.com/questions/64268",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/37716/"
] | I have database session enable, when website got thousands of visitor. It gives me error
<pre><code>[30-Apr-2014 04:27:12 America/Denver] PHP Fatal error: Uncaught exception 'PDOException' with message 'SQLSTATE[HY000]: General error: 1205 Lock wait timeout exceeded;
try restarting transaction' in public_html/lib/Ca... | If you wan't to check the queries/s in live you can use the mysqladmin tool with some options:
<pre><code>[root@db-prod-01 ~]# mysqladmin extended-status -uroot -p -i 1 -r | grep 'Com_insert '
Enter password:
| Com_insert | 59863746 |
| Com_insert | 1 ... | <code>Laravel Database Session</code> also caused similar issue. I think you can refer to it based on situation below:-
The <code>Garbage Collection</code> function of the <code>Laravel Database Session</code> to cause <code>sessions</code> table locked when performing <code>deletion</code> of the <code>expired session... | https://dba.stackexchange.com |
561,399 | [
"https://physics.stackexchange.com/questions/561399",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208833/"
] | I am trying to prove that the angular momentum component operator <span class="math-container">${L}_i$</span> commutes with any function of <span class="math-container">${r}\equiv \sqrt{{\textbf{x}}\cdot{\textbf{x}}}$</span>, i.e.
<span class="math-container">$$[L_i, f( r)]=0.$$</span>
I first worked out that <span ... | There are multiple ways of proving this, as other answers show. Here is another one. There is a general identity that states that if <span class="math-container">$[x, y]=0$</span>, then <span class="math-container">$[x,f(y)]=0$</span>, where <span class="math-container">$f$</span> is some function. The result you are a... | The answers given by Philip and Alexander are correct, but let me add another snippet of information: one could calculate the commutation in the polar coordinates! Then:
<span class="math-container">$$\hat{L}_i = \frac{\partial}{\partial \phi_i},$$</span>
whereas <span class="math-container">$f(r)$</span> is obviously ... | https://physics.stackexchange.com |
25,826 | [
"https://softwareengineering.stackexchange.com/questions/25826",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/934/"
] | Disclaimer: I do not specialize in [desktop] GUI design, but have to do it on occasion. I have seen co-worker's dialogs worse than the once I created, and my major problem with them is that they can be unnecessarily big, and things do not line up.
To be more specific, I mostly do it in .Net Winforms, but occasionally ... | If you want to go the "fixed spacing" way, multibles of 10 are ok. Switching down to multiples of 5 is only necessary when you run out of screen real estate. In one company I'm working for, we use a framework where multiples of 10 are the default setting in the (homegrown) GUI editor. Only in very rare occasions someon... | Forget about "nice round numbers", you will have to experiment with spacing to get something that looks nice, a fixed multiple just gets in the way.
I'd have to say that MSFT programs do tend to look pretty polished when it comes to such details, so despite your disbelief I would guess that the guide you found is prob... | https://softwareengineering.stackexchange.com |
231,609 | [
"https://softwareengineering.stackexchange.com/questions/231609",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/9113/"
] | I have a desktop application where the user has tabular views on some data records. Now we got the requirement to let the user select multiple of these records at the same time and let the him edit some properties of the selected records all at once in a separate edit dialog. The idea is
<ul>
<li>to change only the pr... | I agree that a checkbox could puzzle the user.
My reaction to the problem of how to display an undefined text box and differentiate it from a valid but empty one is to use a placeholder for the undefined one and an empty one for the other.
The valid empty box will look normal to the user and the normal-ness will be... | You could use the system used by Windows. If you open a dialog to edit multiple items, the entries where both pieces of data match is displayed with the data, where they differ a "" or similar string is displayed. The user must select an individual item to edit the multiple-value entries, or they can overwrite it which... | https://softwareengineering.stackexchange.com |
9,703 | [
"https://math.stackexchange.com/questions/9703",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/3356/"
] | My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. I have tried explaining it, but I guess not well enough.
How would you explain the concept to a child, other than the teachers "that is just the rule" approach?
| I want to extend the answer by @Qiaochu Yuan.
I assume the kid accepts $2\times 0 = 0$. In other terms:
"Some number <em>times</em> $0$ yields the no-changer of <em>plus</em>."
Analoguously:
"Some number <em>to the power</em> $0$ yields the no-changer of <em>times</em>."
By no-changer I refer, of course, to the u... | I will give a different answer than the answer I gave in the other thread which tries to appeal to intuition. I am sure your daughter has no problem accepting that $2\times 0 = 0$. Intuitively this is because if you add $2$ to itself zero times, you get zero. Or, to be concrete, if someone gives you two apples zero ... | https://math.stackexchange.com |
406,423 | [
"https://softwareengineering.stackexchange.com/questions/406423",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/359530/"
] | My company works in the field of public infrastructure in Europe, specifically as a software provider and operator. All of our development work is currently outhoused, to two main suppliers relevant for this question. Our company background is in the (semi) public sector, so some development methods take a little longe... | Your understanding is generally correct.
I really like your approach, because one of the big complaints I hear when I discuss pure Agile is "client needs to know exactly what will be done, when will it be done and how much will it cost". The fact that you are willing to accept that uncertainty and take the risk on you... | Agile is about continous feedback. You're going to be seeing the work in progress, and perhaps begin using it, very early on, and very often. Rather than meeting with the developers once a month or even less, you'll want to meet at least weekly -- but these should not be boring meetings, they are more like "demos" wher... | https://softwareengineering.stackexchange.com |
3,714 | [
"https://iot.stackexchange.com/questions/3714",
"https://iot.stackexchange.com",
"https://iot.stackexchange.com/users/8951/"
] | I am doing a home automation project in which I should be able to control the lights on/off but more than that, the brightness of the lights.
I am using Home Assistant (not hassbian) and Node-Red along with MQTT.
I am using a normal bulb I purchased from a hardware store connected to a Sonoff ESP8266 and am able to u... | No, you can't do that using Sonoff since it is an on-off switch with relay.
You need an Triac to do that. Normally the brightness control applications for AC will be done through Triac by changing the firing angle.
| No, most Sonoff devices are just remote controlled relays, they can only turn the power on or off.
You can not use them to dim lights.
| https://iot.stackexchange.com |
128,492 | [
"https://softwareengineering.stackexchange.com/questions/128492",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12206/"
] | I'm a growing programmer who's finally putting unit testing into practice for a library that I'm storing on GitHub.
It occurred to me that I might include the test suites in the repo, but as I look around at other projects, the inclusion of tests seems hit-or-miss.
Is this considered bad form? Is the idea that users ... | You definitely should put your tests into the repository. Tests are in my opinion part of the code and can help others immensely to understand it (if well written). Besides, they can help others when changing or contributing to your codebase. Good tests can give you the confidence that your changes do not inadvertently... | If you <em>don't</em> include the unit tests in the checked-in source code, then:
<ul>
<li>how is someone who downloads and builds their own copy of that code going to verify that it's working the way it was intended? Compiler and library bugs are rare, and data errors (particularly ones that don't render the source c... | https://softwareengineering.stackexchange.com |
5,440 | [
"https://mechanics.stackexchange.com/questions/5440",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/605/"
] | I have purchased a Mazda 323 which has approximately 90k km on the clock. While driving in the rain some water will come in above the brake pedal, approximately 5 or 6 drops during an average local journey (~10 km). A mechanic has said that the firewall has deteriorated and will cost a lot of money (~AU$800) to weld up... | The firewall is typically made up of metal with a layer of fire retardant material. There are holes through the firewall for necessary pipes, wires etc from the engine bay to the passenger compartment.
With old cars (much older than a Mazda 323) I have seen heavily rusted firewalls, but not seen anything like that rec... | My first concern would be getting the firewall inspected by a bodyshop. If it is that rusted the vehicle may not be safe to drive. In the event of a serious accident the firewall deflects the engine under the passenger compartment. In my experience most leaks are due to either a leaking windshield or as @Rory Alsop has... | https://mechanics.stackexchange.com |
29,420 | [
"https://electronics.stackexchange.com/questions/29420",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9098/"
] | So I saw a post talking about the commercial feasibility of an Arduino (http://electronics.stackexchange.com/questions/11333/commercial-use-of-arduino-is-it-suitable) . From this it said a great idea would be writing your own AVR Program i believe.
What does it mean to:
1) Write an AVR Program? What is an AVR Progra... | It's a broad question. I don't think the previous question was meant to imply that an Arduino isn't a 'real' or 'professional' development platform. It has its niche. Every microcontroller has its niche - you have to choose one that helps you do what you're trying to do. Does that sound vague? Yes. Because it all... | Write an Avr program means writing code and loading it to the AVR microcontrollers (*AVR family has many series of microcontrollers such as ATMEGA103, ATMEGA128, ATMEGA1280, ,,,,,, etc and also the popular controllers such as TMEGA8, ATMEGA16 etc....) using the softwares like AVR STUDIO, CODE VISION AVR etc..etc...
... | https://electronics.stackexchange.com |
673,829 | [
"https://physics.stackexchange.com/questions/673829",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/310662/"
] | All resources on standing waves give the same explanation: waves are free to move in and out of the open end of a pipe and, therefore, this open end must be an antinode. This, of course, explains why standing waves can only form in pipes with length <span class="math-container">$(2n-1)\lambda$</span> where <span class=... | Here is a physically intuitive way of thinking about this:
Because the end of the pipe is <em>open</em> (i.e., looking at the impedance of free air), a pressure maximum <em>cannot form</em> at the open end because there is a displacement degree of freedom there which a <em>closed end</em> doesn't have: the freedom to p... | It's good question: it clear why you must have a node at a closed end, and why you shouldn't have a node at the open end. But why do you have to have an anti-node? Couldn't you have neither, where the pressure amplitude is non-zero, but not maximal? I'll call it a "mixed-node" for sake of argument.
Let's call... | https://physics.stackexchange.com |
377,852 | [
"https://mathoverflow.net/questions/377852",
"https://mathoverflow.net",
"https://mathoverflow.net/users/157356/"
] | If <span class="math-container">$\varphi$</span> is a smooth function on <span class="math-container">$\mathbb{R}$</span>, then integration by parts implies that there exists a constant <span class="math-container">$C>0$</span> such that
<span class="math-container">$$
\Big|\int_0^1 \varphi(x)\, e^{i \lambda x}\, dx... | By the substitution <span class="math-container">$tx=u$</span>, the integral in question is
<span class="math-container">$$\int_0^1\frac{e^{itx}}{\sqrt x}\,dx=\frac1{\sqrt t}\,\int_0^t\frac{e^{iu}}{\sqrt u}\,du
\sim\frac1{\sqrt t}\,\int_0^\infty\frac{e^{iu}}{\sqrt u}\,du
=(1+i) \sqrt{\frac{\pi }{2}}\frac1{\sqrt t}$$</s... | You can first substitute <span class="math-container">$u=\sqrt{x}$</span> so that your integral is
<span class="math-container">$$\int_{-1}^1e^{i\lambda u^2}\,du.$$</span>
As <span class="math-container">$\lambda\to\infty$</span>, you can immediately see that most of the contribution from the integral will arise from r... | https://mathoverflow.net |
56,951 | [
"https://security.stackexchange.com/questions/56951",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/45693/"
] | While scanning my website with uniscan it found my <code>robots.txt</code> file which disallows access to <code>/cgi-bin/</code> and other directories, but they are not accessible in browser. Is there a way to access the directories or files which are Disallowed?
| The robots.txt does not disallow you to access directories. It tells Google and Bing not to index certain folders. If you put secret folders in there, Google and Bing will ignore them, but other malicious scanners will probably do the opposite. In effect you're giving away what you want to keep secret. To disallow fold... | The robots.txt file isn't a security measure and has no incidence on access permission.
This file only tells 'good' robots to skip a part of your website to avoid indexation. Bad robots don't even abide by those rules and scan all they can find. So security can never rely on the robots.txt file (that's not its purpose)... | https://security.stackexchange.com |
2,409,292 | [
"https://math.stackexchange.com/questions/2409292",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/475561/"
] | Which is the general formula of this sequence?
$$ x_0 = -1$$
$$ x_{n+1} = ((-1)^n*X_n)/2^n$$
What baffles me more is the sign which is like this: $--++--++--++--++\cdots$
I've been wondering how the sign could change like that, any ideas?
| Let $\,a_n=(-1)^{\lfloor n/2 \rfloor+1}\,$, then by direct computation $a_0=a_1=-1\,$, $a_2=a_3=1\,$, and:
$$
a_{n+4}=(-1)^{\lfloor (n+4)/2 \rfloor+1} = (-1)^{\lfloor n/2 + 2 \rfloor+1}=(-1)^2 \cdot (-1)^{\lfloor n/2 \rfloor+1}=(-1)^{\lfloor n/2 \rfloor+1} = a_n
$$
Therefore the sequence is periodic with period $\,4\... | You can easly prove by induction that $\forall n\in\mathbb{N},x_n\neq0$.
Now let $n\ge 1$. We have $\forall k\in\{0,..,n-1\},x_{k+1}=\left(\dfrac{-1}{2}\right)^kx_k$. Thus
\begin{aligned}
\prod_{k=0}^{n-1}x_{k+1}&=\prod_{k=0}^{n-1}\left(\dfrac{-1}{2}\right)^k x_k\\
\prod_{k=1}^nx_k&=\left(\dfrac{-1}{2}\right)^... | https://math.stackexchange.com |
51,324 | [
"https://datascience.stackexchange.com/questions/51324",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/45603/"
] | After performing clustering and detailed cluster analysis, I am confident that my clusters make sense.
Now, for each cluster, I would like to generate rules in the form of decision tree output. With this, I intend to achieve two things:
<ol>
<li>Most significant variables</li>
<li>Most significant combinations of varia... | I solved this issue with the help of @Franziska W. Thanks!
I currently reverse transform y_test and y_pred and then calculate the metrics as following:
<pre><code># qt_y is a QuantileTransformer instance, gb is a GradientBoostingRegressor
y_pred = gb.predict(X_test)
inv_y_pred = qt_y.inverse_transform(y_pred.reshape(... | Were your rescaled MSE and RMSE appear larger at the end? Should they be equal to the values before applying inverse transform?
| https://datascience.stackexchange.com |
5,649 | [
"https://biology.stackexchange.com/questions/5649",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/-1/"
] | I've read somewhere that after a person has a heart transplant, it is possible that his/her attitude, action or behavior would change slightly or significantly, as though he/she possesses some aspects of the organ donor's personality because he/she is using the donor's heart.
Anything to support this phenomenon? Does... | Although there is clearly no feasible mechanism for such a phenomenon, there is good evidence that transplant patients can <strong>believe</strong> in some sort of transference of qualities from the donor. See for example (my emphasis):
<blockquote>
Inspector, Y. <em>et al</em>. (2004) Another Person's Heart: Magical a... | There are neurons all over the body, not just in the brain. The area with the most neurons, beside the brain, is the heart. It's been theorized that some memory could reside in these cells. I'm a big believer that if you keep an open mind people will throw garbage in it, but this particular phenomena seems worthy of... | https://biology.stackexchange.com |
24,940 | [
"https://softwareengineering.stackexchange.com/questions/24940",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8451/"
] | I'm having a discussion with a co-worker on Linq, I'll copy here:
<blockquote>
Co-Worker: Lets be honest here. Linq
syntax sucks. It's confusing and
non-intuitive.
Me: oh come on, more
confusing than T-SQL?
Co-Worker: uh,
yes.
Me: it has the same basic
parts, select, where, and from
Co-Worker: Linq, to me, is a
bastard... | I can't find the right post anymore, but Eric Lippert (and possibly several other softies) have opined on several occasions about how Linq is <strong>declarative</strong>, which, for several classes of problems, is far more intuitive than <strong>imperative</strong> syntax.
Linq enables you to write code that expresse... | <blockquote>
Co-Worker: Lets be honest here. Linq syntax sucks. It's confusing and non-intuitive.
</blockquote>
You can't argue with that criticism. <em>For your coworker, it sucks</em>. We failed to design a syntax that, for them, was clear and intuitive. That's our failing, and you can pass on my apologies to you... | https://softwareengineering.stackexchange.com |
2,924,718 | [
"https://math.stackexchange.com/questions/2924718",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/524170/"
] | <blockquote>
Let <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> be two random variables with common pdf where
<span class="math-container">$f_X(t) = f_Y (t) =
e^{−t}$</span>
for <span class="math-container">$t > 0$</span>,
and <span class="math-container">$0$</span> othe... | Let <span class="math-container">$Z=2X$</span>, then
<span class="math-container">$$F_{Z}(z)=\Pr[Z\le z]=\Pr[2X\le z]=\Pr[X\le \tfrac z2]=F_X(\tfrac z2)$$</span>
Differentiating:
<span class="math-container">$f_Z(z)=\frac12f_X(\tfrac z2)$</span>.
The pdf of <span class="math-container">$T=Z+Y$</span> is therefore giv... | Your mistake is when you say <span class="math-container">$f_X(2x) = e^{-2x}$</span>. Normally the way you do it is as follows:
<span class="math-container">$$F_{2X}(x) = Pr(2X <x ) = Pr(X < \frac{x}{2}) = \int\limits_{-\infty}^{\frac{x}{2}} f_X(t) \ dt $$</span>
Take a change of variable of <span class="math-con... | https://math.stackexchange.com |
10,085 | [
"https://datascience.stackexchange.com/questions/10085",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/15984/"
] | Which of the below set of steps options is the correct one when creating a predictive model?
Option 1:
First eliminate the most obviously bad predictors, and preprocess the remaining if needed, then train various models with cross-validation, pick the few best ones, identify the top predictors each one has used, then... | I found both of your options slightly faulty. So, this is generally (very broadly) how a predictive modelling workflow looks like:
<ul>
<li><strong>Data Cleaning</strong>: Takes the most time, but every second spent here is worth it. The cleaner your data gets through this step, the lesser would your total time spent ... | Where the feature selection finds a place in your pipeline depends on the problem. If you know your data well, you can select features based on this knowledge manually. If you don't - the experimentation with the models using cross validation may be best. Reducing number of features a priory with some additional techni... | https://datascience.stackexchange.com |
77,290 | [
"https://stats.stackexchange.com/questions/77290",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/35067/"
] | I'm a new R user, and also new to Random Forest modeling. I cannot seem to figure out how to obtain the out-of-bag (OOB) error estimates for cforest models built with the Party Package in R. In the randomForest package, the OOB error estimates are displayed if you simply "print" the model object, but the party package ... | The <code>caret</code> package has a method for getting that. You can use <code>train</code> as the interface. For example:
<pre><code>> mod1 <- train(Species ~ .,
+ data = iris,
+ method = "cforest",
+ tuneGrid = data.frame(.mtry = 2),
+ trControl = tra... | Perhaps to expand a bit on Momo's answer, <em>party</em> doesn't provide an OOB estimate by default, but the computation of it is not too difficult, according to the manual. In the <code>predict</code> function you can use the parameter <code>OOB=T</code>, and leave the parameter <code>newdata</code> with its default o... | https://stats.stackexchange.com |
187,929 | [
"https://mathoverflow.net/questions/187929",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8628/"
] | Let $G$ be a graph, then we define its <em>Hadwiger graph</em> $\textrm{Hadw}(G)$ in the following way:
<ul>
<li>$V(\textrm{Hadw}(G)) = \{S\subseteq (V(G): S\neq \emptyset\textrm{ and } S \textrm{ is connected}\}$;</li>
<li>$E(\textrm{Hadw}(G)) = \{\{S,T\}\subseteq V(\textrm{Hadw}(G)): S\cap T = \emptyset \textrm{ and... | $\def\Hadw{\mathop{\rm Hadw}}$This is true for finite graphs, and false for (not necessarily connected) infinite graphs. Right now I do not know what happens for infinite connected graphs.
<b>1.</b> Each component $G_1\subseteq G$ corresponds to an isolated vertex $v_{G_1}$ in $\Hadw(G)$ and a component $\Hadw(G_1)\se... | $\def\Hadw{\mathop{\rm Hadw}}$If it is not a mauvais ton, I would like to add an easier proof found independently by Sergey Dolgikh and Marat Abdrakhmanov (we used this fact as a contest problem). We assume that $G$ is finite and connected, and again we find all vertices in $H=\Hadw(G)$ corresponding to the vertices of... | https://mathoverflow.net |
2,614 | [
"https://engineering.stackexchange.com/questions/2614",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/1375/"
] | I have a simulation software which shows energy consumption at 30 minutes timestep. If a system consumes 0.06 kWh at 6am, and 0.09 kWh at 630am, how to calculate the energy consumption between 6-7am? Can I assume it is the average of both timestep? Does finer timestep, eg. 10 minutes interval returns a different result... | I think you are getting power and energy confused, so I'll quickly define them before giving an answer.
<strong>Energy</strong> energy is a measure of how much potential for work exists. If you had a battery, it contains a certain amount of energy. Once that energy is used, the battery is "dead" and must be recharged... | In SI units the measure of "amount" of electrical energy is the Joule.<br>
Energy is a measure of "work done".<br>
Energy can be (and often is) expressed in terms of 'rate of doing work'.<br>
The rate at which work is done or at which energy is supplied or utilised is also named "Power".<br>
Work done = 'rate of doing ... | https://engineering.stackexchange.com |
410,213 | [
"https://electronics.stackexchange.com/questions/410213",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/202343/"
] | I'm fairly new to electronics here. But I can't seem to find any clear answer anywhere on the internet.
Are wires special depending on their color? Or they have all the same purpose with just colors to define them so people won't get confused? Say I wanted to reverse the black and red wires on a LED strip connected to... | The colors do not matter electrically. A wire is a wire is a wire, regardless of the color of their insulation. The color of the wire itself may matter when you get into higher voltages, but that's about the type of metal used (aluminum vs copper conductivity, for example).
The colors may matter, for readability, adhe... | Wire colors are like comments in code, even for simple DIY projects. You're talking to your future self. When you take it apart in five years because it stops working, you will have forgotten everything about the original design, so it really helps to follow conventions. For industrial products it is vital to respect n... | https://electronics.stackexchange.com |
158,509 | [
"https://mathoverflow.net/questions/158509",
"https://mathoverflow.net",
"https://mathoverflow.net/users/47383/"
] | Consider a set of $N$ individuals and let their distance be given by $R$, a $N\times N$ matrix. In that, $R(1,2)$ is the distance between individual 1 and 2. Now lets say that I want to separate the individuals into $k$ subsets (or clusters) such that the distance between individuals in each subset is the minimum possi... | No. Take $G=SO(5)$ and $H=SO(3)$, both of which have fundamental group $\mathbb{Z}/2$. I claim that there is no continuous map $f: G\to H$ which induces the identity homomorphism.
If there were, then $f$ would induce a nontrivial homomorphism $f_\ast: H_1(G;\mathbb{Z}/2)\to H_1(H;\mathbb{Z}/2)$, and a graded ring hom... | Not always. Take $G=H=\mathrm{PGL}(n,\mathbb{R})$, with $n\geq 7$. Every nontrivial continuous homomorphism $G\rightarrow G$ is a Lie automorphism; the group of such automorphisms is generated by inner automorphisms and $A\mapsto {}^tA^{-1} $, so it acts on $\pi _1(G)$ through {$\pm 1$}. On the other hand $\pi _1(G)=\... | https://mathoverflow.net |
4,319 | [
"https://physics.stackexchange.com/questions/4319",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I have tried to answer the problem correctly, and I have found similar (and even an identical) problem in my textbook, yet I still can't seem to yield the correct answer with this specific problem.
The example problem in my textbook: A crate is hauled 8m up a ramp under a constant force of 200 N applied at an angle of... | Your answer "(4)(5) cos(30)" with units of "foot-lbs" is correct for the problem as you've stated it, however there are other forces on the box. You might try including gravity.
| I asked my professor. (4)(5)cos(30) is correct when the calculation uses degrees, but it was incorrect because it uses radians. The answer is technically (4)(5)cos(pi/6). Thank you all for the help.
| https://physics.stackexchange.com |
414,057 | [
"https://physics.stackexchange.com/questions/414057",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/187947/"
] | Is it true that an electric current that flows through a conductor creates a magnetic field around the conductor?
If yes, then why doesn't the magnetic sensor of my mobile device react in any way to changes when I bring the device near to the wire connected to 220 V electricity at home?
| There are two wires, the second wire carries the equal (!) return current. The magnetic fields from the two wires cancel out, except at very short distance. For measuring the current from the field you must clamp only one of the wires.
The field at a distance can be further reduced by twisting the wires ("twisted pai... | I can see 2 possible reasons why your phone does not detect a magnetic field.
First, a magnetic field is generated when current flows. A simple wire carries no current. So, unless the wire is part of an active circuit (e.g. a lamp that is turned on) there will be no magnetic field.
Even if there is a current flowing,... | https://physics.stackexchange.com |
120,472 | [
"https://security.stackexchange.com/questions/120472",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/86178/"
] | I've noticed that there is a third-party webservice we utilize programmatically at my job to transmit somewhat sensitive information and I was surprised to see that the endpoint was only using http, rather than https. Upon further investigation it appears that a whilelist is being employed by this webservice, meaning t... | The sniffing problem is about "confidentiality", which whitelisting does not cover, as the traffic can be intercepted and read.
The MitM problem is about "authenticity", which whitelisting does not cover either, as an intercepted packet can be modified without evidence of tampering.
I assume the whitelisting uses IP ... | If the data is unencrypted, anyone sniffing the packets between your server and their server can see it. A whitelist only lets their server verify that the source of the data. It doesn't assure that no one sniffed it during transfer, or that it wasn't intercepted and manipulated at any point during the process.
In sho... | https://security.stackexchange.com |
18,465 | [
"https://mathoverflow.net/questions/18465",
"https://mathoverflow.net",
"https://mathoverflow.net/users/492/"
] | Suppose that $K$ is an $\textit{alternating}$ knot in $S^3$, and let $R_0$ be the space of homomorphisms from $\pi_1(S^3 - K)\to SU(2)$ which send meridians to trace free matrices. Denote the subset of $R_0$ consisting of metabelian representations as $R_m \subset R_0$.
Question: when $K$ is prime, is there any reaso... | I doubt there is such a retraction. Such representations are representations of the $\pi$-orbifold, obtained by killing the square of the meridian (at least if one quotients by $\pm Id$). If one takes a Montesinos knot, these orbifolds are Seifert fibered, and such representations should factor through the quotient orb... | This looks like a good place to start from (if you haven't already read it)
MR2488756 (2009m:57024) Nagasato, Fumikazu . Finiteness of a section of the ${\rm SL}(2,\Bbb C)$-character variety
of the knot group.
Kobe J. Math. 24 (2007), no. 2, 125--136.
This paper shows that for any knot, there are only finitely ... | https://mathoverflow.net |
264,048 | [
"https://security.stackexchange.com/questions/264048",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/58552/"
] | When we encrypt a volume with bitlocker, it takes time to encrypt the data according to the amount of the data but Once the encrypted volume is mounted the contents are transparently accessible to software running on the device as if it weren't encrypted at all.why? I know if I want to turn off bitlocker on that volume... | Bitlocker is like an adapter: encrypted data comes in, unencrypted data goes out. And vice versa.
A filesystem is an abstraction. It creates a layer between the data on the storage device and the application, so accessing a NTFS formatted SSD and accessing a FAT12 formatted floppy disk uses the same procedures.
Bitlock... | Bitlocker encrypts the entire filesystem. When the operating system is running, it decrypts on the fly sections of the disk as they are accessed, giving the user an experience as if the disk is not encrypted at all.
| https://security.stackexchange.com |
387,931 | [
"https://physics.stackexchange.com/questions/387931",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/185723/"
] | I would have a quite stupid question: What is the connection between complex refractive index and the "normal refractive index" that I find in every high school books? Is that the real part of the complex refractive index (and thus corresponding to transmittance?) or is it something like "absolute value", that already ... | The real part of the complex refractive index is the <em>normal</em> refractive index, and is related to the part of wave that transmits through the medium. Let's see what the imaginary part of the refractive index would do to a wave of the form $Ae^{\iota k x}.$ The refractive index is part of $k$ in the medium, so th... | When using refractive indices we usually assume the materials are perfectly transparent and don't absorb any light. In this case we get a real refractive index that is just the ratio of the velocities.
However real materials always absorb some light, and when this happens happens we get a complex refractive index:
$$... | https://physics.stackexchange.com |
373,387 | [
"https://softwareengineering.stackexchange.com/questions/373387",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/260829/"
] | I am new to graph data structure. Everywhere on google it is said to be list(or array ) of linked list.
My question is can not it be represented as list of list(in java array list of array list) or map of list(in java HashMap with key as node and value as array list of connected node ) ?
In all three mentioned appro... | To answer the historical aspects of the question:
The design philosophy is explained in <em>The C Programming Language</em> written by Brian Kernighan and C designer Dennis Ritchie, the "K&R" you may have heard of. The preface to the first edition says
<blockquote>
C is not a "very high level" language, nor a "... | This depends on your definition of high-level and low-level language. When C was developed, anything that was higher-level than assembly was considered a high-level language. That is a low bar to clear. Later, this terminology shifted to the point that some would nowadays consider even Java to be a low-level language.
... | https://softwareengineering.stackexchange.com |
77,175 | [
"https://mathoverflow.net/questions/77175",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1106/"
] | In calculus classes it is sometimes said that the tangent line to a curve at a point is the line that we get by "zooming in" on that point with an infinitely powerful microscope. This explanation never really translates into a formal definition - we instead approximate the tangent line by secant lines.
I seem to have... | In algebraic geometry, this construction is known as the <em>tangent cone</em> to the graph. More generally, suppose we have the zero set of any polynomial $f(x,y) = 0$, and assume $f(0,0)=0$. Then we can write
$f(x,y) = a_m (x,y) + a_{m+1}(x,y) +a_{m+2}(x,y) +\cdots$
where $a_i(x,y)$ is a homogeneous polynomial of... | An animation of your first example, $y=x(x−1)(x+1)$.
I limited the number of frames so that the file would not be too huge (it is ~1MB now).
Frame rate is browser and processor dependent. At best this gives an idea of what a more
professional animation might look like.
<hr /> &... | https://mathoverflow.net |
89,082 | [
"https://cs.stackexchange.com/questions/89082",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/85460/"
] | I just need to know the truth or falsity of a simple statement.
Let $L_1$ be a context-free language over an alphabet which contains some number of characters $\Sigma$, as well as a single, special metacharacter “|”. Suppose that every string in $L_1$ contains exactly one metacharacter. Let the <em>left ha... | Your argument for "no" is flawed, for two reasons:
<ul>
<li>When we say that X reduces to Y, we mean that a solution to Y is one way to solve X. But there might be other ways to solve X that don't rely on solving Y.</li>
<li>Some protocols for consensus elect a leader, but that doesn't necessarily imply that <em>all<... | I've already accepted D.W.'s answer above, but posting some of my later findings for reference of people that end up reading this question:
<ul>
<li>As implied in the question, all consensus algorithms (e.g. Paxos, Raft, Chandra–Toueg) have an elected leader (even a temporary one) which is driving the convergence to t... | https://cs.stackexchange.com |
201,971 | [
"https://softwareengineering.stackexchange.com/questions/201971",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/94300/"
] | How is it possible that written a programming language like CoffeeScript in itself like CoffeeScript? Firstly CoffeeScript doesn't exist that read CoffeeScript scripts and interpret them?
| <ul>
<li>First you design a language <em>A</em> on paper and white board.</li>
<li>Then you write an implementation of a language <em>A</em> (compiler, vm, interpreter, runtime depending on a scope of language) in language <em>B</em>.</li>
<li>Once you have stable environment for language <em>A</em>, you can start writ... | Think of a subset of language to build another language. Don't watch it as building A with A but instead building A with B where B is a small language.
Think of it in this way:
You build a simple interpreter with JavaScript and name it CoffeeScript, later on as your project goes bigger and bigger you start writing par... | https://softwareengineering.stackexchange.com |
73,771 | [
"https://softwareengineering.stackexchange.com/questions/73771",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22218/"
] | I'm developing mobile applications for Windows Phone 7. This application calls some web services and occasionally sends responses out via web services. I recently started looking into MVVM and noticed that, although it is suggested when developing applications in WP7, alot of developers say only to use it if its necess... | If your application uses WPF or Silverlight, use MVVM.
It doesn't matter how simple your application is. It is a very easy pattern to learn and it makes future maintenance/updates extremely easy. It also makes it so new developers, or even someone looking at the code a few years from now can understand what is going o... | It's always <em>possible</em> to build larger scale applications without following a design pattern. However, following a pattern generally allows for greater decoupling of subsystems and therefore, increasing the ease of scaling your system.
Personally, I <em>always</em> follow a pattern when developing my applicatio... | https://softwareengineering.stackexchange.com |
117,608 | [
"https://mathoverflow.net/questions/117608",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29634/"
] | We know that if $G$ is a simple group with $p+1$ Sylow $p$-subgroups, then $G$ is 2-transitive. Now let $G$ be almost simple group with $p+1$ Sylow $p$-subgroups. Is $G$ 2-transitive group?
| I am sure that the answer is yes, but you might have to do a bit of work to write down a completely rigorous proof.
Let $S \unlhd G$ with $S$ simple and $G \le {\rm Aut}(S)$, and suppose that $G$ has $p+1$ Sylow $p$-subgroups. If $p$ divides $|S|$, then $S$ has at most $p+1$ and hence exactly $p+1$ Sylow $p$-subgroups... | I think there is a direct argument. Let $M$ be the unique minimal normal subgroup of $G,$
which is non-Abelian simple. Then $M$ must act faithfully by conjugation
on the $(p+1)$ Sylow $p$-subgroups of $G$- otherwise, $M$
has a normal Sylow $p$-subgroup, which must then be trivial.
But even then, $M$ must normalize, and... | https://mathoverflow.net |
95,047 | [
"https://math.stackexchange.com/questions/95047",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11123/"
] | Consider the sum of the first <span class="math-container">$n$</span> integers:
<span class="math-container">$$\sum_{i=1}^n\,i=\frac{n(n+1)}{2}=\binom{n+1}{2}$$</span>
This makes the following bit of combinatorial sense. Imagine the set <span class="math-container">$\{*,1,2,\ldots,n\}$</span>. We can choose two from ... | Here's a combinatorial proof for $$\sum_{k=1}^n k^2 = \binom{n+1}{2} + 2 \binom{n+1}{3},$$ which is just another way of expressing the sum. Both sides count the number of ordered triples $(i,j,k)$ with $0 \leq i,j < k \leq n$.
<em>For the left side</em>, condition on the value of $k$. For each $k$, there are $k^2... | We give a combinatorial interpretation of the formula
$$
2^2+4^2+6^2+\cdots +(2n)^2=\binom{2n+2}{3} \qquad\qquad (1)
$$
for the sum of the first $n$ <em>even</em> squares.
There are $\binom{2n+2}{3}$ ways to choose $3$ numbers from the numbers $1, 2, \dots, 2n+2$. We organize and count the choices in another way.
Ma... | https://math.stackexchange.com |
629,638 | [
"https://physics.stackexchange.com/questions/629638",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/296328/"
] | If we approximate the Earth's circumference to be <span class="math-container">$40,075\;km$</span> we could say that the the amount of time it takes for a full rotation is about <span class="math-container">$24\; hours$</span>. We could then approximate the rotation of the Earth at the equator to be <span class="math-c... | The latitude of New York is 40°N, which makes a substantial difference in its speed around the earth's axis. The velocity <span class="math-container">$v_\text{earth}$</span> of the earth along the a circle of latitude <span class="math-container">$\theta$</span> is <span class="math-container">$$v_\text{earth} = \frac... | Yes, it does matter that the car is in North America. The amount of time it takes for rotation about the Earth's axis of rotation is the same in North America (still 24 hours), but the distance traveled during this rotation is less so the angular velocity is smaller.
| https://physics.stackexchange.com |
340,443 | [
"https://electronics.stackexchange.com/questions/340443",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/41313/"
] | I need to limit the voltage from AA batteries to 5.25V or less. Essentially, my circuit can operate from (minimum) 3.5V up to 5.25V, and I want to maximize run time by using 4xAA. Should I just run it off 3xAA batteries (giving 4.5V when full) or is there a way this can be done (without the expense of a switching regul... | What is it? Is cost THAT much of an issue?
Using a zener will work, but to work well with such a large load, 1.5A, your going to waste people's batteries IMO, and to be fair 1.5A is not trivial for AA batteries, though good alkaline batteries will be OK.
A linear regulator will burn excess voltage as heat, so if you... | The really inexpensive 5V USB power supply that I purchased many years ago was simply 4- "AA" cells in a battery holder with a couple of 5.1V 1 Watt Zener Diodes soldered right across the battery terminals.
Fresh cells discharged very quickly down to just below the Zener voltage and then stayed at that voltage for man... | https://electronics.stackexchange.com |
640,709 | [
"https://electronics.stackexchange.com/questions/640709",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/146925/"
] | I have a bunch of plants on my balcony and I would like to automate the watering.<br />
I don't want to drill holes in my window frames so I can't provide power from within my apartment.<br />
I'd like to have a self-contained system, a 12v battery (for the pump) and a solar panel to charge it.<br />
Safety is my numbe... | Sealed lead acid batteries are pretty robust. Get sealed ones so they won't leak acid if knocked over.
NiMH is also quite safe. NiCd is now obsolete, as cadmium is toxic, and they offer few advantages over NiMH.
| All lead-acid batteries have the problem that the reaction is <em>between a plate and the acid</em>. The acid's chemical composition changes from full to empty. And as it gets emptier, its freezing point raises.
This is a risk that needs to be managed. But it's unlikely to freeze at -6C, and you shouldn't be dipping ... | https://electronics.stackexchange.com |
112,909 | [
"https://dba.stackexchange.com/questions/112909",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/74109/"
] | My mongod runs out of connections from time to time. But when I restart the instance, it becomes normal.
I check the log and found some connections were created and never be ended. This cause the connection depleted quickly.
My mongo cluster consists of of 3 shards, each with 3 replicasets. So there are 9 mongod ins... | <pre><code>create table #jobhistory (JobOrderID int, dateAdded datetime, Status varchar(10))
go
insert into #jobHistory (JobOrderID, dateAdded, Status)
select 4909, '2015-08-26 18:15:07.527', 'OPEN' union all
select 4909, '2015-08-28 13:35:38.997', 'CLOSE' union all
select 4909, '2015-08-31 12:16:29.787', 'OPEN' union ... | Providing that you'll always close a job before opening another under the same ID (although personally you should never have two seperate jobs running under the same ID without another unique identifier to distinguish (You've opened 4909 and 4910 twice))
if you join the table on itself distinguishing them between Open... | https://dba.stackexchange.com |
226,088 | [
"https://physics.stackexchange.com/questions/226088",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44499/"
] | With the rapidity $\phi$ defined so that $\frac{v}{c}=\tanh{\phi}$, say you have 3 parallel moving reference frames $S$, $S'$ and $S''$ with a constant but different velocity/rapidity.
If the rapidity of $S'$ in relation to $S$ is $\phi_1$,<br>
and the rapidity of $S''$ in relation to $S'$ is $\phi_2$,<br>
then the ra... | Alright here's a very crude heuristic(definitely not a proof) on why(without using velocity composition) rapidity is additive.
Impose these two constraints:
1) the constancy of speed of light in all frames. This means that the rapidity of light $\tanh\phi_c=1$ is the same in all frames of reference.
Consider this c... | Relativistic velocity addition takes the form
$$
V = \frac{v+u}{1+uv/c^2}
$$
The rapidity is defined so that
$$
v = c \tanh \eta
$$
Plugging this into the the velocity addition formula and noting that $V = c \tanh N$, we find
$$
c \tanh N = c \frac{ \tanh \eta + \tanh \eta' }{1 + \tanh \eta \tanh \eta'} = c\tan... | https://physics.stackexchange.com |
4,639,061 | [
"https://math.stackexchange.com/questions/4639061",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1149884/"
] | For another proof I just assumed, that <span class="math-container">$n! < m! \;$</span> for all <span class="math-container">$\;n<m$</span>. And I mean it is kind of obvious that this is the case, but then again I should be able to prove it. However I have no idea where to start there. Can someone give me a hint... | If <span class="math-container">$n<m$</span>,
<span class="math-container">$$n!=1\times2\times...\times(n-1)\times n\qquad\qquad\text{and,}$$</span>
<span class="math-container">$$m!=\underbrace{1\times2\times...\times (n-1)\times n}_{n!}\times (n+1)\times...\times(m-1)\times m\\=n!\times(n+1)\times...\times(m-1)\ti... | <em>Hint</em>: Notice that if <span class="math-container">$n<m$</span>, then <span class="math-container">$$m!=m\cdot (m-1)\cdot(m-2)\ldots\cdot n\cdot(n-1)\ldots \cdot1 = m\cdot (m-1)\cdot\ldots\cdot n!$$</span>
| https://math.stackexchange.com |
25,236 | [
"https://physics.stackexchange.com/questions/25236",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1153/"
] | I have read somewhere that the best/easiest way to watch meteor showers is to lie on the ground or other horizontal surface with your feet oriented towards the "apparent point of origin" (what was that called again?) of the shower and just relax while having eyes open to the heavens.
Last November I actually tried thi... | The only way to observe a meteor shower is naked eye. Any optical instrument will limit your field of view, and you will miss most of the meteors.
The location of the radiant in the sky has no bearing on where you will see meteors. People don't need to worry about exactly where the radiant is. Meteors can occur <em>an... | It's been a while since I set out specifically to watch a meteor shower but back when I used to do so I would typically watch in a prone position. Either lying on a blanket or slightly inclined on a folding lounge chair (and sometimes lying on a picnic table.
The main reason, at least for me, is that you want to tr... | https://physics.stackexchange.com |
93,165 | [
"https://dba.stackexchange.com/questions/93165",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/59767/"
] | I am taking a databases course and i'm learning about functional dependencies. I have searched around and did not find any information on this. My questions is if we are given a table with some tuples, are we able to determine the FDs for this relation instance?
| It's guesswork and detective work. It's a little like what an archaeologist does. You make the most of the data you find, but you realize that some pattern you think you see might be contradicted if you had a wider sample.
| No. The reason why database designers are interested in FDs is because they are a formalisation of Business Rules - rules about the data which accurately reflect the Business Domain to be modelled in the database. The only sound and practical way to identify FDs is by analysing and understanding a set of business requi... | https://dba.stackexchange.com |
289,691 | [
"https://softwareengineering.stackexchange.com/questions/289691",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/171501/"
] | So I'm making a method to create a salutation line based on two people from a database.
There are four parameters: the two names (<code>name1</code> and <code>name2</code>) and the two genders (<code>gender</code> and <code>gender2</code>).
For every gender combination, I have a kind of different output.
For example... | Add the title to the parameters of the printf:
<pre class="lang-c prettyprint-override"><code>char* title1;
switch(gender1){
case 'M':
title1 = "Sir";
break;
case 'W':
title1 = "Madam";
break;
case ...etc.
}
char* title2;
switch(gender2){
case 'M':
title2 = "Sir";... | Radical solution: Let the user specify their <em>own</em> title (from a predefined list that you provide).
Your solution (as viewed through English eyes) only appears to cater for Lords ("Sir") and ladies; most men would be addressed as "Mr", most women as either "Miss", "Mrs" or "Ms", depending on their marital stat... | https://softwareengineering.stackexchange.com |
93,533 | [
"https://physics.stackexchange.com/questions/93533",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10606/"
] | In our quantum mechanics script, it states that $[L^2, X^2] = 0$ and $[L^2, P^2] = 0$, therefore for the following Hamiltonan
$$H = \frac{P^2}{2m} + V(X^2)$$
it is that $[H, L^2] = 0$ therefore $H$ and $L^2$ have the same eigenvectors, and then it continues to calculate orbitals of the hydrogen atom.
My question is:... | Yes there is.
I use the summation convention throughout; repeated indices are summed over 1,2,3.
<ol>
<li>Begin with the canonical commutation relations (CCRs)
\begin{align}
[X_i, P_j] = i\hbar\delta_{ij} I, \qquad [X_i, X_j] = 0, \qquad [P_i, P_j] = 0.
\end{align}</li>
<li>Define the components of orbital angular ... | Another possibility. I directly deal with $X^2$, but the same reasoning can obviously be used for $P^2$, $V(X^2)$ and $H$ (that is a linear combination of scalars) in place of $X^2$ below.
Consider a unitary representation of a rotation $U_\theta = e^{-i\theta L_k}$ along the ${\bf e}_k$ axis. As $X^2$ is a <strong>sc... | https://physics.stackexchange.com |
66,348 | [
"https://dsp.stackexchange.com/questions/66348",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/46133/"
] | So basically information is defined by expected value of Shannon's information i.e. Entropy. I am curious how much information is lost if we simply take the average of the sample given to us. I am also curious if we also take the second moment (variance) of the same signal, how much information do we gain by using the ... | There's a lot of things that influence your choice of sampling rate.
First of all, of course, the Nyquist theorem, which says you need to sample at more than twice of the signal's single-sided bandwidth <span class="math-container">$B$</span> (for real signals)¹.
Then, you often choose a sampling rate that is <em>use... | Only requirement for sampling frequency is that it should be more than twice the maximum frequency component in desired signal. Any other constraint can only be because of the oscillator design of the ADC circuit. So, the sensor you are working with might be able to generate a fundamental frequency of 32Hz and, using s... | https://dsp.stackexchange.com |
31,465 | [
"https://dba.stackexchange.com/questions/31465",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/16753/"
] | I have a set of documents that can have various privacy settings around them:
<ol>
<li>They can be completed public (any registered user) can view them</li>
<li>They can be viewable only by people following you (this
"Followers" array is stored in each User's document)</li>
<li>They can be private to the person who pu... | It's important to remember that since there are multiple ways to design schema in MongoDB for a given set of data, it's critical to consider the types of reads and writes you will be making from your application.
Assuming that you will be querying for a subset of documents that a given user can see, it's likely that y... | Your documents can contain some inline privacy section-document or reference to that document in some security collection (for example) where you can specify whether to access.
On the assumption of your problem it can be looks like:
<pre><code>{
"status":"private", // one of allow-all, private, deny-all
"deny"... | https://dba.stackexchange.com |
6,724 | [
"https://mechanics.stackexchange.com/questions/6724",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3473/"
] | My 2003 focus lx 2.0L L4 SOHC ~18,000 miles has had the engine light so i went to autozone to read the code.
Autozone obd2 printout says "P2195 lack of heated oxygen sensor- Bank 1 Sensor 1 HO2S11 switch- sensor indicates lean."
Autozone said "Your car is burning more fuel. It's a common problem. It's usually the 1s... | <em>since installing new 02 sensor engine light has not reappeared after clearing w/obd2 device and torque free app.</em> TOTAL COST= ~$27
7 31 13 ordered Koolertron F-12 ELM 327 OBDII PC Car Diagnostic Scanner
Electronics EggDeal via amazon $9.50 to use w/android smartphone torque free app to read & clear obd co... | The diagnostic trouble code is not to be looked at as a root cause of the system failure. <em>(example. Replacing a blown fuse is NOT a solution)</em> In all cases there are multiple components that can cause the same code to trigger. For instance, a possible vacuum leak, or EGR problems, and even a PCV issue, could al... | https://mechanics.stackexchange.com |
3,419,182 | [
"https://math.stackexchange.com/questions/3419182",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/446410/"
] | I struggle with the following explanation, and would be grateful if you could help. Thank You.
"Consider a small hole with area <span class="math-container">$a$</span> on the surface of the metal cube through which radiation can
escape. We want to calculate the radiated power though this hole. For radiation at an angl... | The problem is that you are thinking in a 2D world, when the problem is 3D. When you integrate a function <span class="math-container">$f$</span> over all angles on a hemisphere you don't do <span class="math-container">$$\int_0^{\pi/2} f(\theta)d\theta$$</span>
You instead need to do <span class="math-container">$$\in... | The angle isn't the issue; you need to multiply by <span class="math-container">$\sin\theta$</span> beore you integrate, viz. <span class="math-container">$d^3x=r^2dr\sin\theta d\theta d\phi$</span>. Note that<span class="math-container">$$\frac{\int_0^{\pi/2}\sin\theta\cos\theta d\theta}{\int_0^{\pi/2}\sin\theta d\the... | https://math.stackexchange.com |
529,531 | [
"https://physics.stackexchange.com/questions/529531",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/237222/"
] | Reading Sean Carroll's spacetime and geometry he says
<blockquote>
If <span class="math-container">$x^{\sigma_*}$</span> is the coordinate which <span class="math-container">${\mu\nu}$</span> is independent of, let us consider the vector <span class="math-container">$\partial_{\sigma_*}$</span> which we label as
... | There are several different ways to define tangent vectors, eg in terms of coordinates and transformation laws, or as equivalence classes of differentiable curves in first-order contact. In differential geometry, we tend to identify tangent vectors with their corresponding directional derivatives, which can be used as ... | Just think about ordinary vectors. The vector <span class="math-container">$\mathbf{r} = \hat{\mathbf{x}}$</span> has components <span class="math-container">$(1, 0, 0)$</span> in Cartesian coordinates. This is because the components are the numbers you have to multiply the unit vectors with to recover the vector you w... | https://physics.stackexchange.com |
5,159 | [
"https://stats.stackexchange.com/questions/5159",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1636/"
] | The height for 1000 students is approximately normal with a mean 174.5cm and a standard deviation of 6.9cm. If 200 random samples of size 25 are chosen from this population and the values of the mean are recorded to the nearest integer, determine the probability that the mean height for the students is more than 176cm.... | I interpret this question as supposing that an experiment is conducted 200 times. In this experiment, 25 people are independently drawn from the population (with replacement) and their average height is rounded to the nearest centimeter. This process yields 200 whole numbers. You seem to be asking, what is the chanc... | I understand the question as one where we know the theoretical distribution of students height with some precision (i.e., with one decimal place). In the present case, this is a gaussian distribution with parameters $\mathcal{N}(174.5;6.9^2)$.
Now, we have empirical measurements of students height on small samples ($... | https://stats.stackexchange.com |
246,522 | [
"https://stats.stackexchange.com/questions/246522",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/139030/"
] | I have given function values say "$y$" which is dependent on $x$ and $\log(100-x)$, how shall I solve this problem using linear regression - as in I want my model to be like $$y = Ax + B\log(100-x).$$
I could do it by taking $x$ as one variable and $100-x$ as another, but is that wrong?
Is there any other way this c... | If you really want to construct a model such as $y = A x + B \log(100 - x)$ (that is, you know that is how your model SHOULD perform in real life, e.g., based on some physical or biological or chemical arguments), then just do that by treating $x$ and $\log(100 - x)$ as your covariates and perform a linear regression ... | Linear regression can be used in some non linear regression problems if you define new variables that contains the non linearity. You should do the linear regression $y=A X +B U$ , where $U = log(100-x)$. There is no mistake in doing that, you are searching a linear regression function adding a dimension to the proble... | https://stats.stackexchange.com |
34,944 | [
"https://mathoverflow.net/questions/34944",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2665/"
] | Coming up with examples of $D_8$-covers of $\mathbb{C}(x)$ is easy. For example:
$Quot(\mathbb{C}(x)[y,z]/(y^2=x(x-7), z^4=(y+\sqrt{-6})^2(y-\sqrt{-6})^2(y+\sqrt{-10})(-y+\sqrt{-10})^3))$
defines a $D_8$ extension of $\mathbb{C}(x)$. If you view this field extension as an extension of the corresponding smooth project... | As you say, the fixed field by $\langle a\rangle$ is $\mathbb{C}(u)$ with $u^2=-5x/2(x-7)$, and the fixed field by $\langle a^2,b \rangle$ is similarly $\mathbb{C}(v)$ with $v^2=7(x-2)/2(x-7)$ (constants chosen so that $u^2+v^2=1$). So their compositum, the fixed field by $\langle a^2\rangle$, has genus zero and is $\m... | Whenever I need to do something explicit involving a Galois extension of a field whose Galois group is a small 2-group (and it does happen sometimes!) I always find what I need in the paper "Groups of order 16 as Galois groups," by Grundman, Smith, and Swallow.
| https://mathoverflow.net |
45,693 | [
"https://stats.stackexchange.com/questions/45693",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17723/"
] | <strong>Problem</strong> I have a computer algorithm, and am attempting to measure the affect of a parameter (NS) on the output of the algorithm (SC). My hypothesis is that if the level of NS is lowered, there should be a corresponding decrease in SC as well. I'm doing all of my statistical analysis in the R language (... | You're thinking about your ANOVA incorrectly. It's OK, lots of people are taught ANOVA that way. The ANOVA does not mean there are any significant differences between levels of the predictor variable. None of them can be significant and yet the ANOVA is. It means that the pattern of data has meaning. Simply report... | You are running into one of the fundamental problems with p-values: They are partly dependent on sample sizes.
So, when you increase sample size, smaller effect sizes become significant. This accounts for <em>both</em> changes that you report 1) More comparisons become significant because smaller effect sizes are (thi... | https://stats.stackexchange.com |
14,316 | [
"https://quant.stackexchange.com/questions/14316",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/11723/"
] | In exchange rate model explanation,
"...If under the domestic risk neutral measure $Q_d$, the process $X(t)$ satisfies
$\displaystyle \frac{dX(t)}{X(t)}=\sigma dZ_d(t)$
Since $Z_d(t)$ is $Q_d$-Brownian motion, so $X(t)$ is a $Q_d$-martingale."
How does this last line work? I cannot see what theorem has been applied... | The solution of your SDE is known as the Stochastic Exponential:
$$X_t=X_0e^{\sigma Z_t-\sigma^2t^2/2}$$
(You can check this solution by applying Ito to the function $f(t,Z_t)=\ln X_t$.)
Taking the expectation of $X_t$ to check its martingale property, since $Z_t\sim N(0,t)$ then $E(e^{\sigma Z_t})=e^{\sigma^2t^2/2}... | Most of the time, when you have a simple SDE without a drift, it's a martingale because the Wiener process itself is a martingale. In your example, you have a constant with the Wiener process, therefore the whole process must also be a martingale because the expectation is clearly X(t).
However, we can't conclude a dr... | https://quant.stackexchange.com |
677,097 | [
"https://physics.stackexchange.com/questions/677097",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | How can phase diagrams involve volume since it is extensive? perhaps it is understood that we are talking about a specific volume? If the volume and pressure are known but I don't know how much substance is contained in that volume, how can I know the phase? A high pressure in a given volume can occur with a low densi... | <blockquote>
How can phase diagrams involve volume since it is extensive? perhaps it is understood that we are talking about a specific volume?
</blockquote>
Yes, the volume in a phase diagram is either the specific volume, m<span class="math-container">$^3$</span>/kg, or molar volume, m<span class="math-container">$^... | Phase diagrams were developed to monitor the operation of engines. The volume of a cylinder as well as the travel of the piston inside the cylinder can be measured.
Assuming air is not forced into the intake, then it is going to fill up the volume of the cylinder at ambient pressure and temperature. So V, P, and T are ... | https://physics.stackexchange.com |
71,950 | [
"https://mathoverflow.net/questions/71950",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9947/"
] | In Hartshorne IV.2, notions related to ramification and branching are introduced, but only for curves. The main result is the Hurwitz formula.
Now if you have a finite surjective morphism between nonsingular, quasi-projective varieties, then the notion of ramification (divisor) would still make sense and we can also ... | degree of the canonical divisor doesn't make any sense as already pointed out by Mohammed.
On the other hand, by "purity of the branch locus", the branch locus, as well as the ramification locus of $f$ is a sum of irreducible divisors. Denote by $R_i$ the irreducible components of the ramification locus. Then, the lo... | One could argue that Hurwitz's formula boils down to two simple facts:
<ol>
<li>If $f:X\to Y$ is an étale morphism, then $\omega_X=f^*\omega_Y$.</li>
<li>If $f:X\to Y$ is dominant, then $\omega_X\supseteq f^*\omega_Y$</li>
</ol>
"1." is a trivial consequence of an equivalent characterization of being étale, namely th... | https://mathoverflow.net |
30,517 | [
"https://cs.stackexchange.com/questions/30517",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/336/"
] | I often heard that "program = algorithm + data structure".
But I notice that
<ol>
<li>It seems to me that a data structure is (or may be) just a data type or extension thereof. Is it correct? But a data type is a part of a programming language, but a data structure isn't. </li>
<li>the operations/methods in a data st... | When you use recursion to solve a problem, you typically partition your input into one or more smaller instances (and possibly a part that you don't process further). Those smaller instances are what your exercise calls the <strong>small version</strong>.
Upon recursing, your inputs get smaller and smaller until it is... | "Small version" is wrong. What you have to find is a way to operate on the n+1 element assuming that the previous (or next) n elements have already been considered.
E.g.
Is there x in an array?
<ul>
<li>If the array is empty then no.</li>
<li>If the array is not empty then check the first element, if the first eleme... | https://cs.stackexchange.com |
1,072,689 | [
"https://math.stackexchange.com/questions/1072689",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/180015/"
] | So again we study a physics course without studying mathematics course
We are in the work energy chapter , and I'd like to know if you can know the function $f(x,y,z)$ if you know all of its partial derivatives everywhere?
Like $f(x,y,z)$ and we have $$\frac{\partial f}{\partial x} = 5x, \frac{\partial f}{\partial ... | As Robert Soupe says, either $\mathbf{R}$ or $\Bbb{R}$ is unlikely to confuse a reader without explanation.
Until the last decade or two of the 20th Century, $\mathbf{R}$ was common notation for the real numbers in print journals. As Raclette notes, $\Bbb{R}$ is <em>called</em> blackboard boldface because lecturers wo... | The proper notation for the set of all real numbers is either $\mathbb{R}$ or $\textbf{R}$. It really comes down to your choice, and whichever you choose you can back with plenty of precedent. But most of the time people will understand what you mean without you having to explain it.
The problem with $R$ is that in th... | https://math.stackexchange.com |
256,008 | [
"https://stats.stackexchange.com/questions/256008",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/144927/"
] | My question revolves around the Central Limit Theorem. To read from the same page, I quickly state it here:
Let <span class="math-container">$X_{1}, ..., X_{n}$</span> be IID with mean <span class="math-container">$\mu$</span> and variance <span class="math-container">$\sigma^2$</span>. Let <span class="math-container"... | <blockquote>
So here is what I imply from their statement: If that would be true, than any sufficiently large sequence $A_1, \cdots,A_n$ would "form" a normal distribution.
</blockquote>
It's hard to interpret this. If you want to get a single random <em>variable</em>, then you need some operation to reduce this se... | <blockquote>
<em>"I frequently here from people, especially those who have not deeply
studied statistics and use it for example in an application in business, that
not just this very specific term $\bar X_n$ converges in distribution
against a standard normal distribution, but also "any sequence" of
random va... | https://stats.stackexchange.com |
237,581 | [
"https://electronics.stackexchange.com/questions/237581",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/104309/"
] | I am currently designing a circuit where I have typically several IC.
I have a LDO (SGM2019-ADJ) which steps 3.8V down to 3.3V with a max output of 250 mA. This 3.3V rail is dedicated to supplying an audio codec (ALC5616) which consumes a max of 4.3 mA @3.3V if I am not mistaken.
I also have the following devices:
<... | I can not decide it for you, but I can try to suggest what you can base your decision on:
You seem to have 3mA + 30mA + 100mA + 5mA + 45mA + 1mA = 184mA consumption.
<ul>
<li>That is 73% of the 250mA for which the LDO promises to have 225mV drop, so probably enough headroom for now.</li>
<li>You drop ~0.5V you say, w... | If the LDO can handle the current <em>AND</em> it has sufficient heatsinking so that it doesn't get too hot (as long as it's less than 75'C your are probably OK as pretty much all electronics are rated to 125'C), then yes, the LDO will handle having all those devices on the same rail. You are only limited by the maximu... | https://electronics.stackexchange.com |
88,703 | [
"https://physics.stackexchange.com/questions/88703",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/28890/"
] | This is the picture in my mind:
<img src="https://i.stack.imgur.com/VTbX7.png" alt="enter image description here">
For centripetal force, I learned that:
$T-mg\cos\theta= \frac{mv^2}{r}$
In vertical circular motion, the velocity is naturally going to decrease as kinetic energy is converted to potential energy as the... | In the situation at hand, you'll never be able to achieve uniform circular motion.
$\frac{d\vec{v}}{dt} = \frac{1}{m}\sum \vec{F}_{\text{ext}}$
This is a vectorial equation. If you look at the picture you've drawn, you have forces on the radial as well as the tangential direction.
On the radial direction, there is ... | The answer to your question is "Yes, if you want it badly enough.
Uniform vertical circular motion implies that an object is moving in a circle, that the plane of the circle is vertical, and that the speed of the object does not change as it moves around the circle. An example of such motion is that of a point on the... | https://physics.stackexchange.com |
130,949 | [
"https://dba.stackexchange.com/questions/130949",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/88583/"
] | I need to get the rolling sum over a period of 7 days for each row (1 row per day).
For example:
<pre class="lang-none prettyprint-override"><code>| Date | Count | 7-Day Rolling Sum |
------------------------------------------
| 2016-02-01 | 1 | 1
| 2016-02-02 | 1 | 2
| 2016-02-03 | 2 | 4
| 2016-02-... | By far the cleanest solution is to use window function <code>sum</code> with <code>rows between</code>:
<pre><code>with days as (
SELECT date_trunc('day', d)::date as day
FROM generate_series(CURRENT_DATE-31, CURRENT_DATE-1, '1 day'::interval) d ),
counts as (
select
days.day,
... | Ended up using a FOR LOOP, a TEMP table and SELECT on the temp table once the for loop is done:
<pre><code>DO
$do$
DECLARE
curr_date DATE;
BEGIN
-- Create temp table to hold results
DROP TABLE IF EXISTS rolling_7day_sum;
CREATE TEMP TABLE rolling_7day_sum (
date DATE,
count BIGINT
);
-- Iterate dates an... | https://dba.stackexchange.com |
268,546 | [
"https://physics.stackexchange.com/questions/268546",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/123839/"
] | Which are the other ways of transmission if any? If energy does not require any medium for transmission(as for sunlight reaching earth, the heat too), is it transmitted in quanta in particle radiation too?
| Energy transfer can be thought to occur via the exchange of a 'virtual particle'. In nature, there are 4 fundamental forces, namely:
1. Electromagnetic force
2. Gravitational force
3. Strong force
4. Weak force
Each of these forces have a different exchange particle:
For instance, the exchange particle for EM is a p... | To expand on the above answer by @PhysLab (which is very well written), the answer depends on how "in depth" you want to look at it. Before discussing energy transfer, let's cover a few fundamentals, because these are slippery concepts and often misunderstood. (Including by me, so fingers crossed!)
Let's look at what ... | https://physics.stackexchange.com |
47,767 | [
"https://chemistry.stackexchange.com/questions/47767",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/26882/"
] | What causes the transition from smoldering combustion to flame combustion?
From what I have read about it is that, smoldering combustion gives off a lot of flammable gases, primarily, Carbon Monoxide, however, the lower flammability of carbon monoxide is 12.5% and it takes about 2-3 hours to reach a concentration of 1... | The overall reaction is really better given as: $$\ce{2H2SO4 + CaC2O4 -> H2C2O4 + Ca^{2+} + 2HSO4^{-}}$$ since at that strong of a pH the predominate sulfuric acid species is $\ce{HSO4^{-}}$.
Better yet the reaction could be written as $$\ce{2H^+ + CaC2O4 ->C[{0.2 N \ H2SO4, 70 °C}]\ H2C2O4 + Ca^{2+}}$$
As wa... | Calcium sulfate is somewhat soluble in acids (CRC Handbook: "s a"). The previous answer accurately states that the overall reaction is really better given as:
$\ce{2H2SO4 + CaC2O4 -> H2C2O4 + Ca^2+ + 2HSO4−}$.
If only one sulfuric acid per oxalate were used: $\ce{H2SO4 + CaC2O4 -> H2C2O4 + CaSO4}$. Then insolubl... | https://chemistry.stackexchange.com |
260,049 | [
"https://mathoverflow.net/questions/260049",
"https://mathoverflow.net",
"https://mathoverflow.net/users/77969/"
] | suppose I have a matrix $A_{1}\in C^{m*n}, m\geqslant n$ so the QR decomposition of $A_{1}$ is $A_{1}=Q_{1}*R_{1}$. Now, define the augmented matrix $A_{2}=\begin{bmatrix}
A_{1}\\
I_{n*n}
\end{bmatrix}$ where $I_{n*n}$ is $n*n$ identity matrix, so the QR decomposition of $A_{2}$ is $A_{2}=Q_{2}*R_{2}$.<br/> Is there... | First consider the simple case, if $Q_1 = I$, then you want to find $Q_2$ and $R_2$ such that $Q_2 R_2 = \begin{bmatrix} R_1 \\ I \end{bmatrix}$. Split the columns of $Q_2^T$ into left and right halves such taht $Q_2^T = [U V]$. Note that $U^TU = V^TV = I$ and $U^TV = 0$. Then basically you want to find $R_2 = UR_1 + V... | I think the relation is not that simple and here is why:
Since $A_1 = Q_1R_1$ we have
$$
A_2 = \begin{bmatrix}A_1\\ I\end{bmatrix} = \begin{bmatrix}Q_1 & 0\\0 & I\end{bmatrix}\begin{bmatrix}R_1\\I\end{bmatrix}.
$$
Now the QR decomposition of $\begin{bmatrix}R_1\\I\end{bmatrix}$ can be done by $n(n-1)/2$ Givens... | https://mathoverflow.net |
305,106 | [
"https://electronics.stackexchange.com/questions/305106",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/144074/"
] | <em>You are in no way responsible for the effects of the advice you may give.</em>
I have a 5V source that I want to signal to my arduino to start some code when the source is on. I don't have the 5V source with me and want to test my code, and I happen to have an old usb cable handy. I think USB gives a fairly consis... | Unless you short it out, both should be fine. Don't put the arduino gpio in output low mode to avoid that. A series limiting resistor of 10k would helo. Make sure you connect the grounds together or it won't work right.
If you are concerned, an opto coupler would work to isolate the two devices.
| The USB standard calls for voltage to be 5V +0.25 −0.60, so from 4.4V to 5.25V. I would check your USB voltage to make sure it is not over the input voltage of the arduino, but assuming that it should be fine.
| https://electronics.stackexchange.com |
75,453 | [
"https://math.stackexchange.com/questions/75453",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/9054/"
] | I am asked to prove that
<blockquote>
Show that a sequence $x: \mathbb{N} \to \mathbb{R}$ has a limit point iff there $\lim_{n\to\infty} x(n)$ exists as a limit point of a function from a subset of metric space $(\mathbb{N}*, d)$ to metric space $\mathbb{R}$. Note $\mathbb{N}* = \mathbb{N} \cup \infty$ and $d(m, n)... | I believe the following picture might help to get the intuition. (At least for people familiar with the topological spaces.)
<img src="https://i.stack.imgur.com/QEdKC.png" alt="Convergent sequence as a function">
This picture shows the space $\mathbb N\cup\{\infty\}$ (the sets on the picture form the base of the topo... | A function certainly can have a limit as the variable approaches a certain quantity. We have from very early on dealt with such things as $\displaystyle\lim_{x\to 2} \:\:x^3$ and, more interestingly, $\displaystyle\lim_{x\to 0}\frac{\sin x}{x}.$
Showing, for example, that $\displaystyle\lim_{x\to 2} \:\:x^3=8$ involve... | https://math.stackexchange.com |
205,881 | [
"https://physics.stackexchange.com/questions/205881",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/87190/"
] | We have a spin state
\begin{align}
\ |{\Psi}\rangle=a_u|{U}\rangle+a_d|{D}\rangle
\end{align}
where $|U\rangle$ and $|D\rangle$ are $up$ and $down$ basis vectors, and $a_u$,$a_d$ are their complex coefficients.
\begin{align}
\ a_u=x+yi
\end{align}
\begin{align}
\ a_d=w+zi
\end{align}
$x, y, w, z$ are the real para... | The fact that the overall phase factor does not matter means that we can choose it to be whatever we like. This gives us an extra constraint (even if is one we choose arbitrary) and so reduces the number of degrees of freedom by 1.
For example, given that $|a_u|^2 + |a_d|^2 = 1$ we can write our coefficients as
\begi... | An arbitrary normalized quantum state on two dimensions can always be written as
$$
|\psi⟩=e^{i\alpha}\left(\cos\theta|\uparrow⟩+e^{i\phi}\sin\theta|\downarrow⟩\right)
$$
without loss of generality.
The phase factor $e^{i\alpha}$ has no bearing on experiment, as all measurements will be proportional to $⟨\psi|\propto ... | https://physics.stackexchange.com |
357,193 | [
"https://electronics.stackexchange.com/questions/357193",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/53759/"
] | I'm hooking up a microcontroller to be able to turn a bunch of computers on/off remotely. This is via the soft switch on the motherboard which doesn't carry any kind of load.
Looking at relays, the 5v one is slightly cheaper than the 12v one, both are 1A which is far overkill.
Does anyone know if I can save 5 cents b... | Let's say the maximum input voltage is 20 V, just to have a round number and give some margin from the expected 16.8 V.
Now the maximum current through the divider is
$$\frac{20\ {\rm V}}{26.7\ {\rm k\Omega}} \approx 0.75\ {\rm mA}$$
Now you can use the \$I^2R\$ form for resistor power to find the power used in each... | <blockquote>
Once I have these values, how do I calculate the required wattage of the resistors R1 and R2?
</blockquote>
Use the power equations.
$$ P = VI $$
and by various substitutions from Ohm's Law, \$ V = IR \$ we can generate alternatives:
$$ P = VI = I^2 R = \frac {V^2}{R} $$
If you have any two values o... | https://electronics.stackexchange.com |
2,835,407 | [
"https://math.stackexchange.com/questions/2835407",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Determine the kernel of the linear map $T : \mathbb{R}^3 \to \mathbb{R}^2$ with:
<blockquote>
$$T\left(\begin{matrix} x \\ y \\ z \end{matrix}\right)=\left(\begin{matrix} x-y+z \\ x+z \end{matrix}\right)$$
</blockquote>
Can anyone please explain.
| There are 2 ways to write this up, both are named by <em>aston villa</em> but one is explicit and one is not (he just says to pick a basis). I will show you how to pick the basis. Start with the generic $(x,y,z)^T$ and impose $y=0,x=-z$ to get
$$
\begin{pmatrix} x \\ y \\ z \end{pmatrix}
= \begin{pmatrix} -z \\ 0 \\ z ... | We need to find all $v=(x,y,z)$ for which $Tv=0$. Now $Tv=0$ if and only if $Av=0$ (check, it is very easy), where \begin{equation}A=\begin{bmatrix}1&-1 &1 \\1 & 0 &1\end{bmatrix}\sim\begin{bmatrix}1&0 &1\\ 0 & 1 &0\end{bmatrix}=B,\end{equation} where $B$ is a row echelon form of $A$. Ag... | https://math.stackexchange.com |
16,708 | [
"https://dba.stackexchange.com/questions/16708",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8290/"
] | An existing database has a large number of tables stored in the PRIMARY filegroup. I want to move theses tables and their indexes on different filegroups automatically, depending on the "prefix" of the table name.
for example, with 5 tables named like this :
<pre><code>ABC_XXXX
ABC_YYYY
DEF_ZZZZ
DEF_TTTT
GHI_UUUU
</c... | There are a lot of things you are leaving out of your description, which the script will need to accommodate for - is the index a primary key or a unique constraint? are any of the columns descending? is the index filtered? does it have any INCLUDE columns? While you can certainly generate a script manually, why not us... | Had the same problem and this is the script I came up with (tested, and works just as you would expect):
<pre><code>DECLARE @Target_Filegroup sysname = N'XXX';
-----------------------------------------------------------------------------------------
;WITH [IX] AS(
SELECT
[Schema] = SCHEMA_NAME(so.[schem... | https://dba.stackexchange.com |
37,839 | [
"https://mechanics.stackexchange.com/questions/37839",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/23336/"
] | The wording of the question seems a little awkward so let me explain. A few weeks ago I was changing my wife's air filter (2003 Honda Accord). The filter housing is pretty difficult to remove without taking out the battery, so I removed the battery. When I was done with the filter, I reinstalled it. I tried turning the... | Perhaps the bolts of the cable terminals got over-torqued so that the thread got stripped. I would suggest you to control the bolts and in case repair the battery cable terminals.
It is recommended to clean the battery poles with a soft wire brush before installing the terminals
| Are you sure it's not a wire break that you're temporarily suppressing by moving the cable when you press it? You can turn on the lights(with shut off engine) and wiggle and yank the cable a bit. If you see the lights flickering you know theres a wire break. When they don't there can still be a wire break. It's a bit o... | https://mechanics.stackexchange.com |
133,383 | [
"https://mathoverflow.net/questions/133383",
"https://mathoverflow.net",
"https://mathoverflow.net/users/34304/"
] | This is to be confronted with Joseph Gubeladze' paper : "Toric varieties with huge Grothendieck group" !
| Adam Massey showed that K°(P(1,...,1,q)) = K°(P(1,...,1)).On the other hand P(1,...,1,q) is the cone with wertex (0, ...,0,1) which projects the Veronese variety Vq. Who knows any other particular nice geometrical exemples (small dimensions) of weighted projective spaces whith finitely generated algebraic GROTHENDIECK ... | I never did determine whether this was true or not (it was this point that unfortunately required me to use the BOT construction in my paper).
However, at the time I was working on this, it was my suspicion that the torsion part of the $KH_{0}$ of a WPS would be 0. If true, then (at least in characteristic 0) my pape... | https://mathoverflow.net |
562,897 | [
"https://electronics.stackexchange.com/questions/562897",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/277280/"
] | Is there a amplifier that will always put out the same value? The values are ac not dc
Example 1: 1 volt signal in=> 5 volt signal out.
Example 2: 3 volt signal in=> 5 volt signal out.
Example 3: 5 volt signal in=> 5 volt signal out.
Example 4: 10 volt signal in=> 5 volt signal out.
In other words, no matt... | What you’re asking for is a circuit called <em>Automatic Gain Control</em>, or AGC. AGC measures the detected signal level and normalizes the gain to get a constant, useable output level.
AGC is widely used for radio receivers as well as audio (especially microphones).
| Firstly, amplify the signal which can overcome threshold voltage of a FET. Then, connect the output of the amp to gate of the FET.
| https://electronics.stackexchange.com |
207,102 | [
"https://softwareengineering.stackexchange.com/questions/207102",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/91041/"
] | Part of my job is working on line-of-business applications built around client-side databases, such as Access or FoxPro. Other times these local LOBA's have direct document access, such as an exact one-to-one mapping between a logical object an an XML node or references to bookmarks in Word Documents or ranges Excel s... | MVC is a design pattern.<br>
They (design patterns) are not meant to restrain you in how they are used and/or implemented. They are supposed to be a communication mechanism that allows you to convey ideas about your application to other programmers (not an implementation).
And though normally I would expect the model ... | I don't think it's really important how you would call this or that, as long as you get MVC separation of concerns in a correct way.
In my opinion, MVC as a term is only related to code, not to data it's processing. In your example, DB would be storage, while model is whatever in your code "opens" and "exposes" this s... | https://softwareengineering.stackexchange.com |
149,885 | [
"https://softwareengineering.stackexchange.com/questions/149885",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31950/"
] | As the title states, I'd like to know if coding style can cause or influence memory fragmentation in a native application, specifically one written using C++. If it does, I'd like to know how.
An example of what I mean by coding style is using <code>std::string</code> to represent strings (even static strings) and per... | The question and the supporting text don't match up.
Your supporting text is talking about comparing two libraries' memory usage, which can be tested fairly directly and is orthogonal to coding style. Just wrap up the C string operators in a thin C++-style object and you can work with them the same with little-to-any ... | Sure, coding style can impact memory fragmentation since coding style will change your allocation/deallocation patterns which are the largest impact on fragmentation.
That said, using C++ vs C strings isn't a <em>coding style</em>. Further, different coding styles (especially in C++) exist to decrease complexity, incr... | https://softwareengineering.stackexchange.com |
224,368 | [
"https://softwareengineering.stackexchange.com/questions/224368",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/108426/"
] | I'm in the process of integrating a Unit Testing Framework for an existing code base in C++. I've zeroed down on CxxTest, but as it turns out we can use other Mocking Frameworks (like googlemock) in conjunction with CxxTest too.
After reading tutorials on CxxTest (Mocking) and googlemock (the infamous turtle example),... | You could use a factory to create instances of <code>CAnotherClass</code>.
<pre><code>class CCandidateForTest
{
public:
bool foo(int a)
{
std::shared_ptr< CAnotherClassInterface > obj = CAnotherClassFactory::Create();
int b = obj->bar(a+2);
if (a == b) {
return ... | If a class internally creates objects to do its job, then that object isn't a "collaborator" at all. For testing purposes, this is exactly the same situation as if it had a lot of inline code doing the same thing. In other words, you can't mock this object because from the perspective that the test has to assume, it do... | https://softwareengineering.stackexchange.com |
152,796 | [
"https://physics.stackexchange.com/questions/152796",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/61966/"
] | I cannot understand why if
$$J_{i} = -\frac{1}{2}\epsilon_{ijk}M_{jk}$$
then
$$M_{ij}= -\epsilon_{ijk}J_{k}.$$
Here $M_{ij}$ is the generator of the 4 dimensional Lorentz algebra (although I have only taken the rotations here so this is why I only have included latin indices ) and $J_i$ is the rotation around the i-th... | Contract both sides of the first equation with $e^{ijk}$. In three dimensions, we have the identity for the Levi-Civita, $$\epsilon_{ijk} \epsilon^{imn} = \delta_j^m \delta_k^n - \delta_j^n \delta_k^m.$$ Using the antisymmetry of the $M_{jk}$, you obtain the second equation.
| It's a well known identity that
$\epsilon_{ijk}\epsilon_{klm} = \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl}$
Therefore, if
$$J_{i} = -\frac{1}{2}\epsilon_{ijk}M_{jk}$$
then we have:
$$\begin{align}
\epsilon_{lmi}J_{i} &= -\frac{1}{2}\epsilon_{lmi}\epsilon_{ijk}M_{jk}\\
&=-\frac{1}{2}\left(\delta_{lj}\d... | https://physics.stackexchange.com |
715,205 | [
"https://physics.stackexchange.com/questions/715205",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/338901/"
] | I have read about an object, that once at the even horizon the object would be seen as stopped to the observer.
So my question is in regards to the light reflection off of the object. If the object has stopped and my understanding is the light itself is unable to escape, how does the light reflect off of the object for... | The fundamental reason for this - i.e. independent of coordinates and observation methods - is the "one-way" nature of the horizon, in that <em>information</em> cannot flow from the interior region to the exterior.
Consider the counterfactual: suppose that you <em>could</em> see the object cross the horizon a... | At a correct moment enough light to last for an eternity was send after the object. A one second pulse for example, and infinite brightness of course.
The front part of the pulse arrives back after 10 years, the middle part arrives back after 1000 years, the rear end arrives back after eternity.
The middle part will be... | https://physics.stackexchange.com |
112,679 | [
"https://physics.stackexchange.com/questions/112679",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17364/"
] | In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the number of particles. It is semi-classical in the sense that we consider the indistinguishability of the particles, so we di... | Why in the heck are you worrying about the difference between 3/2 and 5/2? Your formulae differ not just by 3/2 and 5/2 but also by $\ln(N)$. For the thermodynamic limit, $\ln(N)$ is infinity, and so a lot bigger than 1.
The number 3/2 has in this context no meaning, except that it is 5/2-1. The number 5/2 gives ... | Semi-classically, from Zemansky:
$$ S = k \ln \Omega \quad , \quad \Omega = \prod_i \left( \frac{g_i^{N_i}}{N_i!} \right) \quad , \quad N_i = \frac{N}{Z} g_i e^{-\epsilon_i / kT} $$
one finds, applying Stirling's approximation: $\ln(x!) \approx x \ln x - x $:
$$ \ln \Omega = \sum_i N_i \ln \frac{g_i}{N_i} + N = \... | https://physics.stackexchange.com |
182,251 | [
"https://security.stackexchange.com/questions/182251",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/69905/"
] | I've noticed that certifications seem to be a big part of the IT Security Professional (non-development), but have not seen the same attention being given/required of the software development engineer that focuses on application security or building security software.
Am I wrong, and just not seeing it? Or is it true... | There are not many security certifications for developers. The simple reason is that there would have to be certs for every language and trend. And considering that trends swing wildly from year to year, there is not enough time to develop a robust security certification that will not be laughed at while the trend is s... | In my experience, true programmers laugh at certifications (most of the time for good reason). They care much more about the projects you have worked on.
Some jobs and companies value industry certificates much higher than others. Many companies really just use it as a check box to weed out applications for jobs. Ther... | https://security.stackexchange.com |
11,309 | [
"https://cs.stackexchange.com/questions/11309",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/6665/"
] | Following question was asked in one of entrance exams for a graduation programme. Please help me try to solve it :
<blockquote>
A computer system has an L1 cache, an L2 cache, and a main memory
unity connected as shown below. The block size in L1 cache is 4 words.
The block size in L2 cache is 16 words. The memory acce... | In order to find that any cache does <em>not</em> contain the value at the requested address you have to access it.
<blockquote class="spoiler">
That means you have to add up the access times of all contributing levels.
</blockquote>
Some of the options seem to suggest one might think that whole blocks from, say, ... | I guess you got the access time wrong. Access time means time to locate a data on a memory. So, whoever accesses the memory (be it CPU or some other device) it will be the same.
Coming to first question here. A block is transferred from L2 to L1. And L1 block size being 4 words and data bandwidth being 4 bytes, it re... | https://cs.stackexchange.com |
587,420 | [
"https://physics.stackexchange.com/questions/587420",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/269663/"
] | There are two forces we know, <strong>Centripetal force</strong> (or Gravity) and <strong>Centrifugal force</strong>. Both are applied to all the planets including earth. Planets are kind of spherical due to gravitational force but also not perfectly round due to this centrifugal force (or any other force idk) applied.... | <blockquote>
Then why none of such planet is torn apart till now ?
</blockquote>
Any planets and stars that <em>would</em> have or <em>could</em> have rotated themselves into pieces have presumably <strong>already done so</strong> (which practically means that they would never have been formed in the first place.) What... | If I am understanding your questions correctly, just because the force of gravity and the centrifugal force are at equilibrium, it doesn't mean the shape has to be spherical. Think for instance of a water balloon flying through the vacuum that is also spinning. The internal force of the water trying to scape and the fo... | https://physics.stackexchange.com |
2,674,768 | [
"https://math.stackexchange.com/questions/2674768",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/466892/"
] | Could anyone please break the following down for me?
$$\sum_{i,t}y_{i,t-2}e_{it}=0$$
I am familiar with $\sum_{i}$ and also $\sum_i\sum_t$. But I have not seen the above before. I will appreciate if someone could explain the first equation. Thanks in advance.
| $\displaystyle\sum_{i,t}$ means the same as $\displaystyle\sum_i \sum_t$. In the second notation, a specific summation order is given, whereas in the first one there isn't.
So the first notation is only appropriate if the order of summation doesn't matter. For example in the finite case.
| Missing are the index sets for $i$ and $t$ respectively. The notation $e_{it}$ indicates that a multiplication of index $i$ and index $t$ is possible.
If e.g. $\{5,7\}$ it the index set of $i$ and $\{2,8\}$ is the index set of $t$ then the LHS equals $$y_{5,2}e_{10}+y_{5,8}e_{40}+y_{7,2}e_{14}+y_{7,8}e_{56}$$
| https://math.stackexchange.com |
7,586 | [
"https://mathoverflow.net/questions/7586",
"https://mathoverflow.net",
"https://mathoverflow.net/users/385/"
] | Here $\zeta(s)$ is the usual Riemann zeta function, defined as $\sum_{n=1}^\infty n^{-s}$ for $\Re(s)>1$.
Let $A_n=${$s\;:\;\zeta(s)=n$}. The behaviour of $A_0$ is basically just the Riemann hypothesis; my question concerns $A_n$ for $n\neq0$.
1) Is determining this just as hard as the Riemann hypothesis?
2) If ... | Regarding 3), this "Big Picard" stuff is serious overkill.
Think like an undergraduate real analysis student:
The p-series <span class="math-container">$\zeta(p)$</span> converges for real <span class="math-container">$p > 1$</span>, whereas <span class="math-container">$\zeta(1)$</span> = sum of the harmonic seri... | There are infinitely many roots of $\zeta(s)-a=0$ for every complex number $a$. When $a\ne 0$, these are called "$a$-values" and there is a whole chapter discussing their distribution in Titchmarsh's book on the zeta-function. Selberg also discusses $a$-values in his (now famous) paper "Old and new conjectures and resu... | https://mathoverflow.net |
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